Asy Mptotic V Alues

V Alues

Threshold Parameter Threshold F Statistic

Keywords: JEL classification: C13, C15, C23, H63, O57 Public debt, Economic growth, Regression kink, Non-linearity, Threshold effects Threshold Parameter Threshold F Statistic Asy mptotic Threshold Parameter Threshold F Statistic Asy mptotic

J'exprime, tout d'abord, ma profonde gratitude et mon entière reconnaissance à Cyriac Guillaumin, mon directeur de thèse, pour avoir accepté d'encadrer ce travail. Je le remercie pour sa grande disponibilité, ses conseils et suggestions utiles et ses encouragements précieux qu'il m'a prodigués tout au long de ma thèse.

Je présente, ensuite, mes plus sincères remerciements aux membres du jury, Jean-Pierre Allegret, Florence Huart, Valérie Mignon et Patrick Villieu, qui ont accepté d'évaluer et de donner leur opinion d'experts sur ma thèse.

Je souhaite également remercier les membres

Table of contents

Introduction

Au cours de la dernière décennie, la dette publique est devenue de plus en plus élevée, atteignant des niveaux inquiétants, pour de nombreux pays avancés, en particulier dans la zone euro. Ces pays avaient mis en oeuvre des mesures de relance budgétaire massives en 2009 en réponse aux graves ralentissements suite à la crise financière de 2008-2009. Deux ans après, les pays de la zone euro ont commencé à inverser le cours des expansions budgétaires, en s'orientant vers des consolidations fiscales, afin de stabiliser les ratios de déficit et d'endettement publics exacerbés par les stimuli budgétaires conjugués à une croissance en berne. En effet, les préoccupations quant aux défauts de paiement de la dette souveraine dans de nombreux pays, notamment de la périphérie de la zone euro, ont conduit aux mesures de consolidations budgétaires et d'austérité. Face à ces mesures, les pouvoirs publics et les économistes ont été partagés entre les effets de court terme des mesures d'assainissement budgétaire et les effets de long terme reliés notamment à l'impact de la dette publique sur la croissance économique.

Pour ce qui est des effets de long terme en particulier, les économistes semblent être au moins unanimes en théorie sur l'impact négatif de la dette publique sur la croissance économique à long terme. Ce constat est devenu tellement ancré dans l'esprit de tout un chacun qu'elle semble légitimer les affirmations quant à l'éventuelle existence d'un seuil de dette publique au-delà duquel la croissance économique serait altérée. C'est ainsi que deux économistes [START_REF] Reinhart | Growth in a time of debt[END_REF] ont déterminé, pour un échantillon de pays développés, l'existence d'un seuil de dette publique (rapportée au PIB) de 90%. À la suite de ce résultat, dont l'implication est forte en termes de politiques économiques, surtout parvenu en temps de crise où les finances publiques sont sous pression, un afflux incessant de travaux a émergé, examinant la relation entre la dette publique et la croissance économique et suscitant plusieurs controverses [START_REF] Caner | Finding the tipping point when sovereign debt turns bad[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Reinhart | Growth in a time of debt[END_REF][START_REF] Lin | High dimensional threshold quantile regression with an application to debt overhang and economic growth[END_REF][START_REF] Bentour | On the public debt and growth threshold: one size does not necessarily fit all[END_REF].

En ce qui concerne les effets de la dette publique à court terme, ils pourraient être appréciés dans un contexte de politique budgétaire en relation avec les multiplicateurs keynésiens. En effet, la dette publique est contractée pour faire face aux besoins de financement des déficits publics, lorsque les recettes publiques ne couvrent pas les dépenses publiques. Ainsi, les effets imminents de la dette publique sur la croissance sont aussi liés aux multiplicateurs de politique budgétaire, dont la valeur peut déterminer la capacité à générer la croissance économique aussi bien que les choix des politiques économiques (programme de stimuli versus austérité). En effet, une valeur élevée (faible) du multiplicateur de dépenses peut générer une croissance élevée (faible) pour une politique budgétaire expansionniste et ainsi réduire (augmenter) le poids de la dette. Étant donné leur importance, les multiplicateurs budgétaires ont aussi fait l'objet d'échanges intenses dans les milieux académiques à la suite de la crise de 2008-2009. Ainsi, si Reinhart et Rogoff (2010) ont été les précurseurs de l'intense débat sur le seuil de la dette publique, c'est grâce à [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF] que le débat autour de la valeur des multiplicateurs notamment budgétaires a été déclenché. Ces auteurs ont révélé la sensibilité des multiplicateurs au cycle conjoncturel, notamment faibles en temps d'expansion et élevés en temps de récession économique. Dès lors, d'autres recherches furent publiées, ayant tendance à confirmer ce résultat et débattant davantage sur la dépendance des multiplicateurs à d'autres déterminants tels que le déficit public, l'endettement public, le régime de change, la politique monétaire, le degré d'ouverture, etc. [START_REF] Romer | What Have We Learned about Fiscal Policy from the Crisis?[END_REF][START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF][START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF][START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], 2013 ;[START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF].

En s'appuyant sur les limites économétriques des études précédentes, mises en évidence dans les différents débats à propos des effets de la dette publique sur la croissance économique depuis la crise de 2008-2009, cette thèse se propose d'analyser la pertinence des arguments en faveur et/ou en défaveur d'un seuil universel présenté supra, que la théorie économique ne semble pas signaler formellement. Nous montrons notamment, que l'existence d'un tel seuil, surtout commun à tous les pays, semble créer un clivage plutôt qu'un consensus au niveau des résultats empiriques. Ainsi, outre la revue de littérature théorique et empirique vigoureusement analysée, nous adoptons une démarche économétrique basée sur des arguments et des modèles économiques pour montrer que la relation entre la dette publique et la croissance économique est davantage un lien endogène émanant des canaux et variables par lesquelles les effets de la dette se transmettent à la croissance économique. De plus, nous montrons que ces canaux et effets qu'ils induisent diffèrent selon l'horizon temporel amenant à une distinction de traitement et de modélisation tenant compte des spécificités propres à chaque pays. Ceci a abouti à une formulation temporelle simulée de la limite de la dette (potentielle) en relation avec les performances de chaque pays en termes notamment de taux d'intérêt de long terme et de productivité potentielle du capital publique.

Contribution de la thèse à la littérature et débats des effets de la dette publique sur la croissance économique

Dans le volet consacré à la revue de littérature, la contribution de la thèse est large et diversifiée. La thèse est constituée de trois chapitres dont chacun assemble et analyse une revue de littérature autour des débats. Le chapitre 1 évoque les récents débats empiriques quant à l'existence d'un seuil de dette publique affaiblissant la croissance économique, sans omettre les différents débats théoriques sur les effets de la dette publique sur la croissance économique distinguant notamment la vision classique de long terme de la vision keynésienne de court terme. Partant de cette dernière, le chapitre 2 étale une riche littérature évaluant ainsi les effets de la dette publique sur la croissance économique à travers l'effet des multiplicateurs de dépenses publiques. La littérature à ce sujet est essentiellement portée sur les différentes nouvelles contributions autour de la taille du multiplicateur qui s'est révélée sensible à une variété de déterminants dont notamment la position de l'économie dans le cycle et la situation fiscale (dette et déficit publics). Le chapitre 3 quant à lui se charge de présenter une revue de littérature très riche et contrastée des modèles évaluant les effets de la dette sur la croissance particulièrement dans l'optique de long terme, tout en résumant les avantages et les critiques à l'encontre de ces modèles.

Résumé du débat théorique sur les effets de la dette publique

En théorie, les effets de la dette sur la croissance économique ont été particulièrement débattus dans l'après-guerre suite à la forte augmentation de la dette publique des pays avancés. La littérature distingue particulièrement la vision keynésienne de court terme qui suppose que les dépenses publiques financées par la dette publique sont susceptibles de stimuler la demande globale dans un contexte de rigidité des prix et des salaires. Cependant, selon la vision classique dont la tendance est le long terme, la dette publique est susceptible de réduire le stock de capital et la productivité, puis de réduire la production.

Divers canaux sont cités pour expliquer les principales raisons de ces effets, comme le résume [START_REF] Hansen | The Public Debt Reconsidered: A Review Article[END_REF]. Une dette publique plus élevée peut déclencher une épargne privée plus élevée (effet Pigou), moins d'incitations à travailler et à investir en particulier pour les détenteurs des obligations d'État (effet Kaldor), un effet d'incitation négatif des impôts supplémentaires nécessaires pour financer le paiement des intérêts et des intérêts plus élevés défavorables pour contrer l'impact inflationniste de "l'effet Pigou". En outre, [START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF] a déclaré que la dette publique peut évincer l'investissement privé en réduisant le crédit à l'économie ou en augmentant les taux d'intérêt à long terme sur les emprunts publics. Les points de vue des keynésiens et des classiques sont résumés dans ce qui est appelée par la suite "l'analyse conventionnelle" des effets de la dette publique, reflétant le paradigme dominant des chercheurs [START_REF] Elmendorf | Government Debt[END_REF].

Une autre contribution théorique importante alimentant le débat sur les effets du financement par la dette publique est "l'équivalence ricardienne". L'idée attribuée à l'origine à Ricardo, affirme que la croissance économique peut être insensible à la dette publique, du fait que les consommateurs, supposés prospectifs (à anticipations rationnelles) peuvent réagir en réduisant leurs dépenses d'un montant équivalent à celui d'une augmentation des dépenses publiques. Ils anticipent en effet des impôts futurs finançant le déficit généré par les nouvelles dépenses publiques et par conséquent épargnent et renoncent à la dépense. Dans le même sens, [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] montre que les obligations d'État constituent un actif pour leurs propriétaires et un passif pour les contribuables. Dans l'ensemble, aucune richesse nette ne serait créée et l'effet serait nul. Les discussions entre économistes sur les effets de la dette publique dans l'optique de l'équivalence ricardienne, ont aussi invoqué les échanges quant à la redistribution de tels effets sur les générations successives. Cette redistribution est surtout reconsidérée dans le cadre des transferts intergénérationnels dans des modèles à générations imbriquées [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF][START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF].

Quant au débat sur l'analyse à court terme, il se concentre en particulier sur la composition des dépenses publiques pour lesquelles les économistes (classiques et néoclassiques notamment) ont tendance à considérer que les dépenses en capital peuvent générer des effets positifs mais pas nécessairement les dépenses courantes. Ce point de vue est contrasté par les keynésiens qui soutiennent que les effets des dépenses sont toujours positifs, avec des différences en termes d'efficacité qui peuvent être plus élevées pour certains types que pour d'autres. Ces opinions opposées sont résumées dans [START_REF] Aschauer | Do states optimize? Public capital and economic growth[END_REF] qui suppose que la relation à court terme entre la dette et la croissance pourrait être positive en raison de l'impact des dépenses d'investissement sur la croissance, tandis que la relation à long terme pourrait être inversée en raison de la prime de risque élevée, à la suite d'une dette publique élevée, augmentant ainsi le coût de la dette. Pour [START_REF] Blanchard | Comments on Alan Blinder's 'The Case Against the Case Against Discretionary Policy[END_REF], l'association négative entre la dette et la croissance pourrait être attribuée au retard des politiques fiscales contracycliques, ce qui signifie que les pays en récession devraient adopter des politiques budgétaires expansionnistes pour stimuler la croissance et, en période d'expansion, des politiques restrictives pour réduire les niveaux d'endettement.

Résumé du débat empirique sur l'effet seuil de la dette publique sur la croissance économique

Dans les économies avancées, l'augmentation de la dette publique pendant la période précédant la crise a été accentuée par les mesures de relance budgétaire mises en oeuvre en 2008-2009. Une année plus tard, [START_REF] Reinhart | Growth in a time of debt[END_REF] ont constaté que, pour un échantillon de 20 pays avancés, il existe un seuil commun de 90% du ratio de la dette publique au PIB au-delà duquel la croissance économique serait altérée. En particulier, ces deux auteurs ont observé que la corrélation entre la dette publique et la croissance est faible pour des niveaux d'endettement modérés et devient forte et négative lorsque le ratio de dette publique, mesuré par le rapport entre la dette publique et le PIB, dépasse 90%. Ils observent que les taux de croissance médian et moyen correspondant aux ratios d'endettement supérieurs à ce seuil diminuent respectivement de 1 et 4 points. Ce résultat, basé sur une approche statistique descriptive simple, a déclenché un afflux de recherches empiriques, utilisant différentes méthodes économétriques, dont la plupart des résultats ont suscité beaucoup de controverses.

Ainsi, certaines études ont tendance à confirmer l'existence d'un seuil de dette publique sans nécessairement parvenir à la valeur de 90% supposée par [START_REF] Reinhart | Growth in a time of debt[END_REF] [START_REF] Caner | Finding the tipping point when sovereign debt turns bad[END_REF][START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Lin | High dimensional threshold quantile regression with an application to debt overhang and economic growth[END_REF]. Néanmoins, le débat autour du seuil de la dette publique s'est intensifié, après que plusieurs auteurs aient contesté les conclusions de Reinhart et Rogoff (2010) comme, par exemple, Fergusson et Johnson (2011), [START_REF] Minea | Is High Public Debt Always Harmful to Economic Growth? Reinhart and Rogoff and Some Complex Nonlinearities[END_REF], [START_REF] Baglan | Government debt and macroeconomic activity: a predictive analysis for advanced economies[END_REF], [START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF], [START_REF] Egert | The 90% public debt threshold: the rise and fall of a stylized fact[END_REF]. Ces contestations ont été notamment alimentées par la révélation de certaines erreurs de codification et de calcul dans l'article de Reinhart et Rogoff (2010) par [START_REF] Herndon | Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff[END_REF].

Le résumé de ces résultats peut être regroupé en trois groupes :

-un premier groupe de recherches empiriques se concentrant principalement sur l'examen d'une relation concave non linéaire entre la dette publique et la croissance économique [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF][START_REF] Eberhardt | Public debt and growth: Heterogeneity and nonlinearity[END_REF][START_REF] Chudik | Is there a debt-threshold effect on output growth?[END_REF] ;

-un deuxième groupe intéressé par la causalité entre la dette publique et la croissance économique [START_REF] Panizza | Public Debt and Economic Growth Is There a Causal Effect?[END_REF], 2013 ;[START_REF] Sanzo | Public debt and growth in the Euro area: evidence from parametric and nonparametric Granger causality[END_REF][START_REF] Gomez-Puig | On the bi-directional causal relationship between public debt and economic growth in EMU countries[END_REF] ;

-un troisième groupe qui examine les effets d'autres variables institutionnelles et macroéconomiques interférant avec la relation entre la dette publique et la croissance économique [START_REF] Greiner | Economic Growth, Public Debt and Welfare: Comparing Three Budgetary Rules[END_REF][START_REF] Kourtellos | The effect of public debt on growth in multiple regimes[END_REF][START_REF] Pan | Co-movement of Government Debt and Economic Growth in the Euro-area: A Bayesian Dynamic Factor Model Analysis[END_REF][START_REF] Sharpe | Institutional arrangements and public debt threshold limits[END_REF][START_REF] Marchionne | Growth, debt and inequality[END_REF].

Les résultats de toutes ces recherches n'ont abouti à aucun consensus. Spécifiquement, certains chercheurs ont repris l'étude de la relation dette-croissance pour le même échantillon de 20 pays avancés utilisé par [START_REF] Reinhart | Growth in a time of debt[END_REF], adoptant différentes approches économétriques, et ont abouti à des résultats différents indiquant généralement de faibles niveaux de seuils d'endettement autour de 20 à 30% [START_REF] Baglan | Government debt and macroeconomic activity: a predictive analysis for advanced economies[END_REF][START_REF] Egert | The 90% public debt threshold: the rise and fall of a stylized fact[END_REF][START_REF] Lee | Testing for a Debt-threshold Effect on Output Growth[END_REF]. D'autres chercheurs ont utilisé différents échantillons et différentes périodes rejetant ainsi l'existence de tout seuil [START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF][START_REF] Eberhardt | Public debt and growth: Heterogeneity and nonlinearity[END_REF][START_REF] Chudik | Is there a debt-threshold effect on output growth?[END_REF][START_REF] Syssoyeva-Masson | The effect of public debt on growth in multiple regimes in the presence of long-memory and non-stationary debt series[END_REF].

En règle générale, les évaluations des effets des politiques budgétaires sont quantifiées par les valeurs du multiplicateur budgétaire. L'efficacité des dépenses publiques dans l'analyse keynésienne/classique (comme mentionné au I.1) dépendant de la composition et du type de dépenses (courantes, en capital, de transferts, etc.) est empiriquement liée aux valeurs de leurs multiplicateurs. De ce côté, un volet important de recherches empiriques a été lancé au lendemain de la crise financière, révélant notamment davantage la sensibilité de ces multiplicateurs à de nombreux déterminants économiques et institutionnels.

Résumé du débat sur la valeur des multiplicateurs de dépenses publiques

Bien que la majorité des recherches précédentes (Section I.2) se concentrent sur l'étude du seuil de la dette publique et considèrent la relation dette-croissance à travers des formulations et modèles économétriques non linéaires, les canaux par lesquels les effets de la dette publique se matérialisent sont proprement liés aux effets des multiplicateurs de dépenses financées par une telle dette, en particulier à court terme. L'évaluation des multiplicateurs budgétaires a été largement reconsidérée à la suite du développement des techniques économétriques. Depuis la crise financière de 2008, une littérature massive évaluant les multiplicateurs budgétaires est apparue [START_REF] Romer | What Have We Learned about Fiscal Policy from the Crisis?[END_REF][START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF][START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF][START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], 2013 ;[START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF].

Les principales conclusions de cette littérature révèlent de grandes différences dans la taille des multiplicateurs. En effet, la taille du multiplicateur s'est montrée sensible à une variété de déterminants qui n'étaient pas (ou rarement) considérés avant la crise de 2008-2009. Les multiplicateurs budgétaires sont particulièrement sensibles à la période d'estimation, propres à chaque pays, et à la méthode d'évaluation [START_REF] Batini | Successful Austerity in the United States, Europe and Japan[END_REF][START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF]. En outre, les multiplicateurs budgétaires se sont révélés sensibles au cycle économique, en particulier, les multiplicateurs de dépenses budgétaires ont tendance à être plus importants dans les récessions que dans les périodes d'expansions [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], 2013 ;[START_REF] Barro | Macroeconomic Effects from Government Purchases and Taxes[END_REF][START_REF] Parker | On Measuring the Effects of Fiscal Policy in Recessions[END_REF][START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF][START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF][START_REF] Fazzari | State dependent effects of fiscal policy[END_REF][START_REF] Glocker | Time-varying fiscal spending multipliers in the UK[END_REF].

Par ailleurs, d'autres chercheurs conduisent à découvrir la vulnérabilité des multiplicateurs budgétaires à d'autres déterminants sans être nécessairement conditionnés par la cyclicité de l'économie. Ces déterminants sont la situation budgétaire mesurée par le niveau des ratios d'endettement et/ou des déficits [START_REF] Corsetti | Sovereign risk, fiscal policy, and macroeconomic stability[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF], la politique monétaire contrainte soit par la tendance des taux d'intérêt à leur borne inférieure zéro (trappe à liquidité) ou par la perte de l'indépendance monétaire comme dans le cas d'un taux de change fixe ou d'une union monétaire [START_REF] Hall | By how much does GDP rise if the Government buys more output?[END_REF][START_REF] Cogan | New Keynesian versus old Keynesian government spending multipliers[END_REF][START_REF] Eichenbaum | When Is the Government Spending Multiplier Large?[END_REF][START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF]. 1Néanmoins, les travaux très récents de [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF] et [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF] considèrent que les multiplicateurs de dépenses publiques sont en moyenne inférieurs à l'unité. Cela contraste la tendance des études conduites après la crise de 2008-2009 et dont les résultats parviennent à des multiplicateurs plus importants, en temps de récessions, pouvant atteindre la valeur de 2. Cela va également dans le sens du même consensus sur les multiplicateurs de dépenses avant la récession de 2008-2009, considéré comme faible et que les effets de la politique budgétaire sont de très courte durée [START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF]. En particulier, les effets de celle-ci tenant compte de la situation budgétaire de l'économie mesurée par le niveau de la dette publique et/ou du déficit public sont fortement débattus au lendemain de la crise financière de 2008de -2009[START_REF] Boussard | Fiscal Multipliers and Public Debt Dynamics in Consolidations[END_REF][START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF]Blot et al., 2014b ;[START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF][START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF],

Résumé du débat sur les effets de la dette publique dans les modèles économiques

Pour évaluer les effets de la dette publique, de nombreux modèles de croissance théoriques ont été conçus. Le modèle de [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF] était la base de la première classe des modèles d'agents à vie infinie (ILA). Plus tard, le débat entre économistes sur l'horizon de vie des agents et le type de liens de transferts opérationnels intergénérationnels entre eux a abouti au développement des modèles à générations imbriquées considérant l'existence/l'absence de continuité, entre les générations, assurée par ces liens [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF][START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF]. Le débat a porté sur l'implication de l'altruisme entre les générations et le cycle de vie des agents pour déterminer l'existence d'effets de la dette publique sur les comportements des agents en termes d'épargne, d'accumulation du capital, d'utilité des consommateurs et du taux d'intérêt. Les contributions importantes dans ce sens remontent à [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF], [START_REF] Yaari | Uncertain lifetime, life insurance, and the theory of the consumer[END_REF], [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF], [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF], [START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF], [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF]Aiyagari ( , 1987)), [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF] et [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF].

Les effets redistributifs d'une génération à l'autre ont fait l'objet de nombreux débats dans l'aprèsguerre. Buchanan (1958) et Meade (1958), discutant des contributions de leurs prédécesseurs, notamment Lerner (1943), montrent que la dette publique ne constitue pas un fardeau pour les contribuables actuels. Ce fardeau est plutôt transféré partiellement ou totalement aux générations futures qui devront payer des impôts pour rembourser la dette (Bowen et al., 1960 ;[START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF]. Dans le même sens, les partisans de l'équivalence ricardienne montrent que la neutralité de la dette peut se produire en fonction notamment de l'existence de liens altruistes opérationnels entre générations [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF]. Ainsi, le débat a émergé modélisant les effets de la politique budgétaire, précisément l'échange (swap) de la dette et son effet sur l'utilité sociale et les taux d'intérêt. Cela a également déclenché un débat controversant entre les néoclassiques et les partisans de l'équivalence ricardienne [START_REF] Barro | Perceived wealth in bonds and social security and the Ricardian equivalence theorem: Reply to Feldstein and Buchanan[END_REF]Feldstein, 1976 ;[START_REF] Cukierman | A Political Theory of Government Debt and Deficits in a Neo-Ricardian Framework[END_REF].

Les effets sur la dette publique sont également pris en compte dans l'économie politique de la dette publique. À cet égard, deux approches ont été débattues. D'une part, l'approche normative où le gouvernement est considéré comme un planificateur social pour qui la priorité est de maximiser le bien-être social de ses individus [START_REF] Barro | On the determination of the public debt[END_REF]Lucas et Stockey, 1983 ;[START_REF] Aiyagari | Optimal Taxation without State-Contingent Debt[END_REF].

D'autre part, l'approche positive considérant la dette publique comme une variable d'État utilisée par chaque gouvernement comme une stratégie pour influencer les choix de son successeur ou comme un moyen de façonner les anticipations des agents économiques privés (Svensson et [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF]. Par conséquent, les idées les plus répandues étaient liées aux effets de la politique budgétaire sous des gouvernements qui suivent des règles d'engagement (commitment) contre des politiques discrétionnaires. En particulier, l'incohérence temporelle du gouvernement a un impact sur la façon dont les agents économiques forment leurs anticipations affectant ainsi leurs décisions économiques [START_REF] Kydland | Rules Rather than Discretion: The Inconsistency of Optimal Plans[END_REF].

Les effets de la dette publique sont également examinés dans la classe des modèles de croissance endogène. Le développement de tels modèles a été essentiellement popularisé par [START_REF] Romer | Increasing Returns and Long-Run Growth[END_REF], [START_REF] Lucas | On the Mechanics of Economic Development[END_REF] et [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]. Ces modèles ont été proposés comme une alternative au modèle de croissance néoclassique de [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF] et [START_REF] Swan | Economic growth and capital accumulation[END_REF]. Celui-ci n'a pas été en mesure d'expliquer les taux de croissance non nuls du PIB par tête persistant dans de nombreuses économies développées, et a donc été remis en cause pour avoir omis les déterminants de croissance à long terme. Ainsi, le cadre de croissance endogène englobe d'autres déterminants de la croissance à long terme, en particulier pour l'évaluation des politiques budgétaires, incorporant le secteur public dans le secteur productif [START_REF] Lucas | On the Mechanics of Economic Development[END_REF]Romer, 1989 ;[START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF][START_REF] Barro | Convergence[END_REF][START_REF] Jones | R&D-Based Models of Economic Growth[END_REF][START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF][START_REF] Jones | R&D-Based Models of Economic Growth[END_REF][START_REF] Jones | Population and Ideas: A Theory of Endogenous Growth[END_REF][START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF][START_REF] Turnovsky | Fiscal policy in a growing economy with public capital[END_REF][START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF][START_REF] Greiner | Public debt in a basic endogenous growth model[END_REF][START_REF] Greiner | Human capital formation and public debt: growth and welfare effects of three different deficit policies[END_REF][START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF][START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF].

Récemment, la politique budgétaire, et en particulier la dette publique a également été modélisée dans la classe des modèles néo-keynésiens. Les travaux pionniers dans ce sens sont principalement dus à [START_REF] Christiano | Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy[END_REF] et [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF]. Ces derniers diffèrent des autres modèles en assumant des taxes générant des distorsions au lieu des taxes forfaitaires comme cela est particulièrement supposé dans les modèles à générations imbriquées. De plus, ils rejoignent la littérature de l'économie politique de la dette en discutant des politiques gouvernementales selon des règles d'engagement ou de discrétion. En particulier, certains auteurs considèrent que la dette publique optimale suivrait un processus de marche aléatoire chaque fois que le gouvernement peut atteindre un engagement politique incohérent dans le temps [START_REF] Benigno | Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach[END_REF][START_REF] Schmitt-Grohe | Optimal Monetary and Fiscal Policy under Sticky Prices[END_REF]. D'importantes recherches empiriques sur ces modèles ont récemment prospéré [START_REF] Leith | Fiscal sustainability in a new Keynesian model[END_REF][START_REF] Mayer | Government debt, inflation dynamics and the transmission of fiscal policy shocks[END_REF].

Malgré les contributions importantes des modèles précédents dans l'évaluation de la dette publique et des effets de la politique budgétaire, les nouveaux modèles keynésiens ont été particulièrement critiqués par [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF]. Celui-ci a contribué par la théorie des "Savings-Spenders" qui a influencé de nombreuses recherches empiriques sur la politique budgétaire en essayant de considérer les comportements suivant des règles empiriques, en particulier dans les modèles d'inspiration de la nouvelle économie keynésienne. Par conséquent, [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] montrent que cette classe de modèle n'est pas à présent utile pour l'analyse des politiques publiques. Ces auteurs se basent en particulier sur la critique du modèle de Smets et Wouters (2007) qui constitue le noyau et la référence fondamentale pour de nombreuses contributions récentes adoptant le cadre d'analyse de la nouvelle économie keynésienne.

Contribution empirique de la thèse

Cette partie résume les principaux résultats empiriques et aboutissements de la thèse à la suite de l'évaluation économétrique des liens entre la dette publique et la croissance économique. Premièrement, nous présentons la contribution économétrique du chapitre 1 étudiant la forme non linéaire entre la dette publique et la croissance économique pour un échantillon de 20 pays avancés. Cette relation fait apparaître l'existence d'un point de retournement dans la relation pour chaque pays permettant de confirmer ou d'infirmer l'existence d'un seuil de dette à ne pas dépasser. Deuxièmement, nous détaillons les résultats du chapitre 2 relatifs à l'étude des multiplicateurs de dépenses publiques en fonction du cycle conjoncturel et le sens d'évolution du ratio d'endettement.

Troisièmement, Nous résumons la contribution empirique du chapitre 3 reliant la dette publique à la croissance économique dans un cadre de croissance endogène, à travers la productivité du capital public.

Les principales conclusions de nos évaluations empiriques conduisent à rejeter le taux d'endettement commun qui s'applique à tous les pays. Nous montrons spécifiquement que la relation entre la dette publique et la croissance économique est plutôt sensible à la période d'analyse et surtout propre à chaque pays. En outre, dans un cadre à court terme, l'accumulation et la contraction de la dette publique ont un impact différent sur la croissance économique via l'effet des multiplicateurs de dépenses. Ces derniers se révèlent, notamment dans notre thèse, sensibles aux autres facteurs liés au cycle conjoncturel (expansion, récession), à l'évolution du taux d'endettement public (accumulation, contraction) et au croisement de ces facteurs. À long terme, la dette publique est liée, dans le cadre d'un modèle de croissance endogène, aux fondamentaux macroéconomiques des économies et à la productivité du capital public.

Présentation et choix de l'échantillon de pays

Compte tenu de l'endettement élevé des économies avancées, nous nous sommes concentrés sur un échantillon de 20 pays de l'OCDE, dont 11 sont membres de la zone euro, à savoir l'Australie, l'Autriche, la Belgique, le Canada, le Danemark, la France, l'Allemagne, la Grèce, l'Irlande, l'Italie, le Japon, les Pays-Bas, la Nouvelle-Zélande, la Norvège, le Portugal, l'Espagne, la Suède, la Suisse, le Royaume-Uni et les États-Unis2 . Le choix de cet échantillon est justifié par de nombreuses raisons dont :

-l'importance économique de ce groupe de pays avancés influençant les économies mondiales notamment du fait qu'ils pèsent sur le système économique et financier international (en termes de risque systémique) ;

-le niveau élevé de la dette publique par rapport au PIB accumulé pour la majorité de ces pays, dont plusieurs d'entre eux ont rencontré des problèmes de dette souveraine lors de la crise financière de 2008-2009, voire même avant ;

-l'échantillon est constitué des pays qui ont été très étudiés dans la littérature et dont les résultats sont débattus après la crise financière de 2008-2009 en termes de dette publique et de politique budgétaire, ce qui nous permet de confronter nos résultats à ceux de la littérature existante ;

-enfin, la disponibilité de séries de données longues, tant annuelles que trimestrielles pour la dette publique et la croissance économique.

Contribution empirique du Chapitre 1 : pas de seuil universel de dette publique

Malgré la diversité des méthodes économétriques utilisées pour étudier la relation croissance-dette, la plupart des analyses précédentes souffrent d'un biais d'échantillonnage (courtes périodes d'analyse). Presque toutes les méthodes économétriques avancées utilisées sont appliquées à des échantillons débutant dans les années 1970. Cette date coïncide avec la fin du système de Bretton Woods et le début de la libéralisation des marchés dans les pays développés. Pour remédier à ce biais, l'analyse a été étendue dans le chapitre 1 sur une longue période, 1880-2008, subdivisée en cinq sous-périodes correspondant aux changements majeurs survenus dans l'ordre monétaire et politique international [START_REF] Rodrik | The Globalization Paradox: Democracy and the Future of the World Economy[END_REF][START_REF] Obstfeld | Globalization and Capital Markets[END_REF]. Ces changements pourraient affecter la stabilité des agrégats macroéconomiques et leurs interdépendances, dont éventuellement la relation dette-croissance. Notre analyse distingue les sous-périodes suivantes :

-1880-1913 : cette période correspond à la fin de la première mondialisation ou la fin de l'ère du mercantilisme ;

-1914-1945 : une période avec deux guerres dévastatrices et la grande dépression économique de 1929. L'ordre économique international a été marqué par le régime de l'étalon-or et le déclin de l'hégémonie britannique remplacé par la suprématie américaine ; -1946-1970 : le monde a connu une croissance et un développement solides au cours de cette période, notamment sous les accords de Bretton Woods et les régimes de taux de change fixes (centrés autour du dollar américain). Cette période de près de trois décennies de prospérité est désignée par le terme des trente-glorieuses ;

- [1971][1972][1973][1974][1975][1976][1977][1978][1979][1980][1981][1982][1983][1984][1985][1986][1987][1988][1989][1990] : ces deux décennies ont connu des événements économiques et politiques turbulents avec la fin de la convertibilité du dollar en 1971 et l'augmentation des régimes de change flottants, les chocs pétroliers des années 1970 avec la coexistence du chômage et de l'inflation et la crise de la dette souveraine des années 1980 ;

-1991-2008 : cette période a connu une large libéralisation financière conformément aux recommandations du Consensus de Washington, entraînant une instabilité financière et des crises pour la plupart des pays émergents. Au cours de cette même période, l'organisation mondiale du commerce (OMC) a été créée, les accords de libre-échange bilatéraux et multilatéraux ont proliféré et la zone euro a été établie.

D'abord, une analyse préliminaire descriptive variée par pays et en panel a été conduite. Puis, une forme quadratique de la croissance économique en fonction du ratio d'endettement sur toute la période 1880-2008 et les sous-périodes susmentionnées a été estimée 3 . La méthode d'estimation GMM a été utilisée corrigeant le problème d'endogénéité dû à la causalité inverse allant de la croissance au taux d'endettement. L'analyse descriptive par pays et par panel ainsi que les régressions ont révélé la sensibilité de la relation à la période et aux échantillons de pays et est altérée par l'hétérogénéité des pays. L'hétérogénéité diminue lorsque l'on omet des pays importants de l'échantillon et se manifeste moins dans l'échantillon des pays de la zone euro.

À la suite de cette hétérogénéité détectée, nous avons jugé primordial le recours à des régressions par pays, ce qui, à notre connaissance, était rarement mené dans les recherches empiriques précédentes. Ainsi, le chapitre a également étudié le lien entre la croissance et la dette publique en utilisant une nouvelle et innovante méthode appelée "regression kink" développée par [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF]. Cette méthode a le pouvoir de détecter de manière endogène les points de tournure dans les relations économétriques étudiées. Appliquée à la relation dette et croissance pour chaque pays, elle met en évidence différentes formes de relations entre la dette publique et la croissance économique. Par conséquent, certains pays peuvent croître avec des ratios d'endettement public élevés, pendant que d'autres pourraient voir leur croissance se contracter par rapport à des ratios d'endettement même faibles, tandis que la croissance dans d'autres pays s'avère insensible à la dette publique. L'étude révèle également l'instabilité de la relation dans le temps. Chaque pays se distingue par des relations différentes selon les périodes d'estimation considérées, en particulier lorsque la transition se fait entre des périodes connues pour certains changements spécifiques du système monétaire international.

Tous ces résultats rejettent l'existence d'un seuil commun et sa valeur de 90% comme le prétendent [START_REF] Reinhart | Growth in a time of debt[END_REF]. Néanmoins, il faut signaler que les travaux précédents n'adoptent pas généralement un cadre de modélisation impliquant d'autres équations et variables par lesquelles la dette publique interagit avec la croissance économique. Par conséquent, il convient d'étudier les effets de la dette publique sur la croissance économique considérant les caractéristiques propres à chaque pays, sans s'affranchir notamment des modèles théoriques pouvant expliquer les canaux de transmission des effets de la dette publique à la croissance économique.

Contribution empirique du Chapitre 2 : sensibilité du multiplicateur budgétaire aux variations de la dette publique et au cycle économique

Le deuxième chapitre est particulièrement consacré à approfondir la relation entre la dette publique et la croissance économique à court terme, notamment via l'évaluation des effets de la dette publique à travers les multiplicateurs de dépense. L'importance de cet exercice s'est inscrite dans le débat déclenché sur les multiplicateurs budgétaires par [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], prouvant qu'ils sont plus élevés en période de récession et plus faibles en temps d'expansion. En conséquence, une grande littérature sur les multiplicateurs budgétaires a émergé en considérant des déterminants autres que le cycle économique, à savoir, les régimes de change, les politiques monétaires, le degré d'ouverture, etc. Ceci a conduit à des résultats suscitant plusieurs controverses entre économistes adoptant des méthodes différentes et/ou des échantillons de pays et des périodes différents.

L'une des méthodes fréquemment sollicitées pour évaluer les multiplicateurs sont les modèles VAR structurels (SVAR), également adoptés dans ce chapitre. Nous utilisons une panoplie de ces modèles pour estimer les multiplicateurs de dépenses à l'aide de données trimestrielles, pour un échantillon de 18 pays de l'OCDE. Nous avons contrôlé les effets du cycle économique et les effets des mouvements de ratio de la dette publique pour déduire les multiplicateurs de dépenses dans ces conditions.

Les résultats montrent que, en contrôlant les effets du cycle économique, les multiplicateurs de dépenses sont beaucoup plus élevés en période de récession qu'en période d'expansion. Ces résultats sont en conformité avec ce qui est observé dans la littérature récente sur les multiplicateurs budgétaires, qui sont importants en période de récession et faibles, voire négatifs en période d'expansion. Compte tenu de ces résultats, les politiques budgétaires devraient être contracycliques. Ces résultats vont également à l'encontre de toute consolidation budgétaire fondée sur une réduction des dépenses en période de récession, ce qui pourrait nuire à l'économie.

En outre, en contrôlant de manière exogène les mouvements de la dette publique, indépendamment du cycle économique, il a été révélé que les multiplicateurs de dépenses sont plus importants en période d'accumulation qu'en période de contraction de la dette. En plus, contrôlant conjointement pour les mouvements de la dette publique et du cycle conjoncturel, les multiplicateurs sont plus élevés sous l'accumulation de la dette dans les deux cas d'expansion et de récession. Cependant, l'endogénéisation de la variable dette publique au PIB dans un SVAR conduit à des multiplicateurs plus élevés en récession qu'en expansion.

De plus, un modèle plus élargi a été établi sur une longue période de données trimestrielles pour les États-Unis (1966q1-2019q2), pays disposant de longues séries chronologiques trimestrielles d'un ensemble de six variables fiscales et monétaires prises en compte dans ce modèle. L'objectif de ce modèle était l'examen et l'explication des canaux de transmission des effets de la dette publique et des dépenses publiques sur la croissance économique en relation avec d'autres variables économiques en l'occurrence le taux d'intérêt, l'inflation et l'investissement privé. Les estimations de ce modèle ont été produites en considérant la variation du cycle conjoncturel.

Les principaux résultats de ce modèle montrent que les dépenses publiques ont des effets positifs mais de courte durée sur la croissance économique. En outre, la dette publique évince l'investissement privé "crowding out", entraînant une baisse du taux de croissance en période d'expansion, tandis qu'en période de récession, les effets de la dette publique sur la croissance sont positifs. Cet effet d'éviction peut jouer le rôle de relais sur les multiplicateurs de dépenses et pourrait expliquer, toutes choses égales par ailleurs, la faible taille des multiplicateurs de dépenses en expansion, alors qu'en période de récession, l'effet positif de la dette "crowding in" conduit à des multiplicateurs plus élevés.

Dans toute la panoplie des modèles SVAR examinés dans le deuxième chapitre, ceux-ci montrent clairement que pendant la période de récession, les effets sur les variables ont généralement tendance à persister. La convergence vers la trajectoire de long terme après les chocs se produit plus rapidement en période d'expansion qu'en période de récession. Cependant, malgré les principales conclusions du deuxième chapitre, l'approche SVAR, exigeant la stationnarité des variables comme condition nécessaire, est restreinte à l'évaluation notamment des effets de court terme des variables de la dette et des dépenses publiques. Cependant, compte tenu des effets théoriques de la dette publique à long terme, leur évaluation s'impose.

Contribution empirique du Chapitre 3 : Le ratio de dette publique potentiel à cibler à long terme est une fonction endogène de la productivité potentielle du capital public

En relation avec le sujet du seuil de dette publique discutée dans le chapitre 1, le troisième chapitre étend l'examen des effets de long terme de la dette publique dans le cadre des modèles théoriques, tenant compte des fondamentaux macroéconomiques propres à chaque pays. Par conséquent, un modèle de croissance endogène a été appliqué au même échantillon étudié dans le chapitre 1 constitué de 20 économies développées. Dans ce modèle, une formule paramétrée a été simulée pour une dette potentielle/limite qu'un pays pourrait cibler pour financer ses investissements productifs sans pour autant la dépasser. Ce potentiel, lié à la croissance économique et à la productivité du capital public ainsi qu'au taux d'intérêt, est dynamique, spécifique à chaque pays et dépendant du temps. De plus, celui-ci a tendance à évoluer à l'opposé de la dette publique réellement observée. Cela répond en particulier à la principale recommandation formulée dans le premier chapitre selon laquelle le seuil de la dette publique est propre à chaque pays et à la période et devrait être étudié compte tenu des fondamentaux économiques du pays. Il apporte notamment une contribution qui se distingue des limitations des recherches mises en évidence dans le premier chapitre, et qui fixent et testent en particulier des valeurs de seuils particulièrement exogènes et atemporels.

De plus, les résultats du troisième chapitre montrent que la dette publique simulée est passée en dessous du niveau observé de la dette en temps de crise pour de nombreux pays avancés, notamment les plus touchés par la crise. Cela constitue un message clair de recommandation de politique économique montrant que les pays sont de plus en plus à l'abri du danger de la dette publique tant que la dette potentielle (simulée) reste supérieure à la dette publique observée. Les résultats montrent que de nombreux pays sont soumis à une pression de la dette publique, en particulier après la crise financière de 2008-2009. Pour certains pays comme l'Irlande, ce stress est de courte durée, et la dette potentielle est rapidement redevenue plus élevée que la dette observée à la suite du redressement de l'activité économique juste quelques années après la crise. Cependant, pour de nombreux autres pays, les effets sont plus prolongés. La dette potentielle a également révélé que des pays comme la Grèce, la Belgique et, dans une certaine mesure, l'Italie, avaient des problèmes de dette accumulée au cours des périodes même avant la crise de 2008.

Empiriquement, la moyenne de la dette potentielle simulée en pourcentage du PIB sur la période étudiée est passée de valeurs plus élevées de 150% à 200% en Suisse, en Suède, au Danemark, en Norvège, aux États-Unis, en Autriche et aux Pays-Bas, à des valeurs moyennes de 80% à 120% enregistrées en France, en Allemagne, en Italie, en Espagne, au Portugal, au Royaume-Uni, en Australie et en Nouvelle-Zélande. Ces valeurs sont même réduites à environ 50% à 80% en temps de crise, notamment pour la Grèce (moins de 50%), le Royaume-Uni (60%), l'Italie et l'Espagne (50%) la France et l'Allemagne (80%) et la Belgique (environ 70%).

Ce chapitre a comme valeur ajoutée la modélisation de la limite d'endettement publique comme fonction endogène dépendante de la productivité du capital public, du taux d'intérêt de long terme et de la croissance économique. La série des dépenses publiques potentielles montre une tendance à la baisse dans le temps mais toujours plus élevée que celle observée dans de nombreux pays de l'échantillon. Cette évolution est due à la tendance générale à la baisse de la productivité du stock de capital public, en particulier pendant l'époque de la grande modération . Le message de politique économique est que l'accroissement de la dette potentielle cible, requière nécessairement l'amélioration de la productivité du capital public. D'où la nécessité de sélectionner les types de dépenses publiques susceptibles d'améliorer cette productivité. Pour reformuler la déclaration de [START_REF] Krugman | The Age of Diminished Expectations: U.S. Economic Policy in the 1990s[END_REF] sur l'importance de la productivité à long terme, "la productivité n'est pas tout, mais à long terme, c'est presque tout". L'amélioration de la productivité pourrait être réalisable par le choix de dépenses publiques plus productives, ce qui implique la sélection de projets ayant des multiplicateurs plus élevés.

Conclusion

Dans les trois chapitres, la thèse s'oppose à tout seuil d'endettement commun s'appliquant à tous les pays. Le sujet de la croissance économique et de la dette publique reste néanmoins l'un des sujets les plus débattus de la macroéconomie après la crise financière de 2008-2009. Cette importance sera maintenue et davantage de recherches à ce sujet sont anticipées à moyen et long terme pour de nombreux événements d'actualité. Effectivement, la crise sanitaire de 2020, en raison de mesures d'urgence rigoureuses et de confinement de la population, conduit à l'hibernation de presque tous les secteurs économiques pendant plusieurs mois. Par conséquent, tous les experts et institutions de prospection prévoient une inévitable récession, et même une dépression prolongée, dans presque toutes les économies mondiales. Toutes les mesures susceptibles d'aggraver les déficits et d'augmenter le niveau de la dette publique, combinées à une contraction du PIB, conduiraient à une flambée des ratios d'endettement public.

Au regard de ces mesures, certains économistes s'attendent à ce que ces ratios augmentent d'environ 20 à 40 points de PIB pour de nombreux pays. Selon [START_REF] Kose | Global Waves of Debt: Causes and Consequences[END_REF], des augmentations similaires ont été observées lors des crises précédentes. En effet, le ratio d'endettement a flambé de 31 et 35 points de pourcentage respectivement pour l'Indonésie et la Thaïlande lors de la crise financière de 1997, et de 27 et 38 points de pourcentage respectivement pour la Lettonie et l'Irlande lors de la crise de 2008-2009. La reprise de la croissance économique, incertaine, est conditionnée par la durée des mesures de confinement sujet à l'évolution de la pandémie Covid-19 et au développement d'un vaccin contre celle-ci.

Dans ces conditions, la politique budgétaire, longtemps subordonnée à la politique monétaire dans la grande modération , est désormais activement sollicitée. La crise sanitaire actuelle conduit notamment à une plus grande implication de la politique budgétaire, surtout que la politique monétaire conventionnelle a déjà atteint ses limites, en particulier dans de nombreuses économies avancées où les taux d'intérêt nominaux atteignent et franchissent pour certains la borne inférieure zéro. Bien que certains points de vue considèrent que la faiblesse des taux d'intérêt réduit le coût de la dette publique, ce qui peut amener à une trajectoire de la dette publique soutenable, la menace du redressement des taux d'intérêt en réponse à une inflation future anticipée, conjuguée à une croissance morose, pourrait prolonger les pays endettés dans des vagues de crise de la dette souveraine.

Par conséquent, les recherches sur la politique budgétaire et les problèmes de l'endettement et la croissance économique resteront désormais très actives. De nombreuses questions méritent notamment d'être soulevées au sujet de la dette publique et la croissance économique au cours de la crise économique actuelle à la suite des retombées économiques et sociales de la crise sanitaire de 2020. Il s'agit notamment d'étudier de nombreux objectifs, notamment conflictuels, de la politique budgétaire visant à sauver des emplois ainsi que des entreprises et secteurs économiques en difficultés d'une part en particulier à court terme, et relancer la croissance économique et ainsi restaurer les recettes publiques, d'autre part à moyen terme. Ces deux objectifs sont inséparables de l'objectif de soutenir la croissance à long terme tout en considérant les effets ultérieurs de l'augmentation de la dette publique. En outre, la nature de la crise économique actuelle est susceptible de soulever de nombreux défis dans les politiques économiques. En particulier, cette crise est caractérisée par la coexistence des chocs négatifs d'offre et de demande, liés notamment aux mesures de confinement des populations et restrictions de mobilité internationale. Notamment, du côté offre, ceci a conduit à limiter les capacités de productions et d'exportations des entreprises et altérer les chaînes de valeurs globales pour certains secteurs. Du côté demande, les mesures du confinement ont limité la demande des ménages notamment en termes des services de voyages, transports, restaurations, ainsi que la demande en produits d'importations. Cette dualité du choc offre-demande pourrait avoir un impact important sur le cadre macroéconomique et particulièrement sur le cadre de la politique budgétaire. Il s'ensuit que la modélisation des effets de la politique budgétaire pourrait sortir du cadre traditionnel, notamment que cette crise ne semble pas ressembler aux crises économiques internationales vécues précédemment (de la grande dépression à la crise des subprimes). De plus, de nombreux défis nécessitant la coordination des politiques monétaires et budgétaires peuvent être à l'ordre du jour, dont les effets devront être évalués, en particulier dans la zone euro.

Public Debt and Economic Growth: A New Assessment

General Introduction

To finance their spending, governments generally have three options: first, they can raise taxes, second, they can create money and, third, they can borrow from domestic and/or foreign markets. The first option is politically not desirable and can even create economic downturns, harming economic growth and employment, especially for countries that have high tax burdens, which is the case for all developed countries. It also takes time to obtain a political consensus in a democratic system to raise taxes. The second option, the creation of money, whenever it is possible, can also cause significant damage to the economy by creating inflation and hence decreasing households' purchasing power. Furthermore, as the central banks in advanced countries are determined to gain and maintain their credibility vis-à-vis the private agents, the moneycreation option is likely to alter such credibility. The third option, namely, raising funds through borrowing, remains the quick option for financing public deficit needs, particularly short-term needs. The choice of borrowing to finance public deficits also has its disadvantages, with doubtful negative effects for economic growth, especially when the borrowed money is destined for expenditure that is not necessarily pro-growth, and the accumulated public debt is higher. The capacity of a country to pay its debt is generally assessed by the level of its total debt reported to its national income (GDP).

Over the last decade, public debt has increasingly become a worrying issue for many advanced countries, especially in the euro area. These countries implemented massive fiscal stimuli in 2009 in response to the severe downturns of the 2008 financial crisis. In around 2011 countries started to reverse the course from fiscal expansion to fiscal consolidation to reduce deficit and debt ratios, which were exacerbated by those fiscal stimuli with slow recovery and long-lasting recession. The fear of a European sovereign debt default by many periphery euro area countries urged them to turn to fiscal consolidation and austerity measures in Europe. This was also fuelled by the triggered debate about the presumable existence of a public debt threshold hampering economic growth [START_REF] Caner | Finding the tipping point when sovereign debt turns bad[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Reinhart | Growth in a time of debt[END_REF][START_REF] Lin | High dimensional threshold quantile regression with an application to debt overhang and economic growth[END_REF][START_REF] Bentour | On the public debt and growth threshold: one size does not necessarily fit all[END_REF].

Following the recession and the fiscal stimuli programmes, almost all the euro area countries have overcome the rule of a 3% and 60% threshold stated in the European Monetary Union (EMU) Stability and Growth Pact (SGP). Consequently, rigorous austerity measures have been implemented to restore confidence, especially across the periphery of the euro area, whereas recessionary effects were more pronounced, and the economic growth rate was still negative. The negative short-term spillovers undermined the incomplete path of recovery, meaning the euro faced a dilemma of boosting economic growth while reducing public debt and deficit. The tradeoff between boosting economic growth by fiscal stimuli to combat negative effects on social welfare and employment, and reducing public debt and deficit through programmes of fiscal adjustment (austerity, consolidation), depends on the size of the fiscal multipliers in each action.

Historical facts of public debt and growth in advanced economies

The history of public debt as a percentage of GDP in advanced economies shows that the period following the 2008 financial crisis has been, in terms of scale, approaching the period of the 1929 Great Depression and the devastating World War II era, where public debt ratios were abnormally high (Figure 1). What makes the difference between the two periods is that, in the recent period, public debt accumulated in peaceful periods of economic expansion and prosperity, which was worsened by the 2008 economic crisis, while the two aforementioned events (the 1929 Great Depression and World War II) were clearly the principal factors contributing to accumulating high public debt to GDP shares in that period.

Following the Great Depression and World War II period (1926-45), the public debt of advanced economies (the G20 advanced) § dropped down from a high average approaching 120% to very moderate levels ranging between 20% and 40%. This stable average was sustained for a period of around thirty years, labelled "Les Trentes Glorieuses" by the French economist Jean Fourastié. This prosperous period was characterized by strong economic growth under the stable Bretton Woods system of exchange rates. However, debt ratios started to rise, albeit not very high, from the mid-1970s, with the end of this system, but also as a result of the two 1970s oil price shocks. This period especially put pressure on the public finances of developing and low-income countries, for which the debt to GDP increased from an average of 24% in 1976 to 100% in 1994. This period is known as the developing countries' public debt crises.

Moreover, following a period of low interest rates and financial liberalization that started after the 1989 "Washington consensus", which contributed to lowering the cost of borrowing and encouraged access to the international financial market, contributing to appeasing the public debt of low-income and developing countries, the public debt to GDP of advanced countries once again started a sustained increase from an average of approximately 40% to more than 90% in 2015. The latter level of public debt ratio is considered by [START_REF] Reinhart | Growth in a time of debt[END_REF] to be an upper limit/threshold that, once passed, may reduce economic growth in advanced countries. This statement triggered an influx of empirical research studying the relationship between public debt ratios and economic growth, fundamentally based, for the majority, on these two variables alone. § The G20 advanced economies here should be distinguished from the G20 group of countries set in 1999 and becoming active after the 2008 economic crisis. The latter contains the big emerging countries (China, India, Brazil, etc.) and the European Union countries block, while the former is only for the advanced OECD countries that have an available long history of public data, as reported in the IMF databases (Abbas et al., 2010;[START_REF] Mbaye | Global Debt Database: Methodology and Sources[END_REF]. Source: Author's own construction using the IMF database [START_REF] Mbaye | Global Debt Database: Methodology and Sources[END_REF].

The previously analysed debt to GDP ratio, representing the burden of public debt of a country normalized by its output, increases when the numerator (the debt in level) grows faster than the denominator (the GDP). From an accounting perspective, the growth rate of the debt in level is the nominal interest rate (the cost of borrowing), the latter is compared to the nominal growth rate of GDP (or to the real growth rate once deflated) from the famous sustainability public debt equation involving the primary deficit/surplus. Figure 2 shows an analysis of the average real growth rate over the same long period, as was done previously for the debt to GDP ratio, for the G20 advanced countries. We notice that the growth rate is weak for the two decades of the Great Depression and World War II (1926-45), averaging 0.4%. On the contrary, the "Trente Glorieuses" period recorded a high average of 4.3%, followed by a declining growth rate performance in the third and fourth periods of 1976-95 and 1996-2015, respectively, to an average of 2.2% and 1.4%. Apparently, this analysis shows that public debt accumulation in advanced economies is linked to the growth rate performances in these countries. This fact is endorsed by putting together GDP growth rate averages by decades and the public debt to GDP ratio in Figure 3. The latter shows that economic growth following the post-war period is a decreasing path from a high level of 5.4% in the decade of 1946-55 until reaching a low level of 0.5% in 2006-15. On the other hand, the public debt to GDP average over decades has increased, from 30.8% in the 1970s to 79% in the last decade. However, this analysis could not show, at high levels, which variable may cause the other, which has been highly debated in the recent literature: high public debt levels may cause

Financial globalisation and the 2008 great recession

World War II and Great Depression

The "Trentes Glorieuses" period Developping countries public debt crises economic growth to slow down [START_REF] Reinhart | Growth in a time of debt[END_REF], especially in a time of peaceful economic expansion, as is the case for the period 1995-2007. 2. Debates about public debt effects on economic growth

The theoretical debate on the public debt effects

In theory, the effects of debt on economic growth were debated particularly in the post-war period following the surge in public debt of advanced countries. The literature distinguishes between the Keynesian short-term view, which assumes that government expenditure financed by public debt is more likely to stimulate the aggregate demand in the context of Keynesian prices and wage rigidities. However, according to the classical vision, which tends to focus on the long-term effects, government debt is likely to reduce capital stock and lower productivity, and then it reduces the output. Diverse channels are cited as the main reasons for these effects, especially as summarized by [START_REF] Hansen | The Public Debt Reconsidered: A Review Article[END_REF]. Higher public debt can trigger higher private saving (the Pigou effect), fewer incentives to work and invest, especially for owners of government bonds (the Kaldor effect), negative incentive effect of the additional taxes needed to finance the payment of interest and higher interest rates that are unfavourable to countering the inflationary impact of the "Pigou effect". Furthermore, [START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF] stated that public debt can crowd out private investment by reducing credit to the economy or by raising long-term interest rates on public borrowing. Both Keynesian and classical views are summarized in what is known as the "conventional analysis" of the effects of government debt, which reflects the dominant paradigm among economists and policy-makers [START_REF] Elmendorf | Government Debt[END_REF].

Another important theoretical contribution that fuels the debate about the public debt financing effects is the "Ricardian equivalence". The idea, originally attributed to Ricardo, states that economic growth can be insensitive to public debt, as consumers, assumed to be forward-looking (with rational expectations) can react by reducing their expenditure following a public expenditure increase by an equivalent amount. The reason is that they expect future taxes to finance the deficit generated by the new public expenditure. The equivalence is implied, as any public expenditure reducing public saving is assumed to be offset by an equivalent increase in private saving. This leads to unchanged total savings, and hence no effect is expected on other macroeconomic variables. Similarly, [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] shows that government bonds constitute an asset to their owners and a liability to taxpayers. Overall, no net wealth will be created, and the effect is null. The ideas of Ricardo-Barro effects of debt somehow invoke the redistribution of such effects across generations. They are especially discussed in the scope of intergenerational transfers and have been analysed in the first models of overlapping generations [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF][START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF].

The debate about the short-term analysis between economists (Keynesians, new Keynesians, classical and new classical) focuses on the composition of public spending, for which classical and neoclassical economists consider that capital expenditure, but not necessarily current expenditure, may have positive effects. This view is contrasted by Keynesians arguing that the effects of spending are always positive, with differences in terms of their efficiency, which may be higher for capital expenditure than other types of expenditure. These opposing views are gathered by [START_REF] Aschauer | Do states optimize? Public capital and economic growth[END_REF], who assumes that the short-term relationship between debt and growth could be positive as a result of the impact of financed capital expenditure on growth, while the long-term relationship could be reversed because of the high-risk premium following high public debt, raising the cost of debt. For [START_REF] Blanchard | Comments on Alan Blinder's 'The Case Against the Case Against Discretionary Policy[END_REF], the negative association between debt and growth could be attributed to delayed counter-cyclical tax policies, which means that countries in recession are adopting expansionary fiscal policies to boost growth and, in times of expansion, restrictive policies to reduce debt levels. The relationship between debt and growth was debated further following the 2008 financial crisis in the wake of much recent empirical research.

The empirical debate on the public debt threshold effects on economic growth

In advanced economies, the trend of public debt in the period of pre-crisis was exacerbated by the fiscal stimulus implemented in the 2008-9 period of crisis. At that time, a controversial paper by [START_REF] Reinhart | Growth in a time of debt[END_REF] reported that, for a sample of 20 advanced countries, there is a 90% common threshold of the government debt to GDP ratio, over which debt has a negative effect on economic growth. This triggered an influx of research, creating an empirical debate with many controversial results about the existence of the public debt threshold, from which the debt-growth relationship changed its sign.

The empirical debate on the effects of public debt on economic growth is of particular importance, as its outcome has significant policy actions. In particular, if economic growth is revealed to be reduced by high levels of public debt, as assumed by [START_REF] Reinhart | Growth in a time of debt[END_REF] and other research supporting their results [START_REF] Caner | Finding the tipping point when sovereign debt turns bad[END_REF][START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Lin | High dimensional threshold quantile regression with an application to debt overhang and economic growth[END_REF], expansionary fiscal policies that may have positive effects in the short term may reduce long-term economic growth, fully or partially offsetting the fiscal stimulus shortterm effects.

The debate about the public debt threshold has intensified, as several authors have contested the Reinhart andRogoff (2010) findings (Fergusson and[START_REF] Ferguson | A world upside down? Deficit fantasies in the great recession[END_REF][START_REF] Minea | Is High Public Debt Always Harmful to Economic Growth? Reinhart and Rogoff and Some Complex Nonlinearities[END_REF][START_REF] Baglan | Government debt and macroeconomic activity: a predictive analysis for advanced economies[END_REF][START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF][START_REF] Egert | The 90% public debt threshold: the rise and fall of a stylized fact[END_REF], especially after the revelation of some codification and calculation errors in the [START_REF] Reinhart | Growth in a time of debt[END_REF] article by [START_REF] Herndon | Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff[END_REF]. The summary of such results could be gathered under three groups: a first group of empirical research focusing mainly on the examination of a concave, non-linear relationship between debt and growth [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF][START_REF] Kumar | Public Debt and Growth[END_REF][START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF][START_REF] Eberhardt | Public debt and growth: Heterogeneity and nonlinearity[END_REF][START_REF] Chudik | Is there a debt-threshold effect on output growth?[END_REF]; a second group interested in the causality between debt and growth [START_REF] Panizza | Public debt and long-term economic growth: the research and policy agenda[END_REF]Presbitero, 2012, 2013;[START_REF] Sanzo | Public debt and growth in the Euro area: evidence from parametric and nonparametric Granger causality[END_REF][START_REF] Gomez-Puig | On the bi-directional causal relationship between public debt and economic growth in EMU countries[END_REF]; and a third group of studies that examine the impacts of other institutional and macroeconomic variables interfering with the relationship between debt and growth [START_REF] Greiner | Economic Growth, Public Debt and Welfare: Comparing Three Budgetary Rules[END_REF][START_REF] Kourtellos | The effect of public debt on growth in multiple regimes[END_REF][START_REF] Pan | Co-movement of Government Debt and Economic Growth in the Euro-area: A Bayesian Dynamic Factor Model Analysis[END_REF][START_REF] Sharpe | Institutional arrangements and public debt threshold limits[END_REF][START_REF] Marchionne | Growth, debt and inequality[END_REF]. The results of all this research did not lead to any confirmed consensus.

Generally, assessments of the effects of fiscal policies are quantified by the fiscal multiplier values. The distinction of public expenditure efficiency in Keynesian/classical analysis (as mentioned in the theoretical debate) by type (current, capital, defence, social, etc.) is empirically linked to their multipliers' estimates. In this vein, another important strand of empirical research was triggered in the aftermath of the financial crisis, revealing more about the sensitivity of such multipliers to many economic and institutional determinants.

The debate on the fiscal multiplier value

Despite the fact that the previous debate about the impact of government debt on economic growth considers the direct relationship between growth and public debt, the channels through which such effects materialize are related to the fiscal multiplier effects, particularly in the short term. The fiscal multiplier assessment has been extensively reconsidered following the development of econometrics and statistics. Since the 2008 financial crisis, a significant amount of literature assessing fiscal multipliers has emerged [START_REF] Romer | What Have We Learned about Fiscal Policy from the Crisis?[END_REF][START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF][START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF]Auerbach andGorodnichenko, 2012, 2013;[START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF].

The main findings of this literature reveal key differences in the size of the multipliers. In fact, the multiplier's value showed sensitivity to a variety of determinants that were not (or rarely) considered before the 2008 crisis. Fiscal multipliers are especially time-and country-specific, and even sensitive to the assessment method [START_REF] Batini | Successful Austerity in the United States, Europe and Japan[END_REF][START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF]. Furthermore, the fiscal multipliers are found to be sensitive to the business cycle; in particular, fiscal spending multipliers tend to be larger in recessions than in periods of expansion (Auerbach andGorodnichenko, 2012, 2013;[START_REF] Barro | Macroeconomic Effects from Government Purchases and Taxes[END_REF][START_REF] Parker | On Measuring the Effects of Fiscal Policy in Recessions[END_REF][START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF][START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF][START_REF] Fazzari | State dependent effects of fiscal policy[END_REF][START_REF] Glocker | Time-varying fiscal spending multipliers in the UK[END_REF]. Other research has led to ascertaining the vulnerability of fiscal multipliers to other determinants and not necessarily conditioned by the state of the economy in the business cycle. These determinants are fiscal position measured by the level of debt ratios and/or deficits [START_REF] Corsetti | Sovereign risk, fiscal policy, and macroeconomic stability[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF], the constrained monetary policy, either by the zero lower bound (ZLB) interest rate (liquidity trap) or by the loss of monetary independence, as in a pegged exchange rate or a monetary union [START_REF] Hall | By how much does GDP rise if the Government buys more output?[END_REF][START_REF] Cogan | New Keynesian versus old Keynesian government spending multipliers[END_REF][START_REF] Eichenbaum | When Is the Government Spending Multiplier Large?[END_REF][START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF].

Nevertheless, the very recent works of [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF] and [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF] consider that government spending multipliers are, on average, lower than unity. This contrasts with the tendency of the post-2008 crisis research confirming larger multipliers, especially in recessions, which could reach the value of 2. This is also in line with the same consensus on spending multipliers before the 2008 recession, considered to be weak, and that fiscal policy effects are short-lived [START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF]. In particular, fiscal policy effects, taking into account the fiscal position of the economy, measured by the level of public debt and/or fiscal deficit, have been highly debated in the aftermath of the 2008 financial crisis [START_REF] Boussard | Fiscal Multipliers and Public Debt Dynamics in Consolidations[END_REF][START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF]Blot et al., 2014b;[START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF][START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF][START_REF] Perdichizzi | Estimating Fiscal multipliers in the Eurozone: A Nonlinear Panel Data Approach[END_REF][START_REF] Poghosyan | How Do Public Debt Cycles Interact with Financial Cycles?[END_REF][START_REF] Auerbach | Fiscal Stimulus and Fiscal Sustainability[END_REF][START_REF] Afonso | Fiscal Multipliers in the Eurozone: A SVAR analysis[END_REF][START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF][START_REF] Broner | Fiscal Multipliers and Foreign Holdings of Public Debt[END_REF]. These contrasting results about spending multipliers still make it interesting to reconsider studying fiscal multipliers and to contribute to this unsettled debate.

Very recently, in a presidential lecture of the American Economic Association, [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] triggered another wave of public debt and growth debate related to the fiscal cost of high public debt, as well as its effect on welfare. He particularly minimized worries about the public debt cost for the American economy as, in historical records, the nominal interest rate has remained, on average (except in some small periods around the 1980s), below the nominal growth rate.

The debate on the effects of public debt in economic models

To assess the effects of government debt, many theoretical growth models have been designed. [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF] model was the basis for the first class of the infinitely lived agents' models.

Later, the debate between economists about agents' lifetime horizon, and the type of intergenerational operative transfer linkages between such agents, led to the concept of modes of overlapping generations (families/dynasties) being built to account for the existence or absence of continuity between generations provided by such linkages [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF][START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF].

The debate was focused on the implications of the altruism between generations and the lifetime agents' horizon in determining the existence of government debt effects on agents' behaviour in terms of saving, capital accumulation, consumers' utility and interest rates. Important contributions in this sense are those of, for example, [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF], [START_REF] Yaari | Uncertain lifetime, life insurance, and the theory of the consumer[END_REF], [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF], [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF], [START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF], [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF]Aiyagari ( , 1987)), [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF] and [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF]. The redistributive effects across generations have been much debated in the post-war period. Buchanan (1958) and Meade (1958), discussing the contributions of their predecessors, particularly Lerner (1943), show that public debt does not constitute any burden for the present taxpayers. The burden is instead transferred, partially or totally, to future generations that will have to pay taxes to service the debt (Bowen et al., 1960;[START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF]. Furthermore, advocates of the Ricardian equivalence show that debt neutrality could happen, depending particularly on the existence of operative altruistic links (bequests) between generations [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF]. In this way, the debate emerged, especially with useful contributions modelling fiscal policy insights, precisely the debttax swap and their effects on welfare utility and interest rates. This also created an intense debate between the neoclassicists and proponents of the Ricardian-equivalence conjecture [START_REF] Barro | Perceived wealth in bonds and social security and the Ricardian equivalence theorem: Reply to Feldstein and Buchanan[END_REF]Feldstein, 1976;[START_REF] Cukierman | A Political Theory of Government Debt and Deficits in a Neo-Ricardian Framework[END_REF].

The public debt effects are also considered in the political economy of public debt. In this regard, two approaches have been debated: the normative approach, where the government is a social planner for whom the priority is to maximize the social welfare of its individuals [START_REF] Barro | On the determination of the public debt[END_REF]Lucas and Stockey, 1983;[START_REF] Aiyagari | Optimal Taxation without State-Contingent Debt[END_REF]; and the positive approach, which considers public debt as a state variable used by each government as a strategy to influence its successor's choices or as a way to shape private economic agents' expectations [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF]. Hence, the most disseminated ideas were related to the effects of fiscal policy under governments following committed rules versus discretionary policies. In particular, the government time inconsistency has an impact on the way the economic agents form expectations affecting their economic decisions [START_REF] Kydland | Rules Rather than Discretion: The Inconsistency of Optimal Plans[END_REF].

The public debt effects are also examined in the class of endogenous growth models. The development of such models was pioneered by [START_REF] Romer | Increasing Returns and Long-Run Growth[END_REF], [START_REF] Lucas | On the Mechanics of Economic Development[END_REF] and [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]. These models were brought as an alternative to the neoclassical growth model of [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF] and [START_REF] Swan | Economic growth and capital accumulation[END_REF], which was unable to explain the persistent per capita non-zero growth rates in many developed economies and was therefore highlighted for missing the determinants of longterm growth. Thus, the endogenous growth framework encompasses other determinants of longterm growth, particularly in assessing fiscal policies, by incorporating the public sector into the productive sector [START_REF] Lucas | On the Mechanics of Economic Development[END_REF]Romer, 1989;[START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]Barro andSala-i-Martin, 1992, 1995;[START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF][START_REF] Jones | R&D-Based Models of Economic Growth[END_REF][START_REF] Jones | Population and Ideas: A Theory of Endogenous Growth[END_REF][START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF][START_REF] Turnovsky | Fiscal policy in a growing economy with public capital[END_REF][START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF][START_REF] Greiner | Public debt in a basic endogenous growth model[END_REF][START_REF] Greiner | Human capital formation and public debt: growth and welfare effects of three different deficit policies[END_REF][START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF][START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF].

Recently, fiscal policy, and particularly government debt, was also modelled under the class of the new Keynesian models. The pioneering works in the new Keynesian modelling framework are principally those of [START_REF] Christiano | Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy[END_REF] and [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF]. The latter differ from the models of the overlapping generations by assuming distortionary taxes instead of lump-sum taxes, as particularly assumed in the overlapping generation models. Furthermore, they join the literature of the political economy of debt by discussing government policies under commitment or discretion rules. In particular, some authors argue that optimal public debt would follow a random walk process whenever the government can achieve a time-inconsistent policy commitment [START_REF] Benigno | Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach[END_REF][START_REF] Schmitt-Grohe | Optimal Monetary and Fiscal Policy under Sticky Prices[END_REF]. The important empirical research of these models has flourished recently [START_REF] Leith | Fiscal sustainability in a new Keynesian model[END_REF][START_REF] Mayer | Government debt, inflation dynamics and the transmission of fiscal policy shocks[END_REF].

Despite important contributions of the previous classes of models in assessing the effects of government debt and fiscal policy, the new Keynesian models have been subject, in particular, to Mankiw's criticism. [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF] contributed by the "savers-spenders" theory, which has influenced much of the empirical research on fiscal policy, trying to consider the behaviour following the rule of thumb, especially in the New Keynesian models. In this way, [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] show that this class of models is not yet useful for public policy analysis. In particular, they address their critics on the model of [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF], which constitutes the fundamental reference for many recent contributions and policy-makers using the new Keynesian analysis framework.

Interest of the thesis

Following the previous preliminary analysis showing the soaring levels of public debt in advanced economies, as well as the debates through the theoretical and empirical literature on the public debt effects on economic growth, the subject of public debt and economic growth linkages, which constitute the core of this thesis, deserves to be reconsidered among academicians, as well as policy-makers. Furthermore, the new reconsideration of fiscal policy effects assessments through fiscal multipliers, which were revealed to be sensitive to the business cycle, and particularly to the fiscal position represented by the public debt or deficit situations, as well as other economic and institutional determinants, adds more enthusiasm to this subject and justifies the choice of thesis subject.

Therefore, the current thesis builds on the very recent literature findings on the fiscal policy debates, particularly on the public debt threshold effects and fiscal multipliers, while also paying attention to the old literature on the public debt effects, which flourished in the post-war era (World War II) and constituted the theoretical core of many public debt effects and economic growth models. Moreover, it contributes empirically to the public debt and economic growth literature using a variety of economic and econometric models across all three chapters of this thesis.

Given the high indebtedness of the advanced economies, our focus was on a sample of advanced countries. It is constituted by 20 OECD advanced countries, of which 11 are euro area members, namely, Australia, Austria, Belgium, Canada, Denmark, France, Germany, Greece, Ireland, Italy, Japan, The Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom and the United States. The focus on this sample was justified for many reasons:

-The economic importance of this group of advanced countries influencing the world economies, and particularly that they weigh on the international economic and financial system (systemic risk).

-The high public debt to GDP accumulated for the majority of these countries, and many of these countries have encountered sovereign debt problems, either in the current financial crisis or previously.

-The sample is constituted by countries that have been highly studied and for which results have been debated in the post-2008 financial crisis in terms of public debt and fiscal policy issues, which allows us to turn our results into important findings in the literature.

-Finally, the availability of a long history of data, annually as well as quarterly, is also an important reason for the choice of this sample.

Plan of the thesis

The first chapter of this thesis, entitled "Public debt and economic growth: one size does not necessarily fit all", highlights the highly-debated issue in the empirical literature about the existence of a debt threshold inversing the relationship between public debt and economic growth from a positive relationship for low and moderate ratios of public debt to a negative one for higher public debt ratios. Our empirical application in the first chapter, applying panel polynomial equation regression, as in [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF] and many other papers that build on it, and a new method of kink regression by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF], applied to individual countries, which searches endogenously the public debt ratio threshold, concludes that the turning point in the relationship between public debt and growth is rather a country-and time-specific one. Following these findings, we recommend in the first chapter studying the relationship between public debt and economic growth, taking into account countries' macroeconomic fundamentals, which should be captured by an appropriate theoretical modelling framework rather than a simple econometric relationship implying two main economic variables (public debt ratio and economic growth), as done by most of the empirical literature following the [START_REF] Reinhart | Growth in a time of debt[END_REF] paper.

As public debt is destined to finance public expenditure, we assess, especially in the short term, the effects and relationship of public debt on growth through the impact of government expenditure on the output. This impact is known as Keynesian multipliers. Therefore, the second chapter, "Short-term effects of public debt on growth: the spending multiplier pass-through", assesses the short-term effects of public debt, particularly through fiscal multipliers. As the body of literature studying the effects of (optimal) fiscal policy is substantial in size, our focus in this chapter, in the literature review and in our application, is dedicated to the fiscal policy effects through spending multipliers (no tax/income multipliers are considered).

Applying the methodology of a structural vector autoregressive (SVAR) model for each country, the results show that the expenditure multipliers are much higher in times of recession than in times of expansion. Moreover, it is observed that, generally, the idea of spending multipliers being weak, and even negative in recent decades compared to the 1960s, 1970s and 1980s, is not well supported by our findings. The previous results are in line with what is observed in the recent literature about fiscal multipliers, in advanced economies, being large in times of recession and weak or even negative in times of expansion.

Furthermore, introducing endogenously the public debt to GDP variable in an SVAR model leads to higher multipliers in recession than expansion for each country of the sample. These results were checked by a large SVAR model conducted on a long history of quarterly data for the United States, as the country with long quarterly times series of six fiscal and monetary variables available, as considered in this model, namely, public debt, GDP, private investment, public expenditure, interest rates and inflation. The main results of this model show that government expenditure has positive but short-lived effects on economic growth. Furthermore, public debt crowds out private investment, leading to a decreasing growth rate in times of expansion, while in times of recession the public debt effects on growth are positive. This crowding-out effect may play pass-through to the expenditure multipliers and could explain, ceteris paribus, the weak size of spending multipliers in times of recession, while the crowding-in effect leads to higher multipliers. Consequently, this chapter concludes on the fiscal policy effects and spending multipliers and contributes to the current economic literature.

The previous chapter considers a short-term approach, while public debt also has prolonged longterm effects, especially in the classical models. Therefore, the third chapter, entitled "Public debt effects in theory-based models with an empirical assessment of the potential public debt", undertakes the essence of the relationship between public debt and economic growth in all theoretical models, citing the over-lapping generations (OLG) models, the infinitely lived agents (ILA) models, the endogenous growth models and the new Keynesian models. For several considerations that were justified in this chapter, the endogenous growth model was chosen as a framework for our application to assess the long-term effects of public debt on economic growth.

The main findings of this chapter are the ability to derive, for each country, an optimal potential endogenous government debt as a time series derived from potential public investment (the government gross fixed capital formation). This parametrized public debt, drawn from an economic model proper to each country, based on a Cobb-Douglas production function augmented by public and human capital, jointly with a public budget constraint equation, is an important result against vehiculating any exogenous threshold, therefore endorsing the conjecture of the first chapter that there is no specific threshold that fits all. Furthermore, for many advanced countries with high actual public debt, potential debt is overcome by actual debt in many periods, especially in times of crisis. Consequently, the third chapter closes with the effects of public debt and contributes to the debate about fiscal policy in the long term.

Figure 4 presents a graphical structure of the thesis, illustrating its main parts and describing its steps as well as the important findings and consequent recommendations.

Results

For each country, optimal public debt is a time series derived from potential public investment -Survey of theoretical public debt models: ILA, OLG, endogenous growth and new Keynesian models -Normative versus positive approach of the public debt effects -Theory of saving-spending [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF]

Introduction

In 2010, the signs of a sovereign debt crisis in Europe and other advanced economies divided economists and policy-makers regarding the efficiency of the economic policies necessary to overcome the recession. Some are in favor of continuing the stimulus packages implemented at the beginning of the crisis, while others call for urgent fiscal consolidation and austerity policies to reduce the public deficit and debt levels. The former, believing in the role of Keynesian multipliers, make growth a priority to stabilize the deficit and debt ratios. The latter hold that high levels of debt hamper growth, which can be explained by a negative causality running from debt to economic growth. In both cases, the relationship between public debt and economic growth is at the forefront implying many controversies.

Thus, in what is an extremely controversial subject, [START_REF] Reinhart | Growth in a time of debt[END_REF] (RR (2010) hereafter) reported that, for a sample of 20 advanced countries, there is a 90% common threshold of the government debt-to-GDP ratio over which debt has a negative effect on economic growth. Several authors 5 have contested this result, especially after the revelation of some codification and calculation errors in RR's (2010) article. 6 This resulted in an influx of research using different methods to study a set of econometric properties likely to alter the link between economic growth and public debt.

The trend among emerging empirical literature has been the examination of a concave non-linear relationship between debt and growth, with some focusing on a variety of econometric issues, such as endogeneity, causality, and heterogeneity rather than using a proper theoretical modeling framework. Despite the use of a variety of econometric tools to overcome such issues, no consensus has been found on the robust existence of a single threshold that fit all and at which debt starts to alter growth. Moreover, despite most researchers agreeing on the negative correlation between high public debt and economic growth, it is difficult to agree on the direction of causality between debt and growth in the long term as suggested by the economic theory. Many economists warn against the hasty interpretation of this research and call for more investigation on this subject [START_REF] Panizza | Public Debt and Economic Growth Is There a Causal Effect?[END_REF][START_REF] Minea | Is High Public Debt Always Harmful to Economic Growth? Reinhart and Rogoff and Some Complex Nonlinearities[END_REF]. According to [START_REF] Minea | Is High Public Debt Always Harmful to Economic Growth? Reinhart and Rogoff and Some Complex Nonlinearities[END_REF], institutions such as the OECD, the EU Commission and the French Report on Public Finance of April 2010 have a tendency to be influenced by the 90% threshold of RR (2010) in acting to reduce their public debt using austerity measures. The authors warn, in particular, against drawing conclusions based on considering exogenous thresholds instead of searching endogenously for such thresholds as the relationship between public debt and growth, which could be altered by complex non-linearities and sudden jumps around high debt thresholds. Their findings also suggest that there may be a regime in which very high public debt is positively correlated with economic growth, similarly to what is observed with low and moderate levels of public debt.

In theory, the effects of debt on economic growth are summarized by the "conventional analysis" which reflects the dominant views among economists and policymakers [START_REF] Elmendorf | Government Debt[END_REF]. This approach adopts the deficit budget Keynesian view in the short term, assuming that a deficit financed by government bonds boosts economic activity. Government expenditures act as a stimulus for the aggregate demand in the context of Keynesian prices and wages rigidities. Nevertheless, for the short term, the debate is rather on the composition of public spending. The debt intended to finance the capital goods, would have positive short-term effects, which may become negative in the long run due to the induced risk premium following high debt [START_REF] Aschauer | Do states optimize? Public capital and economic growth[END_REF]. Keynesians report that the spending effect is positive for all expenditure types, and only differs in efficiency.

In the long term, the economy adheres to the classical vision, for which government debt reduces capital stock and lower productivity, hence, reducing the output. This goes through diverse channels as [START_REF] Hansen | The Public Debt Reconsidered: A Review Article[END_REF] reported: higher debt can trigger higher private saving, less incentives to work and invest especially for the owners of the government bonds and negative incentive effect due to additional taxes needed to pay the debt service. Likewise, public debt can crowd out private investment by reducing credit to the economy or by raising long-term interest rates [START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF].

However, according to [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF], economic growth can be insensitive to public debt. Under the assumption of perfect information, which assumes rational expectations, economic agents expect future taxes to finance the deficit generated by the new public spending and thus reduce their expenditures. This effect is known as Ricardian equivalence 7 : any public expenditure reducing public saving is assumed offset by an increase in private saving by an equivalent amount. Consequently, the national saving is unchanged and no effect is expected on other economic variables.

If theory suggests mainly a causality running from debt to economic growth, few papers examining empirically this issue have not reached any consensus about the direction of the causality [START_REF] Panizza | Public Debt and Economic Growth Is There a Causal Effect?[END_REF]Gomez-Puig and[START_REF] Gomez-Puig | On the bi-directional causal relationship between public debt and economic growth in EMU countries[END_REF][START_REF] Sanzo | Public debt and growth in the Euro area: evidence from parametric and nonparametric Granger causality[END_REF][START_REF] Sanzo | Public debt and growth in the Euro area: evidence from parametric and nonparametric Granger causality[END_REF]. The relationship between public debt and economic growth could also be eclipsed by the interference of other economic and institutional variables. Some authors criticized previous empirical works for the omission of such institutional variables in the debt growth analysis [START_REF] Panizza | Public debt and long-term economic growth: the research and policy agenda[END_REF][START_REF] Kourtellos | The effect of public debt on growth in multiple regimes[END_REF]. Nevertheless, few researches tried to enrich the debt growth relationship 7 The name Ricardian equivalence is due to [START_REF] Buchanan | Barro on the Ricardian Equivalence Theorem[END_REF] who found a similarity between the proposal of [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] and that of David Ricardo. Moreover, O'Driscoll (1977) notes that [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] proposition contradicts Ricardo's conclusions that there is no equivalence of choice between financing a war by taxation or a debt and decides to call it "Ricardian non-equivalence". [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] proposal is also referred to as modern Ricardian equivalence theorem [START_REF] Ahiakpor | the Modern Ricardian Equivalence Theorem: Drawing the Wrong Conclusions from David Ricardo's Analysis[END_REF]. by other macroeconomic and institutional variables (Sharpe, 2013, Pan and[START_REF] Pan | Co-movement of Government Debt and Economic Growth in the Euro-area: A Bayesian Dynamic Factor Model Analysis[END_REF][START_REF] Greiner | Economic Growth, Public Debt and Welfare: Comparing Three Budgetary Rules[END_REF][START_REF] Marchionne | Growth, debt and inequality[END_REF].

Given the absence of consensus on a tolerable level of debt, questions still need to be asked: Does public debt that is too high reduce economic growth? Does the turning point in the relationship between growth and debt exist for all countries and at all times? What is its size? Does it fit all countries or is it a country-specific one?

The purpose of this article is to investigate the existence of the debt threshold effect, its size and whether it fits all countries or varies across countries and periods. The previous empirical studies have several limitations: some, using a long period of analysis as in RR (2010) suffer from methodological issues. They generally adopt simple descriptive statistical approaches to generalize for a common threshold that fits all. While those using different econometric tools could have a short time sample bias. Generally, their samples start after the 1970s. The main papers set exogenous thresholds to test. Furthermore, countries differ in their economic policies affecting the debt-growth relationship, and the panel approach adopted by all the previous empirical literature suffers from a high heterogeneity bias. This paper adds to the existing literature by adopting a different approach. Unlike previous research that has examined the debt-growth thresholds across panels of countries, our methodology gives priority to country specific analysis. Surveying the previous empirical approaches and starting from their limitations, we use a novel econometric method proposed by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] that searches thresholds endogenously for individual countries. We undertake estimations using long time period of 1880-2010 and sub-periods depending on the World major economic and political events. We also run panel regressions by varying countries sample according to some sizeable countries, exchange rate regime and type of government expenditures and effectiveness.

The remainder of the paper is organized as follows. Section 2 reviews the existing literature. Section 3 describes the econometric methodology. Section 4 describes the data and descriptive statistics. Section 5 provides estimation results for country specific regressions. Section 6 presents estimation results for panel analysis. Section 7 concludes.

Literature review

The issue of the government debt threshold has been extensively studied since the 2010 debt crisis, provoking several controversies. Initiated by the early work of RR (2010), researchers have examined public debt thresholds for different panels of countries while correcting for econometric issues. Table 1 summarizes the main contributions.

Insert Table 1 about here RR (2010) found that the correlation between public debt and growth is low for normal debt levels and becomes strong and negative when the debt-to-GDP ratio exceeds 90%. They observe that median and average growth rates corresponding to debt ratios over this threshold shrink by 1 and 4 points respectively. This result, based on a simple descriptive statistical approach, has given rise to much empirical research examining the relationship between debt and growth using increasingly econometric methods.

In a subsequent paper, [START_REF] Reinhart | Public debt overhangs: Advanced economy episodes since 1800[END_REF] emphasized their previous findings of the 90% threshold by analyzing periods of public debt overhangs for a sample of 22 advanced economies going back to the nineteenth century.8 They defined a debt overhang period as a debt-to-GDP ratio of more than 90% lasting for at least five consecutive years. As a result, 26 periods were detected and 23 of these are associated with lower growth. On average, an annual growth lower by 1.2 percentage point than in periods of debt ratios less than 90%. However, from the 22 advanced countries, only 13 have episodes of debt overhang from which two countries (Italy and Greece) have both 8 periods of debt overhang (4 each). Therefore, the sample of countries, with different economic policy experiences, used to emphasize the 90% common rule is reduced. Furthermore, almost all episodes of high debt resulted from costly wars and the Great Depression and, only six countries have had a debt overhang in peacetime: Belgium, Canada, Greece, Ireland, Italy and Japan. So, should this small sample of heterogeneous countries in size, time sample and monetary sovereignty be sufficient for concluding about the common 90% threshold?

In fact, the conjecture of a common threshold does not seem to be accepted by many authors. For example, [START_REF] Ferguson | A world upside down? Deficit fantasies in the great recession[END_REF]) stated that RR (2009, 2010) "jumble big and small countries together from different areas and different political choices. This makes induced policy lessons from such samples a likely misleading exercise". They argue that "political choices for smaller countries are frequently influenced by external factors, while big countries like United States and Japan are the principal players in the international system of which policies affect the rest of the world". Consequently, the authors opposed the idea of a common threshold debt arguing using historical counter-examples. Especially, the United Kingdom constitutes an interesting fact countering Reinhart and Rogoff claim showing that the British industrial revolution flourished while debt-to-GDP ratio exceeded 200% for decades.

Empirically, an important controversy came from [START_REF] Herndon | Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff[END_REF]. By replicating the exercise of RR ( 2010), these authors corrected some data processing errors. Consequently, the average growth rate of countries with government debt-to-GDP ratios of more than 90% is not dramatically different from that calculated for countries with moderate to high debt-to-GDP ratios. This paper triggered an influx of research examining debt thresholds using different econometric tools (Table 1).

A significant amount of research has replicated the same sample of 20 advanced countries used by RR (2010), finding different results that generally point to low levels of debt thresholds. [START_REF] Baglan | Government debt and macroeconomic activity: a predictive analysis for advanced economies[END_REF] used Bayesian inference and found a debt threshold of 20%. [START_REF] Egert | The 90% public debt threshold: the rise and fall of a stylized fact[END_REF] used the [START_REF] Hansen | Threshold effects in non-dynamic panels: estimation, testing, and inference[END_REF] method and found a debt threshold of 20 to 30%. [START_REF] Lee | Testing for a Debt-threshold Effect on Output Growth[END_REF] examining the relationship between public debt and median GDP growth suggest that the debt threshold may exist around 30%. Surprisingly, [START_REF] Minea | Is High Public Debt Always Harmful to Economic Growth? Reinhart and Rogoff and Some Complex Nonlinearities[END_REF], using panel smooth threshold regression (PSTR) models found a convex relationship between debt and growth where the effect is negative below a high debt threshold of 115% and positive above this threshold. However, these results are surrounded by more uncertainties and may result in dangerous consequences when translated into policy decisions.

Other researchers have used different samples and periods to study the long-term effects of debt on economic growth. For example, [START_REF] Pescatori | Debt and growth: Is there a magic threshold?[END_REF] analyzed debt and growth data over long period, considering lead economic growth by 1, 5, 10 and 15 years to be affected by the current debt. Their analysis rejects any threshold from which economic growth is undermined. However, they found that high debt increases output volatility. They also found that countries with high but declining debt grow as fast as countries with lower growth. [START_REF] Eberhardt | Public debt and growth: Heterogeneity and nonlinearity[END_REF] studied nonlinearity by correcting the heterogeneity of the debt-growth relationship across countries. Their results highlighted the negative non-robust relationship between public debt and long-term economic growth, but failed to determine a common debt threshold for all countries. [START_REF] Chudik | Is there a debt-threshold effect on output growth?[END_REF] developed tests for threshold effects in the context of dynamic heterogeneous panel data models and found no evidence of a universally applicable threshold effect. Regardless of the threshold, they found significant negative long-run effects of public debt build-up on output growth. Furthermore, Syssoyeva-Masson and De Sousa Andrade (2017) highlight the long memory of public debt series and recommend studying the debt-growth relationship in a longterm framework.

Nevertheless, other researchers seem to support RR's (2010) findings, albeit not necessarily the 90% debt threshold. [START_REF] Caner | Finding the tipping point when sovereign debt turns bad[END_REF] were the first to review the results of RR (2010) and confirm the negative link between public debt and economic growth above the 90% threshold. [START_REF] Kumar | Public Debt and Growth[END_REF] also highlighted a negative non-linear relationship for higher debt levels for a sample of advanced and emerging countries over the period of 1970-2007. Particularly, the per capita growth is 0.2% lower following a 10-percentage point increase in the debt ratio. Lin (2014) applied a threshold quantile Lasso regression to a sample of 62 cross-sections combining developing and developed countries over the period 1991-2005, and to individual countries for a subsample of data of 22 countries over the period 1961-2010. For cross-country analysis, he confirmed the 90% threshold for the median quintile as defended by RR (2010). However, for country-specific analysis, he demonstrated that tipping points range widely between 10% and 100% across countries. The widespread values of the threshold were emphasized in particular when controlling for macroeconomic and demographic changes. The existence and value of these thresholds increase by quintile, reflecting the asymmetric effects of debt on growth, and are more common in developing than developed countries. [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF] found a significant polynomial term between public debt and per capita economic growth considering a sample of 12 eurozone countries over the period of 1970-2009. Unlike research that has pointed to a defined threshold, their paper indicates an interval (90-100%) from which public debt starts to hamper economic growth.

Econometric Methodology

Unlike the previous research that essentially examined panel groups despite the aforementioned heterogeneity,9 we adopt a different approach in which we give more importance to country specific regressions. For this purpose, we first run an innovative methodology namely a regression kink recently developed by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF]. This method is more appropriate as it permit searching endogenously for unknown thresholds.

To support our results, we also run panel regressions in which we assume that economic growth is a non-linear10 (quadratic) form of debt. Our aim, by this second approach, is to show that we could find thresholds in the relationship between debt and growth in heterogeneous panel groups as shown by partisans of RR (2010) results, but these are instable by time and countries sample as well as other institutional characteristics.

Our approach for panel regressions is different from the previous researches as it considers long period of analysis split according to the major events in the international economic and political order, as well as, varying sample by country size and level of public expenditures and government effectiveness. This approach complements the first one in results: while the individual regressions show different relationship curves by countries that are also instable over time, the panel regressions show that threshold is highly affected by country sample and time period. Both approaches argue against a unique threshold that fit all countries.

Country specific methodology

For the individual regressions, we use the kink regression method developed by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] that searches for endogenous thresholds. 11 The regression function is everywhere continuous except on this threshold where the slope has a discontinuity. Instead of assuming exogenous known thresholds as in many previous empirical researches and by the traditional regression discontinuity models, this method considers that the threshold is unknown and should be estimated.

The recent regression kink with an unknown threshold constitutes an important advancement of the threshold regression models. The first class of such models used the regression discontinuity design (RDD), introduced early by [START_REF] Thistlethwaite | Regression-Discontinuity Analysis: An alternative to the ex post facto experiment[END_REF] and recently enhanced by regression kink design (RKD) [START_REF] Nielsen | Estimating the Effect of Student Aid on College Enrollment: Evidence from a Government Grant Policy Reform[END_REF] and emphasized theoretically by [START_REF] Card | Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design[END_REF]. Both RDD and RKD are especially involved when a policy variable of interest (the outcome) is totally or partially determined by a known assignment rule of an observed treatment variable (covariate). Both methods become important for identifying causal effects in observations settings in many areas such as educational outcomes, election outcomes and unemployment, among others [START_REF] Card | Regression Kink Design: Theory and Practice[END_REF]. 12 The only difference is that RDD uses a "discontinuity" or a "jump" in level of a treatment status at a threshold of an assignment variable, while RKD examines discontinuities in derivatives (slope discontinuities) rather than the level [START_REF] Athey | The State of Applied Econometrics: Causality and Policy Evaluation[END_REF]. Despite their important use, some authors warn that their results could be biased especially for smaller population size, and particularly in the presence of confounding nonlinearities between an assignment variable and an outcome variable [START_REF] Ando | How much should we trust regression-kink-design estimates?[END_REF].

As for [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] regression kink with an unknown threshold, it is the latest method to determine thresholds endogenously without the need for a treatment or an assignment variable as in the previous methods. The conventional regression kink design assumes that the threshold is known. This is suitable in many policy-oriented applications where the threshold is determined by policy [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF]. Instead, we treat the threshold as an unknown to be estimated. This method is particularly appropriate when either the threshold is not set by the policy, or when one wishes to investigate the robustness of this assumption. The features of such regression correspond highly with our aim of examining endogenous thresholds from a direct relationship between economic growth and public debt. We aim to confirm or deny the existence of debt thresholds rather than to measure any policy effects, as the previous methods do. [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] 13 developed an inference and estimation toolkit that tests for the presence of the threshold, estimation, and inference on the regression function and parameters.

Using (𝑎) -= 𝑚𝑖𝑛[𝑎, 0] and (𝑎) + = 𝑚𝑎𝑥[𝑎, 0] to denote the "negative part" and "positive part" of a real number a, Hansen's regression kink model takes the following form:

𝑔 𝑡 = 𝛽 1 (𝑑 𝑡 -𝛾) -+ 𝛽 2 (𝑑 𝑡 -𝛾) + + 𝛽 3 ′ ℎ 𝑡 + 𝜀 𝑡 (1)
where (𝑔 𝑡 , 𝑑 𝑡 , ℎ 𝑡 ) are, respectively, variables describing economic growth, public debt-to-GDP ratio, and a k-vector of other explanatory variables which includes an intercept. 𝜀 𝑡 is the error term, which is independent and identically distributed with zero mean and constant variance (𝜀 𝑡 ~𝑖𝑖𝑑(0, 𝜎 𝜀 2 )). The variables (𝑔 𝑡 , 𝑑 𝑡 , ℎ 𝑡 ) are observed for 𝑡 = 1, … , 𝑛. The parameters to be estimated are the regression slopes 𝛽 𝑖 , with 𝑖 = 1,2,3, and the parameter 𝛾 called the threshold or "kink point". In equation ( 1) the slope with respect to the variable d equals 𝛽 1 for values of 𝑑 𝑡 less than 𝛾, and equals 𝛽 2 for values of 𝑑 𝑡 greater than 𝛾; yet the regression function is continuous in variables 𝑑 and ℎ, except the slope with respect to 𝑑 which is discontinuous at 𝑑 = 𝛾 (kink point).

Equation ( 1) has 𝑝 = 3 + 𝑘 parameters. 𝛽 = (𝛽 1 , 𝛽 2 , 𝛽 3 ) are the regression slopes and are generally unconstrained so that 𝛽 ∈ 𝑅 𝑝-1 . However, for the parameter 𝛾, the model only makes sense if the threshold is in the interior of the support of the threshold variable 𝑑. We thus assume that 𝛾 ∈ Γwhere Γ is compact and strictly in the interior of the support of 𝑑.

To be applied to the debt growth relationship, we rewrite equation (1) with lagged independent variable 𝑑 𝑡-1 (so that this is plausibly pre-determined) and set ℎ 𝑡 = (𝑔 𝑡-1 , 1) and then 𝛽 3 = (𝛿, 𝑐) so that the regression contains a lagged dependent variable to account for dynamic effects and minimize autocorrelations. Equation (1) becomes:

𝑔 𝑡 = 𝛽 1 (𝑑 𝑡-1 -𝛾) -+ 𝛽 2 (𝑑 𝑡-1 -𝛾) + + 𝛿𝑔 𝑡-1 + 𝑐 + 𝜀 𝑡 (2)
Equation ( 2) can be written as 𝑔 𝑡 = 𝛽 ′ 𝑥 𝑡 (𝛾) + 𝜀 𝑡 , where 𝑥 𝑡 = ((𝑑 𝑡 -𝛾) -, (𝑑 𝑡 -𝛾) + , 𝑔 𝑡-1 ) ′ and the least squares criterion for estimation is:

𝑆 𝑛 (𝛽, 𝛾) = 1 𝑛 ∑ (𝑔 𝑡 -𝛽 ′ 𝑥 𝑡 (𝛾)) 2 𝑛 𝑡=1
(3) Minimizing (3) yields the least squares estimator:

(𝛽 ̂, 𝛾 ̂) = 𝑎𝑟𝑔 min 𝛽∈𝑅 𝑘-1 ,𝛾∈Γ {𝑆 𝑛 (𝛽, 𝛾)} (4)
The criterion 𝑆 𝑛 (𝛽, 𝛾) is quadratic in 𝛽 but non-convex in 𝛾. [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] uses a combination of concentration and grid search. Particularly, by concentration we write:

𝛾 ̂= arg 𝑚𝑖𝑛 𝛾∈𝛤 𝑚𝑖𝑛 𝛽∈𝑅 𝑘-1 {𝑆 𝑛 (𝛽, 𝛾)} = 𝑎𝑟𝑔 𝑚𝑖𝑛 𝛾∈𝛤 {𝑆 𝑛 (𝛽 ̂(𝛾), 𝛾)} = 1 𝑛 ∑ (𝑔 𝑡 -𝛽 ′ 𝑥 𝑡 (𝛾)) 2 𝑛 𝑡=1 (5)
Where, for a given 𝛾, the parameters 𝛽 ̂(𝛾) are the least squares coefficients from regressing 𝑔 𝑡 on 𝑥 𝑡 (𝛾). The kink point 𝛾 ̂ is determined by a grid search over 𝛾 ∈ Γ, and once found, the parameters 𝛽 ̂ are determined by standard least squares of 𝑔 𝑡 on 𝑥 𝑡 (𝛾 ̂).

The deduced regression function is then:

𝑔 𝑡 = 𝛽 ̂′𝑥 𝑡 (𝛾 ̂) + 𝑒̂𝑡 (6)
where 𝑒̂𝑡 are residuals with an estimated error variance:

𝜎 ̂2 = 1 𝑛 ∑ 𝑒̂𝑡 2 𝑛 𝑡=1 = 𝑆 𝑛 (𝛽 ̂(𝛾), 𝛾) (7)
In order to test for the unknown threshold, [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] conducted an algorithm14 to test the nested regression model (2) against the following linear model assuming 𝛽 1 = 𝛽 2 = 𝛽 𝑙 :

𝑔 𝑡 = 𝛽 𝑙 𝑑 𝑡-1 + 𝛿𝑔 𝑡-1 + 𝑐 + 𝜀 𝑡 (8)

Panel methodology

To investigate the existence of a threshold at which debt reduces growth, we proceed for the panel approach by the same way as in [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF]. 15 We estimate the following equation:

𝑔 𝑖,𝑡+5 = 𝛼𝑑 𝑖,𝑡 + 𝛽𝑑 𝑖,𝑡 2 + 𝛾 𝑖 + 𝜀 𝑖,𝑡 (9)
where 𝑔 𝑖,𝑡+5 is the 5-years lead economic growth for country 𝑖; 𝑑 𝑖,𝑡 is the debt to GDP ratio for country 𝑖 at time 𝑡, 𝛼 and 𝛽 are parameters associated with the debt and its square, 𝛾 𝑖 is the constant term associated with each country 𝑖 called fixed effect, and 𝜀 𝑖,𝑡 is the error term with zero mean and constant variance (𝜀 𝑖,𝑡 ~𝑖𝑖𝑑(0, 𝜎 𝜀 2 )). The time lag of five years is assumed: the current debt will likely affect growth after 5 years. This is the case where debt is more negatively correlated with growth (Table 1.A).

This equation is analogous to many modelling curves in the economic literature: [START_REF] Mincer | The Human Capital Earnings Function[END_REF] earning equation, Laffer curve (tax rate, Government revenue) and Kuznets curve (income, inequality); where the dependent variable is a quadratic polynomial form of the explanatory variable and thus expected to have a turning point (negative slope of the quadratic term). Similarly, the non-linear term in (9) assumes that the rhythm by which debt affects growth changes from a specific turning point. For example, low public debt could have a positive effect on growth and starting from a certain threshold (high debt), the effect becomes negative.

Equation ( 9) changes its trend if it has a derivative null at a certain level of debt ratio. The debt threshold 𝑑 ̂ is then deduced by deriving (9) according to the debt ratio:

𝑑 ̂= - 𝛼 2𝛽 (10)
Equation ( 9) is to be estimated using Generalized Least Squares (GLS) method. However, to remedy to the major problems raised by the literature in terms of endogeneity, which may be caused in particular by the omission of other explanatory variables or by reverse causality, we use the generalized method of moments (GMM) involving instrumental variables.

Thus, the equation to be estimated by GMM is:

𝑔 𝑖,𝑡+5 = 𝛼𝑑 𝑖,𝑡 + 𝛽𝑑 𝑖,𝑡 2 + 𝜑𝐼𝑛𝑠𝑡 + 𝛾 𝑖 + 𝜀 𝑖,𝑡 (11)
where, 𝐼𝑛𝑠𝑡 are a set of instrumental variables and 𝜑 the set of their associated parameters. The threshold is deduced as in (10).

Another interesting method used previously by some authors is the PSTR models standing for panel smooth transition regression. [START_REF] Gonzalez | Panel smooth transition regression models[END_REF] developed these models as an enhancement for the panel threshold regression (PTR) models of [START_REF] Hansen | Threshold effects in non-dynamic panels: estimation, testing, and inference[END_REF]. These models explain the dependent variable as a linear term of the independent variable augmented with nonlinear terms as a multiplication of the same independent variable with an indicator function. This latter is modelled in the form of a logistic function which depends on a threshold variable. In case the threshold variable is the same as the dependent variable, this yields a polynomial form as in (9). Despite their popularity and advantages of accounting for fixed effects in the panel data, the PSTR do not allow lagged explained variables to be in the right-hand side of the specification [START_REF] Colletaz | Threshold effects of the public capital productivity: An international panel smooth transition approach[END_REF]. This means they do not allow for dynamic effects.

Data and preliminary analysis

In this section, we present the data sources and a preliminary analysis (as the Pearson's correlations and statistical heterogeneity tests) for the data generating process.

Data description

Regarding this work, we consider a sample of 20 developed countries over the period of 1880-2010 from the IMF database. This is the same sample of countries used by RR (2010), in addition to a significant amount of subsequent research. The methodology and description of the data are published in Abbas et al. (2010). 16 The database reports the public debt-to-GDP ratio. The latter comes from the Maddison 17 data according to the Geary-Khamiss method, in international dollar .

For consistency, the Maddison Project data is also used for GDP growth.

The 20 advanced countries are: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Greece, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom and the United States.

Correlations and data heterogeneity tests

Table A.1 (appendix A) shows that Pearson's correlations tend to be negative, especially between current debt and 5-years lead growth. 13 out of 20 correlations are significantly negative over the period of 1950-2008. But, the weak correlations may suggest that the form of the relationship is not necessarily linear, since the Pearson correlations assume linearity. This seems to be revealed by scatter plots for individual countries.

An issue related to data and country samples is heterogeneity. The source of the heterogeneity could be unobserved characteristics as a result of other variables involving economic policies and institutions. The heterogeneity in country behaviors is known as the fixed effect in econometrics. Some of the previous works have warned against the high heterogeneity of countries as a result of differences in fiscal and monetary policies, country size, and quality of institutions. 18

However, to the best of our knowledge, no paper has invoked the issue of data heterogeneity. We take the opportunity to study such heterogeneity. RR (2010), and other researchers, used descriptive statistics based on conditional means and medians to conclude, for all countries, the existence of a common debt threshold beyond which GDP growth slows. This assumes that the data generating process is homogenous for all countries. However, running appropriate statistical tests for the equality of means, equality of medians and equality of variances across countries, for the economic growth categorized by public debt, strongly rejects the null hypothesis of equality for such statistics. This means that the data generating process is highly heterogeneous across countries. Table A.2 presents the results of the equality tests for different periods. The source of variation is several times higher between countries than it is within countries. The heterogeneity seems to decrease as the period shortens. Specifically, over the period of 1991-2008, the null hypothesis of equality of means and medians is accepted at 5% level and the test indicates variances homogeneity.

Country specific analysis

The aim of this section is to analyze the relationship between public debt and economic growth and investigate whether a unique debt turning point exists for all countries. Surveyed empirical studies have not reached any consensus about a clear relationship between debt and growth. Despite the diversity of methods, they showed sensitivity to different econometric problems and data samples shortness. Those using a long period of analysis as in Reinhart andRogoff (2010, 2012) could have methodological issues, especially by adopting simple descriptive statistical approaches to generalize for a common rule that fits all. However, those using somehow advanced econometric analysis could have short time sample bias. Generally, their samples start after the 1970s. Our aim is to reconsider an investigation of the debt-growth relationship, starting from a data descriptive approach and ending to econometric estimations over a long period. We try to remedy to limitations of samples and econometric methods used in the previous literature by using both advanced recent econometric tools and rich statistical data analysis over long period for panel and country specific analyses.

Scatter plots analysis

Despite the diversity of the econometric methods used to study the growth-debt relationship, they are generally applied to samples starting from the seventies. This coincides with the end of the Bretton Woods system and the beginning of market liberalization in developed countries. To remedy this shortcoming, we extend the analysis to the long period of 1880-2008, split to five subperiods corresponding to the main changes in the international economic and political order [START_REF] Rodrik | The Globalization Paradox: Democracy and the Future of the World Economy[END_REF][START_REF] Obstfeld | Globalization and Capital Markets[END_REF]. 19 These world events may affect the stability of the macroeconomic aggregates and their interdependencies, hence the debt and growth linkages. We distinguish the following sub-periods:

-1880-1913. This period fits with the end of the first globalization (mercantilism era);

- . A period with two devastating wars and the 1929 great depression. The international economic order was marked by the gold standard regime;

19 Breakpoint tests based on Dickey-Fuller unit root test emphasized this partition around these dates. For example, break dates in debt series are 1918, 1941, 1964and 2007 for the USA; for the USA;1915[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF], 1969and 1990 for the UK; for the UK;1906, 1944[START_REF]water systems, sanitation systems, and roads. IDR 1.5 trillion devoted to water systems alone was responsible[END_REF]and 1996 for Japan; for Japan;1896, 1960and 1991 for France; for France;1902, 1937, 1974and 1992 for Germany. Detailed results for all countries are available upon request from the author.

- . The world experienced strong growth and development during this period, notably with the Bretton Woods agreements and fixed exchange rate regimes; -1971-1990. A period of turbulent economic and political events with the end of the convertibility of the dollar in 1971 and the tendency to adopting floating exchange rates, as well as the oil shocks of the 1970s with the coexistence of unemployment and inflation, and the sovereign debt crises of the 1980s;

-1991-2008. Countries underwent extensive financial liberalization under the Washington Consensus recommendations, resulting in financial instability for many emerging markets.

The World Trade Organization (WTO) was created, bilateral and multilateral free trade agreements proliferated, and the Euro currency was launched.

We first conduct a scatter plots analysis for the relationship between public debt and growth for individual countries (Figures B.1 to B.9). The relationship is plotted over eight periods: the whole period 1880-2008, the five previous sub-periods, and two other periods (1946-2008 and 1971-2008). Scatter plots are organized for each period for individual countries. We draw scatter plots for 5-years 20 lead economic growth explained by the current public debt. The chart analysis is supported by the Pearson's correlations in Table A.1 for the debt and growth over different eras.

We tend to assume lag effect between debt and growth. We believe that a deficit financed by a government debt will act with a certain delay on economic growth either on the short-term or in the long-term. For example, capital expenditures, which assumed to affect economic growth more than any other type of expenditures are likely to impact growth with a delay. For example, a port or a road financed by bond issuance will make time to be constructed and begins to benefit to the community. Furthermore, other macroeconomic channels by which debt affects economic growth, such as interest rates, openness, population and others, are likely to react with a delay rather than immediately affecting growth. Our statistical data endorsed such assumed delay in the effect of debt on growth where current debt-to-GDP ratio is more correlated with lead growth than current growth (Table A.1).

Individual scatter plot analysis shows that the relationship form changes by countries and periods. We notably distinguish:

-Flat curves for the case of Austria (1991( -2008( and 1880( -2008( ), Denmark (1880( -2008) ) and Portugal (1946Portugal ( -1970));

-Negative linear as in Germany (1880-2008and 1880-1913), the Netherlands (1914-1945), Canada (1971-1990) and, Austria and Italy (1946-1990); 20 The 5 years' lag is justified by the fact that the debt is supposed to affect growth over medium to long-run.

Chapter 1. On the public debt and growth threshold: One size does not necessarily fit all 52 -Positive linear for Belgium , Australia andPortugal (1880-1913), Austria and Germany (1914-1945), France and Switzerland (1946-1970), Ireland and Portugal (1991-2008) and France (1946France ( -1990));

-Convex relationship in Denmark and Norway (1880-1913), Germany and Greece (1946-1970), Italy andUSA (1991-2008), Italy, Portugal, Greece, Sweden, the United Kingdom and Austria and, Japan, Germany, the United States and Greece ;

-Concave relationship as in France, Italy, Switzerland and New Zealand (1880-2013), Australia, Canada, Italy, Spain and the United Kingdom (1914Kingdom ( -1945)), the Netherlands, New Zealand and United Kingdom (1946-1970), Belgium, Denmark, France, Spain, Sweden and Switzerland (1971-1990), France, Norway and Sweden (1991-2008), Belgium, France, Spain and Denmark (1946-2008) and, Australia and Sweden (1946-1990).

Scatter plot analysis highlights that the form of the debt-growth relationship is country and time specific. The economic explanation is straightforward. We note especially differences across countries in the economic and political governance, the structure of debt (external or domestic, currency of denomination, maturity), the aging population (Germany and Japan versus Portugal and Spain), the degree of openness, the size of the economy (Greece and Ireland versus Japan and the United States), the structure of public expenditures, changeable economic policies and political and external environment as well as the level of the development in a country over time. Therefore, the fact that there is neither a unique economic policy, nor a comparable level of institutional and demographic variables across countries, makes less defendable the conjecture of "one size debt threshold that fits all".

Regression kink results

We use the kink regression method of [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF], allowing detecting unknown thresholds. Country specific regressions emphasized what is reported on country specific scatter plots. The regression kink with an unknown threshold shows a variety of forms for the growth-debt relationship. Tables 2 and3 present the regression kink results for the whole and the postwar periods, respectively.

Furthermore, for better visualization of the results, we graph the summary of our findings across more than five landscape pages (Figures 1 to 5 The threshold F-statistic is calculated according to the test of the hypothesis 𝐻 0 : 𝛾 = 𝛾 0 against 𝐻 0 : 𝛾 ≠ 𝛾 0 . The criterion test is to reject for high values of the F-type statistic 𝐹 𝑛 (𝛾 0 ), where

𝐹 𝑛 (𝛾) = 𝑛(𝜎 ̂2(𝛾)-𝜎 ̂2) 𝜎 ̂2
, and

𝜎 ̂2 = 1 𝑛 ∑ 𝑒̂𝑡 2 𝑛 𝑡=1
is from equation ( 7). The threshold 𝛾 ̂ corresponds to the minimum of the threshold F-statistic which is also the minimum of the least squares criterion. [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] presents an algorithm for the bootstrap confidence intervals for parameters and the F-statistic.21

Insert Tables 2 and3 about here

Insert Figures 1 to 5 about here

According to these results, we can distinguish many cases depending on the sign and magnitude of parameters 𝛽 1 and 𝛽 2 :

✓ Case 1: 𝛽 2 > 𝛽 1 > 0
The growth rate is always positively affected by debt and the effect becomes higher after the debt threshold. This case is only supported by Australia over the period 1956-2010.

✓ Case 2: 𝛽 1 > 𝛽 2 > 0

The effect of debt over growth is always positive but is reduced for debt values above the threshold compared to the effect of debt values below the threshold. This case is reported in countries such as Ireland (1929Ireland ( -2010) ) and Norway (1881Norway ( -2010)).

✓ Case 3: 𝛽 2 > 0 > 𝛽 1
The effect is negative for debt ratios below the kink point and then becomes positive after that point. This case is presented by Austria (1956Austria ( -2010)), Denmark, France, Italy, Spain, Sweden and Switzerland over the long period 1881-2010.

✓ Case 4: 𝛽 1 > 0 > 𝛽 2
The effect is positive and then becomes negative after the turning point. This case is presented by the United Kingdom (1956Kingdom ( -2010)), the United States (1791-2010), Austria (1956-2010), Germany (1881-2010) and the Netherlands (1956Netherlands ( -2010)).

✓ Case 5: 𝛽 1 < 𝛽 2 < 0

The effect is always negative but emphasized less after the turning point. This case is observed in Japan over both the long and short periods and Italy over the recent period.

✓ Case 6: 𝛽 1 ≅ 0 (respectively 𝛽 2 ≅ 0) and 𝛽 2 ≠ 0 (respectively 𝛽 1 ≠ 0)

Growth is insensitive to the debt ratio before the threshold (respectively after the threshold) and the effect has the sign of 𝛽 2 (respectively 𝛽 1 ). These special cases are shown by Ireland (1956-2010), Portugal (1881-2010and 1956-2010) and Norway 1881-2010).

✓ Case 7: Flat curves Debt neutrality is shown for the case of the United States and the United Kingdom (1881-2010), Australia (1910-2010), Canada (1881-2010), Denmark (1956-2010), Sweden (1881-2010) and Greece (1884Greece ( -2010)).

The kink regression method emphasizes the differences in the data-generating process of the debtgrowth relationship across countries. It reveals that the thesis of a debt threshold is case-specific and changeable over time. It also suggests that there is no simple formula determining a specified debt threshold or even a range of it, considered a dangerous zone not to reach, just by considering the direct relationship between economic growth and the public debt-to-GDP ratio. This considers more theory-based models, taking into account country fundamentals that are different between countries and impact the debt-growth interactions.

Panel specification analysis

We present in this section, scatter plots analysis and estimation results for the panel groups.

Scatter plots analysis

Figures 6 and 7 present scatter plots for the panel analysis between the 5-year lead economic growth and the public debt ratio. Figures are presented in panel graphs by period for the whole and the euro zone sample. These scatter plots show that economic growth is weakly correlated with the public debt. The trend-line of the relationship is flat in almost all periods for both the whole sample and the eurozone. The relationship is only apparently negative for the whole sample over the period of 1950-2008 and the subsequent postwar period . For the euro zone sample, the analysis is nearly the same except a weak positive correlation over the period of 1991-2008.

Insert Figures 6 and 7 about here

Panel regressions

We first estimate equation (9) using GLS method. However, for the GMM method, a set of convenient instrumental variables is needed. The choice of instrumental variables for the GMM method can be challenging. In practice, these are chosen to be correlated with the explanatory variables and orthogonal to the error term before introducing instruments (error in equation ( 9)), which means weakly correlated to the dependent variable of the initial regression before considering such instruments. We choose a set of variables that can act as potential instruments based on the Pearson's correlations with the explained and explanatory variables (Table A .3). The following variables and their first and second lags are considered to be candidates: old people dependency ratio (ODR), shares to GDP of, respectively; exports (EX), imports (IM), government consumption (GC) and gross capital formation (GCF). The data source of the dependency ratio series is the World Development Indicators of the World Bank, while all other instruments are from the Penn World Tables (version 9.0), which provides data back to 1950 for all the countries of the sample adjusted for purchasing power parity (PPP).

Table A.3 shows first that, gross capital formation is weakly correlated with 5-years lead growth but also weakly correlated with debt. As a result, it is removed from the list of candidate instruments. Second, exports, imports, dependency ratio and government consumption are correlated with the debt variable and weakly correlated with growth. We also used the Sargan test which excluded the GCF at the estimation stage.22

Equation ( 9) is estimated over the periods of [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-1990, 1991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008. The periods of 1880-1913and 1914-1945 were excluded as the debt series experienced breaks for several countries during these periods as a result of the great depression and the World wars. Similarly, estimations start from 1950 instead of 1946 as the debt of many advanced countries stands highly abnormal following World War II. [START_REF] Reinhart | This Time Is Different: Eight Centuries of Financial Folly[END_REF] reported that defaults and restructuring debt in these times are among the highest in history. 23 For a similar reason, the recent financial crisis is not considered in estimation. The main argument is that these points at the end of the period could statistically distort the results in addition to the ambiguous character of the crisis on debt and growth.24

Equation ( 11) is estimated with the fixed effect 25 relative to each country 𝛾 𝑖 . Some authors remove the fixed effect by differentiating their models. However, the fixed effect is important to keep in our case as it considers the heterogeneity of the panel. The fixed effect can be removed if the heterogeneity is rejected. Furthermore, differencing the equation, in our case, will modify the assumed non-linear quadratic form and not allow to easily deduce the concavity of the relation and thus the value of the threshold according to the formula (10). We also run a variety of tests for no cross-section dependence 26 for the estimated panel model over all the periods. Table A .6 summarizes results for the 20 OECD sample of countries and the 10 Euro sample of countries. These tests strongly reject the null hypothesis of no cross-section dependence. Therefore, heterogeneity and cross-section dependence among other problems facing panel methodology support our approach considering studying growth-debt relationship for countries individually. 27 Table 4 presents estimation results by GLS and GMM methods for the five periods of; 1950-1970, 1971-1990, 1991-2008, 1971-2008 and 1950-2008. The results are not significant for the GLS over all periods except the whole period 1950-2008 over which, the form of the equation is convex

(β > 0).
However, the GMM method leads to significant results. For the fixed effects model, two thresholds result from the concavity of the relation (β < 0) over the two periods 1971-1990 and 1971-2008, with respective values of 47.5% and 46.5%. Assuming a model without fixed effects, the estimates are statistically significant over three periods : 1971-1990, 1991-2008 and 1971-2008, with respectively 49.4%, 80.1% and 62.8% thresholds. The J statistics shows the efficiency of the instruments considered in the regressions.

Insert Table 4 about here

These results emphasized the drawbacks from which the GLS method suffers. It reveals also that the relationship is affected by high heterogeneity behaviors across countries. We deal with the first issue by continuing the estimation using the GMM method. For the heterogeneity issue, we considered the size effect between countries and vary the sample by removing sizable countries namely Japan, the United Kingdom, and the United States. We also present the results for the sample of the euro area countries as a group of homogenous monetary and exchange rate regimes. Similarly, we filter countries according to a number of characteristics (government effectiveness and expenditure levels reflecting public economic governance).

For the fixed effects model (Table 5), the results of the estimates show a concave relationship between debt and growth for the periods of; 1950-1970, 1971-1990 and 1971-2008. The results do 26 Testing for cross-sectional dependence is crucial for selecting the appropriate and efficient estimator. We use four tests: Lagrange multiplier (LM) test from [START_REF] Breusch | The Lagrange Multiplier Test and its Application to Model Specifications in Econometrics[END_REF], two tests of [START_REF] Pesaran | General diagnostic tests for cross section dependence in panels[END_REF][START_REF] Pesaran | Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure[END_REF], one based on Lagrange multiplier and the other on pairwise correlation coefficients. The latter has a lower power when the population average pair-wise correlations are zero [START_REF] Pesaran | A bias-adjusted LM test of error cross-section independence[END_REF]. The fourth test is proposed by [START_REF] Pesaran | A bias-adjusted LM test of error cross-section independence[END_REF], which developed a bias-adjusted test that is a modified version of the LM test.

27

For comparison purpose with the regression kink, we also run a dynamic quadratic form (𝑔 𝑡 = 𝑐 + 𝛼𝑑 𝑡-1 + 𝛽𝑑 𝑡-1 not improve by excluding Japan alone. The two periods of 1971-2008 and 1950-2008 on which the relationship becomes significant shows, a convexity of the relationship. Excluding Japan and the United States, the model improves over the period 1950-1970 and the threshold over this period is around 78.4%. Adding the United Kingdom to the excluded countries, the results of the model remain substantially the same. The threshold varies from 40% over 1971-1990 to nearly 78% for the period 1950-1970. For the euro area, the relationship was concave and significant over the subperiods of; 1950-1970, 1971-1990, 1991-2008 and 1971-2008. Estimates for the period of 1950-2008 are rejected. The threshold ranges from a minimum of 45% over the period 1971-2008 to a maximum of 94% over the period 1991-2008.

Insert table 5 about here

We generate fixed effect for this model in Table A.4. This reports the deviation of each country (𝛾 𝑖 -𝛾̅ ) from the homogenous constant term (the average constant for the whole panel). These results emphasize high spreads across countries which makes it possible to conclude that the heterogeneity greatly affects the growth-debt linkages. This may explain the big differences in results across periods and samples. The threshold estimates are not tiny to consider as a claim for a one unique threshold for all countries in all times. On the contrary, this strongly suggests that the growth debt relationship is rather country specific than a common one. Furthermore, even when considering no fixed effects results (Table 6), no substantial improvement is found.

Insert Table 6 about here

For more investigation, we vary the samples by grouping countries according to their level of government effectiveness and expenditure levels reflecting good public economic governance. We split the sample into two groups of high and moderate level based on government effectiveness and shares to GDP of respectively: total final government consumption, military expenditures and, government transfers and subsidies. The first variable is from Worldwide Governance Indicators of the World Bank, while other variables are from the World Development Indicators of World Bank database. Countries are filtered form high to low values on average over time and the frontier between high and moderate groups is determined according to the average of countries averages. Therefore, the average government consumption to GDP over 1960-2008 ranges from 10.1% for Switzerland to 23.6% recorded for Sweden. The average of the sample is 17.7% and this value is used to split the two groups. Similarly, the government effectiveness index average over 1996-2016 ranges from 0.53 for Italy to 2.09 for Finland, and its average over the 20 countries is 1.58 which separates the group of countries with moderate governance from the one with high governance. The same approach was followed for the other variables.

Table A.5 summarizes the estimated thresholds by periods and country samples for the two groups of countries for each of the four considered variables. The estimation is done by GMM method. The results are fuzzy, and many non-significant thresholds are reported especially over the period 1951-2008. However, the recent period seems to point out to more homogeneity in countries behavior and significant thresholds, though different by sample, are reported. These results emphasize the idea of studying the debt-growth relationship on country by country case.

The investigation (both preliminary data analysis and estimation) revealed high heterogeneity in data and behaviors across countries. Despite that we could sometimes prove the existence of a debt threshold by advanced econometric methods, the heterogeneity suggests that this one tend to be rather country specific than common rule for all countries. Furthermore, when dealing with panel cross-section data, it is usually assumed that cross section errors in panel data models are independent, especially for large cross-section size. However, the presence of such cross-section dependence in estimation can result in serious problems of efficiency loss and inappropriate statistical tests.

Conclusion

In this paper, we studied the existence of possible threshold effects in the relationship between public debt and economic growth. We used two econometric approaches. The first method, applied individually to each country of the sample of 20 advanced countries, is the kink regression method developed by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF], which searches endogenously for an unknown threshold. The second method is a technique that previously was explored by some authors especially [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF], which we applied to the panel of the previous countries.

Both methods clearly counter the claim of a common debt threshold that fit all countries. It reveals that the threshold, whenever it exists, is a country specific rather than a common rule to fit all. Unlike all the empirical literature examining the existence and values of debt thresholds on a crosssection data, our analysis undertakes the question on both cross-section and country-specific over a long data span. Country-specific analysis highlighted, in fact, diverse types of relationship between growth and public debt. Accordingly, some countries can grow with high debt to GDP ratios; others could see their growth shrink from even low debt ratios, while growth in some others is insensitive to public debt. The study also reveals the instability of the relationship over time: almost every country exhibits a different relationship by period, especially when considering the whole period and the post-war period .

The results drawn from our study point to further interesting developments since several economic and institutional variables such as interest rate and governance could be integrated into the analysis as they could have some notable effects on the debt-growth nexus beyond the simple model developed here. [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. Coef. prob. [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. Coef. prob [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. Coef. prob. [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. prob Coef. prob a: Coefficients are statistically significant, but the function is convex which means that the debt affects negatively growth for debt ratios below this threshold and positively above this threshold. b: J-statistic is the value of the GMM objective function.

Chapter 1. Tables and Figures

Coef

Coef

The threshold is calculated according to the formulae: 𝑑 ̂= -𝛼 2𝛽 .

Table 5. GMM results for varying countries sample (fixed effects model)

Sample of 20 OECD countries 1950-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. prob (Japan excluded) 1950-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. prob 1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. prob Coef. prob [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-2008[START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF]-2008 Coef. prob Coef. prob 1950-1970 1971-1990 1991-2008 1971-2008 1950-2008 (Japan excluded) 1950(Japan excluded) -1970(Japan excluded) 1971(Japan excluded) -1990(Japan excluded) 1991(Japan excluded) -2008(Japan excluded) 1971(Japan excluded) -2008(Japan excluded) 1950(Japan excluded) -2008 1950-1970 1971-1990 1991-2008 1971-2008 1950-2008 1950-2008 1950-1970 1971-1990 1991-2008 1971-2008 1950-2008 1950-1970 1971-1990 1991-2008 1971 1950-2008 1950-1970 1971-1990 1991-2008 1971-2008 Instrument Growth (t+5)

Debt (t) Growth (t+5) Debt (t) Growth (t+5) Debt (t) Growth (t+5) Debt (t) Growth (t+5) Debt (t) GC -0.

Table A.4. Fixed effects generated across countries and periods

Fixed effects for the quadratic form specification: the sample of 20 OECD countries Country 1950Country -2008Country 1950Country -1970Country 1971Country -2008Country 1971Country -1990Country 1991 1951-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-20081951-2008 Model Without Fixed 1951-1970[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-19901991-2008[START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF]-20081951-2008 Model Without Fixed Notes: significant at 1% (***), 5% (**) and 10% (*). NS is Non-Significant. a: The form of Growth-debt link is convex meaning that the debt affects negatively growth for debt ratios below this threshold and positively above it.

Table A.6. Tests for cross-section dependence for the panel fixed effect model (Least Squares method)

Residual Cross-Section Dependence Test for the 20 OECD countries sample Degrees of freedom = 190 1950freedom = 190 -2008freedom = 190 1950freedom = 190 -1970freedom = 190 1971freedom = 190 -2008freedom = 190 1971freedom = 190 -1990freedom = 190 1991freedom = 190 -2008 Test Test Stat. Prob. Stat. Prob. Stat.

Appendix B. Individual scatter plots for public debt and economic growth

𝑝 𝑛 = 1 𝐵 ∑ 1( 𝐵 𝑏=1
𝑇 𝑛 * (𝑏) ≥ 𝐹 𝑛 ),

6. Compute the level α critical value 𝑐 𝛼 as the empirical (1 -𝛼) of the simulated F statistics

{𝑇 𝑛 * (𝑖), 𝑖 = 1. . 𝐵}. 7. Reject 𝐻 0(𝛽 1 =𝛽 2 ) in favor of 𝐻 1 (𝛽 1 ≠𝛽 2 ) at significance α if 𝑝 𝑛 < α, or equivalently if 𝑇 𝑛 > 𝑐 𝛼 .
The number of bootstrap replications B should set sufficiently large to ensure accuracy of the p-value. We keep the number B=10.000 in our case as reported by [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF]. We also use Γ = [min(𝑑 𝑡 ) , max(𝑑 𝑡 )] for each country and a grid search with the increments of 1. The number of grid points is then: λ = max(𝑑 𝑡 ) -min(𝑑 𝑡 ) + 1. where 𝑒̂𝑡 * = 𝑔 𝑡 * -𝛽 ̂ * ′ 𝑥 𝑡 (𝛾 ̂ * ).

5. Calculate the F-statistic for γ:

𝐹 𝑛 * (𝛾 ̂) = 𝑛(𝜎 ̂ * 2 (𝛾 ̂)-𝜎 ̂ * 2 ) 𝜎 ̂ * 2 ; where 𝜎 ̂ * 2 = 1 𝑛 ∑ 𝑒̂𝑡 * 2 𝑛 𝑡=1
(𝛾 ̂) and

𝑒̂𝑡 * (𝛾 ̂) = 𝑔 𝑡 * -𝛽 ̂ * ′ (𝛾 ̂)𝑥 𝑡 (𝛾 ̂).
6. Repeat this B times to obtain a sample of simulated coefficient estimates (𝛽 * ̂, 𝛾 * ̂) and F statistics 𝐹 𝑛 * . 7. Create (1 -𝛼) bootstrap confidence intervals for the coefficients 𝛽 = (𝛽 1 , 𝛽 2 , 𝛽 3 ) by the symmetric percentile method: the coefficients plus and minus the (1 -𝛼) quantile of the absolute centered estimate bootstrap: for each coefficient

𝛽 𝑖 ; 𝑖 = 1. .3, the interval is 𝛽 ̂𝑖 ± 𝑞 1 * where 𝑞 1 * is the (1 -𝛼) quintile of |𝛽 𝑖 * -𝛽 ̂𝑖|. 8. Calculate the (1 -𝛼) quantile 𝑐 1-𝛼 *
of the simulated F statistics 𝐹 𝑛 * . 9. Create (1 -𝛼) bootstrap confidence interval for γ as the set of γ for which the empirical F statistics 𝐹 𝑛 (𝛾) are smaller than the bootstrap critical value 𝑐 1-𝛼 * :

𝐶 𝛾 * = {𝛾: 𝐹 𝑛 (𝛾) ≤ 𝑐 1-𝛼 * }
Chapter 2

Short-term effects of public debt on growth: The spending multiplier pass-through

Chapter 2

Short-term effects of public debt on growth: The spending multiplier pass-through

Abstract: We examine the relationship between public debt and economic growth in the short term, through spending multipliers. We study the impact of public debt accumulation on the size of the expenditure multipliers, as well as the effects of the business cycle. We adopt the structural vector autoregressive (SVAR) methodology, running a panoply of bi-variate and tri-variate SVAR models on quarterly data for a sample of 18 OECD countries. Furthermore, we estimate an SVAR with six fiscal and monetary variables for the United States to highlight the channels through which public debt affects economic growth. In all the above-mentioned SVAR models, we control for the business cycle and the public debt movement effects. The results show that expenditure multipliers are higher in times of recession than times of expansion, which is in line with the recent findings about fiscal multipliers in advanced economies, being larger in recessions than expansion periods. Moreover, controlling exogenously for public debt, the estimations revealed larger spending multipliers in debt accumulation than in debt contraction periods, independent of the business cycle effects. However, introducing endogenously the public debt ratio leads to higher multipliers in recessions than in expansions. Moreover, the results do not support any tendency for weak spending multipliers for the recent periods compared to older ones. Furthermore, the United States SVAR shows that public debt crowds out private investment, leading to a lower growth rate in times of expansion, while in times of recession the public debt effects on growth are positive. This crowding-out effect may play pass-through to the expenditure multipliers, which could explain, ceteris paribus, the weak size of spending multipliers, while the crowding-in effect in times of recession leads to higher multipliers. The results also revealed that government expenditure has a positive but short-lived impact on economic growth. Besides, the recession period has persistent effects on the responses of variables, for which convergence with the longterm path following the shock is achieved slower than with the expansion time. The policy implication is that fiscal stimulus effects could take time to materialize in recessions, while such effects could be short-lived in expansions, which is something that should be considered by policymakers in their spending decisions.

JEL classification: C30, E62, H50, H60.

Keywords: Business cycle, Dynamic multiplier, Fiscal position, Government expenditure, SVAR.

Introduction

At the height of the 2008 financial crisis, fiscal policy was revived as the main and almost sole active government policy tool to cope with the financial crisis effects, after monetary policy was constrained in many advanced countries by the zero lower bound (ZLB) interest rate or by countries being affiliated to a monetary union, as is the case for eurozone countries [START_REF] Romer | What Have We Learned about Fiscal Policy from the Crisis?[END_REF]. The fiscal policy is solicited in two "distinct" but subsequent events. The first, advanced countries, were urged to implement massive fiscal stimuli plans and bail-out programmes 28 (in 2009-10) designed to dampen the negative effects of the crisis on the private sectors and households at the beginning of the crisis, and therefore boosting growth (OECD, 2009;[START_REF] Ilo | A review of global fiscal stimulus[END_REF]. Consequently, this leads to exacerbating fiscal positions, with the deficit widening and a sharp increase in debt to GDP ratios, which were already high in the pre-crisis year [START_REF] Imf | Group of Twenty[END_REF][START_REF] Taylor | Fiscal Stimulus Programs During the Great Recession[END_REF]. This issue pushed policy-makers, especially in the eurozone, where the debt ratios climbed from the pre-crisis level in almost all countries by 20 percentage points (European Commission, 2012), supported by advisors and economists' views from international institutions and think thank institutes (International Monetary Fund, World Bank, European Central Bank, OECD, G20) and other economists from academia, to reverse the track of the fiscal policy from stimuli programmes to fiscal consolidation. The argument of those economists stands for the modest results obtained from the assessment of fiscal stimuli programmes, 29 as reported by many studies [START_REF] Baldacci | How effective is fiscal policy response in systemic banking crises?[END_REF][START_REF] Freedman | Global effects of fiscal stimulus during the crisis[END_REF][START_REF] Taylor | An Empirical Analysis of the Revival of Fiscal Activism in the 2000s[END_REF][START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF][START_REF] Cogan | What the Government Purchases Multiplier Actually Multiplied in the 2009 Stimulus Package[END_REF][START_REF] Mian | The Effects of Fiscal Stimulus: Evidence from the 2009 'Cash for Clunkers' Program[END_REF][START_REF] Phelps | The Fantasy of Fiscal Stimulus[END_REF], and the likely negative impact of high public debt on economic growth, which triggered a large open debate between economists. 30 However, the prolonged negative impacts of the financial crisis, under the two consequent programmes (fiscal stimulus and fiscal consolidation), have put the focus on another issue related to the role of fiscal multipliers in those programmes, namely, trying to find answers to the weak GDP recovery despite massive fiscal stimuli from one side and the persistent high debt ratios and deficits despite fiscal consolidation from the other. This triggered a permanent influx of empirical studies (re)-assessing the values of the multipliers and reviewing their determinants.

One research strand involves assessing the size of the multipliers due to positive fiscal shocks corresponding to the stimuli programmes (an important list of sample studies and their main 28 Although these fiscal stimuli seem to be large in absolute size, approximately US$ 2 trillion in the G20 countries [START_REF] Ilo | A review of global fiscal stimulus[END_REF], some authors qualified these fiscal stimuli by insufficient and timid programmes [START_REF] Aizenman | Net Fiscal Stimulus During the Great Recession[END_REF]Stiglitz, 2018), especially compared to emerging countries in Asia and the Pacific, not including Japan and the Republic of Korea, where the average stimuli programmes were around 9.1% of GDP compared to just 3.4% of GDP in advanced economies (ILO, 2011). 29 The two important fiscal stimuli that were reviewed are the ARRA programme (the American Recovery and Reinvestment Act), implemented in the United States, and the EERP programme (the European Economic Recovery Plan), implemented in Europe. A very large list of studies, reproduced in Table 1.A. in the appendix, on fiscal stimulus measures and their main findings from the ILO ( 2011), shows very mixed results, especially on the ARRA programme. Among 47 studies and reports of this list, 22 reported mixed effects, 21 positive effects and 4 negative effects.

30 More details about this debate are presented in Chapter 1. See also [START_REF] Bentour | On the public debt and growth threshold: one size does not necessarily fit all[END_REF].

findings about the effects of fiscal stimuli around 2008-10 is reproduced in Table 1.A in the appendix), while the other strand goes the opposite way, evaluating and designing strategies for successful fiscal consolidation31 and austerity measures (Abbas et al., 2010;OECD, 2011OECD, , 2012;;[START_REF] Molnár | Fiscal consolidation: What factors determine the success of consolidation efforts?[END_REF][START_REF] Cogan | Fiscal Consolidation Strategy[END_REF][START_REF] Estevão | The Economic Effects of Fiscal Consolidation with Debt Feedback[END_REF]Blot et al., 2014a;Alesina et al., 2015). In fiscal stimuli programmes, the fiscal instruments used are either related to the increase in spending programmes (and fiscal transfers to households and bail-out programmes) or based on tax cuts for households and investors to boost consumption and investmentor a mixture of the two. However, in fiscal consolidation, which directly aims, ceteris paribus, to sustain and improve the government's fiscal position (reducing debt and deficit) by increasing revenue and rationalizing expenditure, the course of the fiscal instruments is reversed, as in this case, where taxes should be increased and expenditure cut. 32Since the 2008 financial crisis, a significant body of literature assessing fiscal multipliers has flourished [START_REF] Romer | The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks[END_REF]Auerbach andGorodnichenko, 2012, 2013;[START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF][START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF]. 33 Although the story of fiscal multipliers was remounted at the edge of the Keynesian era following the 1929 Great Depression, their empirical assessment has recently been extensively revived as a result of the development of econometrics and statistics. Nevertheless, the renewed importance of fiscal multipliers showed large discrepancies in their values (whether in absolute values or sometimes even in algebraic signs), especially in the recent financial crisis [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF]. These values are time-and country-specific and even sensitive to the assessment method [START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF][START_REF] Batini | Fiscal Multipliers: Size, Determinants, and Use in Macroeconomic Projections[END_REF].

Indeed, in explaining the values of fiscal multipliers, some authors have found those multipliers to be sensitive to the business cycle. In particular, fiscal spending multipliers were revealed to be larger in recessions than expansion periods. Auerbach andGorodnichenko (2012, 2013) were the first to emphasize the tendency of fiscal multipliers to be large in recessions (potentially reaching more than 2) compared to expansions. Consequently, many other researchers confirmed their results, differentiating between fiscal multipliers in recessions and expansions (Barro and Redlick, 2011; Parker, 2011; 34 Corsetti et al., 2012; Caggiano et al., 2015; Fazzari et al., 2015; Glocker et al., 2019). This also pushed some researchers who were not totally convinced, or with opposing results, to refine their analysis, leading to finding out the vulnerability of fiscal multipliers to other determinants and not necessarily conditioned by the state of the economy in the business cycle.

Therefore, fiscal multipliers were revealed to be dependent on the fiscal position measured by the level of debt ratios and deficits [START_REF] Corsetti | Sovereign risk, fiscal policy, and macroeconomic stability[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF], on the monetary policy stance [START_REF] Hall | By how much does GDP rise if the Government buys more output?[END_REF], particularly the constrained monetary policy, either by the ZLB interest rate (liquidity trap) or by the loss of monetary independence, as in the pegged exchange rate or monetary union [START_REF] Cogan | New Keynesian versus old Keynesian government spending multipliers[END_REF][START_REF] Eichenbaum | When Is the Government Spending Multiplier Large?[END_REF][START_REF] Delong | Fiscal Policy in a Depressed Economy[END_REF][START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF].

However, the recent works of [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF] and [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF] consider that government spending multipliers are, on average, lower than unity. This contrasts with the tendency of the post-2008 crisis researchers to confirm larger multipliers, especially in recessions. This also aligns with the consensus on spending multipliers before the last recession, considered to be weak, and that fiscal policy effects are short-lived [START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF]. Furthermore, the debate about the impact of government debt on economic growth (studied in Chapter 1) is directly related and assessed via the multiplier's effects. In particular, fiscal policy effects, taking into account the fiscal position of the economy, measured by the level of public debt and/or the fiscal deficit, have been highly debated in the aftermath of the 2008 financial crisis [START_REF] Boussard | Fiscal Multipliers and Public Debt Dynamics in Consolidations[END_REF][START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF]Blot et al. 2014b;[START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF][START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF][START_REF] Perdichizzi | Estimating Fiscal multipliers in the Eurozone: A Nonlinear Panel Data Approach[END_REF][START_REF] Poghosyan | How Do Public Debt Cycles Interact with Financial Cycles?[END_REF][START_REF] Afonso | Fiscal Multipliers in the Eurozone: A SVAR analysis[END_REF][START_REF] Auerbach | Fiscal Stimulus and Fiscal Sustainability[END_REF][START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF][START_REF] Broner | Fiscal Multipliers and Foreign Holdings of Public Debt[END_REF]. Very recently, in a presidential lecture of the American Economic Association, Blanchard (2019) triggered another wave of public debt and growth debate related to the fiscal cost of high public debt, as well as its effect on welfare, minimizing worries about the public debt costs for the American economy, as, in historical records, the nominal interest rate has remained, on average (except for some small periods around the 1980s), below the nominal growth rate. These contrasting results about spending multipliers make it interesting to reconsider studying fiscal multipliers and contributing to this unsettled debate.

The remainder of this chapter is as follows. Section 2 presents the literature review on fiscal multipliers, focusing particularly on the fiscal spending multipliers and their determinants, especially for highly indebted countries and constrained monetary policies. Section 3 presents a methodology for assessing spending multipliers according to the way the public debt ratio is evolving. Section 4 presents the empirical results. Section 5 concludes.

Literature review

A fiscal multiplier is defined as the output change in response to an (exogenous) change in a fiscal variable in reference to their baseline levels [START_REF] Spilimbergo | Fiscal Multipliers[END_REF][START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF]. 35 The concept of multiplier is generally associated with the general theory of John Maynard Keynes 35 If 𝑌 𝑡 and 𝑍 𝑡 denote, respectively, the output and the fiscal instrument at time 𝑡, the fiscal multiplier is simply expressed as

𝑑𝑌 𝑡 𝑑𝑍 𝑡
. Or, while the effects come with different lag times, the cumulative fiscal multiplier is expressed as [START_REF] Chinn | Fiscal Multipliers[END_REF].

∑ 𝑑𝑌 𝑡+𝑗 𝑗=𝑛 𝑗=0 ∑ 𝑑𝑍 𝑡+𝑗 𝑗=𝑛 𝑗=0
Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 91 (1936). 36 The idea behind fiscal stimulus is that the fiscal multiplier, as the measure of the policy instrument effect, is de facto a Keynesian one, which means that the value of such a fiscal multiplier is larger than unity, making it rewardable/beneficial to go for such fiscal stimulus. In the Keynesian structural models, the simplest way to compute a spending multiplier is via the marginal propensity to consume. 37 The spending multiplier in the Keynesian framework decreases with the marginal propensity to import, as well as the rise in interest rates and increases with the rise of investment due to the expansion of GDP (the accelerator effects). In a vector autoregression (VAR) approach, spending multipliers are determined using the impulse response function and the methodology of identification proposed by [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF].

Despite a continuously growing body of empirical literature on fiscal multipliers in recent years, these tend to bring more confusion than forming a consensus about the size of the fiscal multiplier.

There are many reasons why the size of the fiscal multiplier changes. Besides the proper characteristics of the studied economy, which are obviously due to macroeconomic fundamentals, as well as the institutional environment, the difference of methods and the accuracy of data make an important contribution to these differences. This section surveys the main important contributions of the literature on fiscal multiplier determinants, as well as the challenging issues presented by the methods used to gauge fiscal multipliers.

Recent researchers have mainly been interested in explaining why the recovery slowed in many advanced countries and fiscal consolidation is hurting many others. In this line of research, the frontier is not clear. For some, fiscal consolidation hurts in times of crisis, as fiscal multipliers are larger in recessions than expansions. If this is the case, a legitimate question to consider is why the large size of these multipliers in a time of crisis did not help fiscal stimuli to recover, especially in the eurozone countries. This may be because of the asymmetric effects of the two cases (fiscal stimulus versus austerity). To our best knowledge, very few studies have undertaken the issue of asymmetry. Our investigation of the recent empirical literature found only two papers with contrasting results [START_REF] Baum | The Impact of Fiscal Policy on Economic Activity over the Business Cycle: Evidence from a Threshold VAR Analysis[END_REF][START_REF] Riera-Crichton | Fiscal Multipliers in Recessions and Expansions: Does It Matter Whether Government Spending Is Increasing or Decreasing?[END_REF], while some papers draw conclusions without paying attention to the asymmetry issue [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF]. More details about these papers are provided in Section 2.5.

This also triggered much research exploring the factors determining fiscal multipliers and concentrating on the economic and institutional fundamentals of advanced economies. Researchers in this way studied the effects of fiscal position related to the level of debt and deficit ratios, the exchange rate regime (monetary unions), the degree of openness, agents' expectations (foresight fiscal policy), the constrained monetary policy at the ZLB interest rate and hand-to-mouth consumers, among other things. Some have also found contrasting results while trying to explain the reasons for the failure of fiscal stimuli to deliver a fast recovery. Figure 1 presents the debated determinants impacting the fiscal expenditure multiplier and its relationship with public debt and economic growth linkages. In what follows, as the literature on fiscal multipliers is somehow very rich and large and still evolving, with many different results, we try to highlight some important contributions without pretending to cover all of the literature, particularly the recent works related to the determinants impacting the size of the spending multipliers.

The state dependency of fiscal multipliers on the business cycle

Some works studied fiscal policy in the pre-crisis of 2008 and proved the linkages between fiscal policy and state dependence. The more recent example is the paper of Tagkalakis ( 2008),38 who found, for OECD countries, larger effects of fiscal policy in recessions than expansions, with more emphasized effects in countries with less-developed consumer credit markets.39 However, since the works of [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], research assessing the effects of fiscal policy, considering the state dependency of the economy, have flourished, especially in the period of the 2008 financial crisis. Among these are the works of Bachmann and Sims (2012), [START_REF] Batini | Successful Austerity in the United States, Europe and Japan[END_REF], [START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF], Riera-Crichton et al. ( 2014), [START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF], [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF]. The main result of these papers is confirmation of the dependency of spending multipliers on the business cycle, which is larger during recessions than expansions.

The contributions of [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF], which triggered a series of works studying fiscal multipliers during recessions and expansions, use a regime-switching structural vector autoregression (SVAR) methodology to assess fiscal multipliers in relation to the business cycle. They find large size of spending multipliers in recessions than in expansions, making expansionary fiscal policy more effective in times of recession than expansion. Moreover, at the disaggregated level, expenditure shows large differences in fiscal multipliers, with military spending having the largest multiplier. They also show that multipliers tend to increase once the real-time predictions of fiscal variables are controlled.

Also, focusing on the United States case, [START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF] estimate a non-linear VAR model to assess fiscal multipliers. They show two important results related to fiscal spending multipliers. First, fiscal spending multipliers are greater than 1 in recessions, and, second, they are not necessarily different from, or larger than, those in expansions. The second result opposes the main findings of the previous research, which confirmed that fiscal multipliers are larger in times of recession than expansion. Another important result raised by the authors is related to the nonlinearity effects on fiscal spending multipliers, which seem to be emphasized in extreme events manifested by deep recessions or strong expansionary periods. [START_REF] Auerbach | Fiscal Multipliers in Recession and Expansion[END_REF] extend the same methodology of [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF] to a panel of OECD countries and confirm their earlier results on the average of studied countries.

However, considering the discrepancies between countries in terms of the structure and behaviour of the economies, the fiscal adjustments and policy responses and private agents' expectations, and the impacts of all these factors on the multipliers' size, the results of the papers studying a single country or averaging a group of countries could not be transposed to other countries and remain debatable.

In this regard, [START_REF] Batini | Successful Austerity in the United States, Europe and Japan[END_REF] and [START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF] also confirm that fiscal multipliers tend to be larger in recessions than expansions, but importantly they differ substantially across groups of advanced countries, calling for a fit of fiscal policies and country-by-country assessment of fiscal multipliers. The two papers employ the same methodology of non-linear threshold VAR (TVAR) model. The only difference is that the threshold is endogenously determined by the sign of the output gap in the first paper, and output growth in the second paper. Data is split according to the threshold that separates expansions (positive output gap/growth) and recessions (negative output gap/growth), chosen to maximize the fit of the model and hence allowing different regression slopes for the explanatory fiscal variable. Using the output gap as the threshold variable is argued by the fact that excess capacities are available in the economy under a negative output gap, which reduces the crowding-out effects of private investment in response to government expenditure shocks. Besides, the share of credit-constrained households, adjusting spending in response to a change in disposable income, is higher in recessions. Other studies use output growth or its moving average [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF]. Moreover, according to Bachmann and Sims ( 2012), the role played by household and firm confidence in the transmission of fiscal policy shocks into economic activity is significant, which emphasizes the evidence of countryspecific properties that should be considered when studying the effects of fiscal policy. [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF], using a model of costly financial intermediation based on [START_REF] Curdia | Credit Frictions and Optimal Monetary Policy[END_REF], 40 provide evidence of strong state-dependent fiscal multipliers that can exceed the value of 2 in times of recession and may fall below unity during times of expansion. Furthermore, the size of the fiscal multiplier is inversely dependent on the size of the fiscal stimulus, with a smaller amount of fiscal intervention leading to a larger size of fiscal multiplier, and vice versa. According to the author, "The reason large fiscal interventions are less effective than smaller ones is that the negative marginal wealth effect due to the higher tax liabilities is increasing with the size of the fiscal intervention while the positive marginal effect on the borrowers, from the reduction in the finance premium, is decreasing with the size of the fiscal expansion" [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF]. Using a regime-switching framework, [START_REF] Arin | Fiscal multipliers in good times and bad times[END_REF] also confirmed large spending multipliers for the United States over the period 1949Q1-2006Q4 during 40 The model is a simple extension of the basic-representative-household new Keynesian model (as developed in [START_REF] Woodford | Interest and Prices: Foundations of a Theory of Monetary Policy[END_REF] of the monetary transmission mechanism, allowing for a time-varying wedge between the interest rate available to households on their savings and the interest rate available to borrowers. This model introduces credit frictions and financial intermediation for the allocation of resources due to the introduction of heterogeneity in the spending opportunities currently available to different households. . economic slowdown, while tax multipliers seem to be larger during periods of economic expansion.

The problem of large multipliers is challenging for fiscal consolidation and austerity measures intending, in times of high public debt, to reduce the latter. In this regard, some papers focus on studying the effects of fiscal consolidation on the public debt ratios, particularly in the short term. For example, [START_REF] Eyraud | The Challenge of Debt Reduction during Fiscal Consolidation[END_REF] analyse the short-term fiscal multipliers considered to be the key linkages between instruments of fiscal consolidation, economic growth and public debt reduction. They find that, for many advanced countries, fiscal short-term multipliers in the recent financial crisis have been close to 1, judged to be larger than the average of the short-term multipliers observed before the 2008 recession. With the crisis environment of constrained monetary policy, constrained credit agents and depressed external demand, these are likely to raise the debt ratio in the short term under fiscal consolidation, and this could be emphasized if financial markets react negatively to this short-term behaviour of public debt.

Along the same lines, Egron (2018) estimate a threshold VAR for France, confirming the higher value of spending multipliers in recessions than expansions, and therefore warning about the dangerous effects of fiscal consolidation, particularly in the short term, leading to an increase, rather than reduction, in the government debt to GDP ratio. Nevertheless, the above results should be considered carefully with regard to the likely asymmetric effects of an increase versus a decrease in fiscal instruments (more details on this point in Section 2.5).

Furthermore, using an SVAR model for several MENA countries, Bentour (2020) assessed spending multipliers considering the oil price fluctuations. The spending multipliers found to be sensitive to the oil price movements especially for oil exporting countries, being large (more than 2) in time of oil price decrease and weak in time of oil price increase.

With regard to the researchers tending to confirm larger multipliers in times of economic downturn compared to economic booms, some researchers contrast these results [START_REF] Barro | Macroeconomic Effects from Government Purchases and Taxes[END_REF][START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF][START_REF] Owyang | Are Government Spending Multipliers Greater during Periods of Slack? Evidence from Twentieth-Century Historical Data[END_REF]. For example, [START_REF] Owyang | Are Government Spending Multipliers Greater during Periods of Slack? Evidence from Twentieth-Century Historical Data[END_REF] find multipliers to be smaller and less than 1. The authors use a large constructed quarterly data set for the United States (1980 to 2010) and Canada (1921 to 2011) and the unemployment rate as a measure of slack considering thresholds of 6.5% and 7% for, respectively, the United States and Canada. For a linear model (no threshold of unemployment considered), either in the United States or Canada, spending multipliers are all below unity and slightly larger in the United States than in Canada. However, in periods of high unemployment (period of slack), multipliers are slightly higher than those in Canada and lower than those in low unemployment rates. For the United States, spending multipliers are always less than 1 and comparable across all regimes.

These clashing results about fiscal multipliers have pushed other economists to dig deeper and control for features related to the economic and institutional regimes of the countries, such as fiscal position, monetary policy stance and exchange rate regimes.

Fiscal multipliers' dependency on the fiscal position

Since the first wave of studies triggered by the public debt and economic growth threshold idea of [START_REF] Reinhart | Growth in a time of debt[END_REF], fiscal policy effects have also been revised distinguishing the presence of high debt and deficit impacts on fiscal multipliers. Until now, the results of these studies have continued to fuel the debate about such a subject.

Consequently, using a panel of 17 OECD countries (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Ireland, Italy, Japan, The Netherlands, Norway, Portugal, Spain, Sweden, the United Kingdom and the United States), [START_REF] Corsetti | What Determines Government Spending Multipliers?[END_REF] find that output and consumption multipliers are high during times of financial crisis. In particular, for weak public finances corresponding to "government debt in excess of 100 percent of GDP or net government borrowing above 6 percent of GDP (each lagged once)", they find that government spending responds negatively to a weak fiscal position, thereby contributing to stabilizing public debt.

Depending on the fiscal position, especially with the presence of high public debt, [START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF], adopting a real business cycle (RBC) framework, find that the fiscal multiplier is generally smaller in a high-debt than a low-debt state when general income tax rates serve as an adjustment instrument, but the difference shrinks as the wealth effect on labour becomes strong. Furthermore, uncertainties involving household reactions to the timing and magnitude of the shock, as well as the debt target of fiscal consolidation, also matter. Expecting a higher debt target is not always expansionary, especially when households perceive consolidation to be implemented via adjusting labour tax rates, and expecting a higher debt target produces a positive wealth effect, which reduces the current hours worked and thus offsets positive government spending effects [START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF].

The previous results are in accordance with the findings of [START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF], which confirm that fiscal multipliers are state-dependent of the fiscal position and tend to be systematically smaller when government debt and deficit are high (weak fiscal position). The authors also show that the fiscal multipliers' dependency on the fiscal position is independent of the business cycle effects. In particular, while the size of the fiscal multiplier tends to be larger in recessions and weaker in expansions, the effects of the fiscal position (weak/strong) apply independently of the economy being in recession or expansion.

In relation to fiscal consolidation under high public debt, [START_REF] Boussard | Fiscal Multipliers and Public Debt Dynamics in Consolidations[END_REF] and [START_REF] Berti | Effects of fiscal consolidation envisaged in the 2013 Stability and Convergence Programmes on public debt dynamics in EU Member States[END_REF] tend to confirm the large effect of fiscal multipliers in times of crisis, which push the debt ratio to increase in response to fiscal consolidation, particularly in the short to medium term. However, these undesired effects on the debt dynamics are judged to be short-lived unless these large multipliers persist over time, which may be caused by non-credible fiscal adjustments and the very high (abnormal) impact on interest rates and sovereign yield. These two publications report "critical" fiscal multipliers, defined as "multipliers that can then be defined as the value of the multiplier for which a fiscal shock would leave the public debt ratio unchanged (while a multiplier higher than the critical value would entail a short-term increase in the debt ratio)".

They show that these multipliers are inversely correlated to the change in debt ratio. According to the authors, the true fiscal multiplier could be higher than the critical multipliers, especially for a group of highly indebted countries, namely, Belgium, Bulgaria, the Czech Republic, Ireland, Greece, Spain, France, Italy, Cyprus, Lithuania, Hungary, Portugal, Slovenia and the United Kingdom.

Moreover, Blot et al. (2014b) simulate the dynamic path of public debt and output, under fiscal consolidation, using a simple macroeconomic model for 11 eurozone countries and considering time-varying fiscal multipliers. They analyse the ability of EMU countries to reach public debt ratios below the threshold of 60% in 2032 to comply with the new fiscal rules of the EMU Stability and Growth Pact. The revised Stability and Growth Pact, which was signed in 2012, outlines converging (from an average level of debt ratios of around 80% across the eurozone in 2012) to a 60% debt to GDP ratio, by 1/20th of the adjustment yearly, which allows until 2032 to achieve the target. In this way, Aussilloux et al. ( 2018) make an exercise of simulation on public expenditure reduction for France, expecting that the public debt to GDP ratio could decrease by 25 points from 100% currently to 75% in 2040 for a best-case scenario of fiscal consolidation. [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF] and [START_REF] Broner | Fiscal Multipliers and Foreign Holdings of Public Debt[END_REF] consider studying the type of financing spending to impact fiscal multipliers in times of economic downturn. [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF] find that either tax-financed or debt-financed spending leads to multipliers that are higher than those in recessions, with the multipliers being much larger for debt-financed than tax-financed spending. According to the authors, "The reason is that while higher government spending sets in motion the financial accelerator, higher taxes partly counter this by reducing the quantity of funds available to financially constrained individuals". [START_REF] Broner | Fiscal Multipliers and Foreign Holdings of Public Debt[END_REF] study fiscal multipliers, considering the portfolio of foreign public debt for a panel of 17 advanced countries from 1980 to 2014. In this case, they reveal that fiscal multipliers are stronger when the expenditure is financed by foreign resources. Their size increases, in particular, with the share of foreign public debt and is larger than unity in periods and countries with a high foreign share of public debt (as in the United States and Ireland today) and smaller than those in the opposite case (as in the United States in the 1950s and 1960s, and Japan today).

Moreover, [START_REF] Poghosyan | How Do Public Debt Cycles Interact with Financial Cycles?[END_REF] studies the way that the public debt cycles interact with financial cycles for 57 advanced and emerging economies over the period 1960-2014. He finds that public debt cycles are asymmetrically linked to financial cycles in the way that public debt expansions that are preceded by fuelling in credit and financial markets are longer than any other expansions, while there is no substantial association between public debt contractions and financial cycles.

Afonso and Leal (2018) compute fiscal multipliers for government expenditure in the eurozone for quarterly data over the period 2001-16, using a structural VAR model. They consider the state of the economy, particularly the reaction to the public debt level, the pace of economic growth and the output gap. Government expenditure multipliers accumulate to less than 1 over a year (0.64 yearly and 1.1 after two years), while tax multipliers are negative. Moreover, expenditure multipliers are larger for countries with higher public debt levels during recessions (compared to low public debt levels where the multiplier is close to 0) and in countries showing positive output gaps.

In contrast to the previous findings about the effects of fiscal position on fiscal multipliers, very recently some new studies have minimized the effects of the fiscal position on fiscal multipliers and then minimized the effects of high public debt on reducing the benefits of fiscal expansion in advanced economies [START_REF] Auerbach | Fiscal Stimulus and Fiscal Sustainability[END_REF][START_REF] Perdichizzi | Estimating Fiscal multipliers in the Eurozone: A Nonlinear Panel Data Approach[END_REF][START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF]. For example, using a non-linear panel VAR model controlling for the macroeconomic properties of 12 eurozone countries over 1985-2015[START_REF] Perdichizzi | Estimating Fiscal multipliers in the Eurozone: A Nonlinear Panel Data Approach[END_REF] find that fiscal spending multipliers are insensitive to the level of government debt. Furthermore, these multipliers are larger in times of recession for countries with low degrees of trade openness, high deficit and fixed exchange rate regime, compared to countries with high degrees of trade openness, low deficits and flexible exchange rate regime.

Auerbach and Gorodnichenko (2017) also produce interesting results on this issue for 17 OECD countries. First, the government spending shock effects depend on a country's position in the business cycle, with the fiscal multipliers being larger in times of bad economic conditions than good ones. Second, fiscal expansion while the economy's fiscal position is weak is likely to boost economic output and reduce the debt to GDP ratio, as well as appeasing interest rates and CDS spreads on government debt. Consequently, these findings suggest that fiscal stimulus under a weak fiscal position is likely to boost the economy without worrying about the associated modest cost. However, these results should be considered with caution, as the authors themselves argue, based on the asymmetric effects of fiscal policy shocks (see discussion in Section 2.4). 41 The authors call for more detailed research on this issue using more frequent and variable data on public debt and more disaggregated categories of government spending, as well as structural models for clearer policy recommendations. Besides, [START_REF] Alichi | Fiscal Policy Multipliers in Small States[END_REF] consider the size of the country and focus on estimating government spending effects for 23 small countries across the world. They conclude that fiscal policy in small countries using government primary spending is ineffective at stimulating the level of GDP over the medium term compared to government spending. However, in the short term, multipliers for government current primary spending are higher and sensitive to the level of government debt, the position of the economy in the business cycle, as well as imports as a share of GDP, among other factors. 41 These results should be interpreted with caution, as the authors argue themselves, because of the problem of asymmetric effects "… we recode fiscal shocks series so that the sign of the shocks is negative whenever the shocks take a nonzero value and thus estimated impulse responses show dynamics after an increase in government spending. This recording may be problematic since the effects of government spending cuts are not necessarily symmetric to the effects of government spending increase… thus one should bear in mind the caveat that, although we interpret results as showing responses to increases in government spending, the estimated responses are only based on cuts in government spending" [START_REF] Auerbach | Fiscal Stimulus and Fiscal Sustainability[END_REF].

Along the same lines, in analysing the fiscal and welfare costs of higher debt with reference to the United States, where the safe interest rate42 is less than the growth rate, [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] argues that both the fiscal and welfare costs of debt may be smaller than assumed in current policy debates. [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] seems likely to draw the same conclusions for European economies. His results have triggered a debate, which have been contained until now in economist blogs and some media. This new paper about debt cost nevertheless warns that the cost of austerity measures driven by the fear of high debt is likely to hurt more than the cost of debt build-up, since actual data shows that the interest rate differential/gap growth rate minus interest rate is positive enough to stabilize the public debt ratio while maintaining a small primary deficit. In this case, two important points are worth mentioning. First, the Committee of a Responsible Federal Budget (CRFB), in response to Krugman's "misinterpretation" of Blanchard's (2019)' conclusions, outlined that Blanchard's (2019) conclusions are correct if the primary balance in the United States is small, but the American economy is running a huge primary deficit. 43The second point highlights some arguments and counter-arguments of potential debt finance. The arguments that [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] reports in favour of potential debt finance (standing against fiscal consolidation) are: revised large multipliers, debt hysteresis, higher marginal product of public capital and necessary budget deficits to stimulate demand in the context of constrained monetary policy. Alternatively, the counter-arguments about the potential costs of public debt are as follows: the safe interest rate may be artificially lower than the observed one (which could happen in the case of liquidity discount); the future may be different to the past because of many factors related to total factor productivity (TFP) and an ageing population; and the last counter-argument relies on the existence of multiple equilibria.

However, while some enthusiastic supporters of fiscal stimulus welcome the message of this paper [START_REF] Krugman | Melting Snowballs and the Winter of Debt[END_REF], 44 this has not been commonly agreed by other economists, as historical data showed the opposite for the most important European economies [START_REF] Mazza | Is public debt a cheap lunch?[END_REF][START_REF] Philippon | The True Cost of Public Debt[END_REF]. 45 This paper, while minimizing the effects of high public debt when the safe interest rate is below the nominal GDP growth (which is the case for many advanced economies), is likely to refuel the debate about public debt effects, and [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] himself argues that this should not be taken as an invitation for more debt rollover and calls for more investigation on this issue.

Fiscal multipliers in a constrained monetary policy and exchange rate regime

Just before the financial crisis, economists seemed to agree on the powerful role of monetary policy as a stabilization instrument, eclipsing, to some extent, the role of fiscal policy. However, conventional monetary policy effectiveness is impaired when the interest rate hits the ZLB rate or when it loses its independence because of a currency pegged to another country. 46 In these cases, fiscal policy is more desirable. 47 In assessing the effects of fiscal policy in the case where monetary policy is constrained by the ZLB interest rate (also called the liquidity trap), or by the fixed exchange rate, as when the country participates in a monetary union, the new Keynesian modelling framework is more desirable than other forms of modelling in assessing the effects of fiscal policy. 48Previous important contributions on the effects of zero interest rates have been conducted by many authors in the context of new Keynesian dynamic stochastic general equilibrium (DSGE) models, which have their basis in the real business cycle (RBC). Therefore, [START_REF] Eggertsson | The Zero Bound on Interest Rates and Optimal Monetary Policy[END_REF] and [START_REF] Eggertsson | What fiscal policy is effective at zero interest rates?[END_REF] conduct simulations of an economy with a zero interest rate and find a large effect of temporarily increasing government spending in this situation, much larger than under normal circumstances. Numerical evidence conducted by [START_REF] Eggertsson | What fiscal policy is effective at zero interest rates?[END_REF] suggests a spending multiplier that could attain five times the spending multiplier in normal circumstances.

In the same scope of new Keynesian models49 used in analysing monetary stabilization policy, [START_REF] Woodford | Simple Analytics of the Government Expenditure Multiplier[END_REF] finds that under the severe conditions of a great depression and a lower interest rate, near 0, these models are likely to report larger multipliers, higher than 1, which, to some extent, may also increase welfare. In this situation, an increase in government spending could have a powerful effect, such as offsetting the negative output gap. However, in less severe circumstances, the fiscal policy through expenditure tool is less powerful, even in the case of a binding constraint of a zero interest rate, especially when the disturbance implying it to bind is expected to be transitory. In such a case, although the spending multiplier could stand above unity in such circumstances, it is viewed as insufficient to eliminate the negative output gap. Similarly, [START_REF] Eichenbaum | When Is the Government Spending Multiplier Large?[END_REF] base their analysis on a new Keynesian DSGE model to argue that the government-spending multiplier can be large when the ZLB on nominal interest rates binds, except when the central bank is committed to a Taylor rule, in which case the spending multiplier is smaller than 1. Likewise, in the ZLB, the value of the multiplier is positively related to both the fraction of government spending, as well as the expected duration of the zero bound constraint. Consequently, efficient government spending should fall in line with the state of the ZLB interest rate.

For countries participating in a monetary union, [START_REF] Kilponen | Comparing fiscal multipliers across models and countries in Europe[END_REF] simulate fiscal consolidation effects for 15 structural models from national central banks (NCBs) in the euro area and the ECB (of which 14 out of 15 have a new-Keynesian dynamic general equilibrium framework). They find that short-term multipliers are, in general, negative and smaller than 1 in absolute value, independent of the fiscal instrument, the studied country and the duration of the fiscal shock, with tax multipliers typically smaller in absolute value than government consumption multipliers. However, for permanent fiscal shocks, the short and long-term effects depend on the fiscal instrument, which acts endogenously to stabilize the long-term public debt path. Furthermore, the simulated short-term multipliers seem to be insensitive to the ZLB exchange rates, except when simultaneous fiscal consolidation is implemented across the euro area as a whole. 50 In this case, short-term government consumption multipliers become larger than 1. This result stays valid for non-euro area countries, for which monetary policy is independent and domestically determined.

Furthermore, [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF] differentiate between the fiscal multipliers resulting from liquidity traps from the ZLB interest rate and those arising from the currency union, using a standard new Keynesian model but also considering Ricardian and non-Ricardian (hand-to-mouth) agents. They particularly highlight the differences in fiscal multiplier values in the ZLB case and those in the situation of a monetary union. In the first case (the liquidity trap due to the ZLB interest rate), in the standard Ricardian model (generally assuming Ricardian agents), fiscal multipliers are always larger than 1 in liquidity traps. According to the authors, the mechanism is insured through inflation: higher government spending during liquidity traps stimulates inflation, and with a fixed nominal interest rate the real interest rate is reduced, which increases current household consumption. However, for a country in a monetary union, in the standard Ricardian model, assuming price flexibility, the crowding-out effects of government spending on private consumption, as well as domestic inflation spurred by government spending, which induces a loss of competitiveness and depresses private investment, drags down the multiplier to less than unity. 51 50 As the aim of fiscal devaluation is improving competitiveness when the monetary policy is constrained to do that via the exchange rate devaluation (as in the case of monetary union), and while the competitiveness of a country is enhanced at the expense of the other countries, simultaneous fiscal reforms targeting fiscal devaluation are likely to cancel/compensate the effects of fiscal devaluation between countries (European Commission, 2013). 51 According to [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF], "the liquidity trap analysis implicitly combines a shock to government spending with a one-off devaluation. The positive response of consumption relies entirely on this devaluation. A currency union rules out such devaluation, explaining the difference in the response of consumption".

In contrast to the previous results, [START_REF] Glocker | Time-varying fiscal spending multipliers in the UK[END_REF] do not find the fiscal spending multipliers to be affected by the ZLB interest rate. They only report, using a time-varying parameter factor augmented vector autoregressive (TVP-FAVAR) framework for the United Kingdom, that fiscal multipliers are timely and cyclically variant: in particular, they are larger in times of recession (more than unity) and lower in times of expansion (less than unity). Moreover, and contrary to research showing "non-Keynesian multipliers" (i.e. inferior to 1) for countries participating in a currency union, [START_REF] Combes | The Euro and the Crisis: Evidence on Recent Fiscal Multipliers[END_REF] use panel VAR (PVAR) on quarterly data over the period 1999-2012 to assess the effect of fiscal multipliers on European countries. They reveal that spending multipliers can be larger than 1, especially for countries that are members of the eurozone, or for those expecting to join it. Furthermore, these multipliers tend to be higher in the group of euro countries affected by the 2008 crisis compared to the benchmark of the eurozone countries.

As previously revealed in Section 2.2, spending multipliers are also sensitive to the way they are financed. Spending multipliers are much larger when they are debt-financed compared to when they are tax-financed [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF], and they are also much higher when they are financed by foreign rather than domestic debt [START_REF] Broner | Fiscal Multipliers and Foreign Holdings of Public Debt[END_REF]. Along the same lines, and within a monetary union, (local) fiscal multipliers are also sensitive to the transfers from outside regions/countries for a country participating in a monetary union. Particularly, fiscal multipliers seem to be large (and may even be larger than 1) when there are fiscal transfers from outside regions or countries [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF][START_REF] Auerbach | Local Fiscal Multipliers and Fiscal Spillovers in the United States[END_REF]. 52The degree of openness also plays an important role in this issue, with more closed economies having larger fiscal multipliers than more open ones. This happens particularly in the short term and incomplete financial markets, as prices that are not fully adjusted push up demand for home goods, which stimulates output. Furthermore, the persistency of the fiscal shocks increasing the magnitude of the fiscal multipliers is due to the agents' willingness to save more from foreign fiscal transfers in temporary shocks expecting future lower periods of transfers. Previous to Farhi and Werning's (2017) work on regional multipliers, Nakamura and Steinsson (2014) find that regional fiscal multipliers in the United States, related to military expenditure, are strongly dependent on the business cycle. Using data on military procurement spending across US regions, they estimate a government spending multiplier in a monetary union of approximately 1.5. Erceg and Linde (2012) use a new Keynesian DSGE model for a relatively small open economy to study the effects of fiscal consolidation for a monetary policy constrained either by a monetary union affiliation or by the ZLB on policy rates (for a country with an independent monetary policy). The impacts of fiscal consolidation differ between the two cases, with differences depending particularly on the persistency time of the ZLB (generally more than two years) and on the inflation responsiveness to output gap. Principally, for a sensitive inflation to output gap, fiscal consolidation is more contractionary under the ZLB rate than under currency union.

The impact of the assessment methods

Despite the growing body of literature on fiscal multipliers, their estimation remains very challenging. Generally, methods mostly employed for assessing fiscal multipliers are of three types: first, structural macro-econometric models; second, the multivariate time series, especially the standard vector autoregressive model and its derivatives of linear and non-linear types (structural VAR, threshold VAR, etc.); and, third, the new Keynesian DSGE models.

Macroeconomic structural models were thoroughly developed by public and government institutions, as well as academicians, in the post-war period and are still largely used in fiscal policy analysis. 53 These are based on works associated with the Cowles Commission programme, based on Keynes' general theory and the relative consensus around the IS-LM framework and econometric tools to estimate the structural parameters. Large-scale models were developed following the first attempts to model the United States economy by [START_REF] Tinbergen | Statistical Testing of Business-Cycle Theories. II. Business Cycles in the United States of America 1919-1932[END_REF], [START_REF] Klein | Economic Fluctuations in the United States, 1921-1941[END_REF] and [START_REF] Klein | An Econometric Model of the United States, 1929-1952[END_REF]. 54 These kinds of model, however, were exposed to two important critiques by [START_REF] Lucas | Econometric policy evaluation: A critique[END_REF] and [START_REF] Sims | Money, Income, and Causality[END_REF][START_REF] Sims | Macroeconomics and Reality[END_REF]. 55 Lucas highlighted in his critique the inability of econometric models to catch structural breaks in the behaviour of economic agents visà-vis monetary policy changes. He expressed this critique as follows: "Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with change in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models" [START_REF] Lucas | Econometric policy evaluation: A critique[END_REF].

Sims ' (1972, 1980) critique is directed at exogeneity, causality issues, parameter identification and hypotheses testing. The contributions of the VAR approach to economics science are well 53 For example, [START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF] simulate government spending multipliers under seven structural models from six institutions, namely, the European Commission (QUEST), the International Monetary Fund (GIMF), the Board of Governors of the Federal Reserve System (with two models, FRB-US and SIGMA), the Bank of Canada (BoC-GEM), the European Central Bank (NAWM) and the OECD (OECD Fiscal). The models tend to produce sizeable output multipliers of expenditure and targeted transfers, especially under accommodative monetary policies, although permanent fiscal stimulus can significantly lower such multipliers. 54 See also, for example, [START_REF] Fox | Econometric Models of the United States[END_REF] and Chinn (2013) for a complete literature review. 55 The Lucas critique has revolutionized macroeconomics science by developing many theories such as the theory of rational expectations, which won him the 1995 Nobel Prize, the development of the "time inconsistency" problem by Kydland and Prescott (both Nobel Prize winners in 2004) and the important contribution of Thomas Sargent over the credibility of economic policies. Thomas Sargent also contributed to much empirical research in line with Cristopher Sims, with whom he shared the 2011 Nobel Prize for their contribution to cause and effect in macroeconomics.

summarized and synthesized, for example, in Hoover el al. (2008) or [START_REF] Gossé | L'apport de la représentation VAR de Christopher A. Sims à la science économique[END_REF].

Following these critiques, [START_REF] Sims | Macroeconomics and Reality[END_REF] brought the vector autoregressive (VAR) models and their utilization to diverse applications as an alternative to the macroeconomic structural models. Their strength resides in their simplicity and robust application, especially in forecasting, compared to structural models. However, these models have also attracted many critics, especially the famous [START_REF] Lucas | Econometric policy evaluation: A critique[END_REF] critique. The third type of models based on the real business cycle (RBC) neoclassical model, are the new Keynesian DSGE models (due to the new synthesis theory), largely developed and used in recent years by central banks and monetary institutions. [START_REF] Kydland | Time to Build and Aggregate Fluctuations[END_REF] first confronted the theory with data through the application of calibration methods to real business cycle (RBC) models, avoiding the option of fully econometric estimation, as did the pioneer of structural models.

All these methods have been criticized for caveats on their technical and conceptual design in analysing fiscal policy effects. For example, [START_REF] Cogan | New Keynesian versus old Keynesian government spending multipliers[END_REF] highlighted the role played by the quantitative models in evaluating fiscal policy. In particular, government spending multipliers in the recently used new Keynesian models tend to be much smaller than in the old Keynesian ones. This conclusion came after simulating a new Keynesian model based on the core model of [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF] for the United States and comparing its results to those of Romer and Bernstein (2009), which are based on an old Keynesian model for the same country. They conclude that the models used to assess fiscal policy effects lack robustness and consensus in their results, in which there are stark differences. Their new Keynesian model showed fiscal multipliers and job impact six times smaller than those found by Romer and Bernstein's (2009) old Keynesian model. The principal challenges remain in many differences in assumption, economic issues, as well as econometric and statistical aspects. Generally, the drawbacks and caveats of the new Keynesian models have been discussed in the recent literature, as reported in Chapter 3 (Section 2.4). 56The difference in assumptions, as well as their structure, greatly impacts the size of the multipliers between these three classes of models. Changing assumptions in the same class of models may also lead to a sizeable change in fiscal multipliers. For example, assuming complementarities between public and private capital in the neoclassical RBC models leads to higher spending multipliers than the modest values without this assumption (Baxter and King, 1993). Under its standard framework, the new Keynesian DSGE model leads to smaller spending multipliers, while relaxing some assumptions, such as the presence of the ZLB interest [START_REF] Christiano | On DSGE Models[END_REF][START_REF] Galí | The State of New Keynesian Economics: A Partial Assessment[END_REF], or the relaxation of the Ricardian equivalence assumption in favour of "hand-to-mouth" agents [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF], leading to an increase in spending multipliers.

From an economic perspective, agents' expectations ("fiscal foresight") about future spending and tax policies, the monetary policy reaction, the exchange rate regime, the degree of openness, the state of the economy and the fiscal position (high/low public debt and deficit) are examples of the economic determinants making it difficult to deduce the fiscal multiplier, especially given that, remembering the definition, the fiscal multiplier measures the effects of an exogenous distortionary fiscal instrument on the level of the output. From an econometric and statistical perspective, many problems arise when calculating fiscal multipliers. Important issues are the endogeneity of government spending and non-linearities created by extreme changes, especially in times of extreme events (high expansions or severe downturns). The accuracy of the data and its availability on a disaggregated level is also an important determinant of the correct multipliers' size [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF].

For example, Parker (2011) warned against the impact of the methods and the lack of accurate data used to gauge the effects of fiscal policies through multipliers, especially the use of linear dynamic forms represented by the vector autoregression models and linearized dynamic stochastic general equilibrium models. Accordingly, ignoring the state of the economy (the business cycle) leads to multipliers representing a weighted average of the phases of the cycles over the studied period, which is lower than those estimated in recessions and higher in those emanating from expansions. These caveats can be resolved, according to the author, by considering partial-equilibrium response estimations on a microeconomic level rather than macro and aggregated data. Along the same lines, [START_REF] Canzoneri | Fiscal multipliers in recessions[END_REF] highlighted that studies assessing fiscal multipliers, without distinguishing between recessions and expansions, lead to spending multipliers around unity, while these multipliers could reach more than 2 during recessions and only around 0.5 during expansions.

The new Keynesian models have been criticized for assessing the fiscal multipliers (see also the critiques of this type of model for their assessment of debt effects in Chapter 3, Section 2.4). The new Keynesian DSGE models rely principally on many assumptions that are hard to realize in reality, for example, the assumption about the behaviour of agents generally supposed to be Ricardian, with rational expectations, as well as their poor performance in the recent crisis [START_REF] Chatelain | The Failure of financial macroeconomics and what to do about it[END_REF][START_REF] Wieland | A new comparative approach to macroeconomic modeling and policy analysis[END_REF]Blot et al., 2014b). Furthermore, these models are unable to deal with non-linearities of fiscal multipliers over the business cycle (Blot et al., 2014b).

Furthermore, modelling behaviour is not straightforward. The heterogeneity of economic agents' behaviour adds complexity to the adopted modelling approach conditioning the fiscal policy assessment. For example, [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF] distinguish between Ricardian and non-Ricardian consumers that could affect the size of the fiscal multipliers. Particularly, in a non-Ricardian model where "hand-to-mouth" consumers are considered, marginal propensities to consume are different between Ricardian and non-Ricardian groups of agents. This leads to additional effects of government spending increasing output, whether in a liquidity trap or in a currency union, due to the incidence of taxes, the timing of taxation (on the non-Ricardian agents)

and redistribution from Ricardian agents with low marginal propensity to consume permanentincome to non-Ricardian agents with high marginal propensity to consume. Accordingly, this may raise the multipliers above 1 for a country within a currency union [START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF].

Another issue that is mentioned in the literature belongs to the "fiscal foresight" policy shocks [START_REF] Forni | Fiscal Foresight and the Effects of Government Spending[END_REF][START_REF] Mertens | Measuring the Impact of Fiscal Policy in the Face of Anticipation: A Structural VAR Approach[END_REF][START_REF] Leeper | Quantitative Effects of Fiscal Foresight[END_REF][START_REF] Leeper | Fiscal Foresight and Information Flows[END_REF]. The standard VAR models assess the effects of fiscal policy shocks from current and past information from the data of fiscal variables involved, and they are unable to embed/incorporate the so-called information on "fiscal foresight" policy shocks, that is, shocks related to agents' anticipations/expectations on government fiscal policy spending [START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF]. For example, [START_REF] Caggiano | Estimating Fiscal Multipliers: News from a Non-linear World[END_REF] address this issue by considering state-dependent fiscal multipliers, taking explicit information on such expectations using a measure of anticipated information ("news") on fiscal spending shocks and a group of macro-fiscal variables from the Survey of Professional Forecasters.

For the non-linear effects and behaviour of fiscal relationships, Fotiou (2019) uses a mix of the two methodologies of Auerbach and Gorodrichenko (2012) of the STVAR57 model and the methodology of [START_REF] Nickel | Fiscal stimulus in times of high debt: reconsidering multipliers and twin deficits[END_REF] 58 to study non-linear effects on fiscal multipliers for a panel of 13 countries during 1980-2014. According to the author, non-linearities arise from, first, the state of the economy (recessions versus expansions), second, the composition of the fiscal policy, and, third, the government's fiscal position (high debt ratio versus low debt ratio). He finds that the initial level of debt and the composition of the fiscal adjustments are the most relevant sources of non-linearities. Furthermore, for this author, tax-based consolidation tends to be selfdefeating whenever debt is high. Casalis (2017) also studies the effects of non-linearities controlling for public debt and financial cycles. He reports that non-linearities produce more queries than answers for policy advice and that comparing results is likely to be misleading in this environment.

Do we need a consensus about a unique fiscal multiplier size for all countries?

Despite the important flux of studies about fiscal multipliers, these studies show more uncertainties than certitude about their size. The differences in methods, as well as samples of countries and time periods, play an important role in this issue. Recently, [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF] summarized the main research outcome on fiscal policy since the 2008 financial crisis. According to the author, average fiscal spending multipliers vary in a narrow range between 0.6 and 1. However, there are economic circumstances where spending multipliers lie outside this range, as well as the impact of approaches used to assess those multipliers. In particular, this range may widen if country characteristics, such as the exchange rate regime, and the type of government spending are considered.

Along the same lines, Parraga [START_REF] Rodriguez | The dynamic effects of public expenditure shocks in the United States[END_REF], following an SVAR framework, finds that government spending multipliers and income transfers multipliers in the United States are by far below 1 in the short term (approximatively 0.2). However, compared to government fiscal income transfers multipliers that can reach more than 1 in the long term, the spending multipliers cumulate only to 1 in the long term. [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF], focusing again on the case of the United States, as the single country case for which multipliers are most evaluated in the literature, examine whether the government spending multipliers are sensitive to the zero bound interest rate and the business cycle in the economy.

For [START_REF] Ramey | Ten years after the Financial Crisis: What have we learned from the renaissance of fiscal research?[END_REF], concluding that the average of fiscal multipliers (spending) reported in the previous literature is low and ranges between 0.6 and 1, averaging fiscal multipliers without distinguishing between the sign of the fiscal shocks59 is misleading. Indeed, and surprisingly, to our best knowledge, this flux of very recent studies does not seem to distinguish between multipliers drawn from negative shocks and those from positive shocks, leading us to understand that the effects are similar in the two situations. For example, some studies may draw conclusions on the effect of fiscal multipliers, from fiscal austerity and fiscal consolidation, as if they were the same as in fiscal stimulus, thereby admitting the symmetrical effects in the two opposed shocks.

One of these studies, Ramey and Zubairy (2018), draws the following conclusion "... If multipliers are indeed this low, they suggest that increases in government purchases do not stimulate private activity and that fiscal consolidations based on reducing government purchases are unlikely to do much harm to the private sector". Ramey (2018) also does not seem to distinguish between these situations (fiscal consolidation and fiscal stimuli) in averaging the fiscal multipliers reported in the previous studies. Another study, by Blot and al. (2014b), concludes that "... Recent mainstream literature has emphasized that fiscal multipliers may notably be higher in time of crisis. Then, not only would fiscal consolidation drag down growth more severely, but it could even be selfdefeating".

In line with the literature studying fiscal multipliers' dependency on the business cycle, Ramey and Zubairy (2018) study the state dependency of fiscal multipliers, involving, at the same time, the zero lower bound for the United States. They contrast the findings of the previous research in line with [START_REF] Auerbach | Measuring the Output Responses to Fiscal Policy[END_REF]2013) and report multipliers ranging in a narrow band between 0.6 and 1. The higher magnitude of the fiscal multipliers in the zero lower bound is also of little evidence in [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF].

Ramey and Zubairy's (2018) results should be considered with caution, especially with regards to their data set. Indeed, while they have the advantage of pointing to their long history and more frequent data for the United States (sample between 1889 and 2013), half of the period sample is constructed for the World War periods and before and interpolated using different methods in four different sub-periods. 60 This quarterly constructed data could imply serious problems of accuracy and may have serious problems for the calculated multipliers. This may explain the difference between results where the multipliers seem to be larger in the post-war period when omitting the initial period (although they suggest that these multipliers are not statistically strongly significant). Furthermore, [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF] use narrative methods to extend [START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF] defence news series in order to identify shocks that are unanticipated and exogenous to the state of the economy. 61 Important exceptions to these papers are [START_REF] Baum | The Impact of Fiscal Policy on Economic Activity over the Business Cycle: Evidence from a Threshold VAR Analysis[END_REF] and Riera-Crichton et al. ( 2014), who mention that government spending is not necessarily acting counter-cyclically (going up in times of recessions); rather, it could be, as is the case in many industrial economies, procyclical (decreasing). In this paper, the authors control for the sign of fiscal shocks (increase or decrease in government spending), as well as the size of the fiscal intervention, rather than distinguishing only between recessions and expansions. Their analysis reveals that fiscal expansions are much more expansionary in recession periods than in expansion periods. Using a threshold SVAR (TSVAR) to account for non-linearities, Riera-Crichton et al. ( 2014) find that the long-term multiplier for bad times and an increase in government spending is around 2.3 higher than the value of 1.3 if we control for recession only and expansion is considered. However, using the same methodology of threshold VAR, [START_REF] Baum | The Impact of Fiscal Policy on Economic Activity over the Business Cycle: Evidence from a Threshold VAR Analysis[END_REF] find that public expenditure multipliers vary depending on the size of the shock, its sign and the level of the output gap. Consequently, a positive fiscal shock (increase in government expenditure) in crisis periods leads to a higher spending multiplier, and the latter increases with the size of the fiscal shock. However, in good times, multipliers are lower and seem to behave more linearly.

To sum up this section, the wide spread of results about the size of spending multipliers leads us to conclude that these multipliers, despite their simple definition, reflect:

1-The difference of methods and models used to assess these multipliers: with the same data, and on a single country (the United States, for example), researchers find different results whether the used model is a structural model, a new Keynesian DSGE model or a (non-) 60 The time series are the real GDP, the GDP deflator, government purchases, federal government receipts, population, the unemployment rate, interest rates and defence news. The time series data is interpolated using different techniques depending on the series over the period 1889-1946 and its sub-periods. They follow Gordon and Krenn (2010) by using various higher-frequency series to interpolate existing annual series. Generally, the proportional [START_REF] Denton | Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization[END_REF] procedure, resulting in series that average up to the annual series, is used in the interpolation. This method is robust [START_REF] Chen | Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance[END_REF] and recommended in IMF or Federal Reserve Bank publications [START_REF] Liu | Land-Price Dynamics and Macroeconomic Fluctuations[END_REF][START_REF] Woo | Economic Recovery from Recessions: The Role of Fiscal Policy, and Structural Reforms[END_REF]. 61 The news series is linked to government spending due to political and military events and is likely to be independent of the business cycle. This is an important difference from and other papers using the output gap and economic growth as the instrument variable to determine the turning points of the business Auerbach and Gorodnichenko (2019) cycle.

linear VAR/SVAR model. The assumptions and features, as well as the methods of solving the three types of model, vary widely.

2-The difference in macroeconomic fundamentals of the studied countries, although the most advanced countries share, to some extent, the same level of development and qualified institutions, fiscal policies effects may differ regarding the difference of monetary policy and exchange rate regimes, as well as economic conditions (the business and/or the financial cycle), as represented by the levels of debt and deficit, for example. Other determinants could play an important role as the degree of openness.

3-Consequently, all the differences in empirical results should not be seen as an incongruity between economists. It is a fact rather than a general theory that should apply to all countries. In this regard, a good way to study the effects of fiscal policy is to avoid considering the empirical results of one country or a group of countries as a universal benchmark for all countries. Therefore, studies of fiscal multipliers should be undertaken at country level and avoid drawing conclusions from a single country such as the United States, Japan, the United Kingdom or Germany. When it comes to assessing things empirically, each country's data set represents its own model of economic development and experience across a period of that country, and if this is not even valid to reproduce the future of this economy itself, it is hardly transposable to a different country.

Whether in fiscal stimuli or fiscal consolidation, accurately estimating fiscal multipliers by type of expenditure helps policy-makers to know what categories of spending they should increase (in fiscal stimuli) or cut (in consolidation). The next section undertakes calculations of government spending multipliers in a sample of advanced countries.

Methodology

In our empirical investigation, we use a sample of 18 advanced countries over different periods of time, a panoply of structural vector autoregressive (SVAR) models to assess the fiscal expenditure impacts on the output. We especially test how the business cycle could affect expenditure multipliers, as well as the way accumulating public debt and reducing public debt are impacting the size of the expenditure multipliers. In what follows, we display, first, a detailed methodology of an SVAR model, particularly, its formulation, lag selection and identification of shocks. Second, we discuss the identification restrictions for the considered VAR models linking government expenditure with GDP, augmented exogenously by a dummy variable that controls for the business cycle (expansion/recession) and the public debt evolution (accumulation/decumulation), hence noted an SVAR-X. We also endogenize the public debt variable instead of its exogeneous effects, making a tri-variate VAR of government expenditure, debt and GDP. This model is also controlled for the business cycle impacts.

The general methodology of a VAR/SVAR model

The vector autoregressive (VAR) methodology was popularized by the works of [START_REF] Sims | Money, Income, and Causality[END_REF][START_REF] Sims | Macroeconomics and Reality[END_REF] following the debate between monetarists and Keynesians on exogeneity and causality issues. In particular, [START_REF] Sims | Macroeconomics and Reality[END_REF] points out that the structural models of the Cowles Commission have too many theoretical hypotheses that have not been empirically tested, and he presents the VAR models as an alternative to these models. However, the standard VAR models, which are reduced forms, do not integrate the structural model's simultaneity where there is instantaneous feedback between two endogenous variables [START_REF] Desai | Testing Monetarism[END_REF]. In particular, conditional correlations assimilated with a causal order in the case of the standard VAR can only be justified under determined hypotheses that could not be tested in the absence of a priori restrictions derived from economic theory [START_REF] Cooley | A-theoretical macroeconomics: A critique[END_REF]. To overcome this issue and interpret canonical innovations as exogenous economic policy shocks, Sims transforms the VAR model into a structural VAR (SVAR). Furthermore, to justify the identification restrictions imposed on innovations, Sims refers to [START_REF] Wold | A Study in the Analysis of Stationary Time Series[END_REF] notion of causal chain.

VAR formulation

A system of N equations linking linearly N endogenous variables through their past values to a certain level p, representing the optimal/maximum lag, is called a standard vector autoregressive with lag 𝑝, 𝑉𝐴𝑅(𝑝). It is expressed by Equation ( 1):

𝑌 𝑡 = 𝛷 0 + ∑ (𝛷 𝑖 𝑝 𝑖=1 𝑌 𝑡-𝑖 ) + 𝜖 𝑡 (1)
Where;

𝑌 𝑡 = [ 𝑦 1𝑡 ⋮ 𝑦 𝑁𝑡 ], Ф 0 = [ 𝑎 1 0 ⋮ 𝑎 𝑁 0 ] and 𝜖 𝑡 = [ 𝜀 1𝑡 ⋮ 𝜀 𝑁𝑡
] are vector columns of respectively; endogenous variables 𝑦 1𝑡 … 𝑦 𝑁𝑡 , constant terms and corresponding errors, also called innovations, shocks, of each equation in the VAR, and

𝛷 𝑝 = [ 𝑎 1𝑝 1 ⋮ 𝑎 𝑁𝑝 1 𝑎 1𝑝 2 ⋮ 𝑎 𝑁𝑝 1 … ⋮ … 𝑎 1𝑝 𝑁 ⋮ 𝑎 𝑁𝑝 1
] is the matrix of coefficients associated with lagged terms.

Defining lag time operator 𝐿 as 𝐿𝑋 𝑡 = 𝑋 𝑡-1 , Equation (1) can be written as:

𝑌 𝑡 (𝐼 -∑ 𝛷 𝑖 𝑝 𝑖=1 𝐿 𝑖 ) = 𝛷 0 + 𝜖 𝑡 (2)
Or equivalently also, Ф(𝐿)𝑌 𝑡 = 𝛷 0 + 𝜖 𝑡 , with I as the matrix identity and Ф(𝐿) = 𝐼 -∑ 𝛷 𝑖 𝑝 𝑖=1

𝐿 𝑖

Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 111

Lag selection procedure

To determine the optimal lag 𝑝 to be introduced in the VAR, there is a set of methods commonly used in the economic literature, which select the optimal lag based on the information criteria. The most well known in the literature are Akaike information criterion (AIC) and Schwarz information criterion (SC). However, other tests are also solicited such as sequential modified LR test statistic (LR test), final prediction error (FPE test) and Hannan-Quinn information criterion (HQ). The methodology of these criteria is based on selecting the model that minimizes a defined function.

The methodology consists of estimating the 𝑉𝐴𝑅(𝑝) for lags ranging from 0 to a maximum ℎ 𝑚𝑎𝑥 , where the latter is the maximum number of lags included in the VAR model based on a defined economic theory, a referenced academic article or even sometimes on a simple economic intuition [START_REF] Gossé | L'apport de la représentation VAR de Christopher A. Sims à la science économique[END_REF]. We then retain the number 𝑝 of lags, which minimizes the 𝐴𝐼𝐶 and 𝑆𝐶 criteria defined by the following parametrized functions:

𝐴𝐼𝐶(𝑝) = ln[det(Ω ̂)] + 2 𝑝𝑘 2 𝑇 (3) 𝑆𝐶(𝑝) = ln[det(Ω ̂)] + 2 𝑝𝑘 2 ln(𝑇) 𝑇 ( 4
)
where T is the number of observations, k the number of variables in the VAR model and Ω ̂ the estimated variance-covariance of the residuals.

Identification and analysis of shocks

The reduced form is seen as a "black box", as it is difficult to interpret the reduced form parameters based on an economic theory. Therefore, the structural VAR (SVAR) was developed in the mid-1980s to overcome this issue and allow economic agents' behaviour to be described by the VAR methodology. Since then, many authors have proceeded by including shocks grounded in the economic theory in relation to economic policies, such as supply and demand shocks [START_REF] Shapiro | Sources of Business Cycles Fluctuations[END_REF][START_REF] Blanchard | The Dynamic Effects of Aggregate Demand and Supply Disturbances[END_REF], monetary shocks [START_REF] Sims | Are Forecasting Models Usable for Policy Analysis?[END_REF] or fiscal shocks [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF]. The pass-through from canonical shocks of the reduced form of the equation ( 1), namely, 𝜖 𝑡 , to structural shocks (based on economic behaviour), 𝜔 𝑡 , requires the existence of a matrix 𝑃 such as:

𝜖 𝑡 = 𝑃𝜔 𝑡 (5)
Consequently, identification of structural shocks insured once matrix 𝑃 has been estimated yields:

𝜔 ̂𝑡 = 𝑃 -1 𝜖̂𝑡 (6)
The initial method of identification of shocks, initially suggested by [START_REF] Sims | Macroeconomics and Reality[END_REF], is based on a recursive Cholesky decomposition. Meanwhile, the standard VAR as a reduced form (without any economic theory) requires the variables of the VAR system to be ordered considering the degree of exogeneity/endogeneity of these variables; the order must go from the most exogenous variable to the least exogenous (the most endogenous) one.

However, for a structural VAR, SVAR, the identification method is based on restrictions over structural terms that are not necessarily recursive. The restrictions can be in the short term, as in [START_REF] Bernanke | Alternative Explanations of the Money-Income Correlation[END_REF] and [START_REF] Sims | Are Forecasting Models Usable for Policy Analysis?[END_REF], as well as the long term, as pioneered by [START_REF] Blanchard | The Dynamic Effects of Aggregate Demand and Supply Disturbances[END_REF]. A combination of the two types (short-and long-term restrictions) was developed by [START_REF] Galí | How Well Does The IS-LM Model Fit Postwar U. S. Data?[END_REF]. Recently, restrictions have also targeted specific structural terms, annulling the coefficients associated with these or imposing specific signs. This is done regarding the economic theory [START_REF] Faust | The Robustness of Identified VAR Conclusions about Money[END_REF]Canova and De Nicolo, 2002;[START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF][START_REF] Uhlig | What Are the Effects of Monetary Policy on Output? Results from an Agnostic Identication Procedure[END_REF].

To analyse the shocks of a VAR model, a vector moving average (VMA) (also called Wold decomposition) is required. According to Wold's theorem, every stationary system can be expressed as a weighted average sum to infinity of white noise terms. Considering a stationary 𝑉𝐴𝑅(𝑝) of Equation ( 1), and supposing that the variables are centralized around the mean (i.e. 𝛷 0 = 0), Equation ( 1) can be written in the form of vector moving average, noted 𝑉𝑀𝐴(∞) as:

𝑌 𝑡 = ∑ ѱ 𝑗 ∞ 𝑗=0 𝜖 𝑡-𝑗 = Ѱ(𝐿)𝜖 𝑡 (7)
with

Ѱ(𝐿) = ∑ ѱ 𝑗 ∞ 𝑗=0
𝐿 𝑗 , ѱ 0 = 𝐼 and 𝜖 𝑡 as the vector of innovations (shocks). The impact of these shocks (innovations) over endogenous variables is determined by dynamic impacts defined from Equation (3) as:

ѱ 𝑖𝑗,𝑠 = 𝜕𝑌 𝑖,𝑡+𝑠 𝜕𝜀 𝑗,𝑠 (8)
where ѱ 𝑖𝑗,𝑠 measures the impact of 𝜀 𝑗 in time t over the endogenous variable 𝑌 𝑖 following 𝑠 periods of time. For 𝑠 = 0, this is called immediate impact or instantaneous effect (which can also be assimilated to short-term effect).

Considering (6) and rewriting (7), we can deduct:

𝑌 𝑡 = ∑ (ѱ 𝑗 ∞ 𝑗=0 𝑃)(𝑃 -1 𝜖 𝑡-𝑗 ) = ∑ Ф 𝑗 ∞ 𝑗=0 𝜔 𝑡-𝑗 (9)
Equation ( 9) yields responses to a structural dynamic impact following a structural shock 𝜔 𝑡 :

Ф 𝑖𝑗,𝑠 = 𝜕𝑌 𝑖,𝑡+𝑠 𝜕𝜔 𝑗,𝑠 (10)
Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 113 Furthermore, the structural VAR form (SVAR) can be derived from the reduced form as:

𝑌 𝑡 = ∑ 𝐴 𝑗 𝑌 𝑡-𝑗 ∞ 𝑗=0 + 𝜔 𝑡 (11)
where matrices 𝐴 𝑗 and the structural residual variances of 𝜔 𝑡 are estimated by multiplying the estimated reduced form terms of Equation ( 1) by 𝑃 ̂-1 ; 𝐼 -𝐴 0 = 𝑃 ̂-1 ; 𝐴 ̂𝑗 = 𝑃 ̂-1 Ф ̂𝑗 for 1 ≤ 𝑗 ≤ 𝑝 and 𝑉𝑎𝑟(𝜔 𝑡 ) = 𝑃 ̂-1 𝛺(𝑃 ̂-1 )′. Consequently, the estimation of SVAR is assured once matrix 𝑃 has been estimated. This matrix represents 𝑛 2 unknown parameters comprising 𝑛(𝑛 -1)/2 identifying constraints mandatory to estimate the SVAR model. These constraints must be imposed a priori for the estimation of the model.

Application

For our application, we run a bivariate SVAR linking government expenditure to the GDP to study the effects/multipliers of government consumption on the output. In order to control exogenously for the business cycle (expansion versus recession), debt to GDP evolution (accumulation versus reduction) and the existence of both debt accumulation/reduction under expansion/recession, the SVAR is augmented by variable dummies corresponding to each of the previous prescribed states, hence becoming an SVAR-X (X for exogenous).

Following the previous general methodology, the SVAR, in our case, linking two endogenous stationary variables describing, respectively, the relationship between government expenditure (𝑔 𝑡 ) and GDP (𝑦 𝑡 ) for each country, is formulated as:

{ 𝑔 𝑡 + 𝛽 1,2 𝑦 𝑡 = 𝑐 1,0 + 𝑐 1,1 𝑔 𝑡-1 + 𝑐 1,2 𝑦 𝑡-1 + 𝜀 𝑔,𝑡 𝑦 𝑡 + 𝛽 2,1 𝑔 𝑡 = 𝑐 2,0 + 𝑐 2,1 𝑔 𝑡-1 + 𝑐 2,2 𝑦 𝑡-1 + 𝜀 𝑦,𝑡 (12) 62
where 𝜀 𝑔,𝑡 and 𝜀 𝑦,𝑡 are, respectively, the structural shocks/innovations of the first and second variables in this bivariate SVAR, and could be formulated as:

( 𝜀 𝑔,𝑡 𝜀 𝑦,𝑡 ) = 𝜀 𝑡 ≈ 𝑖. 𝑖. 𝑑. (( 0 0 ) , ( 𝜎 𝑔 0 0 𝜎 𝑦 )) (13)
The real government consumption/expenditure and the real output (GDP) are considered in log differentiated natural logarithm, hence designing the growth rate of the corresponding variables and allowing direct interpretation of simultaneous parameters as elasticities assigned to these variables in the SVAR equations (i.e. ( 𝛽 1,2 𝛽 2,1 ) = 𝛽). Thus, Equation (1) can be formulated as:

[ 1 𝛽 1,2 𝛽 2,1 1 ] [ 𝑔 𝑡 𝑦 𝑡 ] = [ 𝑐 1,0 𝑐 2,0 ] + [ 𝑐 1,1 𝑐 1,2 𝑐 2,1 𝑐 2,2 ] [ 𝑔 𝑡-1 𝑦 𝑡-1 ] + [ 𝜀 𝑔,𝑡 𝜀 𝑦,𝑡 ] (14)
which could be also expressed in the form of:

𝐵𝑣 𝑡 = 𝐶 0 + 𝐶𝑣 𝑡-1 + 𝜀 𝑡 (15)
We deduce the reduced form of the SVAR, called a standard VAR model, by multiplying equation ( 15) by the inverted matrix 𝐵 -1 , assuming it exists, and solving for 𝑣 𝑡 in terms of 𝑣 𝑡-1 and 𝜀 𝑡 :

𝑣 𝑡 = 𝐵 -1 𝐶 0 + 𝐵 -1 𝐶𝑣 𝑡-1 + 𝐵 -1 𝜀 𝑡 = 𝑎 0 + 𝐴𝑣 𝑡-1 + 𝑢 𝑡 (16)
Or equivalently, 𝐴 1 (𝐿)𝑣 𝑡 = 𝑎 0 + 𝑢 𝑡 with 𝐴 1 (𝐿) = 𝐼 -𝐴𝐿.

We can easily deduce the residuals 𝑢 𝑡 as a linear combination of the structural errors 𝜀 𝑡 :

𝑢 𝑡 = 𝐵 -1 𝜀 𝑡 = 1 (1-𝛽 1,2 𝛽 2,1 ) [ 𝜀 𝑔,𝑡 -𝛽 1,2 𝜀 𝑦,𝑡 𝜀 𝑦,𝑡 -𝛽 2,1 𝜀 𝑔,𝑡 ] (17)
Thus:

𝑣 𝑡 = 𝜆 + Ψ(L)𝑢 𝑡 (18)
The structural moving average (SMA) representation of 𝑣 𝑡 is based on an infinite moving average of the structural innovations 𝜀 𝑡 , deduced by substituting 𝑢 𝑡 = 𝐵 -1 𝜀 𝑡 into equation ( 18), which leads to:

𝑣 𝑡 = 𝜆 + 𝛹(𝐿)𝐵 -1 𝜀 𝑡 = µ + Ф(𝐿)𝜀 𝑡 (19)
where

Ф(𝐿) = ∑ 𝜑 𝑘 𝐿 𝑘 ∞ 𝑘=0
.

In order to solve an SVAR, the parameters must be identified, which requires some restrictions to be imposed. Typical identifying restrictions include either assuming no simultaneous equations effects from one variable to another in the SVAR (for example, 𝛽 1,2 = 0 or 𝛽 2,1 = 0) or linear restrictions on the elements of the matrix (for example, 𝛽 1,2 + 𝛽 2,1 = 0). In our case, we follow the methodology of [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF] by identifying government spending shocks using a Cholesky decomposition, ordering government spending first as the variable that is clearly the most exogenous compared to GDP. 63 For our case, we are only interested in government multipliers, and no tax multipliers are considered in the current chapter. As explained in the general methodology, the number of restrictions needed is determined by the number 𝑛 of endogenous variables of the VAR by the formulae, 𝑛(𝑛 -1)/2. Thus, for a bi-variate model, the number of restrictions is only 1 (2(2 -1)/2). Then, the matrix of shocks after restrictions is

[ 𝑐 1,1 0 𝑐 2,1 𝑐 2,2 ].
In our restriction, we especially consider that the response of government expenditure to the output comes with a lag, which means no contemporaneous effects of GDP to government expenditure. Thus, the coefficient 𝛽 1,2 = 0. This is also interesting, as the reverse instantaneous causality from GDP to expenditure may alter, deducing the effect, ceteris paribus, of government expenditure on GDP (fiscal multiplier).

In order to draw fiscal multipliers, the formulae of impulse response functions are required. For the bivariate SVAR model, taking the structural moving average (SMA) representation in Equation ( 18) at the horizon time 𝑡 + ℎ, we have:

[ 𝑔 𝑡+ℎ 𝑦 𝑡+ℎ ] = [ 𝑐 1,1 𝑐 1,2 𝑐 2,1 𝑐 2,2 ] [ 𝑔 𝑡-1 𝑦 𝑡-1 ] + [ 𝜀 𝑔,𝑡 𝜀 𝑦,𝑡 ] (20)
Fiscal multipliers are drawn from structural shocks assigned to each variable; in particular, we are interested in the effect of structural fiscal (expenditure) shocks on GDP in this case. For this purpose, we consider the structural moving average (SMA) representation of the SVAR. At the horizon time 𝑡 + ℎ, the SMA representation is:

[ 𝑔 𝑡+ℎ 𝑦 𝑡+ℎ ] = [ 𝜑 1.1 0 𝜑 1.2 0 𝜑 2.1 0 𝜑 2.2 0 ] [ 𝜀 𝑔,𝑡+ℎ 𝜀 𝑦,𝑡+ℎ ] + ⋯ + [ 𝜑 1.1 ℎ 𝜑 1.2 ℎ 𝜑 2.1 ℎ 𝜑 2.2 ℎ ] [ 𝜀 𝑔,𝑡 𝜀 𝑦,𝑡 ] + ⋯ (21)
Then the structural dynamic multipliers are: impacts in what is referred to as the impulse response functions (IRFs). For the cumulative effects of the structural shock impacts, since the SVAR is designed to be stationary, which means that the effects 𝜑 𝑖.𝑗 ℎ fade away in the long term (i.e. lim ℎ→∞ 𝜑 𝑖.𝑗 ℎ = 0), the long-term cumulative impact of the structural shocks is captured by the instant IFRs to infinity, which means:

∅ = ∑ 𝜑 𝑖.𝑗 ℎ ∞ ℎ=0 ; (𝑖, 𝑗) = (1,2) (23)
The structural dynamic multipliers (short-term or long-term cumulative) defined above are different from the Keynesian concept of the fiscal multiplier, generally associated with the general theory of John Maynard [START_REF] Keynes | The General Theory of Employment, Interest and Money[END_REF]. The latter is defined as the output change in response to a (exogenous) change in a fiscal variable in reference to their baseline levels [START_REF] Spilimbergo | Fiscal Multipliers[END_REF][START_REF] Coenen | Effects of Fiscal Stimulus in Structural Models[END_REF]. Hence, for 𝐺 𝑡 and 𝑌 𝑡 denoting, respectively, the fiscal instrument (government expenditure here) and the output at time 𝑡, the Keynesian or simply fiscal multiplier is expressed as

∆𝑌 𝑡 ∆𝐺 𝑡
. Or, while the effects come with different lag times, the cumulative fiscal multiplier to the time horizon ℎ is expressed by: [START_REF] Chinn | Fiscal Multipliers[END_REF].

∑ ∆𝑌 𝑡+𝑗 𝑗=ℎ 𝑗=0 ∑ ∆𝐺 𝑡+𝑗 𝑗=ℎ 𝑗=0
To compare our results with the findings in the literature and across countries, an exercise of mapping the IRF impacts to Keynesian fiscal multipliers is required. In the explicit SVAR, the government expenditure variable, as well as GDP, are introduced in per cent of first differences of the natural logarithm for the corresponding levels of the variables (i.e. the growth rates in per cent).

The unit root augmented Dickey-Fuller and Phillips-Perron tests show that these variables are integrated of order one in levels. Thus, using the first difference of logarithms ensures stationarity of such variables. Furthermore, introducing the variables in logarithms allows us to draw the Keynesian multipliers directly from the effects of elasticities. Letting 𝜇 𝑌/𝐺 define the elasticity of GDP to government expenditure,64 we have:

𝜇 𝑌/𝐺 = 𝑑𝑙𝑜𝑔(𝑌𝑡) 𝑑𝑙𝑜𝑔(𝐺𝑡) = ∆𝑌𝑡 ∆𝐺𝑡 × 𝐺𝑡 𝑌𝑡 = 𝑘 𝐺𝑡 𝑌𝑡 (24)
The Keynesian multiplier 𝑘 = ∆𝑌𝑡 ∆𝐺𝑡, measuring government expenditure effect on GDP, is then deduced as the elasticity of GDP to government expenditure scaled by 𝐺 𝑡 𝑌 𝑡 ⁄ ̅̅̅̅̅̅̅ representing the averaged share of government expenditure in GDP (or multiplied by (𝑌 𝑡 𝐺 𝑡 ⁄ ̅̅̅̅̅̅̅ )) [START_REF] Gonzales-Garcia | Fiscal Multipliers in the ECCU[END_REF][START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF][START_REF] Barnichon | Understanding the Size of the Government Spending Multiplier: It's in the Sign[END_REF][START_REF] Priftis | Sources of borrowing and fiscal multipliers[END_REF][START_REF] Glocker | Time-varying fiscal spending multipliers in the UK[END_REF]. However, with the latter references, even though they scale their impact IRFs by share of consumption, the results are meaningful in terms of size only if the structural shock is expressed in percentage units. The reason for this is that the structural innovations, especially when using Cholesky innovations in an SVAR, are expressed in standard deviation units. Therefore, in practice, for accuracy of results, the impacts should also be scaled by a standard deviation 𝜎 𝑔 of the fiscal variable (government expenditure), as in [START_REF] Combes | The Euro and the Crisis: Evidence on Recent Fiscal Multipliers[END_REF]. Following this precision, an adjustment coefficient is defined to deduce the short-term (immediate) fiscal (Keynesian) multiplier from the corresponding Cholesky impact multiplier, as:

𝑘 𝑠𝑟 = 𝐼𝑀 𝑠𝑟 × 𝑌 𝐺 ̅ 𝜎 𝑔 (25)
where, from Equation (22.d), 𝐼𝑀 𝑠𝑟 = 𝜕𝑦 𝑡 𝜕𝜀 𝑔,0 = 𝜑 2.1 0 is the immediate effects of government expenditure Cholesky innovations. For the accumulated (long-term) expenditure multipliers 𝑘 𝑙𝑟 , they are deducted in the same way as:

𝑘 𝑙𝑟 = 𝐼𝑀 𝑙𝑟 * 𝑌 𝐺 ̅ /𝜎 𝑔 = (∑ 𝜑 2.1 ℎ ∞ ℎ=0
) * 𝑌/𝐺 ̅̅̅̅̅ /𝜎 𝑔 (26) 65In the previous bivariate SVAR, the effect of public debt on the expenditure multipliers is exogenously tested by a dummy representing the way the public debt ratio is evolving. In the second case, we endogenize the public debt effects and introduce the public debt to GDP ratio in a tri-variate SVAR linking government consumption, GDP and government debt ratio. For the identification in this tri-variate model, two other restrictions are needed. These are simply imposed by assuming that both government consumption and GDP do not have an immediate (simultaneous) effect on the public debt ratio. Thus, the only structural coefficients assumed to be non-null are those capturing the public debt effects on the other variables in the model, while the opposite effects (feedback effects) are delayed by at least one quarter. For the formulations (equations, IRFs, etc.), the methodology is the same as for the previous bi-variate, or as described by the general methodology.

Data

Data source

We first solicited the database of the Federal Reserve Bank of Saint Louis for the quarterly data on real government consumption, GDP and public debt, displayed on their website free of charge, and downloaded country by country, where data is seasonally adjusted. We noticed that this data, which was not available for all the 18 sample countries, has the OECD database as its main source. We therefore avoided the Federal Reserve Bank of Saint Louis data for the two first models and downloaded constructed national accounts of the 18 countries displayed in the OECD database.

For the last model applied to the United States and requiring a long history, data was found and downloaded for all variables from the Federal Reserve Bank of Saint Louis website.

Compared to annual data, high-frequency data, especially quarterly data, is considered to be the most important for assessing fiscal policy effects [START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF]. However, some issues also arise when using such data. The availability of the observed quarterly national account in many of the advanced countries is recent and goes back to the 1990s. Although the data is displayed for the general government consumption and the GDP back to the 1960s, these are estimations rather than observations going back to pre-1990s, as indicated in the OECD database comments. The exception is the United States, the United Kingdom, Canada, Norway and France, where data goes back to before 1990 (Table 1.C in the appendix). Table 2.C presents descriptive statistics for the economic growth rate and government expenditure. The same issue of observed sample data is encountered with government debt, where the observed data starts. for the majority, in the late 1990s (Table 3.C in the appendix), but for the latter variable, there is no estimation back in time. This constrained our estimations for these countries to the corresponding period (except for the United States), where the quarterly public debt is available when the latter is considered an estimation, whether as an exogenous variable or as an endogenous one.

Preliminary analysis of some previous fiscal multipliers with relation to public debt

In this sub-section, we undertake an exercise analysing some previous expenditure multipliers in links with public debt ratios, from previous works for 27 European countries. We especially investigate the calculations and results of [START_REF] Boussard | Fiscal Multipliers and Public Debt Dynamics in Consolidations[END_REF] and [START_REF] Berti | Effects of fiscal consolidation envisaged in the 2013 Stability and Convergence Programmes on public debt dynamics in EU Member States[END_REF]. We draw scatter plots showing short-term expenditure critical multipliers (first year) and public debt to GDP ratios in 2011 and 2012 (Figures 2 and 3 The fiscal multipliers decrease exponentially with public debt to GDP ratios with an "elasticity/country" of -0.539 and -0.597 in 2011 and 2012, respectively. The trendline of the scatter plot is compatible with a negative power curve, with a high coefficient of determination of around 90.8% and 92.6% for the two figures, respectively. We highlight the countries not affiliated with the eurozone countries (with red dots), as well those that joined the eurozone recently (green dots) and the 12 euro core member countries that joined before 2007 (blue dots). The latter group of countries is more concerned with high public debt and lower fiscal multipliers of less than 1, except for the case of Luxembourg. Figures 2 and3 show clearly that all countries with a public debt to GDP ratio exceeding 60% have fiscal multipliers lower than 1.

These figures clearly show a quite different message to the conclusion of the two papers, namely, that large, short-term multipliers are likely to increase debt ratios under initial high public debt. It shows an picture of which high public debt is associated with low spending multipliers, which also raises a legitimate question. On the one hand, could high public debt also have led to lower fiscal multipliers (crowding-out effects, for example)? And it raises a similar debate to the one detailed in Chapter 1 between public debt and economic growth feedback effects (reverse causality). On the other hand, according to these results, fiscal expansion, as opposed to fiscal consolidation, is expected to be less effective under high public debt levels, particularly as the multipliers assumed to be calculated from an exercise of positive fiscal shocks are lower than unity for highly indebted countries (thus assuming assymetry -this issue is discussed in Section 2.4). 2.

Results

In this section, we display the results of the models discussed in the methodology section and argue our results with a robustness check based on the United States data set using a more detailed SVAR with six endogenous (including monetary and fiscal) variables.

We used unit-root tests (augmented Dicky-Fuller and Phillips-Peron) for the stability of the variables, which confirmed that all the variables are integrated of order 1. A summary of the stationarity tests is presented in Table 4.C in the appendix for the three variables of GDP, government consumption and public debt to GDP ratios. Thus, we introduced all the variables in the three models in first differences of the natural logarithm of such variables, except for prices (the interest rate and inflation). The sample of countries that was considered comprises 18 advanced countries, of which the majority are eurozone member countries, namely: Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, The Netherlands, Norway, Portugal, Spain, Sweden, the United Kingdom and the United States. Furthermore, following [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF], we chose not to test for any long-term cointegration relationship, as this might also complicate the exercises of SVAR methodology, especially the way of resolving identification issues, and might deviate from comparing our results to the leading literature and the model results adopting the [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF] approach. Although some pioneer researchers did not test for the number of lags to introduce in their SVAR, simply adopting an SVAR with one lag, we ran the exercise of the determination of such a lag for each country and each model (Table 5.C in the appendix for models with no control of exogenous effects of business cycle or debt movements). We found that 15 out of 18 countries have at least one criterion that indicates that the optimal lag is 1 (more likely indicated by Schwarz information criterion, SC). The three countries are Denmark, Greece and Japan. When controlling, for example, for the business cycle, Greece, Japan and Spain have an order of lags superior to 1 for models in times of recession, while in times of expansion, Austria, Japan, Portugal and Italy have order lags of 2 to 3. As a result of the multiplicity of the exercises undertaken here for each country individually (control for the business cycle, debt movements, etc.), and based on the higher number of countries pointing to only one lag, we preferred to follow the same approach as other researchers who fixed the model for all the countries to a unique optimal minimum lag equal to 1.

The effects of the time periods

Do fiscal multipliers tend to be lower in recent periods than those of the previous decades of the 1960s and 1970s?

There are a set of determinants revealed in the economic literature that may work in reducing the size of the fiscal multipliers. First, there is the increase in trade openness: more closed economies tend to have higher multipliers [START_REF] Barrell | Fiscal Consolidation: Part 2. Fiscal Multipliers and Fiscal Consolidations[END_REF][START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF][START_REF] Batini | Fiscal Multipliers: Size, Determinants, and Use in Macroeconomic Projections[END_REF]. Second, there is labour market flexibility: the more flexible the labour market is, the larger the fiscal multiplier. For example, based on this, it is expected that Europe will show higher multipliers than the United States, as the market in the former tends to be rigid, with the presence of stronger labour syndicates and unions. Rigidities play against wage flexibility, which tend to reduce the response of output to demand shocks [START_REF] Cole | New Deal Policies and the Persistence of the Great Depression: A General Equilibrium Analysis[END_REF][START_REF] Gorodnichenko | The Finnish Great Depression: From Russia with Love[END_REF][START_REF] Batini | Fiscal Multipliers: Size, Determinants, and Use in Macroeconomic Projections[END_REF]. Third, there is the size of automatic stabilizers: larger automatic stabilizers tend to reduce fiscal multipliers, by offsetting part of the initial fiscal shock (Dolls et al., 2012). Fourth, the flexibility of the exchange rate regime tends to lower the multiplier size, as the movements of the exchange rate may cushion the effects of fiscal policy actions (Born et al., 2013;[START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF]. Fifth, the fiscal position, with high public debt and fiscal deficit widening, reduce the size of the multipliers [START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF][START_REF] Bi | Debt-dependent effects of fiscal expansions[END_REF][START_REF] Huidrom | Do Fiscal Multipliers Depend on Fiscal Positions?[END_REF][START_REF] Kirchner | Transmission of Government Spending Shocks in The Euro Area: Time Variation and Driving Forces[END_REF]. Sixth, there is the effect of the active monetary accommodation to fiscal shocks, where expansionary monetary policy can offset the impact of fiscal contraction on demand.

Based on this, fiscal multipliers are likely to be smaller in recent decades, known as the "Great Moderation Era", especially the period 1986-2007, than the pre-1986 period. The reason for this is that, in this period, all the factors previously cited have been strengthened. The degree of openness has increased with the proliferation of the free trade agreements and increased international financial and economic integration. Many exchange rate systems have been switched to greater flexibility, except for countries that have adopted monetary unions. The monetary policy has been more active in fulfilling its role in stabilizing economies, among other things. All this leads us to think that fiscal multipliers may have a smaller size in the recent period than previously.

To examine these facts, we split our sample data for each country, 1966Q1-2019Q2, into two balanced sub-samples, 1966Q1-1991Q4 and 1992Q1-2019Q2, with, respectively, 104 and 110 observations each. We ran a bivariate stationary SVAR with differentiated logarithm of government expenditure and GDP (i.e. growth rates, in per cent) for all 18 countries for the 2 periods.

The results of the impulse response functions 66 (the structural dynamic impacts) are drawn for this exercise in Figures 1.B.a to 1.B.c in Appendix B. These results are also summarized in Table 3.A, which shows that the main sample of countries (12 out of 18) tends to confirm that the expenditure impacts are weak and substantially smaller in the first period than the second one. However, some exceptions were recorded, especially for small-sized economies such as Finland, Greece, Ireland and, to some extent, Italy, Portugal and Spain, particularly in the long term, which reported opposite results: fiscal multipliers tend to be higher in recent periods than previously. This may be in contrast to the idea that more openness decreases fiscal multipliers as the propensity to import increases. However, not only the degree of openness that acts on the size of the multipliers, but also other determinants, could play against the increase of fiscal multipliers, such as the monetary policy accommodation and the exchange rate regimes [START_REF] Batini | Fiscal Multipliers: Size, Determinants, and Use in Macroeconomic Projections[END_REF]. For a few other countries, the impacts are even negative in the second period, namely, Canada, Denmark and Germany in the long term, and France and the United States in the short and long terms. Overall, for the first period, the multipliers average for the sample is around 0.96 (the impact is 0.18) for the first quarter, 1.5 (0.26) for the accumulated fourth quarter (first year) and 1.57 for the accumulated five years. However, for the second period (1992q1-2019q2), the corresponding multipliers are reduced by more than half, recording on average in the sample 0.47, 0.54 and 0.66, respectively for the first, the accumulated 4 and the accumulated 20 quarters (last row in Table 3.A).

Nevertheless, these results should be considered with caution for several reasons. The first, related to the data construction method, is that the quarterly national accounts data for the government expenditure variable, as well as for the GDP aggregate, is for many countries an estimation, rather than an observation, in the first period. OECD data downloaded for the purpose of this exercise displays a comment on each Excel cell data indicating whether the data cell is an observation or estimation. We noticed that for all the countries' samplesexcept for Canada, the United Kingdom and the United States, for which data is observed from the first quarter of 1966, and Norway and 66 In all our applications, we reported the accumulated structural Cholesky IRFs, as defined in the methodology section, deduced from Equation 8(the first impact is ∅ 0 = 𝜑 𝑖.𝑗 0 ; the second accumulated impact ∅ 2 = ∑ 𝜑 𝑖.𝑗 ℎ 2 ℎ=0

; …; until the long-term accumulated impact to time horizon q; ∅ 𝑞 = ∑ 𝜑 𝑖.𝑗 ℎ q ℎ=0

). In all our applications, we considered 𝑞 = 20, which corresponds to five years. The latter accumulated multiplier defined as the sum of effects to 20 quarters is to be differentiated from what some authors reported as the maximum multiplier; namely, the peak of the effects attained in a specific point of time.

Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 123 France, for which the data observed starts in 1978 and 1980, respectivelythe observed data starts after the 1990s (mainly in 1995Q1 for the majority; see Table 1.C in the appendix). The quarterly national account could be estimated using mechanical/statistical methods without any fiscal policy feedback or any business cycle impacts on the data, which may deviate any fiscal policy assessment from accurate outcomes.

The second reason, which is related to the values rather than the method of construction, is that although the Cholesky impact multipliers are higher in the first period than in the period of openness and financial globalization, the fiscal multipliers could be reduced or amplified between the two periods. The trick resides in the coefficient of adjustment enabling the expenditure multipliers to be obtained from the Cholesky impact multipliers. This coefficient has two components, the first being the share of government consumption to GDP, and the second the standard error of the growth rate of government consumption. The common tendency for all advanced economies is for the shares of government consumption to grow as countries prosper and the welfare state is enhanced. Direct factors of this are also related to an ageing population, especially in Japan and many European countries. The increasing/decreasing shares of government consumption could reduce/amplify the fiscal multipliers. The same is true for the second component, which is the standard error of government consumption, which seems to be lower in the second period than the first one (as opposed to the growing of the first component). Variables are less volatile in the second period (the Great Moderation Era). The product of the two components, which correct the Cholesky impacts to get spending multipliers, could then be higher, less or approximately the same for each country between the two periods. Calculus on the countries' data shows that the adjusting coefficient (Table 2.A) is higher for all countries except Ireland, Norway, Portugal and Spain, which may lead to a reduced gap (gap impacts shown by the Cholesky innovations) in government consumption multipliers between the two periods.

A third issue is related to the method of rescaling by the average of the share of government consumption to GDP (𝐺 𝑡 𝑌 𝑡 ⁄ ̅̅̅̅̅̅̅ ). This method, issued from the elasticity of the output of the fiscal instrument, as explained in Equations ( 24), ( 25) and ( 26) and used by many authors [START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF][START_REF] Gonzales-Garcia | Fiscal Multipliers in the ECCU[END_REF][START_REF] Priftis | Sources of borrowing and fiscal multipliers[END_REF][START_REF] Glocker | Time-varying fiscal spending multipliers in the UK[END_REF], may lead to overestimated fiscal multipliers, which is the case here for many countries in periods of recession and long-term accumulated cases. This fact is valid for our results in the current section and subsequent sections, where some countries that have higher expenditure multipliers in the long term under a recession could attain more than five (examples are France, Spain, Portugal). The issue is because 𝑌/𝐺 can display large movements over the sample period [START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF]. To dampen this effect, some authors use an ex ante conversion approach [START_REF] Gordon | The End of the Great Depression 1939-41: Policy Contributions and Fiscal Multipliers[END_REF][START_REF] Ramey | Macroeconomic Shocks and their Propagation[END_REF][START_REF] Barnichon | Understanding the Size of the Government Spending Multiplier: It's in the Sign[END_REF], which consists of re-scaling all the variables by an estimated "potential output" 𝑌 𝑡 𝑝 . Thus, the variables reconsidered for these authors are 𝑌 𝑡 /𝑌 𝑡 𝑝 , 𝐺 𝑡 /𝑌 𝑡 𝑝 , and so on; for our case, we did not consider this issue and rather focused our analysis on comparing changes in both structural impacts and multipliers, among the considered cases (first period versus second period, expansion versus recession, debt accumulation versus debt reduction, etc.), rather than focusing on the size of the fiscal multipliers.

The effect of the business cycle

We ran the same SVAR controlling for the business cycle in the current case. Some authors have used the output gap to control for the business cycle position [START_REF] Batini | Successful Austerity in the United States, Europe and Japan[END_REF]. For our case, we used the growth of GDP, as used by [START_REF] Baum | Fiscal Multipliers and the State of the Economy[END_REF], noted 𝑔𝑔𝑟 𝑡 , instead of the output gap, and we defined a dummy variable for the business cycle, as follows: 𝑏𝑐𝑑 𝑡 = { 1 𝑖𝑓 𝑔𝑔𝑟 𝑡 > 0 0 𝑖𝑓 𝑔𝑔𝑟 𝑡 ≤ 0 . The business cycle dummy indicates expansion, while its complement to unity is a proxy for recession.

The SVAR model is augmented by this variable exogenously (SVAR-X) for considering the effects of the expansion periods only and its complement to unity to account for recessions.

The results of this exercise are displayed in impacts, and their corresponding Keynesian multipliers, shows that these multipliers are either positive and very low or negative and very low (in absolute value) for many countries in the sample in times of expansion (exceptions are recorded for Greece and Ireland, where short-term multipliers are, respectively, 0.92 and 1.02, corresponding to impacts of, respectively, 0.42 and 0.55). However, in times of recession, these impacts are all positive and amplified in size. The maximum of the short-term Cholesky impact is recorded in Ireland by 1.53, corresponding to a multiplier of (1.02), 67 and in Norway by 0.82 (with a multiplier of 2.4). These higher impacts yield multipliers greater than 1 for many countries (11 countries) and approaching unity for the rest (between 0.52 and 0.92). On average, expenditure multipliers in the short term are near 0 (0.09) in times of expansion, while they are more than 1 in recessions (1.55). The long-term accumulated are negative in expansions (-0.24) and very high in recessions (4.8). Our results confirm the conjecture of the higher expenditure multipliers in periods of recession than in those of economic expansion, as revealed by the aftermath of the 2008 crisis literature, especially by Auerbach andGorodnichenko (2012, 2013). Another important point is that, from the IRF plots, the effects are more persistent in times of recession than expansion, as convergence to the long term is more quickly achievable in the latter than in the former (Figures 2.B.a to 2.B.c).

For a general view with relation to the effects of government debt, we plot the impact multipliers, associated with the business cycle, versus debt ratios in Figure 3.B. It seems that these impacts are slightly negatively associated with higher public debt ratios in recessions, while in expansions, the opposite is observed, particularly for the long term. This means that higher debt may weigh on expenditure multipliers in recession periods.

The exogenous effect of the public debt accumulation/reduction

To control exogenously for the effect of public debt, we ran the previous bivariate SVAR, where the accumulation is proxied by a dummy variable equal to 1 whenever the growth rate of public debt to GDP ratio is positive, non-null and zero elsewhere. The public debt reduction case is controlled in the SVARX by the complement of the debt accumulation dummy to unity. The dummy variable for the debt ratio accumulation is defined according to the sign of the debt ratio growth rate (𝑑𝑔𝑟 𝑡 ):

𝑑𝑎𝑑 𝑡 = { 1 𝑖𝑓 𝑑𝑔𝑟 𝑡 > 0 0 𝑖𝑓 𝑑𝑔𝑟 𝑡 ≤ 0
, where 𝑑𝑎𝑑 𝑡 is the dummy indicating debt increase of the debt to GDP ratio (accumulation), and its complement to unity is a proxy for debt reduction.

We do not care whether the public debt ratio is reduced by the high performance of GDP (the denominator) or accumulated because of weak GDP. In both situations, it is the ratio that is important, reflecting the capacity to repay or not based on the performances of the economy.

Table 5.A shows the Cholesky impacts and their corresponding values of expenditure multipliers under public debt movements: in the case where debt to GDP ratio is consequently accumulated; or in the opposite case, where debt is reduced. Overall, the multipliers (impacts) tend to be higher in times of debt accumulation than in times of reduction, except in a few countries, where the two cases are approximately the same, namely, in Finland, Italy, Japan and Norway. The latter has even larger multipliers in debt reduction cases than in debt accumulation. Convergence to the longterm accumulated multiplier varies across countries, where it is fast in more than half of cases, medium in around a third of cases and slow in a few cases (France, Spain and the UK). The convergence is defined as fast if the accumulated long-term multiplier is approximately attained in fewer than five quarters, medium if it is attained in between six and nine quarters, and slow when it is above ten quarters. The size of the expenditure multipliers varies considerably between countries.

The effects of the way the debt is moving, on multipliers, tends not to be different from the business cycle effects, especially if we assume that, generally, the public debt ratio increases in times of recession, which sounds more realistic, due to the double effects of GDP shrinking and the debt level accumulation in times of recession. For further examination of this, an exercise combining the business cycle effects jointly with the public debt movements was run. Table 6.A shows the results. The main conclusion is that, under expansion, multipliers are very low for some countries and negative for most countries, almost independently from the way the debt ratio is evolving. By contrast, under recessions, multipliers are higher and could be larger than unity even in the short term, as is the case for Belgium, Canada, Denmark, Greece, Ireland, Italy, Norway, Spain, Sweden, the United Kingdom and the United States.

To obtain an overall view of the public debt effects on multipliers, we display, for the sample of 18 countries, scatter plots for the average public debt and the short-and long-term multiplier values, under debt accumulation and debt recession cases, as illustrated in four charts presented in Figure 4.B. It seems that, under debt accumulation, there is no clear association between the average of the debt ratio (over the time period) and the multipliers' size. However, a positive correlation (albeit less strong) is observed in the case of debt reduction, which means that expenditure multipliers are higher for high debt ratios conditioned with the case where the debt is decumulated.

The effect of the public debt ratio movements jointly with the business cycle

Controlling for the business cycle effects and the public debt ratio movements is captured by augmenting the SVAR by the product of the two corresponding dummies 𝑏𝑐𝑑 𝑡 and 𝑑𝑎𝑑 𝑡 yielding the following four situations:

1-The effect of public debt accumulation under expansion, captured by (𝑏𝑐𝑑 𝑡 .𝑑𝑎𝑑 𝑡 ), 2-The effect of public debt accumulation under recession, captured by (1 -𝑏𝑐𝑑 𝑡 ).𝑑𝑎𝑑 𝑡 ,

3-The effect of public debt reduction under expansion, captured by (1 -𝑑𝑎𝑑 𝑡 ).𝑏𝑐𝑑 𝑡 ,

4-The effect of public debt reduction under recession, captured by (1 -𝑏𝑐𝑑 𝑡 ).(1 -𝑑𝑎𝑑 𝑡 ).

The results of the structural dynamic impacts (Cholesky IRFs), as well as the corresponding multipliers, are presented in Table 6.A. The latter are deduced from Equation ( 13) for the shortterm (first) multiplier and Equation ( 14) for the long-term multiplier, as explained in the methodology section. For the graphical IRFs, they are presented for each country by case of debt movements under the business cycle. Therefore, Figures 6.B From the results summarized for the short-and long-term impacts and multipliers in Table 6.A, we observe that the effects are negative or positive but near 0 for many of the countries in times of expansion, regardless of the debt development. Exceptions are recorded for Greece, Ireland and Italy. However, in times of recession, all 18 countries have positive important multipliers, whether under debt accumulation or debt reduction, except for The Netherlands and Portugal, which have weak negative multipliers only in the case of debt reduction under recession. Under recession and debt accumulation, many countries have expenditure multipliers higher than 1 in the short term, namely, Belgium, Canada, Denmark, Greece, Ireland, Italy, Norway, Spain, Sweden, the United Kingdom and the United States. However, under recession and debt reduction, the number of countries with multipliers greater than 1 reduced to six countries, namely, Belgium, Italy, Japan, Norway, Spain and the United States.

In order to visualize the previous results in a global view, we scattered the multipliers obtained for these cases against the averages of the debt ratio (Figure 8.B). In two cases of joint expansion with debt accumulation (the first two scatter plots for the short and long terms) and the recession with debt reduction (the last two scatter plots), we observe a positive association of the fiscal multipliers with the average of the debt to GDP ratio. However, there is no clear association for the cases of expansion and debt reduction or recession and debt accumulation. This means that multipliers tend to be higher for countries with high debt to GDP ratios, either in times of expansion, and the debt being accumulated, or times of recession, and the debt ratio being reduced.

The endogenous effect of public debt

Controlling for the business cycle effects, and considering the endogenous public debt ratio, by the tri-variate SVAR model, the results confirm the previous results of the large multipliers under recession, while reporting weak or even negative multipliers in periods of expansion. Tables 7.A and 8.A present, respectively, the dynamic structural impacts and the associated expenditure multipliers for the first quarter (short term), first year, second year and fifth year (long term). The IRFs of these results are shown in Figures 9.B.a to 9.B.c. These results tend to confirm those reported for the case of the bi-variate model, while controlling exogenously for government debt. Furthermore, for the short-and long-term impacts, a positive association with the average of the debt to GDP ratios is noticed in expansion cases, as reported in the scatter plots in Figure 10.B.

We can conclude generally from the previous results of the bi-variate and tri-variate models that: in times of recession, multipliers tend to be higher than in times of expansion, but they tend to decrease with debt reduction rather than debt accumulation in times of recession. This may lead us to consider the self-defeating effects of austerity aimed at reducing public debt and based on expenditure cuts, as it tends to reduce the higher multipliers recorded in times of recession and high public debt.

Robustness check: the public debt crowding-in/out effects

In order to examine why spending multipliers are lower in times of expansion than in recessions, a more disaggregated model containing behavioural equations is required. For this purpose, we chose to study, in particular, whether the crowding-out effect that might be behind lowering spending multipliers originates from public debt. We particularly consider an SVAR with six fiscal and monetary variables for the United States.

In this section, we present the SVAR with six endogenous variables applied to the United Sates only, as the country with a large quarterly data set available (1966Q1-2019Q2). This SVAR is intended to explain and check the robustness of the previous models' outputs, where other variables representing monetary policy aggregates and private-sector investment are introduced, leading to more interactions catching economic behaviour. The endogenous variables considered are the interest rate, the public debt ratio, prices, output, government expenditure and private investment. In this model, we follow nearly the same approach as in [START_REF] Sims | Are Forecasting Models Usable for Policy Analysis?[END_REF]. The difference from Sims's model is that the latter considered money supply equation (which is an interest rate equation explained by money demand), money demand, output, price, unemployment and investment demand equations (the model is detailed in [START_REF] Sims | Are Forecasting Models Usable for Policy Analysis?[END_REF]).

In our case, we modified the model to include fiscal variables that are of interest to us for studying the spending multipliers via the impact of expenditure and public debt. Moreover, in order to assess what is happening on the private demand side, especially the possibility of crowding-in/out effects of government spending and/or debt to private agent decisions, we kept the private investment equation. Private consumption could also be considered but we decided to reduce the size of this model into six variables to gain more degrees of freedom for the quality purpose estimation. The monetary policy action is presented by the equation of interest rate, and the dynamic of prices is captured by the inflation equation.

For the interest rate equation, we used the policy variable, which is the effective federal funds rate.

Assuming that the feds follows a conventional monetary policy based on Taylor's rule, it seems suitable to assume that the feds policy rate (𝑟 𝑡 ) is determined by innovations (𝑒 3 , 𝑒 4 ) corresponding, respectively, to GDP growth rate (𝑦 𝑡 ) and inflation ( 𝑡 ). GDP is a best proxy for the output gap, as we do not consider the output gap in this model. The second equation is related to public debt (𝑑 𝑡 ). For this equation, three variables are important from the classical debt sustainability rule; we could realistically assume that the public debt ratio is determined by the innovations (𝑒 3 , 𝑒 4 , 𝑒 1 ) corresponding, respectively, to innovations from the GDP growth rate, the inflation rate and the interest rate. 68 The third equation is the output assumed to rely on innovations, 𝑒 5 , 𝑒 6 and 𝑒 2 , from, respectively, private investment (𝑖 𝑡 ), government expenditure (𝑔 𝑡 ) (three options are tested: total, current and capital expenditure) and public debt. For the fourth equation of the system corresponding to inflation, the latter is assumed to be determined by the interest rate's innovations (𝑒 1 ) and the investment private innovations (𝑒 5 ). The private investment is assumed to be determined in the fifth equation as the function of innovations coming from the output (𝑒 3 ) and the interest rate (𝑒 1 ) (the accelerator equation). The last equation is an error term corresponding to government expenditure determined by its proper structural innovations (𝑒 6 ). This means that the government expenditure variable does not react simultaneously to the other endogenous variables in this model, but its reaction comes with a delay. We considered the following formulations for the equations of this model, such as: 68 It is possible to provide an SVAR with identities equations such as Taylor's rule for the interest rate and the debt sustainability equation. However, the structural shocks associated with those identities would be zero, and the situation is more complex if the identity is dynamic [START_REF] Cherif | Public debt dynamics: the effects of austerity, inflation, and growth shocks[END_REF][START_REF] Ouliaris | Quantitative Macroeconomic Modeling with Structural Vector Autoregressions -An EViews Implementation[END_REF]. As assessment of the effects of fiscal and monetary policy structural innovations (shocks) on the other endogenous variables is our requirement, we keep such identities as functional structural equations.

{ 𝑟 𝑡 = 𝑓(𝑦 𝑡 ,
Explicitly, the six simultaneous equations of the current model are formulated in the following system, with all the variables log-differentiated: In this exercise, all the variables are made stationary by differentiated natural logarithms, and hence the variables are all in growth rates. The variables, which will appear in outputs and figures, are LGDP for GDP growth rate (𝑦 𝑡 ), LGE for government consumption expenditure, total, current and capital (𝑔 𝑡 = 𝐿𝐺𝐸 = 𝑑𝑙𝑜𝑔(𝐺𝑂𝑉𝐸𝑋𝑃)), LPRC for inflation (GDP deflator inflation, 𝜋 𝑡 = 𝐿𝑃𝑅𝐶 = 𝑑𝑙𝑜𝑔(𝐺𝐷𝑃𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟)), LDR for log differentiated of the debt ratio (𝑑 𝑡 = 𝑑𝑙𝑜𝑔(𝑑𝑒𝑏𝑡𝑟𝑎𝑡𝑖𝑜)), LPINV for the real private investment growth rate (𝑖 𝑡 = 𝐿𝑃𝐼𝑁𝑉 = 𝑑𝑙𝑜𝑔(𝑟𝑝𝑖𝑛𝑣)) and RINTR for the interest rate (𝑟 𝑡 = 𝑅𝐼𝑁𝑇𝑅 = 𝑓𝑓𝑟).

{ 𝑟 𝑡 =
We test the SVAR model with six endogenous variables applied to the United Sates only, as the country with a large quarterly data set. The data set covers, for many variables of this model, a long-observed history of quarterly data going back to 1953. However, the public debt quarterly data starts at 1996. Hence, the model is estimated over the period 1966Q1-2019Q2. This SVAR is intended to check the robustness of the previous models' outputs, where other variables representing monetary policy aggregates and private-sector investment are introduced, leading to more interactions catching economic behaviour. The model functional equations' determinants are discussed in the methodology section. The considered endogenous variables are interest rate, public debt ratio, prices, output, government expenditure and private investment.

In this SVAR we control exogenously for the business cycle and debt movements by introducing as exogenous the dummies controlling for expansion/recession and debt accumulation/reduction, as defined for the previous bivariate model. We also produce the cases where debt movements and business cycle are jointly considered (four cases).

Figure 8 presents a panel of charts showing quarterly data over 1966Q1-2019Q2, by row order and column, from left to right, the public debt ratio development and output growth, the long-term interest rate and the inflation rate for the three first charts. The last chart shows the composition of the total government expenditure, capital and current expenditure growth rates. The dashed grey areas in all four charts of Figure 8 indicate the recession periods where the quarterly negative growth is recorded.

The public debt of the United States stands at around US$ 20.42 trillion at the end of June 2019, from which: 1) about 66% is long-term liabilities, 2) more than 83% is denominated in domestic currency and 7% in foreign currency, and the rest is not allocated (see Table 6.C). For evolution over a long history (Figure 8), we observe that the growth rate is more volatile in the 1966-84 period, but with the public debt ratio in a downward trend. Staring around 1985, the real growth rate becomes less volatile than previously, while the public debt ratio reverses track to generally increase. For the relationship between public debt and interest rate, although the golden rule of public debt and economic growth stipulates that public debt is accumulated whenever the real interest rate is higher than economic growth, the public debt ratio and interest rate are evolving the opposite way. From the 1960s to early 1980s, the interest rate takes an upward trend, while the public debt to GDP ratio is on a downward trend. Starting from the 1980s up to 2019 the interest rate records a sustained decrease, while the public debt ratio reverses its path to a general upward trend (except 1996 until 2001, where it decreases). The same facts are observed when comparing the trend of inflation and GDP growth rate. The period starting from 1986 is known by economists as the "Great Moderation Era". In this period, we can conclude from the previous analysis that public debt in the United States has accumulated over this period of sustained growth and moderate inflation and interest rates, which is the case for many advanced countries in our sample. For the last chart in Figure 8, capital expenditure is less volatile in the second period than the first period (1966-85), compared to current expenditure, which means that current expenditure is more mobilized in times of crisis in recent periods than in the decades of the 1960s and 1970s. The estimation of the structural model (the block of equations described in the methodology by Equations ( 1) to ( 6)), controlling for expansion and recession, yields the following From the previous estimations, we notice significant differences in some estimated elasticities between the two models (expansion versus recession). We also observe that some signs are inverted from positive to negative, or vice versa, between two situations in the equation of interest rate and private investment. This shows that some behaviour is changing over the business cycle, which could explain the differences in fiscal multipliers between periods of expansion and recession. For the rest of the application, we produce the impulse response functions to structural shocks of the interest rate (shock1), public debt variable (shock2), private investment (shock3) and public expenditure (shock6) for the variables output, investment, inflation, interest rate and debt. We produce these IRFs for eight cases: two for the business cycle periods (expansion versus recession), two for debt ratio movements (accumulation versus reduction) and four for the joint business cycle and debt movements (expansion and debt accumulation/reduction and recession and debt accumulation/reduction). These outputs are displayed by the eight figures in Appendix B (Figures 11.B.a to 11.B.h).

To shed more light on the effects of fiscal variables on output, inflation and private investment, we prefer to focus on the corresponding IRFs, which we reproduce in this section. For the effects of the innovations of public debt (shock2) on output, private investment and inflation, Figure 9 clearly shows in the first row corresponding to the expansion model's IRFs that public debt increase has a deflationary effect on the other variables by reducing economic growth, especially through crowding out private investment in the United States, and inducing an increase in government expenditure. However, in times of recession (the second row of Figure 5), an increase in public debt is likely to increase growth by even stimulating inflation and private investment while keeping the interest rate reduced in the second quarter and pushing up government expenditure. We also observe that the effects are generally happening with a delay of one quarter and are at their peaks in the second or third quarter, while fading away (or stabilizing at their long-Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 132 term path) at the fourth or sixth quarter, except for inflation, which has a persistent long-term response.

Figure 5. Responses to a structural shock of the government public debt ratio (shock2) in times of expansion (first row of charts) and recession (second row of charts)

For the effects of the structural innovations of total government expenditure (shock6, in Figure 6) in periods of expansion and recession, we note that the effect is immediate and high (in the first quarter), especially for the response of GDP, private investment and the public debt ratio. The effects of government expenditure are generally independent of the business cycle effects, except for the inflation variable being reduced in times of expansion and pushed up in times of recession.

For the periods of expansion and recession as well, an increase in government expenditure is likely to immediately increase the output and then reduce the public debt ratio, while inducing an increase in the interest rate, especially in the second quarter, to counter the inflationary effects, albeit less important, in times of recession. However, this reduction of the public debt ratio could be a consequence of an algebraic computation of the increase of GDP being the denominator of the debt ratio variable. An important point is that all the responses are very short-lived (the effects occur and fade way within the first year), except for the reaction of the prices. In concordance with the public debt and government expenditure effects, we can conclude that expenditure multipliers are mainly weakened in times of expansion and increased in times of recession (as found in the previous results) by the effects of the public debt that crowd out the private agent decisions of investing, while the effects of fiscal policy (by expenditure side) are positive and short-lived, independent of the business cycle.

- For the effects of debt movements (Figures 7 and8), we observe almost the same findings about the reactions of the variables as those observed for the business cycle, except for prices (inflation and interest rates). A structural innovation of the public debt ratio is likely to reduce output by crowding out investment and may have a deflationary effect when debt is accumulated. However, in times of decumulating public debt, the effects of the public debt increase on output, investment and prices are positive (Figure 7). For the effects of government expenditure, they are positive on output and investment, while reducing public debt. The prices' reactions are slightly different for debt accumulation and debt reduction cases. For the effects of the business cycle and debt movements, we produce the four cases (in Figures 9 to 12). A structural innovation of the debt in periods of debt accumulation and expansion decreases simultaneously the GDP, investment and prices (inflation and interest rate), while increasing government expenditure (first row of the panel in Figure 9). For periods of debt accumulation in recession periods (second row of Figure 9), the effects are opposite (positive) on the first three variables, while the reaction of the interest rate and government expenditure have almost the same shape as in the first case. For the effects of government expenditure (Figure 10), they are shortlived and almost the same, independent of the two considered cases. .0000

.0005

.0010

.0015

.0020

.0025

Figure 10. Responses to a structural shock of government expenditure (shock6) in periods of debt accumulation and expansion (first row of charts) and debt accumulation and recession (second row of charts)

For the government debt reduction case, jointly with the business cycle, unlike the case where debt is accumulated, the responses to the public debt structural shock are slightly different over the business cycle for private investment and interest rate, while they seem to behave the same way for the other variables, between the two situations. In particular, the output, investment and inflation are positively affected in the first year with persistent effects for inflation. This model, containing fiscal and monetary variables, sought to explain why the fiscal multipliers are weaker, or even negative, in times of expansion than recession. In times of high public debt, and particularly expansion, an increase in public debt ratio crowds out private investment, hence reducing output. By contrast, the government expenditure effects on output are all positive in the short term, independent of the public debt evolution (accumulation or decumulation) and business cycle. These results align with what we observed in a preliminary analysis (Section 4.2) of the works of Bouassard et al. ( 2012) and [START_REF] Berti | Effects of fiscal consolidation envisaged in the 2013 Stability and Convergence Programmes on public debt dynamics in EU Member States[END_REF] for 27 European countries, in which we highlighted the apparent decreasing relationship between expenditure multipliers' size and public debt ratio.

Conclusion

In this chapter, we used the methodology of a structural vector autoregressive model (SVAR), augmented by exogenous dummies variables controlling for the business cycle (expansion/recession) and public debt movements (accumulation/reduction). We applied this approach to assess the expenditure multipliers for a sample of 18 OECD countries (Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, The Netherlands, Norway, Portugal, Spain, Sweden, the United Kingdom and the United States) with different exchange rate regimes, monetary policies and degrees of openness.

The results show that, controlling for the business cycle effects, the expenditure multipliers are much higher in times of recession than times of expansion, and could attain, in recessions, more than 1 for many countries in the sample, in the short term, while going beyond the value of 2 in the long term. Moreover, it is noted that, generally, the idea of spending multipliers being weak, Considering these results, the fiscal policy in advanced countries should be designed according to business cycle fluctuations. In particular, fiscal policies should be designed to counter the business cyclicality. In times of recession, it is the role of the government sector to stimulate the economy, while public intervention in times of expansion seems to alter economic growth (as the multipliers are weak or negative for many countries) and less beneficial to the economy than in times of recession. These results also run contrary to any fiscal consolidation based on cutting expenditure in times of recession, which could harm the economy.

Controlling exogenously for the public debt movements, independent of the business cycle, it is revealed that spending multipliers are larger in periods of debt accumulation than in debt reduction periods. Furthermore, controlling jointly for debt movements exogenously and the business cycle reveals the previous tendency, that is, multipliers are higher under debt accumulation in cases of expansion and recession. However, introducing endogenously the public debt to GDP variable in an SVAR leads to higher multipliers in recessions than expansions.

Furthermore, a robustness check of the previous results was conducted on a long history of quarterly data for the United States, as the country with long quarterly time series of the six fiscal and monetary variables considered in this model, namely, public debt, GDP, private investment, public expenditure, interest rate and inflation. The period of estimation covers the range 1966q1-2019q2. The main results of this model show that government expenditure has positive but shortlived effects on economic growth. Furthermore, public debt crowds out private investment, leading to lowering growth rates in times of expansion, while in times of recession, the public debt effects on growth are positive. This crowding-out effect may play pass-through to the expenditure multipliers and could explain, ceteris paribus, the weak size of spending multipliers, while in times of recession the crowing-in effect leads to higher multipliers.

In all our models the recession period generally has a persistent effect on variables for which convergence to the long-term path following the shock is achieved faster in times of expansion than recession. The policy implication of this, for highly indebted countries, is that fiscal stimulus effects could take time to materialize in times of depressed economies, while the effects are shortlived in times of expansion, which should be considered by policy-makers in their spending decisions. Negative Fiscal policies played a small role in Eurozone's recovery, due to the pre-existing Stability and Growth Pact and 3 per cent public deficit ceiling limiting their use. Budget balances as a percentage of GDP were less in France, Germany, and Italy compared to the UK and US, implying that less government funds went towards fiscal stimuli in the former three countries than the latter two. Kandil and Morsy (2010) 34 emerging countries Positive The presence of international reserves allowed emerging economies to be in a good position to weather the economic crisis and have their stimulus measures succeed, while at the same time avoiding a crowding-out effect. For example, China and Brazil have managed to weather the crisis well due to a rapid increase in export prices, robust demand, and constant capital inflows. World Bank (2010a) 14 emerging countries (Mid-1980s-2009 Positive Due to China's economic activity, its monetary and fiscal stimuli, and its inflow of foreign capital, the East Asia and the Pacific region overall has recovered from the crisis and had its employment, exports, and output return to pre-crisis levels. The region is doing so well that many national governments are beginning to end support policies. ADB (2010) 32 countries Positive Asia, the first region to recover from the global financial crisis, (1990s-2010) experienced a strong and fast V-shaped recovery due to large monetary and fiscal stimulus packages. These heavily increased the demand for goods and services and promoted growth, which is projected to reach 7.5 per cent in 2010, which is up from 5.2 per cent in 2009. Bhaskaran and Ghosh (2010)

countries (1981-2009)

Mixed

Indonesia, the Philippines, and Thailand were resilient during the global recession thanks to timely stimulus measures. For example, starting in 2008 Indonesia injected RP 1 trillion into its economy, which successfully increased liquidity and prevented a dramatic depreciation of its currency.

IDB (2010a) 4 Latin American countries

Positive Decreased economic activity, employment, tax rates, and export prices brought about due to the downturn ended Latin America's period of expansion that began in 2002-03 and thus decreased its fiscal surplus. MERCUSOR was still able to respond by implementing measures that showed positive impacts, such as increased government spending, tax cuts, and infrastructure investment. IMF (2010b) 28 North and South America States (1970-2010)

Mixed

The North American and Latin American regions experienced different outcomes due to their fiscal stimuli. The recoveries in the US and Canada are propelled by fiscal stimuli, giving the former a 5.6 per cent GDP increase by Q4 2009 and the latter resilient fiscal credibility, increased demand, and 3 per cent growth in 2010. In most of Latin America, government fiscal stimuli had small multipliers that did not contribute much to growth. Positive The ARRA has dampened the negative impact of the recession on GDP and employment. The most economic activity per federal dollar spent has come from the extension of unemployment insurance benefits and social programs like food stamps and work-share as well as infrastructure spending. Positive The countries in developing Asia rolled out the stimulus measures quickly and decisively in general, proactively using fiscal policy for countercyclical purposes during the global developing crisis. The stimulus packages are tilted toward higher countries) spending, in particular infrastructure investments, consistent with the region's long-standing pro-growth orientation. Partly helped by the healthy public finances' situation in the initial stage, evidences suggest that the stimulus efforts to boost sagging demand have been effective and contributed to the region's remarkable recovery. The Brookings Institution (2009)

G-20

Countries (2008)(2009) Positive The article finds that fiscal stimulus played a crucial role in stabilizing the world economy, especially in the G-20 economies. It suggests that while the effectiveness of fiscal stimulus is questioned, the world economy would have been even worse had there not been stimulus packages. NBER (2010) 22 high income +24 developing countries (1960:Q1 -2007:Q4)

Mixed

Using the panel SVAR methods, the research finds that the effect of government consumption is very small on impact, with estimates clustered close to zero. It supports the notion that fiscal policy may be rather slow in impacting economic activity, raising questions as to the usefulness of discretionary fiscal policy for short-run stabilization purposes.

Mixed

The report verifies the use of fiscal stimulus in virtually all OECD countries. As for the effectiveness of fiscal stimulus, the report suggests after its own review of relevant literatures that the fiscal multipliers are around unity for government spending under normal circumstances. The report suggests that the multipliers may be reduced in the current conjuncture as the propensity of households/businesses to save is likely to increase reducing tax cuts multipliers. OECD Economic Outlook, Volume 2010 Issue 1

OECD Countries (2008-2010)

Mixed

Noting that most OECD countries introduced fiscal packages during the recent crisis, the report recognizes the potentially important role of discretionary fiscal policy during a large and protracted shock. Meanwhile, the report warns that implementing fiscal stimulus may be slow and may result in a pro-cyclical rather than counter-cyclical. Looking at past experience, estimates of discretionary fiscal policy show pronounced counter-cyclicality only in Australia, Canada, Denmark, and the US, while policy has been generally pro-cyclical in Austria, Belgium, Hungary, the Netherlands, Poland, Portugal, and the UK. Also, fiscal policy was poorly prepared to deal with the crisis as countries were financially constrained prior to the outbreak of the crisis.

Source: International Labour Organization (2011). Source: https://ticdata.treasury.gov/Publish/debtb2019q3.html

Introduction

To assess the effects of government debt, many theoretical growth models have been designed.

The first class of these models is the infinitely lived agents' models, initiated by [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF].

Later, the debate between economists about agents' lifetime horizon and the type of intergenerational operative transfer linkages between such agents led to building the concept of overlapping generations' (families/dynasties) models to account for the existence or absence of continuity between generations provided by such linkages [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF][START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF]. In particular, the most debated ideas are the degree of implication of altruism between generations (such as a motive bequest) and the lifetime agents' horizon in determining the existence of government debt effects on agents' behaviour in terms of saving, capital accumulation, consumers' utility and interest rate. Important contributions to this field are those of [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF], [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF], [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF], [START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF], [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF][START_REF] Aiyagari | Equilibrium existence in an overlapping generations model with altruistic preferences[END_REF] and Weil (1989). 69 In this regard, two major propositions emerged. The first, according to the neoclassical framework, is that government debt crowds out private capital by increasing interest rates [START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF].

The second is the Ricardian equivalence for which its advocates show that debt neutrality could happen depending particularly on the existence of operative altruistic links (bequests) between generations [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF]. In this way, the debate in the economic literature emerged especially in the 1970s and 1980s, with useful contributions modelling fiscal policy insights, precisely the debttax swap and its effects on welfare utility and interest rates.

While the most important property characterizing the majority of neoclassical models considering government debt is that they build their reasoning on household behaviour towards public expenditure and government debt, other literature on the political economy of debt assesses the effects of public debt, studying the behaviour of governments and the influence of economic and political institutions. In this regard, two approaches are debated. The first is the normative approach, where the government is considered a social planner (a benevolent social planner), for whom the priority is to maximize the social welfare of its individuals in society [START_REF] Barro | On the determination of the public debt[END_REF][START_REF] Lucas | Optimal Fiscal and Monetary Policy in an Economy Without Capital[END_REF][START_REF] Aiyagari | Optimal Taxation without State-Contingent Debt[END_REF]. The second is the positive approach, considering public debt as a state variable used by each government as a strategy to influence its successor's choices or as a way to shape private economic agents' expectations [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF]. In this regard, the most disseminated ideas are related to the effects of fiscal policy (government debt and spending policies) under governments following committed rules versus discretionary policies. In particular, the government time inconsistent 70 actions have an impact on the way economic agents form their expectations, which affects their economic decisions.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 189

The public debt effects are also assessed theoretically and empirically in the class of endogenous growth models. The pioneering contributions in this modelling area flourished with the development of endogenous growth models, especially by [START_REF] Romer | Increasing Returns and Long-Run Growth[END_REF] and [START_REF] Lucas | On the Mechanics of Economic Development[END_REF]. These models were brought as an alternative to the neoclassical growth model of [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF] and [START_REF] Swan | Economic growth and capital accumulation[END_REF] (the Solow-Swan model). The principal characteristics of such models are focusing on the accumulation of knowledge and its endogenization (whether this is embodied in the form of technological progress or in the form of human capital). Since then, many sources of growth have been integrated, particularly to the production function, as inputs such as innovation, human capital, ideas and government goods, for example [START_REF] Jones | Population and Ideas: A Theory of Endogenous Growth[END_REF][START_REF] Jones | Growth and Ideas[END_REF][START_REF] Jones | Paul Romer: Ideas, Nonrivalry, and Endogenous Growth[END_REF][START_REF] Jones | The New Kaldor Facts: Ideas, Institutions, Population, and Human Capital[END_REF][START_REF] Bloom | Are Ideas Getting Harder to Find?[END_REF]. The latter and similar contributions assess the effects of fiscal policy (taxes, government debt and spending) generally integrating the public sector into the productive sector [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]. However, high government spending (especially unproductive spending), jointly with assumed distortionary taxes, leads to low per-capita growth rates, according to the neoclassical growth theory, or to lower growth, according to endogenous growth theory. These results contrast with the growing empirical evidence that higher government spending and taxes (relative to the size of the economy) are not negatively correlated with the growth rate [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF]. 71 Recently, fiscal policy, and particularly government debt, was also modelled under the class of new Keynesian models, 72 despite these models still actively prioritizing monetary policy analysis (see, for example, [START_REF] Rupert | On the mechanics of New-Keynesian models[END_REF]. These models differ from the overlapping generations models in many aspects. For example, instead of considering all taxes as a lump sum, as assumed in the overlapping generations models, recent new Keynesian models have considered fiscal policy assuming distortionary taxes. Furthermore, they join (intersect with) the literature of the political economy of debt by considering the scope of government actions and discuss government policies under commitment or discretion rules. In particular, some authors argue that optimal public debt would follow a random walk process whenever the government can achieve a time-inconsistent policy commitment [START_REF] Benigno | Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach[END_REF][START_REF] Schmitt-Grohe | Optimal Monetary and Fiscal Policy under Sticky Prices[END_REF].

This chapter is structured as follows. Section 2 reviews the existing literature, namely, the government debt effects in economic growth models, as debated in the old generation models and the endogenous growth models, as well as the very recent new Keynesian models and in the new political economy of debt (positive approach). 73 Section 3 describes the theoretical framework used to assess the effects of government debt (government expenditure) on the economy. Section 4 describes the empirical evidence. Section 5 concludes.

71 [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] interpret such facts by the imprecise distinction between productive and non-productive public spending. Many forms of public spending affect the productivity of the economy differently, either directly or indirectly. The theoretical prediction of a negative tax rate effect on growth is weakened once public spending can be qualified as productive. 72 See, for example, [START_REF] Leith | Monetary and fiscal policy interactions in a New Keynesian model with capital accumulation and non-Ricardian consumers[END_REF], [START_REF] Leith | Fiscal sustainability in a new Keynesian model[END_REF] and [START_REF] Rossi | Designing monetary and fiscal policy rules in a new Keynesian model with ruleif-thumb consumers[END_REF]. 73 These models are categorized, and their main results summarized, in Table A.1 of the appendix.

Literature review

This section is dedicated to the assessment of government debt effects in the theoretical models.

Without claiming completeness, we will make an inventory of the most important contributions, modelling the effect of debt on the behaviour of economic agents and the subsequent consequences on the macroeconomic aggregates. First, we consider the government effects in the infinitely lived agents and the overlapping generations models (henceforward, ILA and OLG models). Second, a summary of the public debt effects in endogenous growth models is presented. Third, the effects of public debt are also considered and discussed in the economic literature of the new political economy of fiscal policy, also known as the positive approach of public debt and fiscal policy. We also present some studies assessing the effects of public spending and debt in the recent class of new Keynesian models, specifically in an integrated framework of fiscal and monetary policy. The fourth section concludes with two critiques of [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF] for the ILA and OLG models and the [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] critique of the new Keynesian models.

Government debt effects in the ILA and OLG models

The main ideas debated in the ILA and OLG models are mostly related to the way government bonds affect the steady state equilibrium interest rate (hence, capital accumulation) and consumption (welfare utility). In this way, two major ideas are contrasted. The proposition that public debt increases equilibrium interest rates in the steady state was confronted by the debtneutrality idea known as Ricardian equivalence. 74 The first idea, as illustrated by [START_REF] Modigliani | Long Run Implications of Alternative Fiscal Policies and the Burden of the National Debt[END_REF], is that, in a full employment model, increasing government debt increases the conception of households' net wealth, which raises consumption and hence reduces saving, resulting in an increase in real interest rates. This reduces the output share resulting from the accumulation of capital. However, for [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF], the idea that the "government debt effect on aggregate demand depends on the assumed increase of the households' net wealth" is only true in the non-full employment framework. In a full employment context, public debt effects could have no wealth effect if agents (generations) were economically connected by operative intergenerational transfers.

In this regard, two slightly different versions of the same neoclassical core model should be distinguished. The first class of model of growth assumes infinitely lived agents (ILA), [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF][START_REF] Cass | Optimum Growth in an Aggregate Model of Capital Accumulation[END_REF]. The second version is OLG models, which instead, have shifted the debate, considering the intergenerational linkages between generations rather than their lifetime horizon 75 [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF][START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF]. The subsequent contributions based on these models show that the debt effect is due to the degree of altruism existing between young and old generations rather than the presence of the infinitely lived agents (linkages that could result in agents with infinite lifetime horizons). This created an intense debate between the neoclassical and proponents of the Ricardian-equivalence conjecture [START_REF] Barro | Perceived wealth in bonds and social security and the Ricardian equivalence theorem: Reply to Feldstein and Buchanan[END_REF]Feldstein, 1976).

Thereby, [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] constructed an OLG model to study the effects of government debt (domestic and foreign) on the long-term competitive equilibrium. The economy assumes an infinitely long life and agents living for two periods, working in the first and retiring in the second.

The model particularly assesses the effects of domestic and foreign debt on both utility level and the equilibrium interest rate. In this model, several key assumptions are made about national debt. First, governments have a one-period maturity avoiding the issue of the expected capital returns. Second, the debt pays the current interest rate. Third, the debt-labour ratio is held constant. Fourth, taxes are assumed as a lump sum on the youth generation.

In this model, the effects of government debt on utility and equilibrium interest rates depend on the coexistence of external and internal debt in the portfolio of government debt. Internal debt raises the interest rate and decreases the utility level in the efficient competitive equilibrium, and may increase or decrease it in the inefficient equilibrium. In particular, in the absence of external debt, domestic debt may increase utility in the case of inefficient competitive equilibrium. External debt increases the gap between the equilibrium interest rate and economic growth. Specifically, it moves the interest rate away from the golden rule solution, 76 which, in turn, reduces utility. In the case of an efficient competitive solution, external debt reduces the utility level of individuals in the long-term equilibrium. However, in the case of an inefficient solution, the external debt effect can raise or lower the utility independently of the existence of internal debt. 77 Furthermore, the debt swap (the substitution of internal debt by external debt) positively influences the interest rate and hence negatively influences utility in the efficient equilibrium, while it could reduce or increase it in the inefficient case. The author differentiates between four effects of public debt on utility: the effect of domestic debt following changes in the taxes required to finance it, the debt effect in the relative factor payments, the effect of external debt, and the debt swap effect.

Nevertheless, [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] constructed a model of overlapping generations based on Samuelson-Diamond's core model [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF][START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] to argue that government bonds displace the interest rate, and utility in the steady-state equilibrium does not necessarily hold and depends, in particular, on the existence of operative altruistic links (bequests) between generations.

75 According to some authors [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF][START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF], having operative linkages in OLG models between some economic agents with defined finite time horizons leads to infinite lifetime connected generations in the OLG models. 76 According to [START_REF] Phelps | The Golden Rule of Accumulation: A Fable for Growthmen[END_REF]: "A golden age means a dynamic equilibrium in which output and capital grow exponentially at the same rate so that the capital-output ratio is stationary over time." 77 The principal findings of the Diamond model, for which government deficits raise long-term interest rates, have been empirically tested in many papers, with a mixture of numerical results [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF].

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 192 Expressly, in the absence of such linkages, the current living generation does not necessarily consider the welfare of its dependants (future generations). Therefore, shifting the tax burden to the future may change the effective lifetime budget of the current living generation. Alternatively, operative altruistic links may cancel the effect on the lifetime budget of the current living generation, as the latter is aware of the welfare of the future generation. Consequently, debt neutrality is guaranteed, as the debt-for-tax swap does not affect the resource allocations and interest rates of the current generation in this case. For [START_REF] Cukierman | A Political Theory of Government Debt and Deficits in a Neo-Ricardian Framework[END_REF], it is sufficient that the bequest motives do not operate for some economic agents only, to conclude under majority rule, for the non-neutrality of government debt.

Unlike [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] model, which considers the infinite lifetime horizon, [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF] studies the effects of debt and accumulation of deficit in a finite lived agent's horizon. 78 This is conducted by constructing what he called an "index of fiscal policy" supposed to capture the effects of current and anticipated fiscal policy. This index has two parts, of which one shows the effect of both changes and levels of government spending on aggregate demand, while the second highlights the effects of government finance; this is reflected by the effects of both government debt and the expected sequence of accumulated deficits on aggregate demand.

The main conclusions are that a government debt increase displaces the steady-state level of foreign assets in agents' wealth in an open economy 79 and decreases the steady-state level of capital and consumption in a closed economy. Consequently, the government can choose any level of steady state of consumption (open economy) and capital (closed economy) by simply choosing its level of debt. Similarly, a decrease in current lump-sum taxes increases human wealth and consumption. The longer the taxes are differed (i.e. shifted to future generations), the larger the effect. In summary, the increase in government debt and taxes creates initial wealth effects on consumption, leading to capital decumulation, which makes capital and consumption lower in the new steady-state level.

For other authors, the way the tax cut is distributed among economic agents plays an important role in determining the effects of fiscal policy. In this way, [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF] used a modified version of the OLG model based on [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF] to show that Ricardian equivalence 80 depends on the way the tax cut is distributed among agents. In particular, debt neutrality holds in an OLG framework where this distribution does not change agents' wealth allocations. The choice of the OLG model (instead of an ILA model) was attributed to the fact that this type of model allows for 78 Blanchard (1985) imposes a constant instantaneous probability of death over agents' lifetime. This makes different agents with different ages and different levels of wealth have the same horizon and assumes the same propensity to consume. This easily enables the aggregation of the consumption function. [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] model adopts, however, specified population and age structures to avoid the aggregation issue. 79 The larger the horizon of agents, the smaller the effect. Specifically, in an infinite horizon, the level of government debt has no effect on the steady-state level of foreign assets [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF]. 80 Ricardian equivalence is summarized as "the debt-tax swap for financing government spending, [which] has no effect on the interest rates and consumption allocations".

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 193 a changeable real interest rate (which may be above or below the real growth rate) to different deficit policy regimes. Furthermore, the OLG models consider heterogeneous agents, which enable taxes to be distributed differently among them. On the contrary, ILA models do not allow the real interest rate to go below economic growth, while, in addition, they assume identical economic agents yielding a uniform tax distribution.

Aiyagari's results were addressed in response to [START_REF] Miller | A reply to Darby[END_REF], for whom "a shift to a different regime with permanently higher deficits will raise the interest rate and may make it exceed the growth rate". [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF] shows that this statement depends on how wealth is distributed, and this does not hold when the distribution of wealth is kept unchanged. His model shows that a higher level of government spending (or similarly a cut in total taxes) can be financed by debt alone at an unchanged (and negative) interest rate and with unchanged total taxes, if the taxes are distributed in a way that maintains wealth distribution. According to the author, this implies reducing taxes for the younger generation as savers and increasing taxes on the older generation of non-savers, while keeping total taxes constant. Thus, any actual effect of higher government spending on interest rates may arise because distributional impacts are not being controlled for, and not simply because the deficit is higher. So, for [START_REF] Aiyagari | Deficits, interest rates, and the tax distribution[END_REF], the validity of Ricardian debt neutrality depends on the way taxes are distributed among taxpayers and not on the length of the lifetime horizon.

Taking into account the operative linkages between agents, other contributions consider instead that the effects of government bonds on economic agents' wealth are related to the way the tax bases are foreseen. In this regard, [START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF] builds on the Yaari-Blanchard version 81 of the overlapping generations model to show that the real equilibrium of the economy (private consumption, capital and relative prices) is independent of the pattern of government debt and lump-sum taxation over time. For the author, the difference between the expected government tax base and the future tax base of individuals that are alive today explains the variations over time in the pattern of lump-sum taxation. The former tax base represents the resources of individuals alive today, and those yet to be born, while the latter represents the resources owned by individuals alive today only, and not the resources of individuals yet to be born. In particular, economic agents that are not linked to their future generations through intergenerational transfers do not integrate the resources of these successors' generations into their inter-temporal budget constraint. In this regard, [START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF] shows that debt neutrality holds if, and only if, the population growth rate and the individual probability of death equal zero. 82 Furthermore, under the latter condition, a nonzero labour productivity rate will not destroy this debt neutrality.

81 Private consumption behaviour is modelled following the Yaari-Blanchard approach [START_REF] Yaari | Uncertain lifetime, life insurance, and the theory of the consumer[END_REF][START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF]. 82 Blanchard (1985) considers that only an uncertain lifetime condition (a positive non-zero probability of death) is sufficient to invalidate the debt-neutrality conjecture.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 194 Contrary to the models that take into account intergenerational transfers and those considering the infinite lifetime horizon induced by such linkages as prerequisites for debt-neutrality validation, 83 [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF] developed a model of "overlapping families of infinitely lived agents" 84 to show that the assumption of the "infinite lifetime horizon" 85 is not necessarily a condition that induces Ricardian debt neutrality, as well as, inversely, finite horizons not necessarily implying the violation of Ricardian neutrality. The model assumes new cohorts entering the economy over time, for which operative intergenerational linkages between some, but not all, agents, result in "partial linkages sufficient to endow any agent alive at any date with an effectively infinite economic horizon". For [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF], newly arriving families are not linked to pre-existing dynasties through operative intergenerational transfers. 86 The infinite lifetime of the agents (dynasties) is guaranteed by the continuous arrival of families who are not linked by operative intergenerational transfers (no intergenerational altruism). The number of newly arriving families (cohorts), which measures economic disconnectedness (and heterogeneity of the population), is also the growth rate of the population. The model is viewed as an extreme version of [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF] version, as it focuses on the birth rate of new arrival families while setting the probability of death to zero -"agents are born but never die". The model of [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF] assumes a constant population by equalling the birth to death rates. Buitter's (1988) model, however, based on Yaari (1965), assumes distinct birth and death rates.

By introducing government bonds in his model, which involves levying lump-sum taxes, [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF] shows that the equilibrium interest rate hinges on the government financing decision and the rate (speed) of newly arriving cohorts (families). In particular, government bonds increase the equilibrium interest rate for a positive non-zero population growth rate. For the author, the anticipated taxes to pay the issued public debt are expected to be compensated by generations that

have not yet been born. However, generations that are alive today do not consider these taxes in their consumption. This makes them better off and pushes them to spend more, "not because they might not be alive when future taxes are levied (they will, as they live forever), but because the future tax base will include new agents to whom they are not economically connected. The real interest rate must hence rise to maintain aggregate consumption at its market-clearing level. Infinite lifetimes are therefore not inconsistent with the violation of the Ricardian debt neutrality 83 The relationship between altruistic intergenerational transfers, infinite time horizons and Ricardian debt neutrality has been widely debated: "It is widely argued that operative intergenerational transfers between all generations, because they imply infinite horizons, lead to Ricardian neutrality (cf. the debate between Feldstein (1976) and [START_REF] Barro | Perceived wealth in bonds and social security and the Ricardian equivalence theorem: Reply to Feldstein and Buchanan[END_REF]). It is also suggested that finite lifespans lead to the violation of the Ricardian proposition [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF]" [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF]. 84 The assumption of "finite lifetime" adopted by OLG models is considered useless in this model by the author. 85 The effective length of consumers' planning horizon is infinite. 86 "Consider, for instance, a primogeniture economy in which a parent only loves his first-born heir, enough to leave him a bequest. Assume that all parents have children, and that children do not love their parents. Each child, whether first-born or not, is, in this economy, linked through operative bequests to the never-ending chain of his first-born descendants, and is thus part of an infinitely-lived family. Children who are not first-born, however, do not belong to any pre-existing dynasty, since they were not loved by their parents: they initiate the dynasty to which they belong. The rate at which new dynasties enter the economy is a reflection, in such an environment, of the proportion of children who are not loved, or not loved enough, by their parents" [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF].

proposition." Furthermore, [START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF] constructed an example for finite horizons, for which Ricardian debt neutrality is not necessarily violated.

Besides the operative intergenerational transfers, the lifetime horizon and the way taxes and tax bases are distributed and perceived among generations, an important contribution adds the degrees of knowledge spillover across generations, as well as the substitutability between consumption and leisure, to the factors impacting equilibrium interest rates and Ricardian equivalence validation. In this way, Ni (1999) extended Diamond's OLG model, where capital is the only variable input, by allowing for capital and labour as inputs, and assuming a learning-by-doing knowledge-based growth economy in the spirit of [START_REF] Arrow | The Economic Implications of Learning by Doing[END_REF] and [START_REF] Lucas | On the Mechanics of Economic Development[END_REF]. [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] model, and others like it, imply that a government deficit always reduces savings and raises interest rates. However, [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF] main model results show that the effect of government deficit on interest rates depends on the spillover of knowledge and the elasticity of labour supply. Precisely, in a neoclassical growth model with elastic labour supply and intergenerational spillover knowledge, public deficits may not necessarily raise real interest rates. 87

The explanation for this is as follows: while a debt-for-tax swap reduces only the capital stock in the [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] model, it reduces both the supply and demand of capital in [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF] model. Then, with consumption and leisure being good substitutes, shifting the tax burden to the future reduces current savings, capital stock and the labour supply of the near future. The overall impact on real interest rates is a result of two opposite effects of reduction in the labour supply and the accumulation of knowledge 88 from one side and capital supply from the opposite side. The reduction in future labour supply and knowledge lowers the equilibrium real interest rate, while the reduction in capital increases it (as in [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF]. The first effect may partially offset and possibly overcome the second one.

To sum up, this section was devoted to the public debt effects in the neoclassical growth models of ILA and OLG. The most debated question in these models is the links between the validity of the Ricardian argument and the lifetime horizon of individuals. Indeed, if the presence of agents with an infinite lifespan in the ILA models (based on [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF] validates the Ricardian equivalence theorem, the OLG (deriving their core framework from [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF] model and [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] model) assign the validity of Ricardian equivalence to the links that tie the people who die and those who will be born [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF][START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF][START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF][START_REF] Weil | Overlapping families of infinitely-lived agents[END_REF]. Beyond debt neutrality and its prerequisites, the neoclassical models show that public debt raises interest rates, in turn crowding out capital and reducing welfare and utility. However, despite important contributions in refining the analysis of government debt effects related to the bequest motives and intergenerational altruistic transfers, the effects are difficult to assess empirically 87 Furthermore, [START_REF] Ni | National Debt, Savings, and Real Interest Rates in a Neoclassical Model with Endogenous Labour Supply and Knowledge-Based Growth[END_REF] suggests, using an empirical investigation, that the dynamics of the interest rate effect are difficult to assess, and the results of empirical studies of the interest rate effect of government deficits should be carefully interpreted. 88 Government deficits reduce the current labor supply and slow down the accumulation of knowledge.

under the ILA and OLG models. This is a result, in particular, of the difficulty gauging the degree of such bequest motives between generations.

Government debt in endogenous growth models

Models of endogenous growth theory were developed to endogenize the role of externalities and their contribution to explaining the persistence of the long-term per-capita growth rate, as an alternative to the rival neoclassical Solow-Swan model [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF][START_REF] Swan | Economic growth and capital accumulation[END_REF]. 89 The latter considers the role of such externalities, or what is assumed to be technical progress, as exogenous. Indeed, the steady-state growth rate in the Solow-Swan model is determined entirely by exogenous elements, and macroeconomic aggregates (capital, output and consumption) grow at a constant exogenous rate of the population growth, which makes the per capita corresponding quantities constant, and hence they do not grow. Therefore, according to Barro and Sala-i-Martin (2004), the main substantive conclusions about the long term are that steady-state growth rates are independent of the saving rate or the level of technology. Specifically, a model without technological change (like the Solow-Swan model) predicts that economies will converge to a steady state with zero per-capita growth as a consequence of the diminishing returns to capital. Solow's model also appeared to be "obsolete", since the total factor productivity (TFP) measure estimated the share of growth explained by technical progress to be more than 50%, as reported by [START_REF] Jones | The New Kaldor Facts: Ideas, Institutions, Population, and Human Capital[END_REF], or ranging between 50% and 70%, according to [START_REF] Hsieh | Development Accounting[END_REF]. This constitutes an "empirical" argument for the emergence of endogenous growth models [START_REF] Hulten | Total Factor Productivity: A Short Biography[END_REF][START_REF] Aiyar | A Contribution to the Empirics of Total Factor Productivity[END_REF][START_REF] Fuentes | On the measurement of Total Factor Productivity: A Latent Variable Approach[END_REF].

With its standard framework, the Solow-Swan model was unable to explain the persistent percapita non-zero growth rates in many developed economies, and hence was highlighted for missing the determinants of long-term growth. Thus, the crucial goal of the pioneers of the endogenous growth theory is to encompass other determinants of long-term growth. This includes broadening the concept of capital, in which the assumption of diminishing return to scale is avoided, to include other determinants as inputs in the process of production, such as human capital [START_REF] Lucas | On the Mechanics of Economic Development[END_REF][START_REF] Romer | Human capital and growth: Theory and evidence[END_REF], innovation, ideas and knowledge 90 [START_REF] Grossman | Quality Ladders in the Theory of Growth[END_REF][START_REF] Jones | R&D-Based Models of Economic Growth[END_REF][START_REF] Jones | Population and Ideas: A Theory of Endogenous Growth[END_REF], public goods and service flows [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF], public capital and productive public capital [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF], public debt [START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF].

To provide explicit contributions involving government spending and public debt in endogenous growth models, we select a benchmark of important contributions. Thus, [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] was the first 89 In 1956 Solow and Swan published two distinct papers on the same issue, and their model is referred to as the Solow-Swan model, or often just the Solow model in reference to the more famous of the two economists. 90 Technological progress is also viewed as a form of generating new ideas by which an economy could escape from diminishing returns to scale in the long term. Consequently, dealing with technological progress as endogenous within economic growth models, instead of exogenous, is an important strand of the endogenous growth theory. However, a technical discussion emerged on how to include ideas and some public goods in the neoclassical production function because of their non-rivalry characteristics (as for the case of ideas) and non-excludable properties (as for some public services: national defence, justice, law and order).

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 197 to introduce government services as flows in the AK modelling framework. This article triggered a series of theoretical extensions (Barro andSala-i-Martin, 1992, 1997;[START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF][START_REF] Turnovsky | Fiscal policy in a growing economy with public capital[END_REF], as well as a variety of empirical contributions [START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF][START_REF] Greiner | Economic Growth, Public Debt and Welfare: Comparing Three Budgetary Rules[END_REF][START_REF] Greiner | Public debt in a basic endogenous growth model[END_REF][START_REF] Greiner | Public Debt, Productive Public Spending and Endogenous Growth[END_REF][START_REF] Greiner | Human capital formation and public debt: growth and welfare effects of three different deficit policies[END_REF]Ghosh andMourmouras, 2004a, 2004b;[START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF][START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF][START_REF] Minea | Debt policy rule, productive government spending, and multiple growth paths: A note[END_REF][START_REF] Yakita | Sustainability of public debt, public capital formation, and endogenous growth in an overlapping generations setting[END_REF]. The aim of the contributions was to establish the effect of public spending and government debt policies on productivity and long-term growth from a perspective of endogenous growth. Public spending encompasses a variety of expenditure and subsidies covering diverse sectors of health, education, research activities, research and development (R&D), public roads and infrastructure, defence and security, justice and law enforcement, and so on. Besides the direct intra-sector effects, some of this spending may also have externalities on other sectors producing knowledge, ideas and powering human capital by affecting their productivity. According to [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], in addition to positive effects either on labor productivity or as rents generated proportionally by a fixed factor, as assumed in previous works (before their paper), productive public spending may also exert an external effect on the productivity of physical capital. 91 The assessment of the external effects of productive public spending is rather an empirical issue.

The [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] model highlights an explicit link between government policy and long-term economic growth in an endogenous growth model by incorporating government investment expenditure into the neoclassical production function with constant returns. The model studies a closed economy with infinite lifetime agents and inter-temporal preferences modelled by a utility function. The author justifies including government services as a separate input of the production function by the fact that private input is not a close substitute for public input. It is difficult to ensure some public activities through private firms as their charges are difficult to implement, as in the case of non-excludable services (national defence and the maintenance of law and order), or because the service is non-rival (ideas) or because external effects cause private production to be too low (as argued for basic education).

The model includes public consumption as an input in the production function, such as:

𝑦 = 𝑘𝜑 ( 𝑔 𝑘 ) (1)
where 𝑦, 𝑘 and 𝑔 are, respectively, the output per capita, the capital per capita and the government consumption of goods and services per capita. φ satisfies the conditions of positive and diminishing marginal products (𝜑 ′ > 0 and 𝜑" < 0). Considering 𝜑, a Cobb-Douglas production function, yields:

91 Internet services is an example of how the same public good might affect the productivity of either final goods and/or human capital accumulation [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF].

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt

198 𝑦 𝑘 = 𝐴 ( 𝑔 𝑘 ) 𝛼 (2)
where A is a constant net marginal product of capital and 0 < 𝛼 < 1. Furthermore, the model assumes a balanced government budget (tax-financed public services) by a flat-rate income tax such as:

𝑔 = 𝑇 = 𝜏𝑦 = 𝜏𝐴 ( 𝑔 𝑘 ) 𝛼 (3)
with 𝑇 being the per capita amount of taxes.

Important implications under the previous assumptions result in different values of government size (𝑔/𝑦 or τ) having different effects on the long-term growth rate. An increase in τ reduces the long-term growth rate, while an increase in 𝑔/𝑦 raises it through an increase in marginal productivity of capital (𝜕𝑦/𝜕𝑘). The two effects cancel each other out for the optimal government size equalizing government expenditure to output:

𝑔 𝑦 = 𝜏 = 𝛼 (4)
Equation ( 4) corresponds to the maximum long-term growth rate. 92 The growth rate function of government size is an inverted U relationship (Figure 1). Hence, for a small government, the effect of raising expenditure 𝑔/𝑦 dominates the effect of raising tax rate τ, while for a large government size the negative effect of taxes on growth dominates. As for the effects on utility, its maximization corresponds to the same conditions that maximize the economic growth rate if the elasticity of substitution of 𝑦 with respect to 𝑔 equals unity.

Particularly in the case of the Cobb-Douglas production function and the same previous notations, government size that maximizes utility corresponds to the condition in Equation ( 4). If the production function is not a Cobb-Douglas form, the relative size that maximizes utility exceeds the one that maximizes growth rate if, and only if, the magnitude of substitution between 𝑔 and 𝑘 is superior to unity.

If [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] considers the flow of public services in the production function, [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF] build on this by considering the accumulated productive public capital as an input in the production function, 93 which generates a sustained per-capita growth rate in the long term. [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF] argue that public investment stimulates aggregate production indirectly via the accumulated stock instead of flows, as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]. Furthermore, the introduction of the productive public stock allows dynamic transitional effects analysis instead of being restricted to steady-state analysis, as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] and others. As a result, they show that a tax rate that maximizes the economic growth rate turns out higher than the one that maximizes utility. However, despite these enhancing elements attributed to Futagami et al.'s (1993) model, the latter still considers that the government budget is balanced at any time, as assumed in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF].

Therefore, instead of assuming that government is restricted to running a balanced budget in every period, as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF], [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF], Barro andSala-i-Martin (1992, 1997) and many other previous works, subsequent research has omitted this assumption and tried to study fiscal policies under an unbalanced government budget. 94 In this area, [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] consider productive public spending to assess optimal fiscal policy (public spending, tax and financial policies) in the same framework as endogenous growth models. They relax the balanced budget assumption to unbalanced budget constraint, thus allowing for government to borrow and lend. Furthermore, they incorporate in their model a separate human capital accumulation as a second sector contrary to many previous papers restricting investigation to one-sector models where public spending can only affect the productivity of the final goods sector. This allows for studying of the properties of government policies on both the final human and non-human capital sectors. In particular, they distinguish optimal tax rates for both types of capital under different 93 This was signalled first by [START_REF] Arrow | Public Investment, the Rate of Return, and Optimal Fiscal Policy[END_REF], but in a non-endogenous growth framework. Assuming diminishing returns to scale in private and public capital given an amount of labor services, the per-capita growth rate depends on the exogenous rate of technological progress alone. 94 Considering an endogenous growth model where the history of debt affects the primary surplus of the government. [START_REF] Greiner | Fiscal and Monetary Policy in a Basic Endogenous Growth Model[END_REF] shows that an economy with a balanced government budget is characterized by a unique balanced growth path. Inversely, with a permanent public deficit, the balanced growth path is either non-existent or non-unique and could be either stable or unstable. Moreover, [START_REF] Greiner | Public Debt, Productive Public Spending and Endogenous Growth[END_REF] shows that a balanced government budget yields higher balanced growth and welfare and lower inflation than a situation with permanent deficits, especially (for welfare) when the government does not put a high weight on stabilizing debt. In the absence of the latter condition, welfare effects hinge on the initial conditions of public debt.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 200 assumptions on technology and distribution, and they analyse the welfare properties of public debt and assets.

The government service flows are introduced in the production sectors, and the effects of fiscal policies and debt are studied by deriving four models depending on whether: public spending is included as input in the output sector, affecting only the productivity of physical capital (Model 1); or affecting only the productivity of human capital (Model 2); or public spending as input in the human capital sector, affecting, respectively, the same variables (Models 3 and 4).

For some useful details, especially when government service flows enter as input only in the final production goods, [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] consider an aggregate social production function in the style of Cobb-Douglas, assuming constant returns to scale to its three inputs, namely, physical capital, human capital and government flows of services, as follows:

𝑌 𝑡 = 𝐴(𝑣 𝑡 𝐾 𝑡 ) 𝛼𝜖 (𝑢 𝑡 𝐻 𝑡 ) 1-𝛼 (𝐺 𝑡 ) 𝛼(1-𝜖) (5)
where 𝑣 and 𝑢 are, respectively, the fraction of total physical and human capital devoted to the production of final goods, and the productivity of public spending is decreasing in the parameter 0 < 𝜀 < 1. It follows that the optimal government size is deduced by:

𝑔 𝑦 = 𝛼(1 -𝜀) (6)
As 𝜀 > 0, the optimal government size in [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] is less than the one provided by [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] in Equation ( 4):

𝑔 𝑦 = 𝜏 = 𝛼 superior to 𝛼(1 -𝜀). According to [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], the optimal government size should be properly regarded as a result of the optimal choice of spending that holds with and without distortionary taxation, while [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] and others consider the (second-best) optimal choice to be the tax rate under an instantaneously balanced budget assumption.

Despite [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] assuming an unbalanced government budget, they include public spending flows as productive input, as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF], instead of accumulated public capital, as in [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF].

Recently, many works95 have concentrated on the issue of public debt, accumulated capital stock of public spending and, generally, fiscal policy and its effects on long-term growth and welfare, in an endogenous growth framework, particularly in the presence of unbalanced budget constraint with debt dynamics. For example, Ghosh and Mourmouras (2004a) extend [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF] to the case of welfare-maximizing fiscal rules, in the presence of government debt. Thus, the public to private capital ratio is lower under a golden rule of public finance (than under other fiscal regimes), minimizing crowding-out effects. However, steady-state welfare may be lowered in a less strict budgetary rule if public consumption rises, leading to crowding-out effects. In the same context, [START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF] construct an endogenous growth model with productive government spending where the government finances expenditure through income tax and government debt and puts a target level of government debt relative to the size of the economy.

The model distinguishes two steady states: a high-growth steady state in which an increase in government bonds reduces the growth rate; and a low-growth steady state where an increase in government bonds raises the growth rate. These results are inverted in the case of an income tax increase. For the level of welfare, it is lower in the low-growth steady state than in the high-growth steady state.

Nevertheless, [START_REF] Minea | Debt policy rule, productive government spending, and multiple growth paths: A note[END_REF] assign the existence of the two steady-state growth rates to the assumption of the public debt target as a ratio to private capital. Therefore, once the target has been defined in terms of public debt-to-GDP ratio, the model leads to a unique and determined balanced growth path. [START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF] build on the models of [START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF] and [START_REF] Minea | Debt policy rule, productive government spending, and multiple growth paths: A note[END_REF] by considering the stock of capital investment rather than flows, as in those models. Hence, they derive an optimal target debt ratio that depends on the tax rates on wage income and consumption, as well as the public investment share in total government spending. The target debt ratio set by the Stability and Growth Pact (SGP) and Maastricht Treaty, namely 60%, is judged to be higher than the optimal level. Moreover, debt reduction based on expenditure cuts alone improves welfare. In particular, fiscal consolidation based on a target level of debt-to-GDP ratio rule (i.e. the well-known 60% rule) improves welfare, and the faster the pace of debt reduction, the greater this improvement is. Furthermore, fiscal consolidation based on expenditure cuts, jointly with a tax increase, does not always improve welfare. In this case, the welfare gains (if any) are lower than those under expenditure cuts only.

In the same context of targeted ratio of public debt, other authors study the sustainability of public finance. Thus, [START_REF] Bräuninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF] uses an endogenous growth model in the form of AK production function to determine a threshold public deficit ratio. [START_REF] Yakita | Sustainability of public debt, public capital formation, and endogenous growth in an overlapping generations setting[END_REF] builds on Futagami et al.'s (1993) production function to determine a sustainable threshold of public finance that increases in public capital stock. Consequently, a larger public capital helps to sustain public finance. Moreover, keeping the debt finance ratio invariable, the threshold of the debt-to-public-capital ratio increases with reduced public investment in GDP ratio. Increasing public capital ratios in [START_REF] Bräuninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF] and Yakita (2008) requires higher taxes and additional bond issuance, leading to higher interest rates and crowding-out effects.

Likewise, Greiner andSemmler (1999, 2000) relax the assumption of government balanced budget and allow for capital market borrowing by the government. Thereby, they analyse the effect of a deficit-financed increase in productive government spending following some predefined budgetary regimes. Hence, fiscal policy effects are significantly determined by such budgetary Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 202 rules. Likewise, [START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF] analyses an endogenous growth model with public capital and sustainable public debt. 96 The model is used to derive the necessary conditions for the existence of a sustainable balanced growth path and to analyse the growth effects of deficit-financed increases in public investment in the sustainable balanced growth path, as well as along the transition path.

Additionally, in a model with elastic labour supply and a government sector in which government levies a distortionary income tax and issues bonds to finance lump-sum transfers and nondistortionary public spending, [START_REF] Greiner | Public debt in a basic endogenous growth model[END_REF] shows that the higher the debt ratio, the smaller the long-term growth rate whenever public spending is adjusted to fulfil the government intertemporal budget constraint. However, the public debt ratio has no effect on the balanced growth rate if the adjustment is on lump-sum transfers.

Analysing the effects of public debt in an endogenous growth model with productive 97 public spending, [START_REF] Greiner | Public Debt, Productive Public Spending and Endogenous Growth[END_REF] shows that higher debt accompanies smaller long-term growth. Moreover, discretionary policy, in general, violates the inter-temporal government budget constraint along a balanced growth path. A balanced government budget gives a unique saddlepoint stable growth path, while a rule-based policy can lead to two saddle-points stable balanced growth, depending on the inter-temporal elasticity of substitution of consumption and on the primary surplus policy. For [START_REF] Greiner | Human capital formation and public debt: growth and welfare effects of three different deficit policies[END_REF], an endogenous growth model with public educational spending shows that the balanced budget policy 98 and the policy with a slight deficit yield higher growth than a debt policy where public debt and GDP grow at the same rate. Furthermore, for high initial debt ratios and low inter-temporal elasticity of substitution, a strong deficit policy yields lower welfare than a balanced budget and a slight deficit policy.

In summary, if the neoclassical ILA and OLG models have been interested in the long-term effects of government fiscal policies (debt and taxation) on the saving-spending behaviour of individuals and generations, through operative linkages and transfers, the endogenous growth models have endogenized such policies to assess their effects on the steady-state growth path. Furthermore, including debt dynamics and/or public capital stock, endogenous models eventually allow for tracing of the transitional dynamics effects of fiscal and debt policies that could not be ensured by the ILA and OLG models. The extensions and development of such models triggered a prolific discussion about the composition of public expenditure (productive as input versus non-productive as utility), the non-rivalry and non-excludable goods, and the associated effects on physical and human sectors for each type of public goods. Accordingly, the differentiated effects between the types of expenditure induce different policies for the government. Despite these important 96 Public debt sustainability is assured by assuming the ratio of the primary surplus to gross domestic income to be a positive linear function of the debt to income ratio. 97 "The productive public spending can be thought of as encompassing very different types of publicly provided goods and services, such as justice, enforcement of law and contracts, police services, educational services and government research activities" [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF]. 98 Greiner (2011) compares the outcome of three budgetary rules: the balanced budget rule, a budgetary rule where debt grows in the long term but at a rate lower than the balanced growth rate, and a rule where public debt grows at the same rate as all other economic variables and where the inter-temporal budget constraint is fulfilled.

contributions, further enhancement remains, especially in considering the heterogeneity of agents' behaviour and welfare, which was also an important drawback of the ILA and OLG models [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF][START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF]. Explicitly, a population could embrace a part of the agents with Ricardian behaviour, while the other part behaves following a rule of thumb.

Government debt in the new Keynesian models and the positive approach

This section presents a summary of some very recent new Keynesian models involving public debt and fiscal policy, as well as the public debt effects in the models, considering a positive approach where the political regime impacts the trajectory of public debt.

Government debt in the new Keynesian models

Instead of assuming that all taxes are a lump sum, especially in the assumptions about overlapping generations models, recent works have considered optimal fiscal policy, assuming distortionary taxes in the class of new Keynesian models in which social welfare is implied from a consumer utility function. The pioneering works in the new Keynesian modelling framework are principally those of [START_REF] Christiano | Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy[END_REF] and [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF]. Government debt effects, especially in the neoclassical models, are studied in the long term and steady-state equilibrium, especially in the ILA and OLG models and some endogenous growth models lacking transitional dynamics. However, the recent generation of the new standard Keynesian models or dynamic stochastic general equilibrium (DSGE) models have studied optimal government policies (monetary and fiscal policies) and fiscal consolidation issues considering economic fluctuations and shocks (in the short and medium term), in which public debt is set in many of these models to zero.

Nevertheless, some authors have studied the trajectory of public debt in relation to committed government actions. Particularly, optimal public debt would follow a random walk process whenever the government can achieve a time-inconsistent policy commitment [START_REF] Benigno | Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach[END_REF][START_REF] Schmitt-Grohe | Optimal Monetary and Fiscal Policy under Sticky Prices[END_REF]. Specifically, the latter study the implications of price stickiness for the optimal degree of price volatility. The model considers a government issuing non-distortionary taxation and can only issue nominally risk-free debt. Specifically, under the assumption of price stickiness in this class of models, the government (social planner) chooses to rely more heavily on changes in income tax rates rather than using surprises as a shock absorber of unexpected innovations in the fiscal budget. The distortions introduced by tax changes are diminished by spreading them over time, which induces a near random walk property in tax rates and public debt.

In the context of new Keynesian models augmented by the government's budget constraint, where public spending is financed by distortionary taxes and/or debt, [START_REF] Leith | Fiscal sustainability in a new Keynesian model[END_REF] analyse the optimal response of government debt to shocks, focusing on the type of involved timeinconsistency policy and its implications for discretionary policies. Like the previous research, Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 204 they find that the optimal pre-commitment policy allows debt to follow a random walk path in the steady state. However, they show that, under a sticky prices framework, governments are tempted to use their monetary and fiscal policy instruments to change the steady-state level of debt in the initial period. The debt will be curved to its initial efficient steady state to encounter this temptation and therefore deter public debt from following the random walk path if following shocks. The new steady-state debt equates the original (efficient) debt level even though there is no explicit debt target in the government's objective function. Analytically, they show that the debt stabilization instrument crucially depends on the degree of nominal inertia. Furthermore, the size of the debt stock, and the welfare consequences of introducing debt, are negligible for pre-commitment policies but can be significant for discretionary policies.

Furthermore, a few studies examine the effects of high debt in fiscal consolidation actions related to the impact on the magnitude and/or sign of the fiscal multipliers. For example, [START_REF] Mayer | Government debt, inflation dynamics and the transmission of fiscal policy shocks[END_REF] use a new Keynesian model to analyse whether, and how, the presence of positive levels of government debt in the steady state influences the responses of macroeconomic variables to a government spending shock. The model assumes that a fraction of the household sector is characterized by rule-of-thumb behaviour, as in [START_REF] Galí | Understanding the effects of Government Spending on Consumption[END_REF]. They show that large levels of government debt in the steady state significantly influence the sign and size of short-and mediumterm fiscal multipliers, which therefore depend substantially on the horizon at which the multiplier is evaluated. Furthermore, there is an interaction between the dynamics of the inflation rate and the debt level in real terms, which is absent in standard new Keynesian models in which government debt is assumed to be equal to zero in the steady state. Overall, in the presence of permanent government debt, the effect of fiscal policy on macroeconomic variables becomes difficult to predict over time.

The positive approach of public debt

In the previous section the ILA and OLG models were generally developed by economists in an environment where governments, being benevolent social planners, maximize the utility of their population. These models are classified under what is referred to in the economic literature as "the normative approach" [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF], the "tax smoothing" theory of the government budget [START_REF] Alesina | The Political Economy of Budget Deficits[END_REF] or "the equilibrium approach to fiscal policy" [START_REF] Roubini | Political and economic determinants of budget deficits in the industrial democracies[END_REF]. The normative theory of debt and fiscal policy considers public debt as a means of smoothing consumption by distributing tax distortions over time [START_REF] Barro | On the determination of the public debt[END_REF][START_REF] Turnovsky | Time consistency and optimal government policies in perfect foresight equilibrium[END_REF][START_REF] Lucas | Optimal Fiscal and Monetary Policy in an Economy Without Capital[END_REF]. The core models of this theory assume, in general, a closed economy without capital where the government is a "benevolent social planner" that maximizes the utility of a representative agent who consumes, works and saves with the same infinite (simplified) time horizon of both government and representative agent [START_REF] Alesina | The Political Economy of Budget Deficits[END_REF].

However, for advocates of the positive approach [START_REF] Roubini | Political and economic determinants of budget deficits in the industrial democracies[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF][START_REF] Grilli | Political and Monetary Institutions and Public Financial Policies in the Industrial Countries[END_REF], normative theory, despite explaining the behaviour of debt in many Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 205 advanced OECD countries, has been challenged by the rapid accumulation over time of debt in almost all developed countries. Therefore, it is unable to provide a complete explanation for such a phenomenon or explain the differences in policies pursued by different countries with comparable economic conditions.

Alternatively, a positive approach has been the subject of modelling government fiscal policy, particularly debt policy, in the field of the new political economy of public debt. 99 This approach is particularly interested in the implied impacts of political process on shaping the path of government debt. The positive approach considers public debt as a state variable used by each government as a strategy to influence its successor's choices or to shape private economic agents' expectations [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF].

In this way, [START_REF] Roubini | Political and economic determinants of budget deficits in the industrial democracies[END_REF] notice that, in several industrialized countries, issues of political management in coalition governments fall behind the slow rate at which fiscal deficits were reduced during the 1975-85 period. In particular, during this period weaker governments 100 had a clear preference for larger deficits. Similarly, [START_REF] Grilli | Political and Monetary Institutions and Public Financial Policies in the Industrial Countries[END_REF] focus on the role played by public institutions in offering constraints and incentives that determine the actions of governments.

Governments' ability to handle growing deficits and debt issues is influenced by the electoral practice and political process. [START_REF] Grilli | Political and Monetary Institutions and Public Financial Policies in the Industrial Countries[END_REF], following [START_REF] Roubini | Political and economic determinants of budget deficits in the industrial democracies[END_REF], note that, in countries with an electoral system favouring many small political parties, governments generally have short horizons and therefore act myopically to avoid tackling the hard choices. [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF] consider the level of public debt as the state variable that gives the current government an instrument to control a rival future government. They compare, in a twoperiod perfect-foresight framework, the policy of a conservative government (one that prefers less debt and deficit), which is certain to be succeeded by a liberal government (a more expansionary government), with the policy where it is certain that it will remain in power. As a result, a conservative government may borrow more if it knows it will be succeeded by a liberal government than it would once certain of remaining in power in the future. Obviously, a conservative government will collect less tax and leave more public debt than the successor would prefer. This increases the conservative government's consumption more than if it remained in government, while the liberal government (successor) with high debt and constrained resources reduces consumption more than it would if it ran alone. Thus, the time-consistent level of 99 Alesina and Perotti (1994) provide a survey of the political economy models of budget deficit organized into six groups: 1-models based upon opportunistic policy-makers and naïve voters with "fiscal illusion"; 2models of intergenerational redistribution; 3-models of debt as a strategic variable, linking the current government with the next one; 4-models of distributional conflicts within social groups and/or political parties in coalition governments; 5models of geographically dispersed interests; and 6-models emphasizing the effects of budgetary institutions. In our case, we are especially interested in the third group, particularly the contributions of [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF] and [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF]. 100 Weaker government is characterized by a short average tenure and by the presence of many political parties in the ruling coalition.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 206 government consumption is somewhere between the two outcomes that the two governments would prefer if ruling on their own.

Meanwhile, the [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF] approach, known as a principal-agent problem, with the conservative government being the principal and the liberal successor government being the agent, simplifies the reality by assuming that the ruling government knows with certainty that it will be succeeded by a more liberal government. They also assume the homogeneity of governments' preferences towards all public goods but different preferences for different levels of the same public good. In this regard, [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF] constitute an advancement in introducing uncertainty about the nature and spending behaviour of successive governments. They also consider different preferences for different items of public expenditure, while [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF] focus on different levels of the same public good.

Therefore, to properly understand the debt build-up and deficits in several industrialized economies, [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF] adopt a positive theory by removing the assumption that fiscal policy is set by a benevolent social planner who maximizes the welfare of a representative consumer. Specifically, their findings suggest that differences in political institutions, leading to different debt policies in different countries, or in the same country at different points in time, help to explain the debt trajectories over time and across countries. Their model101 is derived from [START_REF] Lucas | Optimal Fiscal and Monetary Policy in an Economy Without Capital[END_REF]. In particular, [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF] show that debt accumulation and deficit are accentuated by the alternation of elected governments.

Explicitly, they compare the outcome of debt accumulation and deficit in a situation where governments alternate versus an outcome resulting from a social planning102 government supposedly elected forever. Specifically, a disagreement between different governments on the composition of spending between public goods results in a deficit bias and hence an accumulation of debt higher than would be the case in the situation of a social planner. As explained by [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF]: "The level of debt left to the last period is larger in a democracy than with a social planner; namely the social planner would choose to balance the budget in both periods, while either one of the two parties choose to run a budget deficit in the first period leaving a positive amount of debt to be repaid in the last period. In this sense, the electoral uncertainty creates a sub-optimal deficit bias. This bias is stronger for the party with the smaller probability of reappointment."

Furthermore, the equilibrium level of government debt is higher with: 1/ a higher degree of polarization between alternating governments; and also 2/ with more likelihood of the current government not being re-elected. Moreover, as the ruling government is unable to curve the taxation and expenditure policies of its successors (whether the successor belongs to the same or the opposing party), the law of motion of public debt is the only way in which the fiscal policy of the ruling government can impact the policies of its successors.

Another important result is related to the probability of re-election. In such an uncertain environment, both governments have the same incentive for increasing debt, not certain of being re-elected, and they restrict the next period's public consumption by increasing borrowing for the current ruling period. This leads to a bias towards a larger deficit and higher debt for both governments, which helps to explain the accumulation of public debt in advanced democracies.

Discussion

The first section reviewing the effects of public debt through the ILA and OLG models leads to two principal results. The infinitely lived dynasties models, derived from [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF], and adopted by [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] and others, validate the Ricardian equivalence proposition for which public debt is neutral. It is worth mentioning that the Ricardian equivalence proposition works assuming economic agents' rational expectations. Accordingly, the previous models show that economic agents (some, but not necessarily all) react to fiscal policy redistribution of the tax burden among generations through their bequest motives inducing operative transfers to smooth the pattern of consumption over time. However, because the OLG models of [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] and others lack such bequest motives, a government debt issuance affects the wealth of generations by raising real interest rates, hence crowding out capital and reducing the steady-state utility.

Despite these important contributions for economic theory in assessing government debt and fiscal policy effects, these two types of model have been subject to criticism. [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF] criticized the two modelling approaches, arguing against their adequacy and satisfactory role for analysing fiscal policy. Accordingly, the author is, first, sceptical regarding the assumption that "households smooth their consumption over time" that is adopted by both versions of the model. This assumption is far from perfect, according to [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF]. In particular, current income significantly impacts consumer spending, as many consumers are far from following completely rational expectations, instead adopting rule-of-thumb 103 behaviour (non-Ricardian behaviour) in their spending. Second, some individuals may enjoy long lifetime horizons (due to bequest motives), while others with short time horizons fail to smooth their consumption and accumulate wealth. Third, many households have net wealth near zero (a striking fact reported in the data), and hence no savings, which makes them unable to follow inter-temporal consumption smoothing, as reported by the Barro-Ramsey or Diamond-Samuelson models.

Thus, for [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF], a better model would allow for such heterogeneous behaviour that is apparent in the data. In this regard, [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF] formulated an alternative theory mentioned as "savers-spenders theory of fiscal policy" to address the neoclassical shortcomings in public finance policies. This theory shows, in particular, that, even though government debt does not affect steady-state capital stock and income, it disrupts income distribution and consumption in the steady-state path and, in turn, raises inequality between spenders and savers. Specifically, a higher level of debt yields higher taxation to compensate for the interest payments on the debt. However, the taxes are on both savers and spenders, while the interest payments on debt fall on the savers' side. Therefore, a higher level of debt increases the steady-state income and consumption for savers (with already higher initial income) and lowers it for spenders (with initially a lower income), which raises inequality between the two groups.

The "savers-spenders" theory of Mankiw has influenced many empirical researchers on fiscal policy trying to consider the behaviour following the rule of thumb, especially in the new Keynesian models. However, this type of modelling has also not been immune to criticism. In this way, [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] show that this class of model is not yet useful for public policy analysis. [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] base their critiques on the model of [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF], which constitutes a fundamental reference for many recent contributions and policy-makers using the new Keynesian analysis framework. Accordingly, the [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF] state-of-the-art model adds many free parameters to these models, yielding to shocks that are dubiously structural, as well as many features that are not consistent with the microeconomic evidence.

The drawbacks of the new Keynesian modelling framework were recognized especially after the 2008 financial crisis and are frequently cited in several publications. In this way conferences with different slogans (rethinking macroeconomics, rebuilding macroeconomic theory, etc.) have gathered economists from around the world in an attempt to discover why these models failed to warn about the disaster of the financial crisis. In this way, an important project (the Rebuilding Macroeconomic Theory Project) asked a number of leading economists to describe how the benchmark new Keynesian model might be designed after the financial crisis. Approximately fifteen important articles and contributions [START_REF] Blanchard | On the future of macroeconomic models[END_REF][START_REF] Soskice | Stagnant productivity and low unemployment: stuck in a Keynesian equilibrium[END_REF][START_REF] Ghironi | Macro needs micro[END_REF]Haldane and Turrel, 2018;[START_REF] Hendry | The future of macroeconomics: macro theory and models at the Bank of England[END_REF][START_REF] Krugman | Good enough for government work? Macroeconomics since the crisis[END_REF]Linde, 2018;[START_REF] Mckibbin | Modelling a complex world: improving macro-models[END_REF][START_REF] Reis | Is something really wrong with macroeconomics?[END_REF]Stiglitz, 2018;Vines and Wills, 2018;[START_REF]Ending the microfoundations hegemony[END_REF][START_REF] Wright | On the future of macroeconomics: a New Monetarist perspective[END_REF] by these economists on this question were published in the Oxford Review of Economic Policy (2018, vol. 34 (1-2)). The authors disagreed that the new Keynesian models benchmark of [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF] should not constitute the starting point for the newly designed model. Nevertheless, they agree that the core model should consider four elements, as described in Vines and Wills (2018). The core model should, in particular: i) incorporate financial frictions rather than assuming that financial intermediation is costless; ii) relax the requirement of Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 209 rational expectations; iii) introduce heterogenous agents; and iv) underpin the model with more appropriate micro-foundations.

The theoretical framework

The choice of an endogenous growth model

We showed in Section 2 that the ILA models, derived from [START_REF] Ramsey | A Mathematical Theory of Saving[END_REF], and adopted by [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF] and others, validate the Ricardian equivalence proposition for which public debt is neutral. The latter proposition holds in an environment of perfect information assuming economic agents' rational expectations. Therefore, such models show that economic agents (some, but not necessarily all) react to fiscal policy redistribution of the tax burden among generations through their bequest motives inducing operative transfers to smooth the pattern of consumption over time. However, because the OLG models of [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] and others lack such bequest motives, a government debt issuance affects the wealth of generations by raising real interest rates, in turn crowding out capital and reducing steady-state utility.

Despite their important contributions to the economic theory assessing government debt and fiscal policy effects, the ILA and OLG models have been subject to criticism, to some extent diminishing their contribution. [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF] criticized the two modelling approaches, arguing against their adequacy and satisfactory role in analysing fiscal policy for several reasons:

-First, according to [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF], the assumption that "households smooth their consumption over time" adopted by both versions of the model does not seem convincing. Specifically, many consumers are far from following completely rational expectations and instead adopt the rule-of-thumb behaviour (non-Ricardian behaviour) in their spending; hence, current income significantly impacts consumer spending. For example, [START_REF] Galí | Understanding the effects of Government Spending on Consumption[END_REF] use a new Keynesian model to empirically test the government spending effects on consumption, involving rule-of-thumb agents that only have access to contemporaneous labour income for consumption, and Ricardian agents that can smooth consumption by accumulating capital.

-Second, some individuals may enjoy long lifetime horizons (due to bequest motives), while others with short time horizons fail to smooth their consumption and accumulate wealth.

-Third, many households have net wealth near zero (a striking fact reported in the data), and hence no savings, which makes them unable to follow inter-temporal consumptionsmoothing, as reported by the Barro-Ramsey or Diamond-Samuelson models.

For [START_REF] Mankiw | The Savers-Spenders Theory of Fiscal Policy[END_REF], a better model would allow for such heterogeneous behaviour as is apparent in the data. He therefore formulated an alternative theory mentioned as "savers-spenders theory of fiscal policy" to address the neoclassical shortcomings in the public finance policies. This theory shows that, even though government debt does not affect the steady-state capital stock and income, it disrupts income distribution and consumption in the steady-state path and, in turn, raises inequality between spenders and savers.

The "savers-spenders" theory of Mankiw has influenced many empirical researchers on fiscal policy trying to consider the behaviour of following the rule of thumb, especially in the new Keynesian models. However, the new Keynesian type of modelling has also not been immune to criticism. In this way, [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] show that this class of model is not yet useful for public policy analysis. [START_REF] Chari | The New Keynesian Models: Not Yet Useful for Policy Analysis[END_REF] base their critiques on the model of [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF], which constitutes the fundamental reference for many recent contributions and policy-makers using the new Keynesian analysis framework. Accordingly, the [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF] stateof-the-art model adds many free parameters to these models, yielding to shocks that are dubiously structural, as well as many features that are not consistent with the microeconomic evidence.

Based on the previous critiques, the endogenous growth modelling framework seems to be a suitable candidate for our approach. The endogenous growth models via their productive sector (generally the Cobb-Douglas production function) are extremely flexible in encompassing many other factors to explain the per-capita long-term growth rate. Therefore, fiscal policy variables (productive government expenditure or accumulated government capital) are easily integrated to the production function to assess the effects of such variables in the steady-state (long-term) path and transitional dynamics.

Justification of government capital stock and government expenditure flows in the production function

Many studies have considered the issue of productive government spending, debt and fiscal policies, and their effects on long-term economic growth and social welfare in the context of endogenous growth models. We follow this line of research for several reasons and try to avoid many important issues. We mainly follow the approach of [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] and [START_REF] Barro | Economic Growth[END_REF], but instead consider the public accumulated capital in the production sector rather than the flow of goods and services provided by the public sector. We also consider human capital, as in [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], which could be an interesting measurable input. Our approach differs from [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] and [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], as the latter use productive government flows in the production function, while our study uses accumulated public capital, as in [START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF] and [START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF].

In fact, we judge that models (either theoretical or empirical) using government expenditure flows instead of public capital stock lack some logic and compatibility with the framework of the Cobb-Douglas production function, especially when we consider the government as the production Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 211 sector, which leads to considering productive government expenditure. This results in missing an important contribution of the earlier accumulated stock of public expenditure. As the model of production function, and others considered in the endogenous growth framework, are non-dynamic (no lag or inertia of the endogenous variable is present in the explanatory variable), considering the stock of capital ensures the dynamic effects of public expenditure. This means, economically, that the earlier flow contributions in the output are considered. However, considering only current flows in the production function implies that one considers the earlier accumulated flows (which builds the public stock) fully consumed or as if depreciated with a 100% depreciation rate.

Similar earlier critiques have been addressed to the [START_REF] Scully | Taxation and economic growth in New Zealand[END_REF][START_REF] Scully | Unfinished reform: taxation and economic growth in New Zealand[END_REF][START_REF] Scully | Optimal taxation, economic growth, and income inequality[END_REF] .

The Scully model form is highlighted as having many drawbacks and producing spurious regressions by many authors [START_REF] Chapple | One for the X-files: A critical assessment of Professor Scully's 'Taxation and economic growth in New Zealand[END_REF][START_REF] Easton | The whimpering of the state. Policy after MMP[END_REF][START_REF] Kennedy | On measuring the growth-maximizing tax rate[END_REF][START_REF] Hill | Optimal taxation and economic growth: a comment[END_REF]). [START_REF] Kennedy | On measuring the growth-maximizing tax rate[END_REF] critique is related to the unfounded relationship of this particular production function, which he says as if the public capital were totally used up every year. Moreover, [START_REF] Hill | Optimal taxation and economic growth: a comment[END_REF] shows that this model should use the lagged tax rate in the previous equation instead of a current tax rate. When correcting this error, the growth-maximizing size of the state varies between 9% and 29% for the United States data, while [START_REF] Scully | Taxation and economic growth in New Zealand[END_REF] reports a government size of 19% for the same country.

Beyond that, despite many studies enriching the production function with other variables without paying attention to the nature of these variables, the introduction of stocks rather than flows is more reasonable and in conformity with the logic standard form of the neoclassical production function, which has microeconomic foundations.

Furthermore, this issue is emphasized further when we go through the details of the data of such flows. Indeed, a large part of aggregate government expenditure flows, introduced in the production function, are generally public employees' wages and salaries, direct transfers and subsidies to families and other public and private institutions. Except for some transfers to the latter (which are generally small compared to the total) that could help in the production process of these institutions, wages and salaries and transfers to families and price subsidies go directly to the households' income and constitute an input to their behavioral consumption function (or utility function). Thus, it is logically more suitable to consider it in relation to the latter instead of including it in the production function. 104An interesting issue that is difficult to measure, and which was mainly invoked by what is known as the positive approach of public debt in the domain of the political economy, is the crucial role of institutions in economic growth that uses debt and/or deficit as an instrument variable to curve future governments' (opposing) decisions and economic agents [START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF].

Considering institutions as a sort of game theory between succeeding governments, or between governments and their citizens in a normative modelling approach, is difficult. However, we could also take the role of institutions as endogenous rather than exogenous. One way is to augment the production function by a parameter of the government constraint representing the quality of the institutions. However, the role of institutions could also be considered by encompassing a formula or a parameter describing the inherent discretionary policies of the government, as in [START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF].

In the following section, we present the model.

The model

The productive sector

We use the production function to describe the relationship between accumulated public capital and real GDP. The production function can take different specifications, such as the constant elasticity of substitution (CES) or a trans-log production function, which under some specific restrictions can be reduced to the Cobb-Douglas production function. The latter is a special case of the former; in other words, the former are more flexible forms. The CES, for example, does not require the assumptions of perfect competition and profit maximization. 105We consider the Cobb-Douglas production function, which is well grounded in economic theory and mainly used in practice, to be easy to estimate, and it has good empirical properties [START_REF] Bentour | Do developing countries benefit from foreign direct investments? An analysis of some Arab and Asian countries[END_REF]. The equation106 is as follows:

𝑌 𝑡 = 𝐴. 𝐾 𝑝𝑡 𝛼 𝐾 𝑔𝑡 𝛽 (7)
where 𝑌 𝑡 , 𝐾 𝑝𝑡 and 𝐾 𝑔𝑡 are, respectively, the per capita of output, and the per capita of private and public capital. 𝐴 is a constant designating technical progress, and 𝛼 and 𝛽 are shares in the national income of, respectively, private and public capital stock (also corresponding to elasticities). Private and public capital are evolving according to the following inventory equations:

𝐾 𝑝,𝑡 = (1 -𝛿 𝑝,𝑡-1 )𝐾 𝑝,𝑡-1 + 𝐼 𝑝,𝑡 (8)
𝐾 𝑔,𝑡 = (1 -𝛿 𝑔,𝑡-1 )𝐾 𝑔,𝑡-1 + 𝐺 𝑡 (9)

where 𝐼 𝑝,𝑡 and 𝐺 𝑡 are, respectively, the private and public flows of investments and 𝛿 𝑝,𝑡-1 and 𝛿 𝑔,𝑡-1 are, respectively, the depreciation rate of private and public capital. To simplify, we assume the same constant depreciation rate for the private and public sectors (𝛿 𝑝,𝑡-1 = 𝛿 𝑔,𝑡-1 = 𝛿)

Defining 𝑟 𝑔 as the productivity of public capital, the first-order condition derivation yields for public capital:

𝑟 𝑔,𝑡 = 𝜕𝑌 𝜕𝐾 𝑔 = 𝑌 ∆𝐾 𝑔 = 𝛽 𝑌 𝐾 𝑔 (10)
For a production function with constant returns to scale, 𝛽 = 1 -, we have:

𝑟 𝑔 = (1 -) 𝑌 𝐾 𝑔 .
Equation ( 10) is equal to unity in the optimal steady state path (𝑟 𝑔 = 1), which directly yields a constant optimal government size, as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] and [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], when considering the flows of government services and not public capital. In our case, we prefer to study the economies considering that not all are in the steady state. This leads to a government expenditure size that depends on the return to public capital and its elasticity, which may differ between countries as a result of the differences in public governance and public expenditure productivities.

From Equation (9) we have:

𝐾 𝑔,𝑡 ∆𝑌 𝑡 = -𝛿𝐾 𝑔,𝑡-1 ∆𝑌 𝑡 + 𝐺 𝑡 ∆𝑌 𝑡 = [ -𝛿𝐾 𝑔,𝑡-1 𝑌 𝑡-1 ] 𝑌 𝑡-1 ∆𝑌 𝑡 + 𝐺 𝑡 𝑌 𝑡 𝑌 𝑡 ∆𝑌 𝑡 (11)
From Equation (10) we have the term government productive expenditure share to GDP, we obtain: 107 We used the name "potential", as it is derived from a first-order condition.

Neglecting the depreciation rate yields:

𝑔 ̃𝑡 = [ 𝛾 1+𝛾 ] 1 𝑟 𝑔,𝑡 (14)
Equation ( 14) implies that the potential productive government investment depends on the economic growth rate, as increasing the function of growth as the derivation according to the growth rate is positive, and inversely on public capital expenditure productivity. Hence, the higher the growth rate (higher potential of GDP also), the higher the potential public investment. Furthermore, the higher the productivity (the return 𝑟 𝑔,𝑡 ) of public capital, the lower the potential public investment.

However, once the depreciation rate has been accounted for, the effect of economic growth on the size of the government depends on the current and past productivity of public capital, as well as the elasticity and the depreciation rate parameters. The derivation of the productive share on the growth rate from Equation (13) yields: ].

Furthermore, the optimal government expenditure is an endogenous parameter here and not a constant one, as raised by [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] or [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] (named the size of the government for these authors). The assumption made by these authors is that the marginal product of public capital is equal to one in the optimum, leading to a "constant government size". This is also due to their consideration of government flows instead of public capital, which ensures this relationship.

Proposition: In an endogenous growth framework with the Cobb-Douglas production function encompassing public capital instead of government flows, the potential productive government investment size is an endogenous parameter of economic growth and public capital productivity.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 215

The human capital sector

There is a thorough body of literature on technology diffusion where human capital is an essential element. The theoretical approaches are grounded in [START_REF] Nelson | Investment in Humans, Technological Diffusion, and Economic Growth[END_REF], [START_REF] Grossman | Quality Ladders in the Theory of Growth[END_REF] and [START_REF] Barro | Technological Diffusion, Convergence, and Growth[END_REF], while the empirical literature widely cites, as examples, the works of [START_REF] Benhabib | The roles of human capital in economic development: evidence from aggregate cross-country data[END_REF] and [START_REF] Borensztein | How does foreign direct investment affect economic growth?[END_REF]. Human capital can either be an additional factor of production (Mankiw et al., 1992) or a factor influencing technical progress in the production function [START_REF] Bentour | Do developing countries benefit from foreign direct investments? An analysis of some Arab and Asian countries[END_REF]. Either way, it will appear as an additional repressor. Therefore, we consider having a measure of the stock of human capital as an additional regressor in the production function. The production function takes the form of [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], except that here we consider the stock of public capital instead of flows of government services:

𝑌 = 𝐴. 𝐾 𝑝𝑡 𝛼𝜀 𝐻 𝑡 1-𝛼 𝐾 𝑔𝑡 𝛼(1-𝜀) (15)
where H t is human capital and the other variables are as previously defined.

The quality of public institutions

North (1990) defines institutions as "the rules of the game in a society or, more formally, [they] are the humanly devised constraints that shape human interaction". This characteristic of devised human constraints emphasizes the role of the endogenized character of institutions compared to external/exogenous factors outside human control (geography, for example). Their effects (shape human interactions) are mainly to shape the behaviour of humankind, thus directly impacting economic agents' incentives to invest and consumer choices. Following this effect on the incentives of economic agents, which affects the economic output of their actions, many authors have raised and emphasized the role of institutions in long-term economic growth and economic development [START_REF] Barro | Democracy and Growth[END_REF][START_REF] Acemoglu | The Colonial Origins of Comparative Development: An Empirical Investigation[END_REF][START_REF] Rodrik | Institutions Rule: The Primacy of Institutions over Geography and Integration in Economic Development[END_REF][START_REF] Acemoglu | The Role of Institutions in Growth and Development[END_REF]. Such a role is embedded (and hence endogenous) in different forms of dynamic interaction between economic, organizational, political and social factors [START_REF] Aoki | Endogenizing institutions and institutional changes[END_REF]. The fiscal policy sector, in general, and the public debt/deficit management issues, in particular, are very important domains of public policy that are heavily determined and impacted by the institutional framework of the country.

The institutional framework plays its role in two dimensions. The first is related to the quantitative effects of government fiscal variables, which is summarized as the dimension size via the amount of expenditure and investments allocated by the government. The second is related to the qualitative aspects of government actions, which could be summarized by the quality of institutions encompassing the effects of many areas of government reform, programmes and actions (economic freedom, justice, rule of law, order and security, enforcing contracts, protecting investors, property rights, etc.). The dimension size, proxied by the stock or flows of government Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 216 expenditure, has been embedded in models of endogenous theory, as described in Section 2.2 [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF][START_REF] Futagami | Dynamic analysis of an endogenous growth model with public capital[END_REF][START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF][START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF]. However, the second aspect of the institutions relates to their quality in its broad sense and is not easy to observe, although this plays a crucial role in shaping the effects of the institutional framework on fiscal policy input (government expenditure, government debt, deficits, etc.) and also output variables (economic growth, society welfare, income distribution, etc.).

Modelling the quality of public institutions is a challenging and complex task for economists. So, while the economic models and the endogenous growth theory struggle to clearly include the institutions' role in the production process, the task is hardly emphasized, as the political side of the institutions plays an important role that is difficult to consider. The political character of the institutions implies removing the frontiers between the two disciplines: economic science and political science. Nevertheless, some economists have attempted to include empirically the role of institutions considering the data produced on governance indicators from international institutions, such as economic and political freedom of the heritage foundation, worldwide governance indicators of the World Bank, country risk profile of the international risk country group (IRCG), business indicators of the World Bank, and so on, with fuzzy results. 108 Instead, some economists have calibrated the role of institutions to some reduced parameters.

In our case, we also limit modelling the role of institutions by considering the effect of the institutions in the production process, represented by a parameter 𝜃 ≥ 1 representing the quality of institutions. For 𝜃 = 1, the quality of institutions has no effect on the production function, which turns out to be the same as in the previous section. The production function then becomes:

𝑌 𝑡 = 𝐴. 𝐾 𝑝𝑡 𝛼𝜃𝜀 𝐻 𝑡 (𝜃-1) 𝐾 𝑔𝑡 𝛼(1-𝜃𝜀) 𝐿 𝑡 (1-𝛼𝜃) (16)
with 𝐿 𝑡 as the quantity of labour and the other variables as previously defined.

We notice that this production function exhibits constant returns to scale 109 in all its inputs as:

(𝛼𝜃𝜀 + (𝜃 -1) + 𝛼(1 -𝜃𝜀) + (1 -𝛼𝜃) = 1). For 𝜃 = 1 and 𝜀 = 0, the production function is a function of only public capital and labour.

108 As a result of the non-convincing measures and fuzzy results of considering such measures representing the qualitative dimension of the institutions, we limit our next empirical application (Section 4) to the dimension size represented by the public capital stock, for which we add human capital, as discussed in Section 3.3.4. The quality of human capital is also questioned, as the measures considered are mainly based on the educational attainments represented generally by the average years of schooling for adults. In order to compare countries based on this measure, the main assumption is that: one year acquired in a society is the same across all other societies, neglecting by this the differences between educational systems between countries. Nevertheless, we consider that those differences are reduced, as the sample of countries enjoys a nearly equivalent level of development. 109 The condition of constant returns to scale is crucial for an endogenous growth model.

The lowercase variables describe the per capita of the respective higher-case quantities, as defined previously. While the original production exhibits constant returns to scale, the normalized production function's returns to scale depend on the quantity 𝛼𝜃 as the sum of the corresponding elasticities:

-𝛼𝜃 = 1: constant returns to scale. The higher the quality of institutions, the lower the input share 𝛼 needed for producing -𝛼𝜃 > 1: increasing return to scale -𝛼𝜃 < 1: decreasing return to scale

We define 𝜌 𝑥 as the rate of return of the input 𝑥 to the output 𝑦 as the marginal rate of that input, so as:

𝜌 𝑥 = 𝜕𝑦 𝜕𝑥
. Accordingly, for public capital we have:

𝜌 𝑘 𝑔 = 𝜕𝑦 𝜕𝑘 𝑔 = 𝜕𝑌 𝜕𝐾 𝑔 = 𝛼(1 -𝜀𝜃) 𝑌 𝐾 𝑔 (18)
Similarly:

𝜌 ℎ = 𝛼(𝜃 -1) 𝑌 𝐻 (19)
And:

𝜌 𝑘 𝑝 = 𝛼𝜀𝜃 𝑌 𝑘 𝑝 (20)
From the inventory public capital accumulation, the equation assuming the inventory stock is calculated in the beginning of the period and not in the last part of the period: 110

𝐾 𝑔,𝑡 = (1 -𝛿 𝑔,𝑡-1 )𝐾 𝑔,𝑡-1 + 𝐺 𝑡 (21)
where 𝛿 𝑔,𝑡-1 is the depreciation rate of public capital accumulation 𝐾 𝑔,𝑡-1 . 110 The other alternative equation is to assume that the inventory stock is assessed at the end of the period (31 December instead of 1 January), and thus the equation changes slightly to: 𝐾 𝑔,𝑡+1 , where 𝛾 is the growth rate of the economy, the dimension size yields:

𝑔 = 𝛼(1-𝜀𝜃) 𝜌 𝑘 𝑔 ( 𝛾 1+𝛾 ) (24)
The dimension size of the state is an endogenous function of quantitative quantities related to the growth of the economy and the productivity of public capital, and to a qualitative variable representing the efficiency of human capital and the quality of government institutions. In detail:

-The dimension size of the government is a function of the economic growth rate via the term 𝛾 1+𝛾

: the impact of the latter depends on the sign of quantity . In particular, the size is a growing function of the economic growth rate if 𝜀𝜃 < 1 and the efficiency of the public capital is positive (the derivative is positive in this case).

-The dimension size is inversely dependent on the efficiency of public capital: the higher the productivity of public expenditure, the lower the size of the government. Alternatively, lower efficiency of public capital leads to a higher government size.

-The dimension size of the government is negatively related to the human capital efficiency and the quality of institutions. A high efficiency of human capital, as well as good quality of institutions, should lead to a small size of government.

Alternative equations for the dimension size:

𝜌

The government sector

The budget constraint is defined as:

𝐵 𝑡 = (1 + 𝑖 𝑡 )𝐵 𝑡-1 + 𝐺𝐼 𝑡 + 𝑆𝐺 𝑡 -𝑇 𝑡 (28)
where 𝐵 𝑡 is government bonds, 𝑖 𝑡 is the nominal interest rate, and, 𝐺𝐼 𝑡 , 𝑆𝐺 𝑡 and 𝑇 𝑡 are, respectively, government flows of expenditure on productive capital, social and security government spending, and tax revenue. The quantity 𝐺𝐼 𝑡 + 𝑆𝐺 𝑡 -𝑇 𝑡 is the primary balance (primary surplus or deficit, depending on its sign). Some authors [START_REF] Obstfeld | Dynamic Seigniorage Theory[END_REF][START_REF] Haslag | Money creation, reserve requirements, and seigniorage[END_REF][START_REF] Terra | Principles of International Finance and Open Economy Macroeconomics: Theories, Applications and Policies[END_REF] 111 add a term of seigniorage revenue, which we assume to be non-existent or negligible112 in our case.

We assume that state dependency on seigniorage revenue is likely to happen when the government fails to fulfil its financing needs for expenditure through conventional taxes or bond sales. Furthermore, the option of seigniorage (fiat money) may lead to hyperinflation, which may be selfdefeating. These conditions are of less importance in advanced economies (which are the focus of the case study of this chapter).

Dividing both sides of this equation by the nominal output production 𝑝 𝑡 𝑌 𝑡 with 𝑝 𝑡 the price deflator of real output 𝑌 𝑡 , and manipulating the left-hand-side equation term (LHS) to raise the real growth rate and inflation terms yields:

𝑏 𝑡 = 1+𝑖 𝑡 1+𝛾 𝑡 𝑏 𝑡-1 + 𝑔𝑖 + 𝑠𝑔 𝑡 -𝜏 𝑡 (29)
where 𝑏 𝑡 , 𝑔𝑖 𝑡 , 𝑠𝑔 𝑡 and 𝜏 𝑡 are the ratios to the output of public debt, government productive investment, government social and security spending and tax revenue, respectively, while 𝛾 𝑡 is the current nominal economic growth. This equation describes the law of motion in an inter-temporal balanced government budget.

The productive potential government capital and potential government debt

In this section, we link the results of the productive sector (Section 3.3.1) to the government sector (Section 3.3.2). Equation ( 14) leads to an endogenous potential government investment (which will be simulated in the first step).

Equations ( 14) and ( 17) could be jointly used to derive a potential endogenous (limit) of public debt in relation to economic and monetary conditions (economic growth, public capital productivity, interest rate). For example, [START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF] consider that the government could have a targeted potential level of debt in the long term (𝑏 𝑡-1 = 𝑏 𝑡 = 𝑏 ̃𝑡). We assume that this potential debt limit will be designated only to financing the potential government investment needs (-𝑔 ̃𝑡), while we can assume that social and security spending are financed by tax revenue; this means that 𝑠𝑔 𝑡 -𝜏 𝑡 = 0 and 𝑔𝑖 𝑡 = -𝑔 ̃𝑡 (𝑔𝑖 𝑡 is negative, as it is a financing need to be filled by the new issuance of debt; otherwise, there is a positive primary surplus and accumulating new debt is not necessary). Considering this case, Equation ( 17) yields:

𝑏 ̃𝑡 = (1+𝛾 𝑡 ) (𝛾 𝑡 -𝑖 𝑡 ) (-𝑔 ̃𝑡) = (1+𝛾 𝑡 ) (𝑖 𝑡 -𝛾 𝑡 ) 𝑔 ̃𝑡 (30)
Replacing 𝑔 ̃𝑡, as described in ( 14), leads to:

𝑏 ̃𝑡 = (1+𝛾 𝑡 ) (𝑖 𝑡 -𝛾 𝑡 ) ([ 𝛾 𝑡 1+𝛾 𝑡 ] 1 𝑟 𝑔,𝑡 + [ 𝛿𝛽 1+𝛾 𝑡 ] 1 𝑟 𝑔,𝑡-1 ) (31)
Equation ( 30) (or 31) delivers an endogenous potential (optimal/maximal/limit) debt that a country could target in the long term based on its economic fundamentals related to its potential productive expenditure, economic growth rate and interest rate. As we are considering the long term, the interest rate considered is the long-term interest rate. Note that the denominator is the difference between interest rates and economic growth. The higher this denominator, which means a higher interest rate than economic growth (unfavourable economic conditions), the lower the potential debt that a country could issue. This denominator constitutes an inertia bringing down potential debt in bad economic conditions, where interest rate spreads are higher. Inversely, the higher the growth rate, the higher the potential debt (the derivation of the potential debt to growth rate is strictly positive).

The overall average of accepted elasticities over the two periods is around 20%. This value is somewhat below the average value, which we estimated using panel data for the whole sample of the same countries. The estimated value for the panel group is around 25% and corresponds exactly to what is found by [START_REF] Barro | International comparisons of educational attainment[END_REF] panel estimations for government investment flows. Focusing on the United States' data, the elasticity is around 0.19 and 0.21 over the two periods and is very robust to data sample variations in our estimations.

A conducted robustness check generally shows that the elasticity of public capital flows for the United States varies between 17% and 0.23% following sample time variations. Furthermore, [START_REF] Hill | Optimal taxation and economic growth: a comment[END_REF] shows that the growth-maximizing size of the state varies between 9% and 29% for the United States (large interval), while [START_REF] Scully | Taxation and economic growth in New Zealand[END_REF], with a different specification to ours, reports a government size of 19% for the same country. For the countries for which government investment flow elasticities are rejected over the two periods of estimation, we can consider the average of all elasticities (0.20) as a calibrated elasticity for all these countries in the subsequent calculations. We can also adopt calibrated parameters based on similarities between countries. For the case of Japan, however, an estimation over earlier samples gives highly accepted positive but decreasing elasticities over time. Belgium also has a sensitive elasticity to sample changes. The elasticity becomes accepted starting from 1980, where we find a positive accepted elasticity of 7.6% over 1980-2015.

Inspecting the elasticities of public and private capital, we notice that higher government capital elastictities (and also higher government flow elasticities) are accompanied by lower or negative private capital (flow) elasticities or rejected private capital elasticties. This is particularly the case for countries such as Ireland, Norway, Spain and Sweden. This might be attributed to the crowdingout effect of private investment by government investment. Drawing scatter plots for private and public capital elasticities for the two periods clearly shows this tendancy. Figures 3 and4

Simulations of targeted/potential public debt ratios

Based on the results of Table 1 for capital stock elasticities, we note that there are no big differences between elasticities for the two periods (1960-2007 and 1960-2015). Therefore, to save space, we pursue our calculations considering the results of elasticities over the whole period of 1960-2015.

To conduct simulations and calculus, we decided to produce two simulated exercises. The first one is based on the estimated elasticity of each country, and the second is based on the average of all countries' elasticities (equal to 0.3).

However, for the countries for which elasticities are not accepted across the simulated period, we decided to consider only the average of elasticities as the benchmark for their elasticities. These countries are Australia, Austria, Denmark and New Zealand. Greece, over both periods, and Japan, over the period 1960-2007, although they have negative accepted elasticities, are analysed assuming these are the true elasticities. Hence, the simulation is done considering their negative elasticities 118 and the average of the elasticities (0.30). For the rest of the countries, we simulate the rest of our calculations considering the countries' elasticities and the average of countries' elasticities (0.3).

Simulation steps

-First, we use the previous government capital values' elasticities (Table 1), estimated for the period 1965-2015, to generate the "return" of the government productive investment -Second, we generate the public potential investment based on Equation ( 13)

(𝑔 ̃𝑡 = [ 𝛾 𝑡 1+𝛾 𝑡 ] 1 𝑟 𝑔,𝑡 + [ 𝛿𝛽 1+𝛾 𝑡 ] 1 𝑟 𝑔,𝑡-1
).

-To avoid high fluctuations generated by data, we use the Hodrick-Prescott filter 119 to smooth the generated potential public investment, before introducing it in the next step.

118 Having negative elasticities does not mean that this should lead to negative simulated investment. These two countries have positive simulated investment (see 119 To obtain a smooth estimate of the long-term trend component of a series, the Hodrick-Prescott filter (HP filter hereafter) is a widely used smoothing method among researchers. The method first appeared in a working paper in the early 1980s, was applied to analyse the post-war US business cycles and published later in 1997 [START_REF] Hodrick | Postwar U.S. Business Cycles: An Empirical Investigation[END_REF]. A time series 𝑌 𝑡 could be decomposed to its long-term trend 𝐺 𝑡 (a sum of growth component) and cyclical component 𝐶 𝑡 : 𝑌 𝑡 = 𝐺 𝑡 + 𝐶 𝑡 . The HP filter algorithm works to smooth the original series by estimating its trend component, while the cyclical component results as the difference between the original series and its trend. The trend component is the one that minimizes ∑ (𝐶 𝑡 )

2 + 𝜆 ∑ [(𝐺 𝑡 -𝐺 𝑡-1 ) -(𝐺 𝑡-1 -𝐺 𝑡-2 )] 2 𝑇 1 𝑇 1
, where T is the number of observations and λ is a positive parameter of smoothing that depends on the frequency of the time series. The higher the data frequencies, the larger the value of λ, and the larger λ, the higher the penalty of changes in the trend's growth rate (represented by the second term of the previous equation) and the smoother the trend component. In practice, λ is set empirically to be 1,600 for quarterly data, as suggested by [START_REF] Hodrick | Postwar U.S. Business Cycles: An Empirical Investigation[END_REF], while for annual data, λ is set to 100 in many applications, which we also consider in ours.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 230 Focusing on the long-term tendency and avoiding fluctuations seems to be in line with our focus on the long-term analysis.

-Third, we simulate the potential public debt using Equation (30) (𝑏 ̃𝑡 = (1+𝛾 𝑡 ) (𝑖 𝑡 -𝛾 𝑡 ) 𝑔 ̃𝑡).

First, generating public capital returns/productivity shows, on average, big differences between countries due, mainly, to differences in elasticities. The public capital productivity averages are widely different across countries, ranging from low values of 5% to 15% in Austria, Denmark, Portugal and Spain, and very high values of 80% recorded in countries with high values of elasticities, namely, Ireland and Switzerland (Figure 5).

Second, we simulate the potential government investment based on the public capital marginal productivity (derived from the marginal product of capital, Equation ( 13)). For comparison, we produce the descriptive statistics for both observed and simulated government productive investment (gross capital formation) and draw the averages in Figure 6. This shows that, overall, the simulated variable overcomes the actual one in all countries by about one to three percentage points, except for Japan and Greece, where the actual one is, on average, slightly above the simulated one (by 0.4 percentage points). In particular, the simulated debt ratio is double the actual one in Australia and Ireland. Figures B.3 and B.4 in Appendix B show the tendency for all countries towards actual and simulated potential government investment, respectively. 120 In all countries, government investments (actual and simulated) tend to decrease over time (Figure B.5). 120 For all figures and tables when it applies, we point to variables in the form of "Y_XXX", where Y is the variable presented (simulated) and XXX is the three-character country code. Table A.4 (in the appendix) presents these codes. Third, we simulate the results for the debt limit that a country could target, considering the previously simulated potential government investment and the conditions of economic and monetary performance, reflected by the average long-term interest rates and economic growth, respectively. Data on long-term interest rates is extracted from the OECD database. 121 We call this simulated debt "potential debt". We use the term "potential", as this is related to "potential" government investment (potential, as it is derived from the first condition of maximizing output, that is, marginal productivity of capital). It is, in fact, the optimal (maximal) public debt that a country can issue to finance its potential government productive investment and is directly related to public capital productivity (efficiency). This potential public debt is like a mirror (an opposite picture) of the actual debt. This is due to the differential between interest rates and economic growth that appears in the denominator of the potential debt with an opposite sign of the actual accumulated debt formula. This constitutes an inertia lowering potential debt when interest rates are higher than economic growth, which pushes down potential debt under actual debt, attracting the attention of policy-makers to the danger of the debt situation. The danger of public debt could be measured by the distance between simulated and actual debt. The higher this distance, the safer the debt is.

AUS

First, we consider the simulation using the growth and long-term interest rate differential average over the period 1960-2015. We produce a set of figures that show the tendencies of simulated The first set of graphs (Figure 7) presents six countries where the debt is not threatening, as we could still target potential debt that is higher than actual debt over history. These countries are Australia, New Zealand, Denmark, Switzerland, Norway and Sweden. The average potential debt to GDP is approximately 96.9% for Australia, and 100.5% for New Zealand, with lower values of around 80% for both countries. The remaining countries have higher potential average of public debt based on their performances, which are around 230% in Denmark, 250% in Switzerland, 150% in Norway and 170% in Sweden, respectively. *: countries having only two curves are those for which elasticities aren't significant, and thus we limit the exercise of simulated public debt to their elasticities as the average of all significant elasticities (0.3). Figure 8 shows a group of four non-euro area countries with floating exchange rates and largersized economies, namely, the United States, Japan, the United Kingdom and Canada. The sustainable path of the first three countries is undermined during the financial crisis. Actual public debt remains with a long history under targeted public debt until around the period of crisis (2008-10), although the two paths (simulated and observed) converge over time, showing that these countries accumulate public debt over time during the prosperity periods of the 1960s and the Great Moderation Era of the 1990s. For Japan, the formula shows negative explosive potential debt based on the average long-term interest rate and growth rate over the whole period. However, for this country, the long-term interest rate is observed over 1989-2015 only. A robustness check for countries is conducted based on their performances over certain specific periods and not the whole period. However, simulation is always produced over the whole period to visualize the track of simulated debt over the entire period.

For the other countries, the United States and Canada, although potential debt has a tendency to decrease over time to converge towards actual increasing debt, it still does not constitute a threat to public finance sustainability. However, the United Kingdom presents a different picture compared to the United States and Canada. Simulated debt is exceeded by actual debt in the year 2008 and stays under actual debt for the period 2008-15, despite an upward shift. The average potential debt ratios to target to finance potential expenditure is around 195.5% for the United States, 100.2% for the United Kingdom and 145.5% for Canada. Figure 9 presents the results for a set of euro area countries, namely, Austria, Germany, France, Italy, The Netherlands and Spain. 122 For Austria and The Netherlands, potential debt remains higher than actual debt over the whole period. However, for Italy, Spain and, to some extent, France, potential debt falls below actual debt in 2002 for Italy (with potential equalling actual around 100%), in 2012 for France (with equality in 91%) and in 2010 for Spain (with equality in around 60%). Germany also has a negative trend of potential debt approaching actual debt in around 2010 (at nearly 90%) without crossing it. Potential debt stays below actual debt at around 55% in Spain, 58% in Italy and 88% in France. Therefore, these could be the safer limits of debt (not altering growth) for these countries, and they could keep their public debt under control at lower ratios than these values. In conclusion, for this set of countries, the potential debt to target 122 As a reminder, note that Austria's estimated elasticity is not statistically significant, and the graph shows the simulated debt for Austria based on the average of elasticities equalling 0.3. Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 235 in bad times is around 60% to 90%, based on an average of their economic and monetary performances. However, in normal economic conditions, potential debt could reach more than double these values. The last group of countries (Figure 10) focuses on the rest of the eurozone countries, namely, Greece, Portugal, Ireland and Belgium. Except for Portugal, which has the same tendency for potential debt as Spain and Italy (Spain and Italy are described in Figure 9), the three other countries have different stories of their own. Belgium's potential debt goes below its actual debt in the early years of the 1980s and follows the same tendency as actual debt until 2008, where it drops and the two curves disconnect and evolve oppositely. Potential debt continues to decrease until it reaches a lower value of 68% at the end of the period.

For Greece, potential debt crosses actual debt in 1985 at a lower rate of public debt around 47% and remains with the trend of actual debt for a decade, where potential debt once again surpasses actual debt in 1995 and stays until 2002, where it drops again below actual debt (as in Italy). Potential debt continues to decrease under actual debt until the end of the period and even becomes negative starting in 2010, reaching around -10% in 2011-15. The negative number should be interpreted in the sense that Greece in this period should not hold any public debt based on its economic performance at this time.

Nevertheless, some results create serious questions about the validity of the data of interest rates, inflation, growth, and so on, used to simulate the formulae for those countries and their sensitivity to the actual data. 123 For Ireland, there are two periods where debt is unsustainable (targeted debt is below actual debt), in 1983-93 and 2008-14. However, Belgium shows an apparently unsustainable path from the 1980s. The data on long-term interest rates from the OECD database is unfortunately short samples for some countries such as Japan, where the data time series starts in 1989, and for Greece in 1998. 124 Therefore, for robustness check and to avoid the problem of data shortness, we produce estimations for potential debt, calibrating the differential of growth and interest rate in the denominator of Equation ( 30) by the data of the United States (but we leave the growth rate in the numerator unchangeable and proper to the country itself). This is also a test for our formula against some irregular observations in the data. In fact, countries such as Japan, Greece and Ireland are 124 For this purpose we checked many other international sources reporting data on interest rates for government bonds, securities and treasury bills, such as the International Financial Statistics (IFS) of the IMF, the Bank for International Settlements (BIS) and the Federal Reserve Bank of Saint Louis (https://fred.stlouisfed.org/tags/series?t=interest+rate%3Blong-term). These sources report data on long-term interest rates for different periods, depending on the country, which is the same data as reported by the OECD database. Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 238 interesting cases to study, with higher accuracy and deep investigation of the data, and even specifications to be re-estimated. Along the same lines, [START_REF] Barta | In the Red: The Politics of Public Debt Accumulation in Developed Countries[END_REF] analyses and compares the cases of Belgium, Canada, Denmark, Greece, Ireland, Italy and Japan, since the 1970s, to identify factors that differentiate countries accumulating threatening debt from those that keep their debt under control. He notes that practices in fiscal policy management make a difference rather than the political bias impact of debt accumulation, as proposed by some authors in reference to the positive approach of public debt [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF][START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF].

Figure 11 shows the results for Greece and Japan for this exercise. According to the new simulated debt for Japan, this becomes positive and high with a downward tendency until crossing the increasing accumulated debt in 2008 at the ratio of 192%. The results produced for Greece are also improved compared to its own data on interest rates, as previously explained. The intersection between actual and potential debt is materialized in 2005 at an average ratio of debt equivalent to 100%. Indeed, an IMF note on fiscal space calculating the debt limit based on the fiscal reaction function, and the interest rate growth differential, shows that the public debt dynamics are not on a sustainable path to converge to a finite steady-state ratio for the following countries: Greece, Italy, Japan and Portugal [START_REF] Ostry | Fiscal Space[END_REF]. An exercise of simulation is also conducted for all the other countries calibrating the gap (longterm interest rategrowth) by the United States one, but although the tendency changes slightly for many countries, the years of intersections between actual and simulated debt are delayed for some countries, such as Belgium, until the year of the financial crisis (the intersection using its own data is around 1982). For the United Kingdom, potential debt stays higher even in times of crisis when calibrating with the United States' interest rates, and for many other countries the average of the simulated debt increases substantially, especially for Australia, Austria, New Zealand, Belgium, France, Italy, Spain, Greece and The Netherlands. However, for some countries, such as Denmark, Sweden, Norway and The Netherlands, the average is almost stable between the two exercises, while it decreases substantially for Switzerland. The results for all the sample countries are stacked in Figure B.6 in Appendix B.

The impact of elasticity

To gauge the effects of elasticity changes, we assess the effects of three valuesthe estimated one from the model, then the one calibrated to 0.15 and 0.30 valueson potential government investment and debt (Table 3). First, we see that the impact of variation of elasticities is higher for small countries than sizeable countries. Doubling the value of elasticity (for example, from 0.15 to 0.30) leads to a decrease in simulated public debt, on average, by around three points of GDP for small countries such as Greece and Ireland. This impact is, however, contained, on average, at around 1 to 2 points of GDP for sizeable countries (the United States, Japan, Germany, France, the United Kingdom). Since the elasticity impact is not highly determinant on the results, as previously shown, we keep constant the elasticity of public capital at the average of 0.30 125 for all countries and simulate the impacts of the gap between interest rate and growth. In fact, as shown in the previous paragraph, the elasticity impact is very low on the results compared to what we will show for the differential in interest rates and economic growth. Furthermore, we focus on some countries where long-term interest rate data is available over the whole history. We choose, for example, sizeable countries, namely, the United States of America, France, the United Kingdom and Canada (Japan and Germany were excluded for reasons of data shortness on interest rates). We simulate results considering the whole period, and the two sub-periods 1960-84, as well as in the so-called Great Moderation Era, 126 1985-2015, to see the effects of the gap between interest rates and growth (the denominator in Equations 30 or 31). Descriptive statistics of long-term interest rates and economic growth for these countries are displayed in Table 4. We note that the difference between long-term interest rates and economic growth is higher in the period 1960-84 than in the period 1985-2015. 125 We should remember that this is the average of the significant estimated public capital elasticities over the sample of countries. Fixing the elasticity for all countries to a common value allows comparison of the countries' results based on the impact of the interest rate and economic growth gaps alone. 126 The Great Moderation Era is first described by [START_REF] Stock | Forecasting Output and Inflation: The Role of Asset Prices[END_REF] analysing, over the period 1960-2002, the United States quarterly GDP volatility, shown to be highly reduced after 1985 compared to the previous period. This tendency of output and price stability is mainly attributed to the macroeconomic stabilization policies followed by independent central banks [START_REF] Bernanke | The Great Moderation[END_REF]. Some economists argue that this period came to an end in 2007 with the 2008 financial crisis, while others argue that the GDP volatility averages are still lower than pre-1985, assuring the continuity of the Great Moderation Era [START_REF] Clark | Is the Great Moderation Over? An Empirical Investigation[END_REF].

The effects of interest rates and economic growth differences are produced in Table 5 and Figure 11. Overall, there are sizeable and substantial effects on potential debt for the four selected countries. The averages of simulated public debt, over the period 1960-84 (Scenario 1), is around 168% for the United States, 118% for France, 78% for the United Kingdom and 135% for Canada. These averages are, respectively, higher in the Great Moderation Era, 1985-2015 (Scenario 2), by around 38 points of GDP in France, 52 points in the United States, 57 points in the United Kingdom and 20 points in Canada. For the whole period, the averages of simulated debt are 137% in France, 195% in the United Sates, 100% for the United Kingdom and 145% for Canada.

Discussion

Contrary to the second chapter, where we adopted a short-term approach assessing the impact of the presence of public debt on GDP via the effects on the fiscal multipliers, as well as the interaction with the business cycle and other economic variables, this chapter has adopted a longterm approach based on an endogenous growth model to assess the relationship between public debt and economic growth. Economists (classical and new classical) adopting this approach generally try to avoid the role of empirical estimations and data in their calculations (adhering to the [START_REF] Lucas | Econometric policy evaluation: A critique[END_REF] and [START_REF] Sims | Money, Income, and Causality[END_REF] critiques). They prefer calibration to estimation and argue as if all economies are in the steady state in the long term, which is not necessarily true. Furthermore, calibration is another way of deriving parameters that are under the control of economic theory and do not necessarily reflect the behaviour and data-generating process proper to each country. Furthermore, the results of the calibrated models are theoretical and not so easy to interpret by the policy-makers. In our case, we judge it useful that countries are not necessarily in the steady-state path and hence considered in transitional dynamics, even in the long term; we prefer to run estimations in the long term, being suitable for the approach of endogenous theory, and we stay away from calibrated elasticities. The only calibrations adopted in some variables are based on data averages.

Chapter 1 of this thesis reported detailed literature on the public debt threshold, which reported different numerical thresholds revealing sensitivity to the countries' sample (for panel regressions), to the period and the country on individual levels (for single-country regressions).

The importance of the debt limits has already been taken into consideration before the recent financial crisis, first by the Europeans in the establishment of the European Monetary Union (Maastricht criterion of 60%), and by multilateral institutions in designing their loan programmes, especially the International Monetary Fund and the World Bank institutions. These Breton Woods Institutions designed an approach called debt sustainability analysis (DSA) for low-income countries (LIC) and market access economies (i.e. emerging economies and advanced economies). This practical framework became operational and was applied especially to LIC in 2002 (IMF andthe World Bank, 2005, 2013). However, since the 2008 crisis, this approach is permanently revised and has been updated to include other highly indebted countries, which is the case for advanced countries (IMF, 2013). The DSA is a kind of stress test for debt sustainability based on limits of some important financial indicators, namely, bond yield spreads, external financing requirements (as a percentage of GDP), public debt held by non-residents (share of total), public debt in foreign currency (share of total) and annual change in the share of short-term public debt at original maturity. A safer benchmark gross government debt of 60% and 70% of GDP was calculated for the groups of emerging countries and advanced countries, respectively. The 70% limit was able to reach 85% for the group of advanced countries. This threshold is less than the 90% threshold that fits all countries suggested by [START_REF] Reinhart | Growth in a time of debt[END_REF].

In this section, we compare our results with some results produced in the recent literature that have adopted modelling techniques derived from economic theory, although the approaches differ. Some papers that conclude debt limits, and then the fiscal space defined as these debt limits minus actual debt, are influential and have important policy implications [START_REF] Ostry | Fiscal Space[END_REF][START_REF] Ostry | When Should Public Debt Be Reduced?[END_REF][START_REF] Ghosh | Fiscal Fatigue, Fiscal Space, and Debt Sustainability in Advanced Economies[END_REF][START_REF] Pienkowski | Debt Limits and the Structure of Public Debt[END_REF]. For many of these researchers, the debt limit is assessed around the period of the financial crisis of 2008/2009. Therefore, to compare our results with those raised by some authors, we limit this comparison to a very short period or a specific year of comparison (for example, around the 2008 financial crisis).

Returning to our earlier results, Table 6 shows the average limits over the crisis period, 2009-12, for the 20 countries in the sample. The second column shows observed average debt over the period 2009-12, the third, fifth and seventh columns show, respectively, the averages of simulated potential debt over the same period considering the economic performances proper to each country (Potential1), then simulation based on the calibration of economic growth and long-term interest rates to the Great Moderation Era (1985-2015) performances (Potential2), and the simulation calibrating long-term interest rates and economic growth to those of the United States for all countries (Potential3). The other columns, Gap1, Gap2 and Gap3, present the difference between the previous simulations (Potential1, Potential2 and Potential3) and observed debt (actual), respectively. When actual debt overcomes simulated debt, the gap is negative, and the country should curve the accumulation of debt by rapid de-leveraging.

A negative gap over the years of the financial crisis (2008-12) is recorded for Belgium, the United Kingdom and Spain, and highly negative for Japan, Greece and Italy (Gap1). Portugal, Germany and France also recorded very low but positive gaps. Considering the Great Moderation Era, Gap2 is negative for Portugal, in addition to the previous countries cited for Gap1, except the United Kingdom and Japan. The latter recorded high potential debt in contrast to high negative potential debt for Gap1. Considering the third simulation, Greece, Italy, Japan and Portugal are countries Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 244 with worrying debt, even considering the United States' benchmark for economic growth and interest rate performances. However, some countries' potential debt has significantly increased in this simulation. This is the case for Australia, New Zealand, France, the United Kingdom, Spain and, to a lesser extent, Germany. Other countries, however, have seen their potential debt decrease in this last simulation, namely, Austria and Switzerland. In the same way, [START_REF] Ghosh | Fiscal Fatigue, Fiscal Space, and Debt Sustainability in Advanced Economies[END_REF] use the approach of [START_REF] Ostry | Fiscal Space[END_REF] to calculate the debt limits for advanced countries and to produce a fiscal space defined as the difference between that debt limit and the actual debt-to-GDP ratio, based, in particular, on the interest rate and economic growth differential and considering the primary balance. They find that Greece, Italy, Japan and Portugal have no fiscal space as their debt is unsustainable. However, the other countries have enough fiscal space, especially given that the assessed debt limits range from minimum values of 152% and 154% for Canada and Germany, respectively, to high values of 246% and 263% for Ireland and Norway, respectively. For the set of countries with positive fiscal space, the latter values are around low values of 50% to 70% recorded for the United States, Ireland and Belgium, medium values from 75% to 100% recorded for the United Kingdom, France and Germany, and higher values of higher than 100%, especially in northern countries (Norway, Sweden and Denmark) and Australia and New Zealand. These results are generally in line with our results in Table ( 6).

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 245

The same exercise was updated by the international rating agency, Moody's, adopting the same approach as [START_REF] Ostry | Fiscal Space[END_REF] and [START_REF] Ghosh | Fiscal Fatigue, Fiscal Space, and Debt Sustainability in Advanced Economies[END_REF], to calculate a distance to debt limit for a sample of advanced and emerging economies. The sample of countries also covers the 20 advanced countries that we studied in this chapter, in addition to other countries. The results are reproduced in [START_REF] Ostry | When Should Public Debt Be Reduced?[END_REF] in a figure summarizing these distances to debt limit, which are reproduced in Figure 13. The latter indicates that Japan, Italy and Greece have zero fiscal space, which was also confirmed by our results in Table 6 (Gap1). Belgium, Spain and the United Kingdom also report negative differences between potential debt and actual debt in Table ( 6), concordant to some extent with Moody's results, where fiscal space is very low, except for the United Kingdom. Our results (Table 6) also show that Switzerland, Austria, Sweden, Denmark, Australia, Norway, New Zealand, The Netherlands, The United States and, to some extent, Ireland and Canada have safer potential debt higher than actual debt, while France, Germany and Portugal have average potential debt approaching actual debt. These results are also generally in line with Moody's calculations, as reported in [START_REF] Ostry | When Should Public Debt Be Reduced?[END_REF], which are reproduced in Figure 13. Note: For comparison purposes, distance to debt limit, as defined in [START_REF] Ostry | When Should Public Debt Be Reduced?[END_REF], is reproduced and reported for our sample jointly with the distance from actual to potential debt calculated by our method (Gap1 in Table 6). For negative Gap1 (potential tolerable debt below observed debt), we report zero instead of negative numbers. In another IMF paper [START_REF] Pienkowski | Debt Limits and the Structure of Public Debt[END_REF], the debt limit for advanced countries is found to be 137% of GDP. This debt tolerance can be enhanced by issuing GDP-linked bonds, which can increase this limit to 238% of GDP for all advanced countries (when the bonds issuance is 100% linked to GDP). The author concludes that this linked debt to GDP clearly shows that there is no one-size-fits all, which endorses our results.

Another important point revealed in this chapter is the effects of the interest rates and economic growth differential (gap) in shaping the curve of potential public debt over time. The effects are higher on potential public debt in the Great Moderation Era (1986Era ( -2015) ) than in 1960-85. This is due to the gap being higher, on average, in the 1960-85 period and narrowing in the Great Moderation Era (Table 4). This latter period is characterized, on average, by lower interest rates, but also lower economic growth compared to 1960-85, which makes the differential between longterm interest rates and economic growth lower than the one in 1960-85, as revealed in Table 4. As a consequence of lower interest rates, the Great Moderation Era has played a bigger role in the accumulation of public debt that countries nowadays struggle to decrease (Cecchetti el al., 2011).

A recent debate was triggered by [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] assuming that, on average (opposite to the case here for long-term interest rates), interest rates are lower along history than economic growth, which makes debt safer in advanced economies and means that there is nothing to be concerned about. Some economists interpreted this as an appeal for fiscal expansion and avoiding fiscal austerity. More details of this debate are presented in the Chapter 2, as well as a recent discussion about the type of interest rates by [START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] in his analysis.

The third result is that potential government investment to GDP ratios are, on average, higher than the observed government investment ratios, and they tend to decrease over time. This may indicate that, first, countries are not reaching their potential productive investments, and, second, that the issued public debt may drift from financing productive capital to other government expenses as an enhancement of the welfare state needs and ageing population expenditure. In fact, the size of social spending in OECD countries increased from 18% in 1980 to 26% in 2014 [START_REF] Alesina | The Political Economy of Government Debt[END_REF].

Despite the importance of such results, some caveats should be considered, and future development could enhance the results of our approach. First, we assumed that potential debt is only issued to finance potential public capital derived by the model, while the finance of the other current government expenditure is supposedly filled by collecting taxes. This may have led to generating simulated higher potential public debt, which stays high, above actual debt, especially in good times for many countries. However, tax revenue is not sufficient to compensate the financing needs of total expenditure. For example, according to the OECD database website, tax revenue in France was around 45% of GDP in 2015 (above an average of 34% for OECD countries), while general expenditure stood at around 57% (social expenditure 43% plus social protection 14% In this chapter, the adopted theoretical framework of the Cobb-Douglas production function has focused on the long-term approach to simulate the potential debt that a country could target without undermining its public finances. However, this long-term approach omits the short-term effects of fiscal policies, which are highly determinant in public debt management. The framework of endogenous growth models could be suitable for long-term analysis, while debt related to fiscalpolicy short-term effects is omitted. Furthermore, we derived potential debt from potential public productive investment, neglecting the effects of other public expenditure such as social spending in education, justice, health, and so on. In fact, as stated by [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF], "The productive public spending can be thought of as encompassing very different types of publicly provided goods and services, such as justice, enforcement of law and contracts, police services, educational services and government research activities". Social spending in education, health, justice, and others, is to enhance human capital, and to create qualified political and economic institutions, which develop the business environment. The rule of law and order, as well as security, are also crucial determinants ensuring stability for the business environment. Taking this into consideration, it is highly recommended to consider the effects of such categories of expenditure and to analyse their impacts on economic growth in both the short and long terms.

Conclusion

Contrary to the first chapter, which examined the purely statistical-econometric relationship between economic growth and public debt, albeit with advanced econometric tools (Hansen's regression kink method), this chapter has extended the investigation to the role of theory-based models, taking into consideration country-specific fundamentals. Therefore, the chapter first surveyed the effects of public debt on economic growth in different classes of theoretical and empirical public debt models (OLG, ILA, endogenous growth models, new Keynesian DSGE models, and the normative versus the positive approach). In the second part, an endogenous model was applied to the sample studied in the first chapter, made up of 20 developed economies.

Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt

248

In this model, we simulated a parameterized formula for a potential/limit debt that a country could target to finance its productive investments. These limits, linked to economic growth and public capital productivity, as well as the interest rate, are dynamic, country-and time-specific and tend to evolve contrary to actual accumulated public debt. Simulated public debt, in particular, drops under actual levels of debt in times of crisis, especially for many advanced countries severely affected by the crisis. This sends a clear message of policy recommendation that countries are safe from the danger of public debt as long as potential debt (simulated/targeted) stays higher than actual public debt. The results show that many countries are under the stress of public debt, especially after the financial crisis of 2008. For countries such as Ireland, this stress is short-lived, and potential debt quickly remains higher than actual debt following the redressing in economic activity a few years after the crisis. However, for many other countries, the effects are prolonged.

The results also revealed that countries such as Greece, Belgium and, to some extent, Italy, had problems of accumulated debt, in the early 1980s for the two first countries, and the early 2000s for Italy.

The potential (limit) public debt is country-specific and evolves contrary to actual accumulated debt over time. Indeed, it moves in line with the public capital productivity trend, which historically tends to decline while actual public debt is rolling over. The story of the debt limit was intensely debated at the forefront of the 2008 financial crisis. The different results found in the literature supporting the debt limit existence, whether for all countries (or at least for countries of the same level of development), or case-specific countries, tend to discuss the threshold debt generally, as a one-size-fits-all for countries, whether determined endogenously or set exogenously. However, the added value of the present work is that the debt limit is an endogenous parametrized function linked to the economic returns (productivity) of public capital financed by such issued debt. Another point to note is that, although we found that the endogenous debt limit, whenever it exists, is country-and time-specific, using [START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] regression kink method in the first chapter, this chapter added the finding that potential debt limits are determined yearly based on the country's principal macroeconomic fundamentals. -Governments have a one period maturity.

-Debt pays the current interest rate.

-Taxes are lump-sum.

-Debt labor ratio is kept constant.

-Domestic debt raises interest rate and lowers utility in the efficient case.

-Results for the inefficient case depend on the existence of the foreign debt with domestic debt.

-Foreign debt widen the gap between the interest rate and growth, lowers utility in the efficient case.

-Results for utility are mixed for the inefficient case. Debt Swap has the same effects. -The model's hypotheses are mainly based on the [START_REF] Samuelson | An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money[END_REF] and [START_REF] Diamond | National Debt in a Neoclassical Growth Model[END_REF] models' assumptions.

-Government bonds effects on the interest rate and utility does not necessarily hold and depends especially on the existence of operative altruistic links (bequest motives) between generations.

-Intergenerational transfers guarantee debt-neutrality as the debt-for-tax swap does not affect the resource allocations and interest rates of the current generation.

Blanchard (1985) ILA

-A finite lived agents' horizon.

-Studies the effects of debt and deficit accumulation.

-Design an "index of fiscal policy" capturing the effects of current and expected fiscal policy.

-Taxes are lump-sum.

-Constant probability of death.

-Debt increase (in the steady state): changes the foreign assets in agents' wealth in an open economy, and, decreases the level of capital and consumption in a closed economy.

-Taxes decrease: raises wealth and consumption. Effect is larger the longer taxes are shifted to future generations. Debt and taxes increases create an initial wealth effects on consumption, leading to capital decumulation which makes capital and consumption lower in the new steady-state level.

Aiyagari (1985) OLG

-Use a modified version of the OLG model of Samuelsson (1958).

-Assess the Ricardian equivalence validation.

-Enabling changeable interest rate to deficit policy regimes.

-Taxes distributed differently across heterogeneous agents.

-Ricardian equivalence validation depends on the way taxes are distributed among agents and not on the length of the lifetime horizon. The debt-neutrality holds if the tax distribution does not change agents' wealth allocations. A higher level of spending can be financed by debt at an unchanged interest rate, if taxes' distribution maintains wealth distributions.

Buiter (1988) OLG

-The model is based on the Yaari-Blanchard models.

-Evaluates the effects of government bonds on economic agents' wealth.

-Private consumption behavior is modelled following [START_REF] Yaari | Uncertain lifetime, life insurance, and the theory of the consumer[END_REF] and [START_REF] Blanchard | Debt, Deficits, and Finite Horizons[END_REF] approaches.

-The equilibrium is independent of the pattern of the public debt and lump-sum taxation over time.

-The difference between expected government tax base and the future tax base of the current individuals explains the lump-sum taxation variations over time. Agents not linked to the future generations by bequest transfers omit their successors' resources from their budget constraint.

-Debt-neutrality holds if and only if the population growth and the probability of death sums to zero. Under this condition, a non-zero labor productivity rate will not destroy this debt-neutrality.

Weil (1989) ILA -A model of "overlapping families of infinitely lived agents", aims to show that: 1 st , the "infinite lifetime horizon" assumption do not necessarily imply debt-neutrality; 2 nd , the "finite horizons" don't necessarily violate debt-neutrality.

-Assumes new cohorts over time, and new families aren't linked to the existing by transfers.

-Operative transfers between some but not all agents result in partial linkages leading to infinite economic horizon.

-Agents' infinite lifetime is assured by the arrival of the families who are not linked by transfers.

-The equilibrium interest rate hinges on the government financing decision (government bonds by levying lump-sum taxes in this case) and speed of new arrival cohorts/families.

-Government bonds increase the equilibrium interest rate for a positive non-zero population growth rate: expected taxes to pay the issued debt are compensated by generations that are not yet born and are not considered by the current generations.

The real interest rate must hence rise to maintain aggregate consumption at its marketclearing level. Infinite lifetimes are so not inconsistent with the violation of the debtneutrality assumption. Also, finite horizons do not necessarily violate the latter. [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] EGT -Aims at establishing the effect of public spending and government debt policies on utility and long-term growth in a perspective of endogenous growth theory.

-The model studies a closed economy with infinite lifetime agents and intertemporal preferences modelled by a utility function.

-Adopts an AK modeling framework assuming constant returns to scale and including the flows of public services as input in the production function.

-Argues that private inputs are not a close substitute for public inputs as some public activities are difficult to be insured by private firms (defense, law and order), or the service is non-rival (ideas), or as external effects cause lower private output (basic education).

-Assumes timely balanced-budget.

-In case of a Cobb-Douglas production function, -The two effects cancel for the optimal government size equalizing government expenditure to tax rate and the share of the capital ( 𝑔 𝑦 = 𝜏 = 𝛼). The growth rate function of the government size is an inverted U curve: for a government small size, raising expenditures' effect dominates raising tax rate's effect, while for a large government size, the negative effect of taxes on growth dominates.

-Maximum utility corresponds to same conditions maximizing growth if the elasticity of substitution of 𝑦 to 𝑔 = 1.

-In non-Cobb-Douglas case: maximum growth depends on the elasticity of substitution between public services and private capital and, the relative size maximizing utility exceeds the one maximizing growth rate if and only if the magnitude this elasticity substitution is superior to 1.

Futagami et al. (1993) EGT

-Same approach as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF].

Study the effect of public capital stock (instead of government services flows) and public debt policies on utility and growth.

-Adopts an AK modeling framework.

-The model includes the stock of public capital as an input in the production function.

-Assumes timely balanced-budget.

-Public investment stimulates aggregate production indirectly via the accumulated stock instead of flows as does [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF]. The introduction of the productive public stock allows dynamic transitional effects analysis instead of being restricted to the steady state analysis as in [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF].

-Tax rate maximizing economic growth rate is higher than the one maximizing utility. [START_REF] Corsetti | Optimal Government Spending and Taxation in Endogenous Growth Models[END_REF] EGT -Multi-sector model encompassing productive public spending to assess optimal fiscal policy in the approach of endogenous growth models.

-Incorporate a separate human capital accumulation as a second sector.

-The production function is a Cobb-Douglas with physical capital, human capital and flows of public goods.

-Assume unbalanced budget constraint allowing government borrowing/lending.

-4 models are derived depending whether: public spending as input in the output sector, affects the productivity of capital (model 1); affects the productivity of human capital (model 2); or public spending as input in the human capital sector, affects respectively the same previous variables (models 3 and 4).

-Distinguish an optimal tax rates on both types of capital under different assumptions on technology and distribution and analyze the welfare properties of public debt and assets.

-If the government spending is an input in the production function only (not in the human sector), the optimal choice of the government spending leads to a constant ratio of expenditures to output in every time independently of the tax policy. This ratio is less than the one found by [START_REF] Barro | Government spending in a simple model of endogeneous growth[END_REF] ( 𝑔 𝑦 = 𝛼(1 -𝜀) < 𝛼 𝑎𝑠 𝜀 > 0). In model 1, the optimal tax on human capital is zero and the one on physical capital is positive. This result is inverted in model 2. In both models (1 and 2), a government optimal choice of both government spending and tax rates leads to an instantaneous balanced budget and the optimal public debt is zero. -Aim at analyzing the optimal response of government debt to shocks focusing on the type of the involved timeinconsistency policy.

-New Keynesian framework based on [START_REF] Christiano | Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy[END_REF] and [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF].

-Assume sticky prices in the short run.

-Expenditures are financed by nondistortionary taxes and or by issuing only nominal risk-free debt.

-Optimal public debt would follow a random walk path if the government can achieve a time-inconsistent policy commitment. Under the assumption of price stickiness, the government (social planner) chooses to rely more heavily on changes in income tax rates rather than using surprises as a shock absorber of unexpected innovations in the fiscal budget.

-The distortions introduced by tax changes are diminished by spreading them over time which induces a near random walk property in tax rates and public debt.

Leith and Wren-Lewis (2013) NKT -New Keynesian models augmented by the government's budget constraint.

-Aim at analyzing the optimal response of government debt to shocks involving time-inconsistency policy and its implications for discretionary policies.

-New Keynesian (DSGE) framework based on [START_REF] Christiano | Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy[END_REF] and [START_REF] Smets | Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach[END_REF].

-The model assumes sticky prices in the short run.

-Public spending is financed by distortionary taxes and/or by debt.

-Optimal pre-commitment policy allows debt to follow a random walk path in the steady state.

-However, under sticky prices framework, government is tempted to use its policy instruments to change the steady state level debt in the initial period. Debt is curved to initial efficient steady state to encounter this temptation and thus deter the public debt to follow random walk path if following shocks; the new steady state debt equates the original (efficient) debt level despite there is no explicit debt target in the government's objective function. Debt stabilization instruments depend on the degree of nominal inertia. The size of the debt stock and welfare consequences of introducing debt are negligible for pre-commitment policies but can be significant for discretionary policies. -Large government debt in steady state impact the sign and size of short/medium run fiscal multipliers, depending on the horizon's evaluation of these multipliers.

-Presence of dynamic interactions between inflation and debt level in real terms (absent in standard New Keynesian models where debt is set to zero in the steady state).

-In the case of permanent debt, the fiscal policy effect becomes difficult to predict over time. [START_REF] Persson | Why a Stubborn Conservative would Run a Deficit: Policy with Time-Inconsistent Preferences[END_REF] PAD -A principal-agent problem, aiming at comparing the policy of a conservative government, certain of been succeeded by a liberal government, to the policy where he is certain of his reelection. The level of public debt is an instrument of the current government to control the rival future government.

-Two-period perfect-foresight framework, -Assume the ruling government is certain that he will be succeeded by a liberal government. Assume homogeneity of governments' preferences towards all public goods but different preferences for different levels of the same public good.

-A conservative government may borrow more if he knew that he will be succeeded by a liberal government than it would do once certain of remaining in power in the future; A conservative government will collect less tax and leave more public debt than what the successor would prefer.

-This raises the ruler government consumption than it would be if he will stay in the government, while the successor with high debt and constrained resources reduces consumption than it would be if he runs solely. Thus, the time-consistent level of government consumption is somewhere in between the two outcomes of what each of the two governments would prefer if ruling on his own.

Alesina and Tabellini (1990) PAD A political/positive theory of debt aiming at understanding the debt buildup and deficits in several industrialized economies Explicitly, they compare the outcome of debt accumulation and deficit in situation where governments alternate versus an outcome resulting from a social planner government supposed elected forever.

-Assume uncertainty about the nature and spending behavior of succeeding governments.

-Assume different preferences for different items of public spending and a constant population of identical individuals with the same time horizon.

-Individuals differ only by their preferences for public goods, supplied by the government and financed by means of distortionary taxes on labor.

-Government is elected among two parties maximizing each the electorate utility function.

-Differences in political institutions, leading to different debt policies, help explain debt paths over time and across countries. Debt accumulation and deficit are emphasized by the alternation of the elected governments. Disagreement of different governments on the structure of the spending results in a deficit bias and an accumulation of debt higher than it would be in case of a social planner.

-The debt left to the last period is larger in a democracy than with a social planner.

-The electoral uncertainty creates a sub-optimal deficit bias. This bias is stronger for the party with the smaller probability of reappointment". The equilibrium level of government debt is higher; 1/ the higher the degree of polarization between alternating governments and 2/ the more likely the current government will not be reelected. Moreover, as the ruling government is unable to curve the taxation and expenditure policies of its successors, the law of motion of the public debt is the only way by which the fiscal policy of the ruling government can impact the policies of its successors. [START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF]2012;2015;2016) EGT -2007: Endogenous growth model with public capital and sustainable debt.

-2012: Endogenous growth with elastic labor supply and a government sector.

-2015: Endogenous growth model with productive public spending.

-2016: An endogenous growth model with public educational spending -2007: Assume the ratio of the primary surplus to gross domestic income to be a positive linear function of the debt ratio.

-2012: Government levies distortionary income tax and issues bonds to finance lump-sum transfers and non-distortionary public spending.

-2015: Rational identical households with perfect foresight maximizing their utility.

-2016: Same assumptions as in [START_REF] Greiner | Public Debt, Productive Public Spending and Endogenous Growth[END_REF].

-2007: The model is used to derive necessary conditions for the existence of a sustainable balanced growth path and analyze growth effects of deficit financed increases in public investment.

-2012: The long-run growth rate is smaller the higher the debt ratio whenever public spending is adjusted to fulfill the government inter-temporal budget constraint.

-2015: Higher debt goes along with smaller long-run growth. Moreover, discretionary policy violates the intertemporal government budget constraint along a balanced path.

-2016: Balanced budget policy and a slight deficit policy yield higher growth than a policy where debt and GDP grow at the same rate. For high debt and low elasticity of substitution, a high deficit policy yields lower welfare than a balanced budget and a slight deficit policy.

Maebayashi et al. (2017) EGT

-Consider a stock of capital investment in endogenous framework.

-Examine how reducing public debts in the economy with large public debts affects transition of the economy and welfare.

-Builds on [START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF] assumptions but instead consider public capital not flows as input.

-Assume the depreciation rate of public capital is zero.

-Derive an optimal target debt ratio that depends on the tax rates on wage income and consumption, and the ratio of public investment to total spending. Fiscal consolidation based on a debt ratio target rule improves welfare and this improvement is more the fastest the pace of debt reduction is.

-Fiscal consolidation based on expenditure cuts jointly with a tax increase does not always improve welfare. In this case, the welfare gains (if any) are lower than those under expenditure cuts only.

Mankiw (2000) SST

-A critic of ILA and OLG models and alternative theory mentioned as "Savers-Spenders Theory of fiscal policy" to address the neoclassical shortcomings considering that "households smooth their consumption over time" is inaccurate as many consumers are far from following complete rational expectations.

-Assume the role-of-thumb behavior (non-Ricardian) in the consumers spending.

-Some individuals may enjoy long lifetime horizons (due to bequest motives) while others having short time horizons fail to smooth their consumption and accumulate wealth.

-Even if debt does not affect the steady state capital stock and income, it disrupts the income distribution and consumption leading to raise inequality between spenders and savers. A higher level of debt yields higher taxation to compensate for the interest payments on the debt. But taxes are on both savers and spenders while interest payments on debt fall on the savers side. Thus, a higher level of debt increases the steady sate income and consumption for savers and lowers it for the spenders which raise inequality between the two groups.

-Many agents have no saving (data fact), so unable to smooth intertemporal consumption as reported by the ILA or OLG models. A better model would allow for such heterogeneous behaviors.

Chari et al. (2009) CNK

-A critic to the New Keynesian models based on the study of Smets and Wooters (2007) core model.

-Critics based on the examination of Smets and Wooters (2007) properties and assumptions.

-New Keynesian models are not yet useful for public policy analysis. These models include many free parameters yielding to shocks that are dubiously structural as well as many features that are not consistent with microeconomic evidence.

General Conclusion

The aim of this thesis was to examine the relationship between public debt and economic growth, particularly the impact of the former on the latter. Although this issue was mainly debated in the post-war era, leading to a variety of theoretical models involving the long-term effects of public debt, as well as the short-term effects, the debate about this subject was revived for the advanced countries following the 2008 crisis. This thesis re-examined, first, the validity of [START_REF] Reinhart | Growth in a time of debt[END_REF] conjecture of a common debt threshold, which stated that debt to GDP ratios above 90% reduce economic growth for a sample of advanced countries, thus creating a controversial debate among economists and policy-makers. Second, it assessed the short-term and, third, long-term effects of public debt on economic growth.

At this level, the methodology used the most recent advanced econometrics methods, focusing on the relationship between the two variables, based purely on the data-generating process and comparing it to a large body of empirical literature on this issue that flourished after the 2008 crisis (Chapter 1). Then, the relationship was analysed considering the economic channels through which public debt acts on economic growth, first, in the short term (Chapter 2) and, second, in the long term (Chapter 3). In the short term, as public debt is generated to finance government expenditure (including government investments), the public debt and economic growth linkages were examined by adopting a fiscal policy assessment framework invoking the expenditure multipliers.

In the long term, public debt and economic growth are linked by adopting a theoretical framework of endogenous growth models.

The principal conclusions of our thesis lead us to reject the common debt ratio that applies to all countries for a sample of 20 advanced countries. It shows, specifically, that the relationship between public debt and economic growth is rather time-and country-specific. Furthermore, in a short-term framework, public debt accumulation and contraction have different impacts on economic growth through expenditure multipliers. The latter are also revealed in our thesis to be sensitive to other factors related to the business cycle (expansion, recession), the public debt ratio development (accumulation, contraction) and the coexistence of cross-cutting of these factors. In the long term, public debt is linked, in the context of the endogenous growth framework, to the macroeconomic fundamentals and public expenditure's productivity.

Specifically, Chapter 1 made important contributions to the empirical debate about a common public debt threshold that applies to all countries. Without claiming exhaustivity, this chapter summarized a large survey covering the main body of important empirical literature econometrically studying the relationship between public debt and economic growth, following the controversial paper of [START_REF] Reinhart | Growth in a time of debt[END_REF]. Furthermore, the empirical contribution of Chapter 1 focused particularly on analysing a sample of 20 advanced economies, including 10 euro countries, considering a long period of analysis that goes back to 1880. In the first step, we ran a variety of panel regressions for an economic growth function as a quadratic polynomial of the public debt ratio following [START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF]. In the second step Chapter 1 addressed the debt-growth link with a novel and innovative approach for individual countries using the Hansen (2017) "regression kink" method. This method has the power to detect endogenously the turning point between explained and explanatory variables compared to models fixing the exogenous threshold.

For the panel regressions, we used appropriate methods of estimations and tests to deal with several econometric issues such as endogeneity, sample bias, heterogeneity, non-linearity and reverse causality. Panel estimations were conducted varying the country sample, as well as considering sub-periods of time, by break points following world events occurring in the international system. All these analyses show that the debt-growth nexus changes widely over time and by sample countries. Furthermore, the revealed relationship is altered by data and cross-country heterogeneity. The heterogeneity decreases when omitting sizeable countries from the sample and is less manifested in the sample of 10 euro countries.

Applied to the debt and growth relationship by country, the regression kink method sorted out a variety of different curves depending on the country. Therefore, some countries could grow with high debt to GDP ratios, others could see their growth shrink from low debt ratios, while growth in others was insensitive to public debt. The study also reveals the instability of the relationship over time. Every country exhibits a different relationship by period, especially when the transition is between periods known for specific changes in the international monetary system. All of the results in Chapter 1, whether panel regressions or Hansen (2017) regression kink, stand in contrast to the existence of a common threshold and its 90% value, as claimed by [START_REF] Reinhart | Growth in a time of debt[END_REF]. It not only argues against the 90% threshold value but also clearly rejects any common threshold. The threshold, whenever it exists, is country-specific rather than following a common rule to fit all. Consequently, as the public debt and economic growth relationship is country-specific (one size does not fit all), the main recommendation of Chapter 1 is for more investigation using models based on theory to study the effects of public debt on economic growth considering the economic properties and fundamentals.

Chapter 2 was dedicated, in particular, to examining the relationship between public debt and economic growth in the short term, through Keynesian multipliers. Specifically, we studied the impact of public debt accumulation on the size of the expenditure multipliers, as well as the effects of the business cycle. We adopted, in this chapter, the structural vector autoregressive (SVAR) methodology, running a panoply of bi-variates and tri-variate SVAR models on quarterly data for a sample of 18 OECD countries with different exchange rate regimes, monetary policies and degrees of openness. Besides, we estimated an SVAR with six fiscal and monetary variables for the United States to highlight the channels by which public debt affects economic growth. In all the above-mentioned SVAR models, we controlled for business cycle and public debt movement effects to deduce spending multipliers for these cases.

The results show that, controlling for business cycle effects, the expenditure multipliers are much higher in times of recession than times of expansion. Moreover, our results do not support the general tendency of spending multipliers being weak, and even negative, as revealed by some researchers, in recent decades compared to the 1960s, 1970s and 1980s. The previous results are in line with what was observed in the recent literature regarding fiscal multipliers, in advanced economies, namely, being large in times of recession and weak, or even negative, in times of expansion. Furthermore, controlling exogenously for public debt movements, independent of the business cycle, it was revealed that spending multipliers are larger in periods of debt accumulation than in debt contraction periods. Also, jointly controlling exogenously for debt movements and the business cycle reveals that multipliers are higher under debt accumulation in cases of expansion and recession. However, introducing endogenously the public debt to GDP variable in an SVAR leads to higher multipliers in recessions than expansions.

Furthermore, the main results of the United States model show that government expenditure has positive but short-lived effects on economic growth. Furthermore, the public debt crowds out private investment, leading to a lowering growth rate in times of expansion, while in times of recession the public debt effects on growth are positive. This crowding-out effect may play passthrough to the expenditure multipliers and could explain, ceteris paribus, the weak size of spending multipliers, while in times of recession the crowing-in effect leads to higher multipliers.

In the panoply of SVAR models considered in Chapter 2, it was noted that recession periods generally have a persistent effect on variables for which convergence to the long-term path following the shock is achieved more slowly compared to expansion time. The policy implication of this is that fiscal stimulus effects could take time to materialize in depressed economies, while the effects could be short-lived in times of expansion, which should be considered by policymakers in their spending decisions.

As the public debt and growth relationship also involves long-term effects, Chapter 3 extends the investigation of the public debt effects in relation to the role of theory-based models of public debt on long-term economic growth, considering country-specific fundamentals. Therefore, an endogenous growth model was adopted for the same sample studied in Chapter 1, constituted by 20 developed countries. Specifically, a Cobb-Douglas production function was augmented by the stock of public capital and linked to a public debt equation through the productivity of public capital. Therefore, theoretical formulae and empirical simulations were derived based on this framework. For the theoretical results, we concluded that, in an endogenous growth framework, with the Cobb-Douglas production function encompassing public capital instead of government flows, the potential productive government investment is an endogenous parameter of economic growth and public capital productivity.

Furthermore, we simulated a parameterized formula for a potential/limit debt that a country could target to finance its productive investments. This potential, linked to economic growth and public capital productivity, as well as the interest rate, is dynamic, country-and time-specific and has a tendency to evolve in contrast to the actual accumulated public debt. This, in particular, responds to the main recommendation made in Chapter 1, that the public debt threshold is time-and countryspecific, which should be studied considering a country's economic fundamentals. It also responds to the caveats of the research highlighted in Chapter 1, which set and tested, in particular, the exogenous values of thresholds.

Moreover, the results of Chapter 3 show that the simulated public debt drops under the actual levels of debt in times of crisis for many advanced countries that are severely affected by the crisis. This has a clear message regarding policy recommendation that countries are safer from threats of public debt as long as the potential debt (simulated/targeted) stays higher than the actual public debt. The results show that many countries are under stress of public debt, especially after the financial crisis of 2008. For some countries, such as Ireland, this stress is short-lived, and the potential debt quickly remains higher than the actual one following economic recovery. However, for many other countries, the effects are prolonged. The potential debt also revealed that some countries (Greece, Belgium and Italy) had debt issues in periods before the 2008 crisis.

The added value of Chapter 3 is that the debt limit is an endogenous parametrized function linked to the economic returns (productivity) of public capital financed by such issued debt. The potential public expenditure series shows a decreasing trend over time, albeit still higher than the observed one in many countries of the sample. This is driven by the general decreasing trend of public capital stock productivity, especially in the great moderation era . The policy message to increase potential public expenditure, and hence the targeted potential debt, is to enhance such productivity. To rephrase [START_REF] Krugman | The Age of Diminished Expectations: U.S. Economic Policy in the 1990s[END_REF] statement about the importance of productivity in the long term, "productivity isn't everything, but in the long run it is almost everything". Productivity enhancement could be achievable through the choice of higher productive public capital, which implies selective public capital projects with higher output multipliers.

Across the three chapters, the thesis counters any common debt ratio threshold that applies to all countries. The subject of growth and public debt remains one of the most debated subjects in fiscal policy after the 2008 financial crisis. This importance will continue, and we expect more research about it in the medium and long term in relation to many current events. Indeed, the current sanitary crisis of 2020, qualified by many politicians as a time of war because of the harsh measures of emergencies and confining and locking down populations, leads to hibernation of almost all economic sectors for months. Consequently, all the experts and national and international forecasting institutions are at least unanimous about the inevitable recessions, if not prolonged depressions, in the world and in almost all economies of advanced, emergent and developing countries. All government financial measures (monetary and fiscal), which are likely to deepen the deficits and increase public debt levels, once combined with a shrinkage in GDP, lead to soaring ratios of public debt. In this way, some economists expect public debt ratios to jump for many countries by 20 to 40 percentage points of GDP. Historical examples, according to [START_REF] Kose | Global Waves of Debt: Causes and Consequences[END_REF], show similar differences in accumulated debt to GDP ratios, comparing before and after the crises, where, for example, it reached approximately 31% and 35%, respectively, for Indonesia and Thailand in the 1997 financial crisis, and around 27% and 38%, respectively, for Latvia and Ireland in the 2008 financial crisis. The recovery and economic growth levels, which are highly uncertain, are conditioned by the prolonged measures, depending on the evolution of the Covid-19 pandemic and the development of a vaccine.

In the current trend, fiscal policy, which was subordinated to monetary policy in the Great Moderation has, since the 2008 crisis, become active and is leading the scene. The Covid-19 crisis will lead to greater involvement of fiscal policy; in particular, the conventional monetary policy has already reached its limit in using the conventional framework, particularly in many advanced economies, where nominal interest rates are reaching, or near to reaching, the zero lower bound. Although some views postulate that the trend of low interest rates is in favour of reduced public debt costs, which seems to point to a sustainable public debt path around higher levels, the threat of reverting the interest rates path in response to expected inflation in the future in an environment of low economic growth would plunge many highly-indebted countries into other waves of unsustainable and sovereign debt crisis.

Therefore, research on fiscal policy, and particularly the public debt overhang issues and economic growth, is likely to remain hotly debated for a long time to come. Many questions are, hence, worth raising regarding public debt and economic growth in the post-Covid-19 economic crisis. These include studying many conflictual objectives of fiscal policy aimed at saving jobs, as well as rescuing firms from bankruptcy, and raising growth, hence, countries' revenues in the short term, while dealing with the subsequent effects of raising public debt, particularly in the medium to long term. Moreover, the nature of the current economic crisis is likely to raise many issues in economic policies. An example revealed by the 2008 crisis is that fiscal multipliers are sensitive to the business cycle and many other determinants related to countries' economic fundamentals. The current crisis is qualified as a dual shock of demand and supply shocks, which may have an important impact on the global macroeconomic framework, and particularly on the fiscal policy framework. Therefore, modelling public debt and fiscal policy effects may fall outside the regular traditional framework. At the country level, many challenges and coordination issues may seem to be highly solicited, and their effects should be assessed, especially across the eurozone.

  Résumé de la thèse en français .............................................................................

Figure 1 :

 1 Figure 1: Public debt as a percentage of GDP over the period 1926-2015

Figure 2 :

 2 Figure 2: G20 Real GDP Growth Rate during 1926-2015 (%, Average)

Figure 3 :

 3 Figure 3: Debt to GDP ratios and Real GDP Growth rate over decades for G20 advanced countries

Figure

  Figure 4: Thesis Structure

  ), where each page contains four countries' results for two periods:1881-2010 and 1950-2010. For each figure, two panel charts are presented: the left-hand-side chart for the whole period, and the right-hand side for the post-war period. Each part contains a chart with three components: the first part (left) simply draws the debt ratio variable over time. This shows a mixture of high upward and downward sloping trends over time, indicating possible structural breaks. The second part (in the middle) shows kink regression plots, where the red point corresponds to the turning point (kink point or threshold), along with the regression line corresponding to equation (2). The third part (on the right) presents the threshold parameter in axis with the F-statistic showing the minimum of the Fisher test that indicates the threshold. Asymptotic values (confidence intervals) are displayed in dashed blue lines.

  Figure 1. Regression kink results for United States, Japan, United Kingdom and Australia

FigureFigureFigureFigureFigure

  Figure B.1. 5-year lead economic growth and current public debt, 1880 and 2008

Algorithm 2 :

 2 Wild Bootstrap confidence intervals for parameters 1. Generate n iid draws 𝑢 𝑡 from the N(0,1) distribution. 2. Set 𝑒 𝑡 * = 𝑒 𝑡 ̂𝑢𝑡 where 𝑒 𝑡 ̂ are the OLS residuals from the fitted regression kink model (2). 3. Set 𝑔 𝑡 * = 𝛽 ′ ̂𝑥𝑡 (𝛾 ̂) + 𝑒 𝑡 * , where (𝛽 ̂, 𝛾 ̂) are the Least-Square estimates. 4. Using the observations (𝑔 𝑡 * , 𝑔 𝑡-1 , 𝑑 𝑡-1 ), estimate the regression kink model (2

Figure 1 :

 1 Figure 1: Fiscal spending multiplier determinants and the link to government debt and GDP growth

  multipliers/impacts measure how a unit impulse of the structural shocks at time 𝑡 affects the level of endogenous variables at the horizon time 𝑡 + ℎ. In particular, the two first equations (22.a and 22.b) represent the response of, respectively, government expenditure and GDP growth rates to their proper innovations. The two other equations (22.c and 22.d) assess the crossing effects of the structural innovations between the endogenous variables of the SVAR. In particular,Equation (22.d) represents the response of the GDP growth rate to a structural unit shock of government expenditure, which will be our emphasis in this application. Drawing the structural dynamic impacts 𝜑 𝑖.𝑗 ℎ for the shocks (𝑖, 𝑗) = (1,2) allows us to visualize such dynamic

  ) for the 27 European Union countries. The calculations are simulated under fixed interest rates. The 27 countries are Belgium (BE), Bulgaria (BG), Cyprus (CY), the Czech Republic (CZ), Denmark (DK), Estonia (EE), Finland (FI), France (FR), Germany (DE), Greece (EL), Hungary (HU), Ireland (IE), Italy (IT), Latvia (LV), Lithuania (LT), Luxembourg (LU), Malta (MT), The Netherlands (NL), Poland (PL), Portugal (PT), Romania (RO), Slovakia (SK), Slovenia (SI), Spain (ES), Sweden (SE) and the United Kingdom (UK).

Figure 2 .•Figure 3 .

 23 Figure 2. Critical multipliers for EU member states versus the public debt to GDP ratiosyear 2011

•

  Euro member joined before 2007 • Euro member joined after 2007 • Non euro member Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through 121

  .a to 6.B.c present the impulse response functions for the case of debt accumulation and the two business cycle cases. Similarly, Figures 7.B.a to 7.B.c show the impulse response functions for the case of debt contraction and the two business cycle cases.

Figure 4 .

 4 Figure 4. Evolution of some SVAR variables vis-à-vis public debt for the United States

Figure 6 .

 6 Figure 6. Responses to a structural shock of government expenditure (shock6) in times of expansion (first row of charts) and recession (second row of charts)

Figure 7 .

 7 Figure 7. Responses to a structural shock of the public debt ratio (shock2) in periods of debt accumulation (first row of charts) and debt contraction (second row of charts)

Figure 8 .

 8 Figure 8. Responses to a structural shock of government expenditure (shock6) in periods of debt accumulation (first row of charts) and debt contraction (second row of charts)

Figure 9 .

 9 Figure 9. Responses to a structural shock of the government debt ratio (shock2) in periods of debt accumulation and expansion (first row of charts) and debt accumulation and recession (second row of charts)

Figure 11 .

 11 Figure 11. Responses to a structural shock of the government debt ratio (shock2) in periods of debt reduction and expansion (first row of charts) and debt reduction and recession (second row of charts)

Figure 12 .

 12 Figure 12. Responses to a structural shock of government expenditure (shock6) in periods of debt reduction and expansion (first row of charts) and debt reduction and recession (second row of charts)

Figure 3 .Figure

 3 Figure 3.B. Expenditure multipliers effects under the business cycle versus the public debt ratio average

Figure 1 .Chapter 3 .

 13 Figure 1. The relationship between per-capita long-term economic growth and government size

  = 𝑔 ̃𝑡 the "potential" 107

Chapter 3 .

 3 Public debt effects in theory-based models with an empirical assessment of the potential public

Chapter 3 .

 3 Public debt effects in theory-based models with an empirical assessment of the potential public debt 217 Normalizing by the labour quantity 𝐿 and labelling using lowercase, Equation (21) yields: 𝑦 𝑡 = 𝐴. 𝑘 𝑝𝑡 𝛼𝜀𝜃 ℎ 𝑡 (𝜃-1) 𝑘 𝑔𝑡 𝛼(1-𝜀𝜃)

Chapter 3 .

 3 Public debt effects in theory-based models with an empirical assessment of the potential public

Figure 4 :

 4 Figure 3 : Scatter plot elastictities of Public Investment stocks versus Private capital stocks (Kp, Ig): Sample 1960-2007

Figure 5 . 231 Figure 6 .

 52316 Figure 5. Scatter plot of public capital productivity versus elasticity

Chapter 3 .

 3 121 https://stats.oecd.org/ Public debt effects in theory-based models with an empirical assessment of the potential public debt 232 public debt for each country. Figures7, 8, 9 and 10 produce such simulated debt results, along with actual public debt, over the period 1960-2015 for the 20 sample countries.

Figure 7 .

 7 Figure 7. Simulated potential paths of public debt versus the actual path based on potential simulated government investment and economic and monetary performances for Australia, New Zealand, Denmark, Norway, Sweden and Switzerland*

Figure 8 .

 8 Figure 8. Simulated potential paths of public debt versus the actual path based on potential simulated government investment and economic and monetary performances for the United States, Japan, the United Kingdom and Canada

Figure 9 .Chapter 3 .

 93 Figure 9. Simulated potential paths of public debt versus the actual path based on potential simulated government investment and economic and monetary performances for Austria, Germany, France, Italy, The Netherlands and Spain*

Figure 10 .

 10 Figure 10. Simulated potential paths of public debt versus the actual path based on potential simulated government investment and economic and monetary performances for Belgium, Greece, Ireland and Portugal

Figure 11 .

 11 Figure 11. Simulated potential public debt for Greece and Japan using the US long-term interest rate and economic growth differential

  [interet rates -economic growth] of the period 1985-2015 Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 243

Figure 13 .

 13 Figure 13. Fiscal space: distance to debt limit (percentage points)

  -term growth while an increase in expenditures raises it by raising marginal productivity of capital.

Chapter 3 .

 3 Public debt effects in theory-based models with an empirical assessment of the potential public debt models augmented by the government's budget constraint.

  model analyzing the responses of macroeconomic variables, in the steady state, to a government spending shock in the presence of positive levels of government debt.-Derived assumptions of New Keynesian models.-The model assumes a fraction of the household sector to follow a rule-of-thumb behavior as in Gali et al. (2007) (non-Ricardian agents).

Chapter 3 . 261 FigureChapter 3 . 262 FigureChapter 3 .Figure B. 7 .

 3261326237 Figure B.1. Scatter plot elastictities of public investment fLows versus private capital stocks (Kp, Ig): Sample 1960-2007

Table 1 . Empirical studies survey of the public debt and economic growth threshold Authors Samples Econometric methodologies Debt thresholds Other notes on methods and results

 1

	Reinhart and Rogoff	20 developed countries and 24	Growth mean and the median analysis	90% for advanced	Arbitrarily set thresholds: 30%, 60%
	(2010)	developing countries: 1946-	according to pre-established thresholds	countries	and 90% and conclude that growth is
		2009			altered from 90%
	Caner et al. (2010)	26 developed and 75	Hansen's (2000) OLS threshold	77% and 64%	77% for the whole sample, 64% for
		developing countries: 1980-	econometric estimate		developing countries
		2008
	Herndon et al.	The 20 developed countries of	Replication of RR's (2010) work after	No threshold found	The relationship is sensitive to country
	(2013)	RR (2010)	correction of data errors		and period
	Kumar and Woo	38 countries, most of which are	Econometric estimation by various	High level but not	Correction of problems of reverse
	(2010)	OECD countries: 1970-2007	methods such as GMM	reported	causality, endogeneity and
					heterogeneity
	Checherita and	12 euro area countries: 1970-	Estimation of a polynomial form of	Interval [70% to 100%]	The degree of the polynomial form is
	Rother (2010)	2009	growth explained by the debt ratio		around 1.2 to 3
	Checherita et al.	11 euro, 22 OECD and 14 EU	Cobb-Douglas optimization	65%: OECD; 63%: the	The debt threshold is a non-linear
	(2014)	countries: 1960-2010	augmented by public spending	EU; 50%: euro	function of the elasticity of the public
					expenditure/private capital ratio
	Pescatori et al.	34 mainly developed countries:	Analysis of growth (t + k) and debt (t);	No threshold found	High government debt tends to
	(2014)	1875-2011	k = {1,5,10,15} using a descriptive		increase economic growth volatility
			approach
	Chang and Chiang	15 OECD countries: 1990-	Threshold method for non-dynamic	32.3% and 66.25%	The relationship is positive over the
	(2009)	2004	panel		three regimes delimited by the two
					thresholds
	Cecchetti et al.	18 OECD countries: 1980-	Threshold method for non-dynamic	85%	Debt negatively influences growth
	(2011)	2010	panel		above 85% threshold
	Minea and Parent	20 developed countries of RR	Estimation of econometric relationship	60%, 90% and 115%	Between 90% and 115%, negative
	(2012)	(2010) and Abbas et al. (2010)	with changing thresholds		effect, between 60% and 90% and
		data			above 115% positive
	Egert (2015)	The RR (2010) data and	Estimation and detection of	20%: central debt; 50%:	Individual estimate confirms threshold
		countries sample	endogenous thresholds (Hansen, 1999)	general debt	for some countries around 30%
					(United States)
	Baglan and Yoldas	20 developed countries of RR	Inference techniques to remedy	Between 18% and 53%	No robust threshold and subject to
	(2013)	(2010): 1954-2008	endogeneity and heterogeneity issues		uncertainty
	Baum et al. (2013)	12 euro countries: 1990-2010	Threshold method for dynamic and	67%	Study of short-term impact
			non-dynamic panel
	Kourtellos et al.	Sample of 82 countries: 1980-	Threshold regressions using the Solow	No threshold found	Heterogeneity and influence of
	(2012)	2009	growth model		institutional quality

Table 1 (continued) Authors Samples Econometric Methodologies Debt thresholds Other notes on methods and results

 1

	Eberhardt and	Sample of 105 countries: 1970-	Techniques addressing heterogeneity	No common	Estimation of dynamic and static non-
	Presbitero (2015)	2008	and dependence in cross-sections	threshold	linear models by GMM method
	Panizza and Presbitero	17 OECD countries: 1981-	Estimation by GMM of linear and non-	No threshold found	No negative effect of the debt on growth
	(2012)	2008	linear relationships
	Sharpe (2013)	12 euro countries: 1998-2011	Estimated relationship of debt and	40% and 133%	Negative effect for debt ratios over 40%,
			interest rate by GMM and TSLS		emphasized above the 133% threshold
	Pan and Wang (2013)	12 euro countries: 1970-2009	Bayesian analysis using dynamic	Negative	Common factors and shocks affect
			factor models	relationship	positive growth and negative debt
	Gomez-Puig and	11 euro countries: 1980-2013	Granger (1969) causality method	56% to 103%	Causality dependent on the country, the
	Sosvilla-Rivero (2015)				threshold found only for four countries
	Di Sanzo and Bella	12 countries of the euro: 1970-	Studies of individual causality by non-	Threshold not	Causality results vary across countries
	(2015)	2012	parametric tests	examined
	Greiner (2011)	Long-term simulation for Italy,	Simulated endogenous growth model	Threshold not	The impact of debt on growth is positive
		Germany and the eurozone		examined	if the pace of debt remains lower than
					the pace of GDP
	Marchionne and	Sample of 27 countries: 1994-	Estimation considering the GINI index Non-linearity; no	The results suggest non-linear link that
	Parekh (2015)	2010		threshold reported	depends on the income distribution
	Lin (2014)	62 developing and developed	Threshold quantile Lasso regression	Thresholds ranging	Thresholds vary by country and quintile
		countries: 1991-2005		from 10% to 100%	and more common in developing than in
					developed countries
	Lee et al. (2017)	RR (2010) database for 20	Test for threshold effects by regressing	Around 30%	The median real GDP growth falls
		developed countries	growth median on public debt		abruptly above a debt-to-GDP ratio of
					30%
	Gomez-Puig and	11 euro area countries: 1961-	Time-series regressions based on	Variable threshold	Threshold varies across countries from
	Sosvilla-Rivero (2017)	2015	economic growth literature	from 21% to 61%	21% in France to 61% in Belgium
	Chudik (2017)	40 advanced and developing	Test for thresholds in dynamic	No evidence of any	Significant negative long-term effects of
		countries: 1965-2010	heterogeneous panel with cross-	threshold	public debt build-up on output growth
			sectionally dependent errors
	Syssoyeva-Masson and	60 developed and developing	Panel regression using time-series	Two regimes: 44%	Highlight the debt long-memory process
	De Sousa Andrade	countries, IMF data: 1970-	cointegration and Hansen (1999)	and 48%	and recommend long-term analysis
	(2017)	2012

Table 2 . Regression kink results over long periods

 2

	Specification		𝑔 𝑡 = 𝛽 1 (𝑑 𝑡-1 -𝛾) -+ 𝛽 2 (𝑑 𝑡-1 -𝛾) + + 𝛿𝑔 𝑡-1 + 𝑐 + 𝑒 𝑡
	Country	β 1	β 2	δ	c	γ	Period
	Australia	0.002 (0.321) 1.719 (0.234)	0.49 (0.503)	1.11 (2.996)	134 (167.9) 1901-2010
	Austria	0.070 (0.072)	-0.04 (0.039) 0.584 (0.085) 2.389 (1.335)	35.6 (6.4) 1881-2010
	Belgium	0.000 (0.000) 0.088 (0.394) 0.214 (0.135) 1.487 (0.333) 173.4 (231.3) 1881-2010
	Canada	1.016 (1.133) 0.002 (0.016) 0.314 (0.127) 1.471 (0.978)	22.7 (4.1) 1881-2010
	Denmark	-0.067 (0.058)	0.048 (0.04) 0.016 (0.174) 0.679 (0.793)	33.4 (6.8) 1881-2010
	France	-0.029 (0.01) 0.167 (0.064) -0.203 (0.147) -0.306 (1.22)	161 (20.4) 1881-2010
	Germany	0.318 (0.127) -0.051 (0.033) 0.459 (0.148) 2.587 (0.904)	20.1 (2.3) 1881-2010
	Greece	-0.008 (0.016) -2.063 (0.194)	0.027 (0.07) 1.172 (2.576)	215 (1.5) 1884-2010
	Ireland	0.177 (0.191)	0.04 (0.016)	0.435 (0.15)	1.07 (0.829)	35.1 (7.9) 1929-2010
	Italy	-0.058 (0.035) 0.053 (0.053) 0.371 (0.146) 0.001 (1.051)	66 (18.8) 1881-2010
	Japan	-0.434 (0.159) -0.006 (0.008)	-0.11 (0.104) 2.564 (0.671)	22.8 (4.9) 1881-2010
	Netherlands	0.04 (1.806) -0.009 (1.182) 0.233 (3.205) 3.235 (26.27) 110.9 (2439) 1881-2010
	New Zealand	-0.005 (0.01) 0.074 (0.112) -0.048 (0.107) 0.814 (0.973)	163.3 (78.2) 1881-2010
	Norway	2.647 (0.87) 0.032 (0.028)	-0.123 (0.14) 2.501 (0.705)	14.6 (1.4) 1881-2010
	Portugal	125.31 (17.9) -0.069 (0.022) -0.106 (0.137) 4.482 (0.954)	13.6 (0.0) 1881-2010
	Spain	-0.059 (0.018) 0.017 (0.028) 0.014 (0.098) 0.399 (0.796)	74.6 (16.2) 1881-2010
	Sweden	6.189 (0.01) -0.001 (0.048) 0.109 (0.102)	2.092 (1.21)	13.4 (16.3) 1881-2010
	Switzerland	-0.023 (0.016) 3.977 (0.595) 0.047 (0.119)	0.272 (0.63)	74.3 (0.6) 1899-2010
	United Kingdom -30.542 (0.02)	0.00 (0.235) 0.362 (0.067) 0.932 (1.571)	27.5 (55.0) 1881-2010
	United States	34.306 (8.17)	-0.013 (0.02) 0.292 (0.107) 3.082 (0.936)	7.6 (0.1) 1881-2010
	Note: Standard errors are given in parentheses.

Table 3 . Regression kink results over the period 1956-2010

 3

	Specification	𝑔 𝑡 = 𝛽 1 (𝑑 𝑡-1 -𝛾) -+ 𝛽 2 (𝑑 𝑡-1 -𝛾) + + 𝛿𝑔 𝑡-1 + 𝑐 + 𝑒 𝑡
	Country	β 1	Β 2	δ	c	γ
	Australia	0.034 (0.033) 0.614 (0.155) 0.119 (0.167) 2.259 (0.697)	37.4 (1.1)
	Austria	-0.086 (0.038) 0.039 (0.025) -0.017 (0.141) 1.555 (0.517)	44.0 (7.7)
	Belgium	51.31 (4.898) -0.016 (0.024) 0.157 (0.107) 2.923 (0.694)	38.9 (3.8)
	Canada	0.149 (0.238) -0.006 (0.019) 0.328 (0.138) 1.587 (0.634) 52.7 (10.9)
	Denmark	-36.619 (0.028) -0.007 (0.095) 0.033 (0.024) 2.390 (1.191)	4.4 (15.4)
	France	0.521 (0.478) -0.024 (0.014)	0.476 (0.16) 1.705 (0.667)	16.1 (1.3)
	Germany	-0.132 (0.061) 0.005 (0.033) 0.038 (0.183) 1.326 (0.817)	34.8 (7.7)
	Greece	-0.058 (0.035) 0.053 (0.053) 0.371 (0.146) 0.001 (1.051)	66 (18.8)
	Ireland	3.28 (1.227) 0.037 (0.015) 0.346 (0.128) 1.456 (0.667)	27.3 (1.0)
	Italy	-0.053 (0.014) 0.091 (0.045) 0.100 (0.197) 0.502 (0.438) 105.4 (4.7)
	Japan	-0.339 (2.241) -0.011 (0.016)	0.299 (0.2) 2.171 (2.383) 18.1 (75.7)
	Netherlands	0.083 (0.039) -0.064 (0.113) 0.162 (0.179) 2.821 (0.962) 61.7 (10.2)
	New Zealand	1.81 (0.055) -0.014 (0.023) -0.074 (0.169) 2.058 (0.771)	19.4 (0.4)
	Norway	-0.037 (0.023) 0.793 (0.007) 0.337 (0.139) 0.926 (0.677)	57.9 (0.7)
	Portugal	10.74 (2.203) -0.066 (0.021) 0.377 (0.132)	3.998 (0.95)	14.5 (0.2)
	Spain	-0.064 (0.078) 0.038 (0.026) 0.549 (0.126) 0.543 (0.841) 34.5 (18.7)
	Sweden	-0.119 (0.044) 0.056 (0.025) 0.394 (0.156) -0.198 (0.579)	40.2 (5.6)
	Switzerland	-0.083 (0.036)	0.05 (0.037) 0.177 (0.144) 0.288 (0.492)	39.9 (8.8)
	United Kingdom	0.124 (0.072) -0.021 (0.019)	0.154 (0.18) 3.037 (0.873)	59 (8.5)
	United States	1.892 (0.617) -0.072 (0.028) 0.028 (0.156) 4.650 (0.800)	34.4 (0.7)
	Note: Standard errors are given in parentheses.

Table 4 . GLS and GMM panel estimation results Regression

 4 by Generalized Least Squares method (GLS). Specification: 𝑔 𝑖,𝑡+5 = 𝛼𝑑 𝑖,𝑡 + 𝛽𝑑 𝑖,𝑡 2 + 𝛾 𝑖 + 𝜀 𝑖,𝑡

	Model with fixed effects

  .

				Coef.	prob. Coef.	prob.	Coef.	prob. Coef.	prob.
		0.038	0.808	0.234*	0.069 0.161**	0.043	0.106**	0.016 0.566	0.186
		-0.001	0.529	-0.002*	0.081 -0.001** 0.034	-0.001*** 0.005 -0.006	0.157
		4.176*	0.099	-2.845	0.277 -3.684	0.202	-0.682	0.616 -6.376	0.397
	J-statistic b 4.526	0.339	2.949	0.399 0.786	0.675	1.143	0.565 0.666	0.717
	Threshold NS		49.4	80.1		62.8	NS
	Notes: Significant at 1% (***), 5% (**) and 10% (*). NS is Non-Significant.

Table 6 . GMM estimation results for reduced samples for model without fixed effects Sample of 20 OECD countries

 6

			. Coef.	prob. Coef.		prob. Coef.	prob. Coef.	prob.
		1.929*	0.096 0.100*	0.057 1.063**	0.013 0.064*	0.071 -0.123**	0.019
		-0.014*	0.095 -0.001**	0.027 -0.006*	0.092 -0.001**	0.021 0.001	0.126
	γ	-37.593	0.136 0.655	0.557 -41.709*** 0.006 1.443*	0.085 6.689*** 0.000
	J-statistic b 2.191	0.534 3.652	0.161 4.996		0.172 0.765	0.382 4.387	0.112
	Threshold 69.6	46.1	94.0		45.0	NS
	Notes: Significant at 1% (***), 5% (**) and 10% (*). NS is Non-Significant.
	a: Coefficients are statistically significant, but the function is convex which means that the debt affects negatively
	growth for debt ratios below this threshold and positively above this threshold.
	b: J-statistic is the value of the GMM objective function. The threshold is calculated according to the formulae: 𝑑 ̂= -	𝛼 2𝛽 .

Table A .1. Public debt and economic growth correlations by countries and periods

 A

	Correlation of debt(t) and growth(t)	Correlation of debt(t) and growth(t+5)
	Countries

Table A .2. Data heterogeneity tests across sections and periods

 A Test for Equality of means, medians and variances of GROWTH Categorized by values of DEBT Notes: df is degrees of freedom. Prob. is the probability. Count is the number of observations. Sum of Sq. is the sum of square. Mean Sq. is the mean of square. Std. Dev. is the standard deviation. Std. Err. of mean is the standard error of mean.

	Equality of means	Sample: 1881 2008			Sample: 1950 2008			Sample: 1971 2008	Sample: 1991 2008
	Method		df	Value		Prob.	df		Value	Prob.	df	Value	Prob. df	Value	Prob.
	Anova F-test	(2, 2248)	12.655	0.000	(4, 1119)	10.675	0.000	(3,	2.498	0.059 (3, 353)	2.365	0.071
	Analysis of Variance									741)
	-2008 Mean Sq. -0.22 Sum of Sq. 25.42 8.47 -0.38** 1264.73 3.58 -0.44** 1290.15 3.62 -0.44** Sample: 1991 2008 -0.44 df 0.39 11.42 3 -0.07 Mean Sq. -0.52 -0.72** -0.17 4.57 353 -0.34 -0.61 4.60 356 -0.06 0.27 -0.06 -0.49 0.31 Prob. df Value Prob. -0.25 -0.21 -0.10 0.004 3 6.76 0.080 -0.30 -0.11 0.72** 0.011 3 5.11 0.164 0.17 -0.51 -0.31 0.012 3 7.77 0.051 -0.36* -0.17 -0.16 0.012 3 7.77 0.051 -0.28 -0.23 -0.24 0.028 3 7.24 0.065 -0.55** -0.41 -0.23 Sample: 1991 2008 -0.21 0.02 -0.40 Prob. df Value Prob. -0.25 -0.69** -0.74** 0.000 3 5.82 0.121 -0.74*** -0.26 -0.24 0.032 (3, 353) 0.36 0.781 -0.21 -0.85** -0.26 0.034 (3, 353) 0.38 0.771 -0.36* -0.28 -0.67* 2.14 1.89 -0.43** -0.03 0.73** -0.02 -0.09 -0.58 Sample: 1991 2008 -0.42 -0.18 -0.35 -0.21 -0.14 -0.23 -0.11 3/20 4/20 Count Mean Std. Std. Err. of Dev. Mean 8/20 19/20 16/20 2.080 2.372 0.126 95 -0.07 -0.11 Mean Sq. df 0.13 Sum of Sq. -0.3 -0.51*** 0.12 70.44 3 34.26 -0.28* Sum of Sq. 281.74 -0.47*** -0.12 7383.49 6.60 741 3387.23 -0.10 -0.37** -0.27 7665.23 6.83 744 3421.50 0.08 -0.28** -0.18 Sample: 1950 2008 0.26 0.14 df -0.28 0.15 4 -0.21 -0.19 1119 -0.07 0.14 1123 0.08 0.25 Sample: 1971 2008 -0.12 0.21 -0.28* -0.54*** -0.17 df Value Prob. df Value -0.29 -0.13 -0.19 -0.57*** 0.00 4 35.61 0.000 3 13.44 -0.14 0.15 0.04 -0.43** 0.01 4 32.55 0.000 3 11.14 0.13 0.41* 0.32** -0.22 0.16 4 49.99 0.000 3 10.88 0.00 0.25 -0.38** -0.66*** -0.22 4 49.99 0.000 3 10.88 0.06 -0.03 -0.44** -0.75*** -0.05 4 45.27 0.000 3 9.10 0.16 0.00 0.12 -0.21 -0.1 Sample: 1950 2008 Sample: 1971 2008 -0.05 0.06 -0.08 -0.02 0.07 df Value Prob. df Value -0.22 -0.19 -0.30 -0.47*** -0.22 4 34.49 0.000 3 22.05 -0.04 -0.28 -0.23 -0.32** 0.18 (4, 1119) 5.66 0.000 (3, 2.95 -0.14 0.54** -0.16 -0.50*** -0.3 741) (4, 1119) 5.63 0.000 (3, 2.91 0.16 0.01 0.11 -0.52*** -0.23 741) 2.57 -0.23 0.58** 0.04 -0.19 0.21 0.24 0.55** 0.36** -0.14 -0.3 Sample: 1950 2008 4.31 Mean Sq. 235.26 41792.62 18.59 -0.25 Sum of Sq. -0.54*** 0.08 0.20 470.52 -0.40** -0.30 -0.1 -0.02 42263.14 18.78 -0.13 -0.26 Sample: 1881 2008 df 2 2248 2250 -0.44*** -0.25 df Value Prob. -0.51*** -0.26 2 22.29 0.000 -0.30** 0.30 2 21.67 0.000 0.27** -0.22 2 26.97 0.000 -0.70*** 0.09 2 26.97 0.000 -0.68*** -0.11 2 25.71 0.000 0.06 -0.23 Sample: 1881 2008 0.11 0.22 df Value Prob. -0.25* -0.18 2 143.47 0.000 -0.35** 0.21 (2, 2248) 36.73 0.000 -0.29** -0.36 (2, 2248) 32.60 0.000 -0.23* 0.04 Bartlett weighted standard deviation Australia Source of Variation Austria Between Belgium Within Canada Total Denmark Equality of medians France Method Germany Med. Chi-square Greece Adj. Med. Chi-square Ireland Kruskal-Wallis Italy Kruskal-Wallis (tie-adj.) Japan Van der Waerden Netherlands Equality of variances New Zealand Method Norway Bartlett Portugal Levene Spain Brown-Forsythe Sweden Switzerland -0.28** 0.37* Category statistics of debt United Kingdom -0.04 -0.20 Sample: 1881 2008 Sample: 1971 2008 United States 0.01 0.11 0.06 -0.17 -0.09 -0.1 0.03 Total Sample -0.25* -0.34 -0.02 -0.04 -0.07 -0.29** -0.24 Significant Correlations 13/20 1/20 0/20 4/20 6/20 13/20 0/20 Debt Debt Count Mean Std. Dev. Std. Err. of Mean Count Mean Std. Dev. Std. Err. of Mean Count Mean Std. Dev. Std. Err. of Negatives correlations 15/20 12/20 11/20 6/20 12/20 20/20 12/20 Mean [0, 100) 1928 2.256 4.062 0.093 [0, 50) 612 3.156 2.828 0.114 353 1.678 2.107 0.216 19/20 [100, 300 1.023 4.582 0.265 [50, 100) 434 2.278 2.235 0.107 334 2.204 1.946 0.106 211 2.025 1.847 0.127 Note: Significant at 1% (***), 5% (**) and 10% (*). 200) [200, 23 3.918 12.991 2.709 [100, 150) 64 1.790 2.198 0.275 50 1.453 1.668 0.236 43 1.358 1.700 0.259
	300)				[150, 250)	13	1.578 1.534 0.425	8	0.993 1.162 0.411 8	0.993 1.162 0.411
	All	2251	2.109 4.334	0.091	All		1124	2.718 2.613 0.078	745	2.082 2.144 0.079 357	1.829 1.904 0.101

Table A .3. Instruments correlations of public debt ratio and economic growth

 A

Table A .5. Sensitivity of debt thresholds to government expenses and government effectiveness.

 A

						-2008
	Australia	-1.78	-2.57	0.39	-0.65	15.10
	Austria	-0.56	3.74	0.08	-0.05	-1.78
	Belgium	2.79	-4.60	1.29	1.98	-4.19
	Canada	0.45	-5.51	-0.50	-0.43	-5.90
	Denmark	-1.22	2.08	-0.09	0.00	-0.93
	France	-1.18	0.86	-0.31	-0.53	0.68
	Germany	-1.44	2.14	-0.48	-0.47	0.21
	Greece	1.04	4.70	0.59	-0.46	-4.92
	Ireland	1.11	-3.46	1.13	2.14	1.11
	Italy	1.46	0.29	0.19	1.00	-6.57
	Japan	2.03	8.80	0.85	0.88	-2.14
	Netherlands	0.40	-4.78	-0.50	-0.27	-1.92
	New Zealand	-1.10	-6.50	-1.17	-1.10	4.62
	Norway	-0.84	0.45	0.43	0.49	6.82
	Portugal	-0.22	4.00	0.25	0.65	0.79
	Spain	-0.12	4.60	0.37	0.00	0.40
	Sweden	-0.57	0.88	-0.46	-0.99	-2.77
	Swiss	-2.03	-0.73	-1.18	-1.45	0.01
	United Kingdom	2.05	1.61	-0.25	-0.19	3.27
	United States	-0.78	-5.06	-0.55	-0.37	-1.83
		Fixed effects for the quadratic form specification: the sample of 10 Euro countries
	Austria	-0.80	8.13	-0.26	-0.23	-0.27
	Belgium	1.78	-12.25	1.44	1.02	-6.01
	France	-1.35	1.05	-0.77	-0.29	5.35
	Germany	-1.53	4.48	-0.87	-0.58	4.48
	Greece	0.60	7.66	0.41	-0.71	-7.76
	Ireland	1.22	-9.45	0.97	1.13	4.67
	Italy	0.99	-1.88	0.24	-0.12	-9.32
	Netherlands	0.44	-12.01	-0.70	-1.10	-0.50
	Portugal	-0.35	7.03	-0.13	0.43	5.32
	Spain	-0.40	7.59	-0.08	0.27	4.00

High Government effectiveness (13 countries): Finland, Denmark, Sweden, Norway, Netherlands, Canada, New Zealand, Austria, Australia, United Kingdom, Belgium, Germany and United States.

  Moderate Government Final Consumption as % of GDP (11 countries): New Zealand, Italy, Ireland, Austria, Australia, United States, Greece, Portugal, Japan, Spain and Switzerland. Moderate Military Expenditures as % of GDP (11 countries): Belgium, Germany, Italy, New Zealand, Denmark, Spain, Canada, Switzerland, Ireland, Austria and Japan.

	Effect	NS	NS	80.7***	73.8***	61.2*** a
	Model With Fixed Effect	114.7**	NS	95.4*	60.8**	92.8*** a
	Moderate Government effectiveness (7 countries): Ireland, France, Japan, Spain, Portugal, Greece and Italy.
	Model Without Fixed Effect	40.3**	41.6**	NS	49.3*	NS
	Model With Fixed Effect	NS	NS	102.5***	NS	NS
	High Government Final Consumption as % of GDP (9 countries): Sweden, Denmark, Netherlands, France, Canada, Belgium,
	Germany, United Kingdom and Norway.
	Model Without Fixed Effect	NS	NS	NS	72.2*	61.4*** a
	Model With Fixed Effect	NS	NS	NS	52.3**	101.4*** a
	Model Without Fixed Effect	60.7** a	NS	NS	67.5***	NS
	Model With Fixed Effect	NS	NS	91.5***	58.4*	NS
	High Military Expenditures as % of GDP (9 countries): Unites States, United Kingdom, France, Greece, Portugal, Norway,
	Netherlands, Sweden and Australia.
	Model Without Fixed Effect	NS	NS	NS	45.2**	122.0* a
	Model With Fixed Effect	NS	NS	65.3**	51.4**	118.9*** a
	Model Without Fixed Effect	46.0* a	NS	89.3**	NS	51.1***
	Model With Fixed Effect	NS	NS	114.2**	NS	NS
	High Government Transfers and Subsidies as % of GDP (7 countries): Belgium, Switzerland, Netherlands, Canada, Sweden,
	United States and Japan.
	Model Without Fixed Effect	53.4***	73.0*	93.0***	81.5***	NS
	Model With Fixed Effect	NS	NS	NS	71.6***	NS
	Moderate Government Transfers and Subsidies as % of GDP (13 countries):

  Table 4.A, while the IRFs are plotted in Figures 2.B.a to 2.B.c in Appendix B. The table reporting short-term (first quarter) and long-term (five years)

  𝑐(1)𝑦 𝑡 + 𝑐(2)𝜋 𝑡 + 𝑒 1𝑡 ;

		𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛	(1)
	𝑑 𝑡 = 𝑐(3)𝑦 𝑡 + 𝑐(4)𝜋 𝑡 + 𝑐(5)𝑟 𝑡 + 𝑒 2𝑡 ;	𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑑𝑒𝑏𝑡 𝑟𝑎𝑡𝑖𝑜 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛	(2)
	𝑦 𝑡 = 𝑐(6)𝑖 𝑡 + 𝑐(7)𝜋 𝑡 + 𝑐(8)𝑟 𝑡 + 𝑒 4𝑡 ;	𝑜𝑢𝑡𝑝𝑢𝑡 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛	(3)
	𝜋 𝑡 = 𝑐(9)𝑟 𝑡 + 𝑐(10)𝑖 𝑡 + 𝑒 5𝑡 ;	𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛	(4)
	𝑖 𝑡 = 𝑐(11)𝑦 𝑡 + 𝑐(12)𝑟 𝑡 + 𝑒 6𝑡 ;	𝑝𝑟𝑖𝑣𝑎𝑡𝑒 𝑖𝑛𝑣𝑒𝑠𝑚𝑒𝑛𝑡 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛	(5)
	𝑔 𝑡 = 𝑒 3𝑡 ;	𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 (6)

  table. Standard errors of the estimated coefficients are displayed between parentheses below the estimated values of those coefficients.

	Model's estimation controlling for expansion	Model's estimation controlling for recession
	𝑟 𝑡 = . 129 (.256)	𝑦 𝑡 +. 311 (.287)	𝜋 𝑡 + 𝑒 1𝑡	𝑟 𝑡 = -. 071 (.192)	𝑦 𝑡 +. 383 (.279) 𝜋 𝑡 + 𝑒 1𝑡
	𝑑 𝑡 = -1.05 (.174)	𝑦 𝑡 -1.12 (.355) 𝜋 𝑡 -.308 (.087) 𝑟 𝑡 + 𝑒 2𝑡	𝑑 𝑡 = -.639 (.181)	𝑦 𝑡 -1.20 (.354) 𝜋 𝑡 -.269 (.088) 𝑟 𝑡 + 𝑒 2𝑡
	𝑦 𝑡 =. 167 (.018)	𝑖 𝑡 +. 209 (.029)	𝜋 𝑡 -. 017 (.020) 𝑟 𝑡 + 𝑒 4𝑡	𝑦 𝑡 =. 163 (.021)	𝑖 𝑡 +. 245 (.032)	𝜋 𝑡 -. 016 (.024) 𝑟 𝑡 + 𝑒 4𝑡
	𝜋 𝑡 = -.024 (.030)	𝑟 𝑡 -.005 (.021) 𝑖 𝑡 + 𝑒 5𝑡	𝜋 𝑡 = -.022 (.031)	𝑟 𝑡 -.009 (.021) 𝑖 𝑡 + 𝑒 5𝑡
	𝑖 𝑡 = -.636 (.605)	𝑦 𝑡 -2.13 (2.07) 𝑟 𝑡 + 𝑒 6𝑡	𝑖 𝑡 =. 378 (.368)	𝑦 𝑡 -1.15 (1.25) 𝑟 𝑡 + 𝑒 6𝑡
	𝑔 𝑡 = 𝑒 3𝑡						𝑔 𝑡 = 𝑒 3𝑡
	(…) are standard errors	(…) are standard errors

  in recent decades, compared to the 1960s, 1970s and 1980s, is not well supported by our findings. The previous results are in line with what was observed in the recent literature about fiscal multipliers, in advanced economies, being large in times of recession but weak, or even negative, in times of expansion.

	Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through
	and even negative
	Response of LGDP to Shock6	Response of LPINV to Shock6	Response of LPRC to Shock6	Response of RI NTR to Shock6	Response of LDR to Shock6
	.008	.04	.0008	.004	.002
	.006	.03	.0006	.003	.000
			.0004	.002	-.002
	.004	.02
			.0002	.001	-.004
	.002	.01
			.0000	.000	-.006
	.000	.00	-.0002	-.001	-.008
	-.002	-.01	-.0004	-.002	-.010
	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20
	Response of LGDP to Shock6	Response of LPINV to Shock6	Response of LPRC to Shock6	Response of RI NTR to Shock6	Response of LDR to Shock6
	.008	.04	.0006	.003	.002
	.006	.03	.0004	.002	.000
			.0002	.001
	.004	.02			-.002
			.0000	.000
	.002	.01			-.004
			-.0002	-.001
	.000	.00	-.0004	-.002	-.006
	-.002	-.01	-.0006	-.003	-.008
	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20	2 4 6 8 10 12 14 16 18 20
			137

Table 1 .A: Sample of studies on the effectiveness of stimulus measures

 1 Positive Between 7 and 11 million jobs were saved due to the G20's 2009 fiscal policies, representing 29-43 per cent of the G20's total unemployment in the first half of 2009. In comparison, the Asian region's policies were successful overall in offsetting the loss of exports and kept regional 2009 GDP dropping at 4.2 per cent instead of 7.8 per cent, a possible outcome had the fiscal policies not been enacted.MixedFiscal stimuli have provided an essential impetus for recovery in developed and developing countries alike. Following a decline of 0.5 per cent in 2009, the world output is projected to increase by 4.25 per cent in 2010. However, growth and recovery in the job market have varied across countries of different socio-economic levels, even with similar fiscal responses.Positive During the crisis, many EU countries implemented reforms to combat the discouraged worker effect and keep workers in the labour market, such as decreasing the average hours worked per week. This made the early reduction in economic activity less drastic than originally projected.

	Author(s)	Countries/Periods Effects	Main Findings
	Verick and Islam	60 countries (2008-	Positive Fiscal stimuli have proven more effective in creating jobs when they focus on capital expenditures for employment-intensive infrastructure and labour
	(2010)	2009)			market measures. The US in 2009 enacted ARRA to restore employment mostly through tax cuts with a goal to create 3.5 million jobs by Q4 2010. By Q3
					2009, 300,000-1.5 million jobs were made; 8.4 million jobs were lost since 2007.
	Van Doorn,	20 countries	Mixed	A nation's original fiscal stance determines how it can respond during a crisis. Hungary, for example, now has greater foreign exchange risks because its
	Suri, and Gooptu	(1995-2010)		external debt surpassed its domestic debt prior to the crisis. Brazil, India, and Egypt have less risky exchange rates by accumulating more domestic debt
	(2010)				than external debt before the economic downturn hit.
	UNESCAP (2010)	37	countries
		(1990s -2009)
	IMF (2010a)	186 countries
		(1970-2010)
	Arpaia and Curci	27 EU countries
	(2010)	(1980s-2009)
	EEAG (2010)	27 countries
		(1990s-2009)
	Wyplosz (2010)	Eurozone -16
		countries
		(1996-2009)

Mixed

The EU's stimulus measures succeeded in curbing deflation and preventing a second depression. As example, Germany see its investment and domestic demand recover by the end of Q2/2009; however, consumption and GDP drop after an initial increase brought about by fiscal stimulus measures. ILO (2010a) EU (2006-2009) Mixed Mixed As a result of the European Globalization Adjustment Fund (EGAF) component of the European Economic Recovery Plan (EERP), 25,000 people received support in the form of skills training, job and career search help, promotion of entrepreneurship, and training for self-employment. This allowed many EU citizens to find jobs after losing work due to outsourcing.

Table 1 .A continued: Sample of studies on the effectiveness of stimulus measures

 1

	Kucera, Roncolato,	India and South	Negative Fiscal stimuli did not contribute much to GDP or job growth in India or South Africa. India's employment growth rate was 1.7% in Q4/2009 but only 0.2%
	and Uexkull (2010)	Africa (19602010)	in Q1/2010.

South Africa experienced 3 negative quarters of growth in 2009 and observed positive growth in Q4/2009 (0.7%), but growth decreased again in Q1/2010 (-1.3%). Employment declined by 770,000, 833,000, and 870,000 in Q3/2009, Q4/2009, and Q1/2010 respectively.

  Negative The US government's early response to the 2007 crisis worsened the situation by focusing on liquidity and bank credit market problems rather than risk, providing no help to other than banks and creditors. Measures such as term auction facilities, cash infusions, and interest rate cuts failed to substantially increase consumption, but it increased dollar inflation and raised oil prices. successful in allowing most state governments to maintain pre-crisis levels of employment in government and educational institutions, in spite of the massive decrease in tax revenue. This did come at the cost of decreased wages and working hours though. The bill also gave a 9-month subsidy for the unemployed that covered 65 per cent of former employers' healthcare.Positive The ARRA was able to slow down the rate of job and output loss while also returning GDP to positive levels. In Q2 2009, 2-3% was added to GDP, and in Q4/2009, 1.5-3% was added to GDP. Employment significantly increased under the ARRA, specifically between 1.5-2 million jobs by the end of 2009.Positive Unemployment insurance should not be reduced, as it both creates jobs and aids those without one. The unemployment insurance measures in the ARRA retained 1.7 million current jobs and created 1.2 million new jobs by July 2010.

	Taylor (2009)	United	States
		(2006-2008)
	Burtless (2010) The ARRA was US Government United States (2007-2010) Mixed United States Mixed Due to US stimulus packages, the decline in national GDP slowed from -6.4% in Q1/2009 to -0.7% in Q2/2009, and then turned around to 2.2 and 5.7% in
	(2010)	(1940s -2009)		Q3 and Q4 of 2009. The rate of job losses also has been reduced substantially, from a high of 691,000 in Q1/2009 to a low of only 69,000 in Q4/2009.
	Council of Economic	United	States
	Advisors (2010)	(2007-2009)
	Joint Eco. Committee	United	States	Mixed	By Q1 2010, the ARRA increased GDP by 1.7 to 4.2 per cent and decreased the national unemployment rate by 0.7 to 1.5 percentage points. This resulted
	-US Congress (2010)	(1950s-2010)			in the creation of 1.2-2.8 million jobs since the ARRA was enacted a year prior.
	Mishel and Shierholz	United	States
	(2010)	(2007-2010)
	Weller (2010)	United	States
		(1950s-2010)
	Flaherty (2010)	Canada	(2000-	Positive As a result of Canada's stimulus package, in 2009 both aggregate employment and GDP levels increased. Since its inception in July 2009, the Canada
		2010)				Action Plan has created 135,000 jobs out of its target of 225,000. The GDP increased by 0.9 per cent in Q3 of 2009 and by 5 per cent in Q4 of 2009. Canada
						also experienced the smallest decline in GDP out of all G7 nations, since the crisis began.
	ILO (2010g)	Canada			Positive The earnings protection and work sharing components of Canada's Action Plan were successful in saving many Canadian jobs during the crisis. In 2009,
		(20072010)			13,500 workers received C$3,323 in financial assistance for unpaid wages due to company closures and termination. Also, in 2009, 6,000 work sharing
						agreements were signed by Canadian employees, securing the employment of 167,410.
	Asian Development	Asia	(4	G20
	Bank, ADB (2010)	members and 10
		other developing
		countries)

Mixed

The ARRA allowed the private sector to start recovering prior losses in investment, production, and hiring. The US in Q2 2010 experienced a 2.4% growth rate and gained 630,000 new private sector jobs in the first 7 months of 2010, but unemployment still high and 7.7 million jobs lost since 2007.

  The medium-to long-run effects of increases in government consumption vary considerably depending on the level of development, exchange rate flexibility, openness to trade, and debt of the central government.

	OECD Economic	34 OECD
	Outlook,	Interim	Countries
	Report (2009)		(2008-2010)

Table 2 .A: Coefficient of correction to get fiscal multipliers from Cholesky impacts innovations by periods and countries samples

 2

		Government consumption growth rate standard error (𝜎 𝑔 )	Average of GDP to government consumption (𝑌/𝐺 ̅̅̅̅̅ )		𝑌/𝐺 ̅̅̅̅̅ /𝜎 𝑔
	Countries	1966Q1/ 2019Q2	1966Q1/ 1991Q4	1992Q1/ 2019Q4	1966Q1/ 2019Q2	1966Q1/ 1991Q4	1992Q1/ 2019Q4	1966Q1/ 2019Q2	1966Q1/ 1991Q4	1992Q1/ 2019Q4
	Austria	0.721	0.469	0.882	4.796	4.575	5.002	6.65	9.75	5.67
	Belgium	0.679	0.700	0.599	3.877	3.643	4.096	5.71	5.20	6.84
	Canada	1.056	1.288	0.704	4.091	3.616	4.536	3.88	2.81	6.45
	Denmark	0.821	0.850	0.751	4.156	4.215	4.101	5.06	4.96	5.46
	Finland	1.800	1.809	1.724	3.818	3.605	4.018	2.12	1.99	2.33
	France	0.468	0.498	0.291	4.275	4.298	4.253	9.14	8.62	14.63
	Germany	1.178	1.459	0.823	5.179	5.103	5.251	4.40	3.50	6.38
	Greece	1.827	1.026	2.272	5.558	5.967	5.174	3.04	5.82	2.28
	Ireland	1.898	1.116	2.415	5.002	3.717	6.205	2.64	3.33	2.57
	Italy	0.706	0.456	0.713	5.050	4.829	5.257	7.15	10.58	7.38
	Japan	0.928	1.119	0.576	5.758	6.067	5.469	6.20	5.42	9.49
	Netherlands	1.415	1.821	0.884	4.165	4.163	4.167	2.94	2.29	4.71
	Norway	1.423	1.444	1.350	4.590	4.756	4.435	3.22	3.29	3.28
	Portugal	1.096	1.010	0.671	6.890	8.262	5.606	6.28	8.18	8.35
	Spain	1.035	1.060	0.912	6.842	8.128	5.638	6.61	7.67	6.18
	Sweden	0.923	1.013	0.749	3.236	2.994	3.463	3.51	2.96	4.62
	United Kingdom	1.101	1.162	1.046	4.727	4.251	5.173	4.29	3.66	4.95
	United States	0.830	0.952	0.680	5.298	4.400	6.139	6.38	4.62	9.03

Table 3 .A. Sensitivity of government expenditure Cholesky impacts and the corresponding multipliers to different periods of time

 3

	1966Q1-1991Q4

Table 4 .A: Business cycle effects on government expenditure short run and long run multipliers

 4

	1992Q1-2019Q2 Country	Short run impact (1st quarter) Expansion Recession Expansion Recession Expansion Recession Expansion Recession Long run accumulated impact (5 years) Short run multiplier (1st quarter) Long run accumulated multiplier (5 years)	Short run multiplier (Recession Minus Expansion)	Long run accumulated multiplier (Recession Expansion) Minus
	Austria	-0.029	0.375	-0.085	1.292	-0.137	1.793	-0.404	6.175	1.93	6.58
	Belgium	-0.014	0.276	0.025	1.196	-0.071	1.429	0.131	6.201	1.50	6.07
	Canada	-0.027	0.383	-0.239	1.413	-0.137	1.907	-1.190	7.043	2.04	8.23
	Denmark	0.009	0.419	-0.158	0.814	0.033	1.506	-0.570	2.929	1.47	3.50
	Finland	0.071	0.366	0.108	0.752	0.141	0.728	0.215	1.498	0.59	1.28
	France	-0.080	0.153	-0.461	1.428	-0.318	0.611	-1.835	5.689	0.93	7.52
	Germany	-0.104	0.359	-0.307	0.805	-0.500	1.723	-1.474	3.861	2.22	5.33
	Greece	0.423	0.514	0.457	0.603	0.917	1.113	0.990	1.308	0.20	0.32
	Ireland	0.550	1.533	0.486	2.165	1.022	2.846	0.903	4.019	1.82	3.12
	Italy	0.112	0.195	0.213	0.515	0.641	1.120	1.226	2.956	0.48	1.73
	Japan	-0.085	0.322	-0.240	0.915	-0.461	1.745	-1.302	4.953	2.21	6.25
	Netherlands	-0.065	0.279	-0.069	1.538	-0.246	1.051	-0.261	5.796	1.30	6.06
	Norway	0.145	0.819	-0.004	0.906	0.427	2.405	-0.011	2.659	1.98	2.67
	Portugal	0.109	0.234	0.295	1.623	0.488	1.051	1.323	7.280	0.56	5.96
	Spain	0.085	0.407	0.087	1.481	0.396	1.893	0.406	6.895	1.50	6.49
	Sweden	-0.099	0.377	-0.200	1.012	-0.303	1.158	-0.614	3.109	1.46	3.72
	UK	-0.014	0.346	-0.117	1.414	-0.065	1.588	-0.535	6.488	1.65	7.02
	USA	-0.024	0.310	-0.181	1.060	-0.174	2.224	-1.298	7.608	2.40	8.91
	Average	0.05	0.43	-0.02	1.16	0.09	1.55	-0.24	4.80	1.46	5.04

Table 5 .A. Short run and long run government expenditure multipliers under debt accumulation and debt reduction

 5 Impact multipliers (IM) are adjusted by the corresponding adjustment coefficient from table 2.A to obtain fiscal multipliers (FM) according to the formulae 𝐹𝑀 = 𝐼𝑀 * 𝑌/𝐺 ̅̅̅̅̅ /𝜎 𝑔 . Convergence to the long run is fast if it is approximately attained in less than 5 quarters, medium between 6 and 9 quarters and slow in case it is reached in more than 10 quarters (this is clearly visible from the GDP responses charts).

			Cholesky impacts			Multipliers impacts
		Under debt	Under debt	Under debt	Under debt	Convergence to long run multiplier
		accumulation	reduction	accumulation	reduction
	Country	Short run	Long run	Short run	Long run	Short run	Long run	Short run	Long run	Under debt accumulation	Under debt reduction
	Austria	0.19	0.38	0.14	0.24	0.90	1.80	0.65	1.15	Fast	Fast
	Belgium	0.34	1.23	0.21	0.48	1.76	6.36	1.11	2.48	Medium	Medium
	Canada	0.31	0.85	0.10	0.03	1.54	4.21	0.51	0.13	Medium	Medium
	Denmark	0.31	0.34	0.14	0.08	1.12	1.22	0.50	0.28	Fast	Fast
	Finland	0.14	0.22	0.15	0.20	0.28	0.44	0.30	0.39	Fast	Fast
	France	0.09	0.63	0.03	0.40	0.35	2.49	0.13	1.60	Medium	Slow
	Germany	0.18	0.38	0.07	0.10	0.87	1.81	0.32	0.47	Fast	Fast
	Greece	0.77	1.20	0.67	1.01	1.67	2.61	1.44	2.18	Fast	Fast
	Ireland	1.48	1.70	0.38	0.14	2.75	3.16	0.70	0.27	Fast	Fast
	Italy	0.35	0.90	0.31	0.74	1.99	5.19	1.79	4.22	Medium	Medium
	Japan	0.09	0.16	0.07	0.21	0.48	0.89	0.37	1.12	Fast	Fast
	Netherlands	0.12	0.88	-0.06	0.09	0.45	3.32	-0.23	0.35	Medium	Fast
	Norway	0.52	0.30	0.62	0.50	1.54	0.89	1.83	1.48	Fast	Fast
	Portugal	0.20	0.70	0.04	0.31	0.88	3.16	0.20	1.38	Medium	Medium
	Spain	0.33	2.95	0.26	1.25	1.55	13.72	1.20	5.81	Slow	Slow
	Sweden	0.32	0.75	0.04	0.04	1.00	2.30	0.12	0.13	Fast	Fast
	UK	0.36	1.43	0.21	0.47	1.65	6.58	0.95	2.16	Slow	medium
	USA	0.15	0.28	0.03	-0.11	1.09	2.02	0.22	-0.76	Medium	Fast
	Average	0.35	0.85	0.19	0.34	1.22	3.45	0.67	1.38	--	--
	Notes:

Table 7 .A. Short run and long run GDP response to a structural government expenditure innovation from an SVAR with endogenous public debt

 7

			Short run Impact (1st quarter)	Impact in one year	Impact in two years	Long run impact (5 years)	Convergence to the long run
	Country	Sample	Expansion	Recession	Expansion	Recession	Expansion	Recession	Expansion	Recession	Expansion	Recession
	Austria	2000:1-2019:2	-0.05	0.29	-0.12	0.63	-0.12	0.69	-0.12	0.70	Fast	Medium
	Belgium	1995:4-2019:2	0.03	0.17	-0.07	0.62	-0.08	0.84	-0.08	0.95	Fast	Slow
	Canada	1990:1-2019:2	-0.02	0.29	-0.20	0.89	-0.22	1.16	-0.22	1.24	Fast	Medium
	Denmark	2000:1-2019:2	0.09	0.30	-0.07	0.56	-0.07	0.58	-0.07	0.58	Fast	Fast
	Finland	2000:1-2019:2	-0.05	0.23	-0.10	0.38	-0.10	0.38	-0.10	0.38	Fast	Fast
	France	1998:4-2019:2	0.03	0.21	-0.08	0.70	-0.12	1.02	-0.13	1.22	Medium	Slow
	Germany	1998:1-2019:2	-0.16	0.20	-0.35	0.68	-0.35	0.72	-0.35	0.72	Fast	Fast
	Greece	1997:4-2019:2	0.45	0.57	0.60	0.82	0.60	0.83	0.60	0.83	Fast	Fast
	Ireland	2000:1-2019:2	0.08	0.28	-0.05	0.61	-0.05	0.62	-0.05	0.62	Fast	Fast
	Italy	1995:4-2019:2	0.11	0.19	0.23	0.54	0.24	0.59	0.24	0.59	Fast	Fast
	Japan	1997:4-2019:2	0.00	0.24	-0.11	0.41	-0.12	0.42	-0.13	0.42	Fast	Fast
	Netherlands	1999:4-2019:2	-0.11	-0.02	-0.06	0.33	-0.05	0.45	-0.05	0.48	Fast	Medium
	Norway	1995:4-2019:2	0.13	0.70	0.02	0.83	0.03	0.82	0.03	0.82	Fast	Fast
	Portugal	1999:4-2019:2	-0.04	0.12	-0.07	0.33	-0.10	0.39	-0.10	0.40	Medium	Medium
	Spain	1995:4-2019:2	0.03	0.06	0.04	0.53	0.04	0.96	0.04	1.51	Medium	Slow
	Sweden	1995:4-2019:2	-0.10	0.36	-0.18	0.97	-0.18	1.10	-0.18	1.11	Fast	Medium
	UK	1995:1-2019:2	0.04	0.35	-0.02	1.07	-0.03	1.47	-0.03	1.68	Fast	Slow
	USA	1995:1-2019:2	0.05	0.42	-0.06	1.17	-0.06	1.41	-0.06	1.46	Fast	Medium
	Average	0.03	0.28	-0.04	0.67	-0.04	0.80	-0.04	0.87	--	--

Note: Convergence to the long run is fast if it is approximately attained in less than 5 quarters, medium between 6 and 9 quarters and slow in case it is reached in more than 10 quarters (this is clearly visible from the GDP responses charts).

Table 8 .A. Short run and long run government expenditure multipliers from an SVAR with endogenous public debt

 8

			Short run multiplier (1 st quarter)	1 st year multiplier	2 nd year multiplier	Long run multiplier (5 years)
	Country	Sample	Expansion	Recession	Expansion	Recession	Expansion	Recession	Expansion	Recession
	Austria	2000:1-2019:2	-0.25	1.40	-0.58	3.01	-0.57	3.31	-0.57	3.35
	Belgium	1995:4-2019:2	0.16	0.90	-0.37	3.21	-0.41	4.37	-0.41	4.91
	Canada	1990:1-2019:2	-0.11	1.44	-0.98	4.45	-1.08	5.79	-1.09	6.20
	Denmark	2000:1-2019:2	0.33	1.06	-0.25	2.02	-0.25	2.07	-0.25	2.07
	Finland	2000:1-2019:2	-0.10	0.47	-0.21	0.75	-0.20	0.76	-0.20	0.76
	France	1998:4-2019:2	0.13	0.84	-0.32	2.78	-0.47	4.07	-0.51	4.84
	Germany	1998:1-2019:2	-0.77	0.96	-1.69	3.25	-1.68	3.44	-1.68	3.44
	Greece	1997:4-2019:2	0.98	1.23	1.31	1.78	1.31	1.80	1.31	1.80
	Ireland	2000:1-2019:2	0.15	0.52	-0.10	1.14	-0.09	1.15	-0.09	1.15
	Italy	1995:4-2019:2	0.65	1.11	1.31	3.09	1.36	3.39	1.36	3.41
	Japan	1997:4-2019:2	0.00	1.30	-0.62	2.23	-0.67	2.25	-0.68	2.25
	Netherlands	1999:4-2019:2	-0.42	-0.07	-0.21	1.23	-0.20	1.70	-0.20	1.79
	Norway	1995:4-2019:2	0.39	2.04	0.07	2.44	0.08	2.42	0.08	2.42
	Portugal	1999:4-2019:2	-0.18	0.54	-0.31	1.46	-0.45	1.74	-0.46	1.78
	Spain	1995:4-2019:2	0.15	0.27	0.19	2.47	0.17	4.47	0.17	7.02
	Sweden	1995:4-2019:2	-0.31	1.09	-0.55	2.99	-0.55	3.37	-0.55	3.41
	United Kingdom	1995:1-2019:2	0.17	1.60	-0.09	4.90	-0.11	6.73	-0.12	7.69
	United States	1966:1-2019:2	0.23	1.86	-0.25	5.15	-0.27	6.22	-0.27	6.43
	Average		-0.25	1.40	-0.58	3.01	-0.57	3.31	-0.57	3.35

Note: Impact multipliers (IM) are adjusted by the corresponding adjustment coefficient from table 2.A to obtain fiscal multipliers (FM) according to the formulae 𝐹𝑀 = 𝐼𝑀 * 𝑌/𝐺 ̅̅̅̅̅ /𝜎 𝑔 . Figure 1.B.

a: Sensitivity of GDP responses to expenditures impact multipliers by period of time (1 st set of countries)

					Figure 1B.b:
					Austria					Austria					Belgium					Belgium
	.35					.035					.5					.20
	.33 .34					.034					.4					.18
	.32					.033										.16
	.31					.032					.3					.14
	.30			Period: 1966/Q1-1991/Q4	.031			Period: 1992/Q1-2019/Q2	.2			Period: 1966/Q1-1991/Q4	.12			Period: 1992/Q1-2019/Q2
	.29					.030										.10
	.27 .28					.029					.1					.08
	.26					.028					.0					.06
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Canada					Canada					Denmark					Denmark
	.28					.06					.50					.10
	.24 .26					.02 .04					.45					.06 .08
	.22					.00					.40					.04
	.20			Period: 1966/Q1-1991/Q4	-.04 -.02			Period: 1992/Q1-2019/Q2	.35			Period: 1966/Q1-1991/Q4	.02			Period: 1992/Q1-2019/Q2
	.18					-.06					.30					.00
	.14 .16					-.10 -.08					.25					-.04 -.02
	.12					-.12					.20					-.06
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Finland					Finland					France					France
	.06					.48					.20					-.1
	.02 .04					.44					.15					-.2
	.00					.40					.10					-.3
	-.02			Period: 1966/Q1-1991/Q4	.36			Period: 1992/Q1-2019/Q2	.05			Period: 1966/Q1-1991/Q4				Period: 1992/Q1-2019/Q2
	-.04					.32					.00					-.4
	-.08 -.06					.28					-.05					-.5
	-.10					.24					-.10					-.6
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18

Sensitivity of GDP responses to expenditures impact multipliers by period of time (2 nd set of countries)

				Figure 1.B.c:
				Germany					Germany				Greece				Greece
	.27				.06					.8				.95
	.25 .26				.02 .04					.6				.90
	.24				.00					.4				.85
	.23			Period: 1966/Q1-1991/Q4	-.02			Period: 1992/Q1-2019/Q2				Period: 1966/Q1-1991/Q4	.80			Period: 1992/Q1-2019/Q2
	.22				-.04					.2				.75
	.20 .21				-.08 -.06					.0				.70
	.19				-.10					-.2				.65
	2	4	6	8 10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18
				Ireland					Ireland				Italy				Italy
	1.0				.788					.36				.52
	0.9				.784					.32				.48
	0.3 0.4 0.5 0.6 0.7 0.8			Period: 1966/Q1-1991/Q4	.760 .764 .768 .780 .776 .772			Period: 1992/Q1-2019/Q2	.16 .28 .24 .20			Period: 1966/Q1-1991/Q4	.28 .44 .40 .32 .36			Period: 1992/Q1-2019/Q2
	0.2				.756					.12				.24
	0.1				.752					.08				.20
	2	4	6	8 10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18
				Japan					Japan				Netherland				Netherland
	.12				.07					.26				.20
	.10				.06					.24				.16
	.08				.05					.22
					.04									.12
	.06			Period: 1966/Q1-1991/Q4	.03			Period: 1992/Q1-2019/Q2	.20			Period: 1966/Q1-1991/Q4	.08			Period: 1992/Q1-2019/Q2
	.04				.02					.18
	.02				.01					.16				.04
	.00				.00					.14				.00
	2	4	6	8 10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18

Sensitivity of GDP responses to expenditures impact multipliers by period of time (3 rd set of countries)

	Figure 2.B.
				Norway				Norway				Portugal				Portugal
	.32				.3				.84				.9
									.82				.8
	.31				.2				.80				.7
	.30				.1				.78				.6
				Period: 1966/Q1-1991/Q4				Period: 1992/Q1-2019/Q2	.76			Period: 1966/Q1-1991/Q4	.5			Period: 1992/Q1-2019/Q2
	.29				.0				.74				.4
	.28				-.1				.72				.3
									.70				.2
	.27				-.2				.68				.1
	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18
				Spain				Spain				Sweden				Sweden
	.224				1.2				.34				-.01
	.222 .223				1.0				.32 .33				-.03 -.02
	.221				0.8				.31				-.04
	.219 .220			Period: 1966/Q1-1991/Q4	0.6			Period: 1992/Q1-2019/Q2	.30			Period: 1966/Q1-1991/Q4	-.05			Period: 1992/Q1-2019/Q2
	.217 .218				0.4				.28 .29				-.07 -.06
	.216				0.2				.27				-.08
	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18
				UK				UK				USA				USA
	.00				.070				.04				-.05
	-.02 -.01				.055 .060 .065				.01 .02 .03				-.15 -.10
	-.04 -.03			Period: 1966/Q1-1991/Q4	.035 .040 .045 .050			Period: 1992/Q1-2019/Q2	-.02 -.01 .00			Period: 1966/Q1-1991/Q4	-.30 -.25 -.20			Period: 1992/Q1-2019/Q2
	-.05				.030				-.03				-.35
	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18 20	2	4	6	8 10 12 14 16 18

a: The effects of the business cycle (expansion verusus recession) on GDP responses to government expenditure dynamic structural shock (1 st set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

	Figure 2.B.
					Au stria					Austria					Belgium					Belgium
	-.02					1.4					.03					1.4
	-.03					1.2					.02					1.2
	-.04					1.0										1.0
	-.05										.01
	-.06		EXPANSION	0.8			RECESSION	.00			EXPANSION	0.8			RECESSIO N
	-.07					0.6										0.6
	-.08					0.4					-.01					0.4
	-.09					0.2					-.02					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Can ada					Canada					Denmark					Denmark
	.00					1.6					.04					.9
	-.04					1.4					.00					.8
	-.08					1.2
	-.12					1.0					-.04					.7
	-.16		EXPANSION	0.8			RECESSION	-.08			EXPANSION	.6			RECESSIO N
	-.20					0.6
	-.24					0.4					-.12					.5
	-.28					0.2					-.16					.4
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Fin land					Finland					France					France
	.110					.8					.0					1.6
	.105															1.4
	.100					.7					-.1					1.2
	.095					.6					-.2					1.0
	.090		EXPANSION				RECESSION				EXPANSION	0.8			RECESSIO N
	.085					.5					-.3					0.6
	.080					.4					-.4					0.4
	.075															0.2
	.070					.3					-.5					0.0
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18

b: The effects of the business cycle (expansion verusus recession) on GDP responses to government expenditure dynamic structural shock (2 nd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Germany					Germany					Greece					Greece
	-.08					.9					.47					.62
	-.12					.8					.46					.60
	-.16					.7										.58
											.45
	-.20			EXPANSION	.6			RECESSION				EXPANSION	.56			RECESSION
											.44
	-.24					.5										.54
	-.28					.4					.43					.52
	-.32					.3					.42					.50
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Ireland					Ireland					Italy					Italy
	.56					2.2					.22					.52
	.54 .55					2.1					.20					.44 .48
	.53					2.0					.18					.40
	.51 .52			EXPANSION	1.8 1.9			RECESSION	.16			EXPANSION	.36 .32			RECESSION
	.50					1.7					.14					.28
	.48 .49					1.6					.12					.20 .24
	.47					1.5					.10					.16
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Japan					Japan					Netherland
	-.08					1.0					-.065					1.6
	-.12					0.9					-.066					1.4
						0.8										1.2
	-.16					0.7					-.067					1.0
	-.20			EXPANSION	0.6			RECESSION	-.068			EXPANSION	0.8
						0.5										0.6
	-.24					0.4					-.069					0.4
	-.28					0.3					-.070					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 RECESSION Netherland Figure 2.B.c: The effects of the business cycle (expansion verusus recession) on GDP responses to government expenditure dynamic structural shock (3 rd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

	Chapter 2. Short-term effects of public debt on growth: The spending multiplier pass-through
					Norway				Norway					Portugal					Portug al
	.15					.92					.300					1.8
	.10					.90					.250 .275					1.4 1.6
	.05					.88					.225					1.2
				EXPANSION	.86			RECESSION	.200			EXPANSION	1.0			RECESSION
	.00					.84					.175					0.8
	-.05					.82					.125 .150					0.4 0.6
	-.10					.80					.100					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Spain					Spain					Sweden					Sweden
	.0880					1.6					-.08					1.1
	.0875					1.4					-.10					1.0
	.0870					1.0 1.2					-.14 -.12					0.8 0.9
	.0860 .0865			EXPANSION	0.6 0.8			RECESSION	-.18 -.16			EXPANSION	0.5 0.6 0.7			RECESSION
	.0855					0.4					-.20					0.4
	.0850					0.2					-.22					0.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					UK					UK					USA					USA
	.00					1.6					.00					1.1
	-.04 -.02					1.0 1.2 1.4					-.08 -.04					0.8 0.9 1.0
	-.10 -.08 -.06			EXPANSION	0.4 0.6 0.8			RECESSION	-.16 -.12			EXPANSION	0.4 0.5 0.6 0.7			RECESSION
	-.12					0.2					-.20					0.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
									156

a: The effects of the debt ratio movments (accumulation versus contraction) on GDP responses to government expenditure dynamic structural shock (1 st set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

	.20 .24 .28 .32 .36 .40 Figure 5.B..16 DEBT ACCUMULATION Austria		.12 .14 .16 .18 .20 .22 .24 .26			DEBT REDUCTION Austria		0.2 0.4 0.6 0.8 1.0 1.2 1.4			DEBT ACCUMULATION Belgium	.20 .25 .30 .35 .40 .45 .50	DEBT REDUCTION Belgium
		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18
						Canada								Canada								Denmark			Denmark
	.9								.11								.340							.15
	.8								.09 .10								.335							.13 .14
	.7								.08								.330							.12
	.6				DEBT ACCUMULATION		.06 .07			DEBT REDUCTION		.325			DEBT ACCUMULATION	.11	DEBT REDUCTION
	.5								.05								.320							.10
	.4								.03 .04								.315							.08 .09
	.3								.02								.310							.07
		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18 20		2	4	6	8	10 12 14 16 18
						Finland								Finland								France
	.24								.20								.7							.45
	.22								.19								.6							.35 .40
	.20								.18								.5							.30
	.18				DEBT ACCUMULATION		.17			DEBT REDUCTION		.3 .4			DEBT ACCUMULATION	.20 .25
	.14 .16		Short run multipliers under debt accumulation .15 .16			200	.1 Long run multipliers under debt accumulation .2		.05 .10 .15
	.12	2	4	6	8	10 12 14 16 18 20	.14	2	4	6	8	150 10 12 14 16 18 20	.0	2	4	6	8	10 12 14 16 18 20	.00	2	4	6	8	10 12 14
														100
														50
														0
				.50	1.00	1.50	2.00	2.50	3.00		0.00	5.00		10.00			15.00
			200 Short run multipliers under debt reduction					200 Short run multipliers under debt reduction
			150													150
			100													100
			50													50
			0													0
	-0.50	0.00	0.50	1.00	1.50		2.00		-2.00	0.00	2.00		4.00			6.00	8.00

16 18 DEBT REDUCTION France Figure 5.B.b: The effects of the debt ratio movments (accumulation versus contraction) on GDP responses to government expenditure dynamic structural shock (2 nd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Germany					Germany					Greece					Greece
	.40					.100					1.3					1.05
	.36					.095					1.2					1.00
	.32					.085 .090					1.1					0.90 0.95
	.24 .28			DEBT ACCUMULATION	.075 .080			DEBT REDUCTION	0.9 1.0			DEBT ACCUMUL ATION	0.75 0.80 0.85			DEBT REDUCTION
	.20					.070					0.8					0.70
	.16					.065					0.7					0.65
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Ireland					Irelan d					Italy					Italy
	1.84					.4					1.0					.8
	1.76 1.80					.3					0.8 0.9					.7
											0.7					.6
	1.72			DEBT ACCUMULATION	.2			DEBT REDUCTION	0.6			DEBT ACCUMUL ATION	.5			DEBT REDUCTION
	1.64 1.68					.1					0.5 0.4					.4
	1.60					.0					0.3					.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Japan					Jap an					Neth erlan d
	.17					.22					.9					.12
	.16					.20					.8
	.15					.18					.7					.08
	.11 .12 .13 .14			DEBT ACCUMULATION	.12 .14 .16			DEBT REDUCTION	.4 .5 .6			DEBT ACCUMUL ATION	.00 .04
	.10					.10					.3					-.04
	.09					.08					.2
	.08					.06					.1					-.08
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 DEBT REDUCTION Netherland Figure 5.B.c: The effects of the debt ratio movments (accumulation versus contraction) on GDP responses to government expenditure dynamic structural shock (3 rd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Norway					Norway					Portugal					Portugal
	.55					.64					.8					.32
	.50					.62					.7					.28
						.60
	.45					.58					.6					.24
	.40					.56					.5					.20
	.35			DEBT ACCUMULATION	.54			DEBT REDUCTION	.4			DEBT ACCUMULATION	.16			DEBT REDUCTION
	.30					.52					.3					.12
						.50
	.25					.48					.2					.08
	.20					.46					.1					.04
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					Spain					Spain					Sweden					Sweden
	3.0					1.4					.8					.0428
	2.5					1.2					.7					.0420 .0424
	2.0					1.0										.0416
	1.5			DEBT ACCUMULATION	0.8			DEBT REDUCTION	.6 .5			DEBT ACCUMULATION	.0412 .0408			DEBT REDUCTION
	1.0					0.6										.0404
	0.5					0.4					.4					.0396 .0400
	0.0					0.2					.3					.0392
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18
					UK					UK					USA
	1.6					.48					.30					.04
	1.4					.44					.28					.02
	1.2					.40					.26					.00
	1.0					.36					.24					-.02
	0.8			DEBT ACCUMULATION	.32			DEBT REDUCTION	.20 .22			DEBT ACCUMULATION	-.06 -.04
	0.6					.28					.18					-.08
	0.4					.24					.16					-.10
	0.2					.20					.14					-.12
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 DEBT REDUCTION USA Figure 6.B.a: The effects of the debt ratio accumulation and the business cycle on GDP responses to government expenditure dynamic structural shock (1 st set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Austria					Austria					Belgium					Belgium
	.104					.65					.9					1.6
	.100					.60					.8					1.4
	.096					.50 .55					.6 .7					1.0 1.2
	.088 .092		DEBT ACCUMULATION and EXPANSION	.35 .40 .45		DEBT ACCUMULATION and RECESSION	.4 .5		DEBT ACCUMULATION and EXPANSION	0.6 0.8		DEBT ACCUMULATION and RECESSION
	.084					.30					.3					0.4
	.080					.25					.2					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Canada					Canada					Denmark					Denmark
	.60					1.6					.226					.55
	.45 .50 .55					1.2 1.4					.220 .224 .222					.45 .50
	.30 .35 .40		DEBT ACCUMULATION and EXPANSION	0.6 0.8 1.0		DEBT ACCUMULATION and RECESSION	.212 .214 .216 .218		DEBT ACCUMULATION and EXPANSION	.35 .40		DEBT ACCUMULATION and RECESSION
	.25					0.4					.210					.30
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Finland					Finland					France
	.055					.34					.40					1.4
	.050					.32					.35					1.2
	.045					.28 .30					.25 .30					0.8 1.0
	.035 .040		DEBT ACCUMULATION and EXPANSION	.22 .24 .26		DEBT ACCUMULATION and RECESSION	.10 .15 .20		DEBT ACCUMULATION and EXPANSION	0.4 0.6
	.030					.20					.05					0.2
	.025					.18					.00					0.0
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT ACCUMULATION and RECESSION France Figure 6.B.b: The effects of the debt ratio accumulation and the business cycle on GDP responses to government expenditure dynamic structural shock (2 nd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Germany					Germany					Greece					Greece
	.11					.7					1.3					.85
	.10					.6					1.2					.80
	.09										1.1					.75
						.5
	.08		DEBT ACCUMULATION and EXPANSION			DEBT ACCUMULATION and RECESSION	1.0		DEBT ACCUMULATION and EXPANSION	.70		DEBT ACCUMULATION and RECESSION
						.4
	.07										0.9					.65
	.06					.3					0.8					.60
	.05					.2					0.7					.55
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Ireland					Irelan d					Italy					Italy
	1.72					1.80					.7					.8
	1.68					1.76					.6					.7
	1.64					1.72					.5					.6
			DEBT ACCUMULATION and EXPANSION			DEBT ACCUMULATION and RECESSION			DEBT ACCUMULATION and EXPANSION			DEBT ACCUMULATION and RECESSION
	1.60					1.68					.4					.5
	1.56					1.64					.3					.4
	1.52					1.60					.2					.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Japan					Jap an					Neth erlan d
	-.10					.60					.7					1.0
	-.15					.55					.6					0.8 0.9
						.50					.5					0.7
	-.20					.45					.4					0.6
	-.25		DEBT ACCUMULATION and EXPANSION	.40		DEBT ACCUMULATION and RECESSION	.3		DEBT ACCUMULATION and EXPANSION	0.5
						.35					.2					0.4
	-.30					.30					.1					0.2 0.3
	-.35					.25					.0					0.1
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT ACCUMULATION and RECESSION Netherland Figure 6.B.c: The effects of the debt ratio accumulation and the business cycle on GDP responses to government expenditure dynamic structural shock (3 rd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Norway					Norway					Portu gal					Portugal
	.48					.80					.50					.50
	.44					.79					.45					.45
	.36 .40					.78					.40					.35 .40
	.28 .32		DEBT ACCUMULATION and EXPANSION	.76 .77		DEBT ACCUMULATION and RECESSION	.30 .35		DEBT ACCUMULATION and EXPANSION	.20 .25 .30	DEBT ACCUMULATION and RECESSION
	.24					.75					.25					.15
	.20					.74					.20					.10
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Spain					Spain					Sweden					Sweden
	2.4					3.0					.55					1.2
	2.0					2.5					.50					1.0 1.1
	1.6					2.0					.45					0.9
	1.2		DEBT ACCUMULATION and EXPANSION	1.5		DEBT ACCUMULATION and RECESSION	.40 .35		DEBT ACCUMULATION and EXPANSION	0.8 0.7	DEBT ACCUMULATION and RECESSION
	0.8					1.0					.30					0.6
	0.4					0.5					.25					0.4 0.5
	0.0					0.0					.20					0.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					UK					UK					USA
	1.0					1.6					.32					1.1
	0.9					1.4					.30					1.0
	0.8					1.2					.28					0.9
	0.7					1.0					.26					0.8
	0.5 0.6		DEBT ACCUMULATION and EXPANSION	0.8		DEBT ACCUMULATION and RECESSION	.22 .24		DEBT ACCUMULATION and EXPANSION	0.6 0.7
	0.4					0.6					.20					0.5
	0.3					0.4					.18					0.4
	0.2					0.2					.16					0.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT ACCUMULATION and RECESSION USA Figure 7.B.a: The effects of the debt ratio reduction and the business cycle on GDP responses to government expenditure dynamic structural shock (1 st set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Austria					Austria					Belgium					Belg ium
	-.06					.28					.02					.60
	-.08					.26					.00					.55
	-.10					.22 .24					-.04 -.02					.45 .50
	-.14 -.12		DEBT REDUCTION and EXPANSION	.18 .20		DEBT REDUCTION and RECESSION	-.08 -.06		DEBT REDUCTION and EXPANSION	.30 .35 .40		DEBT REDUCTION and RECESSION
	-.16					.16					-.10					.25
	-.18					.14					-.12					.20
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Canada					Canada					Denmark					Denmark
	-.04					.36					.02					.22
	-.08					.32					-.02 .00					.20 .21
	-.20 -.16 -.12		DEBT REDUCTION and EXPANSION	.24 .28		DEBT REDUCTION and RECESSION	-.10 -.04 -.08 -.06		DEBT REDUCTION and EXPANSION	.17 .19 .18		DEBT REDUCTION and RECESSION
	-.24					.20					-.14 -.12					.15 .16
	-.28					.16					-.16					.14
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Finland					Finland					France
	-.04					.168					-.10					.8
	-.06 -.05					.160 .164					-.25 -.20 -.15					.5 .6 .7
	-.09 -.08 -.07		DEBT REDUCTION and EXPANSION	.152 .156		DEBT REDUCTION and RECESSION	-.45 -.40 -.35 -.30		DEBT REDUCTION and EXPANSION	.2 .3 .4
	-.10					.148					-.50					.1
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT REDUCTION and RECESSION Fran ce Figure 7.B.b: The effects of the debt ratio reduction and the business cycle on GDP responses to government expenditure dynamic structural shock (2 nd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Germany					Germany					Greece					Greece
	-.20					.20					.84					.40
	-.24					.18					.80					.38 .39
	-.28					.16					.76					.37
	-.32		DEBT REDUCTION and EXPANSION	.14		DEBT REDUCTION and RECESSION	.72 .68		DEBT REDUCTION and EXPANSION	.36 .35		DEBT REDUCTION and RECESSION
	-.36					.12					.64					.34
	-.40					.10					.60					.32 .33
	-.44					.08					.56					.31
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Ireland					Ireland					Italy					Italy
	.30					.36					.44					.52
	.25					.32					.40					.48
						.28
	.20					.24					.36					.44
	.15					.20					.32					.40
	.10		DEBT REDUCTION and EXPANSION	.16		DEBT REDUCTION and RECESSION	.28		DEBT REDUCTION and EXPANSION	.36		DEBT REDUCTION and RECESSION
	.05					.12					.24					.32
						.08
	.00					.04					.20					.28
	-.05					.00					.16					.24
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Japan					Japan					Netherland
	-.16					.55					-.115					.150
	-.20					.50					-.120					.125
	-.28 -.24					.40 .45					-.125					.075 .100
	-.36 -.32		DEBT REDUCTION and EXPANSION	.30 .35		DEBT REDUCTION and RECESSION	-.135 -.130		DEBT REDUCTION and EXPANSION	.000 .025 .050
	-.40					.25					-.140					-.025
	-.44					.20					-.145					-.050
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT REDUCTION and RECESSION Netherland Figure 7.B.c: The effects of the debt ratio reduction and the business cycle on GDP responses to government expenditure dynamic structural shock (3 rd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

					Norway					Norway					Portugal					Portugal
	.20					.76					.13					.20
	.16					.72 .74					.11 .12					.16
	.12					.70					.10					.12
			DEBT REDUCTION and EXPANSION	.68		DEBT REDUCTION and RECESSION	.09		DEBT REDUCTION and EXPANSION	.08		DEBT REDUCTION and RECESSION
	.08					.66					.08					.04
	.04					.64 .62					.07 .06					.00
	.00					.60					.05					-.04
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Spain					Spain					Sweden					Sweden
	.17					1.0					-.14					.24
	.16					0.9					-.15					.22
	.15					0.8					-.16					.20
	.14					0.7					-.17					.18
	.13		DEBT REDUCTION and EXPANSION	0.6		DEBT REDUCTION and RECESSION	-.19 -.18		DEBT REDUCTION and EXPANSION	.16		DEBT REDUCTION and RECESSION
	.12					0.5					-.20					.14
	.11					0.4					-.21					.12
	.10					0.3					-.22					.10
	.09					0.2					-.23					.08
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					UK					UK					USA
	.00					.50					.00					.16
	-.02					.45					-.04					.15
	-.04					.40					-.08					.14
	-.06		DEBT REDUCTION and EXPANSION	.35		DEBT REDUCTION and RECESSION	-.12		DEBT REDUCTION and EXPANSION	.13
	-.08					.30					-.16					.12
	-.10					.25					-.20					.11
	-.12					.20					-.24					.10
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 DEBT REDUCTION and RECESSION USA Figure 8.B. Eexpenditure multiplier under business cycle and public debt movements versus the public debt ratio average

	Figure 9.B.
	Short run multipliers in expansion and		Long run multipliers in expansion and
			200 debt accumulation						200 debt accumulation
			150									150
			100									100
			50									50
	-1.00	-0.50	0 0.00	0.50		1.00	1.50	-3.00	-2.00	-1.00	0 0.00	1.00	2.00	3.00
		Short run multipliers in expansion and		Long run multipliers in expansion and
			200 debt reduction						200 debt reduction
			150								150
			100								100
				50								50
	-1.50	-1.00	-0.50	0 0.00	0.50	1.00	1.50	-3.00	-2.00	-1.00	0 0.00	1.00	2.00	3.00
		Short run multipliers in Recession and			Long run multipliers in Recession and
	200		debt accumulation			200		debt accumulation
	150								150
	100								100
	50								50
	0 0.00	0.50	1.00	1.50	2.00	2.50	3.00	0 0.00		5.00	10.00	15.00
		Short run multipliers in Recession and debt		Long run multipliers in Recession and
		200		reduction			200			debt reduction
		150							150
		100							100
		50							50
		0							0
	-0.50	0.00	0.50	1.00	1.50	2.00	0.00	1.00	2.00	3.00	4.00	5.00

a: The endogenous effects of the public debt ratio and the business cycle on GDP responses to government expenditure dynamic structural shock from a trivarite SVAR model (1 st set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

				Austria				Austria				Belgium				Belg ium
	-.05				.8					.04					1.0
	-.07 -.06				.7					.02					0.8 0.9
	-.08				.6					.00					0.7
	-.09		EXPANSION	.5			RECESSION	-.02			EXPANSION	0.6 0.5			RECESSION
	-.10				.4					-.04					0.4
	-.12 -.11				.3					-.06					0.2 0.3
	-.13				.2					-.08					0.1
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
				Canada				Canada				Denmark				Denmark
	.00				1.4					.12					.60
	-.04				1.2					.08					.55
	-.08				1.0										.50
										.04					.45
	-.12		EXPANSION	0.8			RECESSION	.00			EXPANSION	.40			RECESSION
	-.16				0.6										.35
	-.20				0.4					-.04					.30
	-.24				0.2					-.08					.25
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
				Finland				Finland					France
	-.04				.40					.04					1.4
	-.06 -.05				.36 .38					.00					1.2
	-.09 -.08 -.07		EXPANSION	.28 .30 .32 .34			RECESSION	-.08 -.04			EXPANSION	0.6 0.8 1.0
	-.11 -.10				.24 .26					-.12					0.4
	-.12				.22					-.16					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 RECESSION Fran ce Figure 9.B.b: The endogenous effects of the public debt ratio and the business cycle on GDP responses to government expenditure dynamic structural shock from a trivarite SVAR model (2 nd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

				Germany				Germany					Greece					Greece
	-.12				.8					.62					.84
	-.16				.7					.58 .60					.80
	-.20				.6					.56					.76
	-.24		EXPANSION	.5 .4			RECESSION	.54 .52			EXPANSION	.72 .68			RECESSION
	-.28				.3					.50					.64
	-.32				.2					.48 .46					.60
	-.36				.1					.44					.56
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
				Ireland				Ireland					Italy					Italy
	.12				.65					.24					.6
	.04 .08				.50 .55 .60					.18 .20 .22					.4 .5
	-.08 -.04 .00		EXPANSION	.30 .35 .40 .45			RECESSION	.12 .14 .16			EXPANSION	.2 .3			RECESSION
	-.12				.25					.10					.1
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Japan					Japan				Netherlands
	.00				.44					-.05					.5
	-.02				.40					-.06					.4
	-.04				.36					-.07					.3
	-.06									-.08
	-.08		EXPANSION	.32			RECESSION	-.09			EXPANSION	.2
	-.10				.28					-.10					.1
	-.12				.24					-.11					.0
	-.14				.20					-.12					-.1
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 RECESSION Netherlands Figure 9.B.c: The endogenous effects of the public debt ratio and the business cycle on GDP responses to government expenditure dynamic structural shock from a trivarite SVAR model (3 rd set of countries)

  Note: Shaded area bar corresponds to the fourth quarter.

				Norway				Norway				Portugal				Portugal
	.16				.88					-.03					.40
	.12				.84					-.05 -.04					.35
	.08				.80					-.06					.30
			EXPANSION				RECESSION	-.07			EXPANSION	.25			RECESSION
	.04				.76					-.08					.20
	.00				.72					-.09 -.10					.15
	-.04				.68					-.11					.10
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					Spain					Spain				Sweden				Sweden
	.042				1.6					-.08					1.2
	.040				1.2 1.4					-.10					1.0 1.1
	.038				1.0					-.12					0.9
	.036		EXPANSION	0.8			RECESSION	-.14			EXPANSION	0.8 0.7			RECESSION
	.034				0.6					-.16					0.6
	.032				0.2 0.4					-.18					0.4 0.5
	.030				0.0					-.20					0.3
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20
					UK					UK					USA
	.04				1.8					.06					1.4
	.03				1.6					.04					1.2
	.01 .02				1.2 1.4					.00 .02					1.0
	-.01 .00		EXPANSION	0.6 0.8 1.0			RECESSION	-.04 -.02			EXPANSION	0.6 0.8
	-.02				0.4					-.06					0.4
	-.03				0.2					-.08					0.2
	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14 16 18 20	2	4	6	8	10 12 14

16 18 20 RECESSION USA Figure 10.B The expenditure multipliers from the trivariate SVAR with endogenous debt varibale and controlled for the business cycle, scattered with the average level of the public debt ratio

					Figure 11.B.a.
		200	Short run impact in Expansion			200 Long run impact in Expansion
		150						150
		100						100
		50						50
		0						0
	-0.20	0.00	0.20	0.40	0.60	-0.40 -0.20	0.00	0.20	0.40	0.60	0.80
		200	Short run impact in Recession	200	Long run impact in Recession
		150					150
		100					100
		50					50
		0					0
	-0.20	0.00	0.20	0.40	0.60	0.80	0.00	0.50	1.00		1.50	2.00

Impulse response functions in time of economic expansion

													Figure 11.B.b.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RINTR to Shock2					Response of LDR to Shock2
	.0004									.002										.0004										.0004										.016
	.0000									.000										.0002										.0000										.012
										-.002										.0000
																														-.0004										.008
	-.0004									-.004										-.0002
																														-.0008										.004
										-.006										-.0004
	-.0008									-.008										-.0006										-.0012										.000
	-.0012									-.010										-.0008										-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RINTR to Shock6					Response of LDR to Shock6
	.006									.04										.0004										.0008										.002
	.005									.03										.0002										.0004										.000
	.004																			.0000
	.003									.02																				.0000										-.002
																				-.0002
	.002									.01																				-.0004										-.004
	.001																			-.0004
	.000									.00										-.0006										-.0008										-.006
	-.001									-.01										-.0008										-.0012										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RINTR to Shock5					Response of LDR to Shock5
	.0002									.001										.003										.0005										.004
										.000																				.0004
	.0000																																							.002
										-.001										.002										.0003
	-.0002									-.002																				.0002										.000
	-.0004									-.003										.001										.0001										-.002
										-.004																				.0000
	-.0006																																							-.004
										-.005										.000										-.0001
	-.0008									-.006																				-.0002										-.006
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RINTR to Shock1					Response of LDR to Shock1
	.0015									.012										.0010										.005										.001
	.0010									.008										.0008										.004										.000
																				.0006										.003										-.001
	.0005
										.004										.0004										.002										-.002
	.0000
																				.0002										.001										-.003
	-.0005									.000										.0000										.000										-.004
	-.0010									-.004										-.0002										-.001										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of economic recession

													Figure 11.B.c.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RINTR to Shock2					Response of LDR to Shock2
	.0025									.006										.0008										.0004										.016
	.0020									.004																				.0000										.012
	.0015																			.0004
										.002																				-.0004										.008
	.0010
										.000										.0000										-.0008										.004
	.0005
	.0000									-.002										-.0004										-.0012										.000
	-.0005									-.004																				-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RINTR to Shock6					Response of LDR to Shock6
	.005									.04										.0004										.0004										.002
	.003 .004									.03										.0002										.0000										.000 .001
										.02										.0000																				-.001
	.002																													-.0004
										.01										-.0002																				-.002
	.000 .001									.00										-.0004										-.0008										-.004 -.003
	-.001									-.01										-.0006										-.0012										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RINTR to Shock5					Response of LDR to Shock5
	.0025									.005										.0030										.0006										.001
	.0020									.004										.0025										.0005										.000
	.0015									.003										.0020										.0004										-.001
																														.0003
	.0010									.002										.0015																				-.002
																														.0002
	.0005									.001										.0010										.0001										-.003
	.0000									.000										.0005										.0000										-.004
	-.0005									-.001										.0000										-.0001										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RINTR to Shock1					Response of LDR to Shock1
	.0012																			.00100										.005										.001
	.0008									.008										.00075										.004										.000
	.0004									.004										.00050										.003										-.001
	.0000																			.00025										.002
																																								-.002
	-.0004									.000										.00000										.001
	-.0008																													.000										-.003
																				-.00025
	-.0012									-.004																				-.001										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt accumulation

														Figure 11.B.d.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RINTR to Shock2					Response of LDR to Shock2
	.0010									.004										.0004										.0005										.016
	.0005									.000										.0000										.0000										.012
	.0000
																				-.0004										-.0005										.008
	-.0005									-.004
																				-.0008										-.0010										.004
	-.0010
	-.0015									-.008										-.0012										-.0015										.000
	-.0020									-.012										-.0016										-.0020										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RINTR to Shock6					Response of LDR to Shock6
	.008									.04										.0006										.0008										.002
	.006									.03										.0004										.0004										.000
																				.0002
	.004									.02																				.0000										-.002
																				.0000
	.002									.01																				-.0004										-.004
																				-.0002
	.000									.00										-.0004										-.0008										-.006
	-.002									-.01										-.0006										-.0012										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RINTR to Shock5					Response of LDR to Shock5
	.0010									.002										.0028										.0005										.002
	.0006 .0008									.000 .001										.0016 .0020 .0024										.0002 .0003 .0004										-.001 .000 .001
	.0004																			.0012
	.0000 .0002									-.002 -.001										.0000 .0004 .0008										-.0001 .0000 .0001										-.004 -.003 -.002
	-.0002									-.003										-.0004										-.0002										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RINTR to Shock1					Response of LDR to Shock1
	.0020									.012										.0012										.005										.001
	.0015																													.004										.000
	.0010									.008										.0008										.003										-.001
	.0005									.004																				.002										-.002
																				.0004
	.0000																													.001										-.003
										.000
	-.0005																			.0000										.000										-.004
	-.0010									-.004																				-.001										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt reduction

											Figure 11.B.e.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RI NTR to Shock2					Response of LDR to Shock2
	.0028									.008										.00100										.0004										.016
	.0020 .0024									.004										.00075										.0000										.012
	.0016																			.00050										-.0004										.008
	.0012									.000										.00025										-.0008
	.0008																			.00000										-.0012										.004
	.0000 .0004									-.004										-.00025										-.0016										.000
	-.0004									-.008										-.00050										-.0020										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RI NTR to Shock6					Response of LDR to Shock6
	.008									.04										.0006										.0008										.002
	.006									.03										.0004										.0004										.000
																				.0002
	.004									.02																														-.002
																				.0000										.0000
	.002									.01																														-.004
																				-.0002
	.000									.00										-.0004										-.0004										-.006
	-.002									-.01										-.0006										-.0008										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RI NTR to Shock5					Response of LDR to Shock5
	.0012									.003										.0030										.0008										.002
	.0008									.002										.0025										.0006										.001
										.001										.0020																				.000
	.0004																													.0004										-.001
										.000										.0015
	.0000																													.0002										-.002
										-.001										.0010																				-.003
	-.0004									-.002										.0005										.0000										-.004
	-.0008									-.003										.0000										-.0002										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RI NTR to Shock1					Response of LDR to Shock1
	.002									.0100										.00100										.005										.001
										.0075										.00075										.004										.000
	.001									.0050										.00050										.003										-.001
	.000									.0025										.00025										.002										-.002
										.0000										.00000										.001
	-.001									-.0025										-.00025										.000										-.003
										-.0050																				-.001										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt reduction and expansion

											Figure 11.B.f.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RI NTR to Shock2					Response of LDR to Shock2
	.004									.008										.00100										.0004										.016
	.003																			.00075										.0000										.012
										.004										.00050
	.002																													-.0004										.008
																				.00025
	.001									.000																				-.0008										.004
																				.00000
	.000									-.004										-.00025										-.0012										.000
	-.001																			-.00050										-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RI NTR to Shock6					Response of LDR to Shock6
	.008									.04										.0006										.0008										.002
	.006									.03										.0004										.0004										.000
																				.0002
	.004									.02																				.0000										-.002
																				.0000
	.002									.01																				-.0004										-.004
																				-.0002
	.000									.00										-.0004										-.0008										-.006
	-.002									-.01										-.0006										-.0012										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RI NTR to Shock5					Response of LDR to Shock5
	.0012									.002										.0030										.0005										.002
	.0008									.001										.0025										.0004										.001
										.000										.0020										.0003										.000
	.0004																													.0002										-.001
										-.001										.0015
	.0000																													.0001										-.002
										-.002										.0010										.0000										-.003
	-.0004									-.003										.0005										-.0001										-.004
	-.0008									-.004										.0000										-.0002										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RI NTR to Shock1					Response of LDR to Shock1
	.002									.012										.00100										.005										.001
	.001									.008										.00050 .00075										.003 .004										-.001 .000
	.000									.004										.00025										.002										-.002
	-.001									.000										-.00025 .00000										.001 .000										-.003
										-.004																				-.001										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt reduction and recession

										Figure 11.B.g.
			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RI NTR to Shock2					Response of LDR to Shock2
	.0016									.004										.0008										.0004										.016
	.0012									.002																				.0000										.012
										.000										.0004
	.0008																													-.0004										.008
										-.002
	.0004																			.0000										-.0008										.004
										-.004
	.0000									-.006										-.0004										-.0012										.000
	-.0004									-.008																				-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RI NTR to Shock6					Response of LDR to Shock6
	.006									.04										.0006										.00050										.002
	.005									.03										.0004										.00025										.000
	.004																			.0002										.00000
	.003									.02																														-.002
																				.0000										-.00025
	.002									.01																														-.004
	.001																			-.0002										-.00050
	.000									.00										-.0004										-.00075										-.006
	-.001									-.01										-.0006										-.00100										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RI NTR to Shock5					Response of LDR to Shock5
	.0020									.005										.0030										.0008										.001
	.0015									.004										.0025										.0006										.000
										.003										.0020																				-.001
	.0010																													.0004
										.002										.0015																				-.002
	.0005																													.0002
										.001										.0010																				-.003
	.0000									.000										.0005										.0000										-.004
	-.0005									-.001										.0000										-.0002										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RI NTR to Shock1					Response of LDR to Shock1
	.0015																			.0012										.005										.001
	.0010									.008										.0008										.004										.000
																														.003
	.0005									.004																														-.001
																				.0004										.002
	.0000																																							-.002
	-.0005									.000										.0000										.001 .000										-.003
	-.0010									-.004										-.0004										-.001										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt accumulation and expansion

										Figure 11.B.h.
			Response of LGDP to Shock2					R esponse of LPIN V to Shock 2					Response of LPRC to Shock2					Response of RINTR to Shock2					Response of LDR to Shock2
	.0004									.004										.0004										.0004										.016
	.0000
										.000										.0000										.0000										.012
	-.0004
	-.0008									-.004										-.0004										-.0004										.008
	-.0012									-.008										-.0008										-.0008										.004
	-.0016
										-.012										-.0012										-.0012										.000
	-.0020
	-.0024									-.016										-.0016										-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					R esponse of LPIN V to Shock 6					Response of LPRC to Shock6					Response of RINTR to Shock6					Response of LDR to Shock6
	.008									.04										.0004										.0008										.002
	.006									.03										.0002										.0004										.000
																				.0000
	.004									.02																				.0000										-.002
																				-.0002
	.002									.01																				-.0004										-.004
																				-.0004
	.000									.00										-.0006										-.0008										-.006
	-.002									-.01										-.0008										-.0012										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					R esponse of LPIN V to Shock 5					Response of LPRC to Shock5					Response of RINTR to Shock5					Response of LDR to Shock5
	.00100									.002										.003										.0005										.004
	.00075									.001																				.0004										.002
	.00050									.000										.002										.0003 .0002										.000
	.00025									-.001										.001										.0001										-.002
	.00000									-.002																				.0000
	-.00025									-.003										.000										-.0001										-.004
										-.004																				-.0002										-.006
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					R esponse of LPIN V to Shock 1					Response of LPRC to Shock1					Response of RINTR to Shock1					Response of LDR to Shock1
	.0020									.012										.0012										.005										.001
	.0015																													.004										.000
	.0010									.008										.0008										.003										-.001
	.0005									.004																				.002										-.002
																				.0004
	.0000																													.001										-.003
										.000
	-.0005																			.0000										.000										-.004
	-.0010									-.004																				-.001										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Impulse response functions in time of debt accumulation and recession

			Response of LGDP to Shock2					Response of LPINV to Shock2					Response of LPRC to Shock2					Response of RINTR to Shock2					Response of LDR to Shock2
	.0028									.008										.0008										.0004										.016
	.0016 .0020 .0024									.004 .006										.0004										-.0004 .0000										.008 .012
	.0012									.002
	.0008									.000										.0000										-.0008										.004
	.0000 .0004									-.002										-.0004										-.0012										.000
	-.0004									-.004																				-.0016										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock6					Response of LPINV to Shock6					Response of LPRC to Shock6					Response of RINTR to Shock6					Response of LDR to Shock6
	.006									.04										.0004										.0008										.002
	.005
										.03										.0002										.0004										.000
	.004
	.003									.02										.0000										.0000										-.002
	.002									.01										-.0002										-.0004										-.004
	.001
										.00										-.0004										-.0008										-.006
	.000
	-.001									-.01										-.0006										-.0012										-.008
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock5					Response of LPINV to Shock5					Response of LPRC to Shock5					Response of RINTR to Shock5					Response of LDR to Shock5
	.0020									.004										.0030										.0005										.002
	.0015									.003										.0025										.0004										.001
										.002										.0020										.0003										.000
	.0010									.001																				.0002										-.001
																				.0015
	.0005									.000																				.0001										-.002
										-.001										.0010										.0000										-.003
	.0000									-.002										.0005										-.0001										-.004
	-.0005									-.003										.0000										-.0002										-.005
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18
			Response of LGDP to Shock1					Response of LPINV to Shock1					Response of LPRC to Shock1					Response of RINTR to Shock1					Response of LDR to Shock1
	.002									.012										.00100										.005										.001
										.008										.00075										.004										.000
	.001									.004										.00050										.003										-.001
	.000									.000										.00025										.002										-.002
																				.00000										.001
	-.001									-.004										-.00025										.000										-.003
										-.008																				-.001										-.004
	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18	20	2	4	6	8	10	12	14	16	18

Table 2 .C: Descriptive statistics for government consumption growth rate

 2

	1966Q1-2019Q2	AUT	BEL	CAN DEN	FIN	FRA	GER	GRC	IRE	ITA	JAP	NED	NOR	POR	SPA	SWE	GBR	USA
	Mean	-0.11	-0.07	-0.09	0.09	-0.04	-0.01	0.04	0.13	-0.38	-0.08	-0.04	-0.07	0.13	0.28	0.20	-0.07	-0.12	-0.28
	Median	-0.09	-0.09	-0.13	0.08	-0.06	-0.06	0.03	-0.10	-0.15	-0.08	-0.13	-0.09	0.14	0.16	0.10	-0.21	-0.13	-0.39
	Maximum	3.92	3.51	3.47	3.49	8.27	8.14	6.25	9.95	8.44	3.56	6.13	6.20	8.24	6.16	3.50	4.93	3.91	3.61
	Minimum	-3.50	-3.34	-3.41	-3.6	-14.55	-6.76	-4.89	-10.2	-18.48	-5.12	-5.13	-11.08	-4.35	-3.14	-4.66	-4.93	-5.47	-4.47
	Std. Dev.	1.04	0.87	1.18	1.19	2.28	0.97	1.36	2.94	2.55	1.04	1.28	1.85	1.56	1.27	1.11	1.45	1.31	1.12
	Skewness	0.18	0.39	0.25	-0.1	-1.19	1.45	0.65	0.21	-1.63	-0.15	0.59	-0.82	0.19	1.33	-0.09	0.32	-0.21	0.46
	Kurtosis	4.53	5.26	3.32	3.57	13.60	36.03	6.54	4.09	15.40	5.63	6.74	10.12	6.58	7.59	5.19	4.38	4.24	4.87
	Jarque-Bera	21.94	50.70	3.08	3.66	1047.14 9755.39 125.99 12.01 1458.86 62.24 136.80 473.17 115.01 249.98 42.71 20.46 15.11 38.48
	Probability	0.00	0.00	0.21	0.16	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	1966Q1-1991Q4	AUT	BEL	CAN DEN	FIN	FRA	GER	GRC	IRE	ITA	JAP	NED	NOR	POR	SPA	SWE	GBR	USA
	Mean	-0.16	-0.02	0.07	0.22	0.20	0.03	-0.04	0.25	-0.13	-0.07	-0.32	-0.16	0.26	0.61	0.31	0.21	-0.17	-0.20
	Median	-0.30	0.07	0.05	0.32	0.32	0.06	-0.07	-0.14	0.06	-0.06	-0.36	0.06	0.29	0.46	0.33	0.03	-0.09	-0.32
	Maximum	2.76	2.22	3.47	3.49	8.27	8.14	5.43	9.83	2.88	2.80	6.13	5.72	8.24	6.16	3.50	4.93	3.91	3.61
	Minimum	-3.50	-3.34	-3.41	-3.0	-14.55	-6.76	-4.89	-10.2	-3.36	-5.12	-5.13	-11.08	-4.22	-3.14	-4.66	-4.93	-5.47	-4.47
	Std. Dev.	1.03	0.95	1.40	1.23	2.52	1.24	1.60	3.44	1.22	1.17	1.48	2.41	1.61	1.55	1.30	1.68	1.49	1.35
	Skewness	0.24	-0.27	0.01	-0.3	-1.70	1.23	0.44	0.05	-0.42	-0.63	0.71	-0.95	0.66	0.95	-0.64	-0.19	-0.38	0.14
	Kurtosis	3.64	3.89	2.62	3.40	14.24	27.03	4.48	3.25	3.19	5.28	6.27	6.48	8.56	5.67	4.64	3.90	3.92	3.85
	Jarque-Bera	2.72	4.70	0.64	2.75	591.33	2505.17	12.74	0.31	3.16	29.03	54.47	67.45	140.38	46.10	18.64	4.06	6.13	3.44
	Probability	0.26	0.10	0.73	0.25	0.00	0.00	0.00	0.86	0.21	0.00	0.00	0.00	0.00	0.00	0.00	0.13	0.05	0.18
	Observations	103	103	103	103	103	103	103	103	103	103	103	103	103	103	103	103	103	103
	1992Q1-2019Q2	AUT	BEL	CAN DEN	FIN	FRA	GER	GRC	IRE	ITA	JAP	NED	NOR	POR	SPA	SWE	GBR	USA
	Mean	-0.06	-0.11	-0.24	-0.0	-0.27	-0.04	0.11	0.02	-0.61	-0.10	0.23	0.00	0.00	-0.03	0.11	-0.34	-0.08	-0.35
	Median	-0.08	-0.13	-0.32	-0.0	-0.34	-0.11	0.05	-0.10	-0.49	-0.08	0.19	-0.14	-0.01	-0.10	-0.03	-0.41	-0.20	-0.42
	Maximum	3.92	3.51	2.60	3.36	7.58	2.30	6.25	9.95	8.44	3.56	5.17	6.20	3.62	3.48	3.48	3.65	3.21	3.16
	Minimum	-3.12	-1.53	-2.93	-3.6	-10.96	-1.42	-3.11	-6.32	-18.48	-2.32	-2.10	-2.74	-4.35	-1.90	-1.79	-2.98	-3.14	-2.00
	Std. Dev.	1.05	0.79	0.91	1.14	2.02	0.61	1.09	2.39	3.34	0.92	1.01	1.11	1.51	0.83	0.89	1.13	1.13	0.86
	Skewness	0.13	1.38	0.34	0.02	-0.44	1.03	1.39	0.44	-1.22	0.76	1.21	2.55	-0.38	0.77	1.18	1.02	0.26	1.12
	Kurtosis	5.34	7.87	4.27	3.96	12.11	5.94	11.34	5.26	9.84	5.56	7.30	15.07	3.83	5.10	5.82	5.46	3.81	5.81
	Jarque-Bera	25.49 143.62	9.50	4.20	383.94	59.03	354.38 27.09	241.32	40.60 111.52 786.52	5.79	31.14	61.93 47.02	4.27	59.30
	Probability	0.00	0.00	0.01	0.12	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.06	0.00	0.00	0.00	0.12	0.00

Table 3 .C: Descriptive statistics for government debt to DGP ratio (in percent): different country samples (number of observations)

 3

		AUT	BEL	CAN	DEN	FIN	FRA	GER	GRC	IRE	ITA	JAP	NED	NOR	POR	SPA	SWE	GBR	USA
	Mean	78.7 111.2 110.0 48.4 52.4 90.0 68.0 145.4 65.0 119.4 182.5 62.9 36.5 101.8 72.0 60.0 62.5	92.0
	Median	77.9 110.2 108.7 50.3 48.9 91.7 66.5 136.7 62.7 116.8 176.4 62.7 42.5	86.2	66.2 58.7 50.4	83.7
	Maximum	94.0 136.0 133.8 62.7 70.5 113.8 82.4 191.6 129.4 138.8 240.8 78.7 57.9 146.7 106.9 77.2 92.6 138.4
	Minimum	65.0 91.4	86.1 29.9 33.2 68.2 57.5 106.0 26.4 103.9	78.2	49.6	4.0	64.9	40.6 47.4 38.6	68.9
	Std. Dev.	9.4	9.9	11.9	7.2 10.9 16.2	7.4	34.6	33.5	11.3	45.8	7.8	16.4	30.8	22.4	8.0	21.7	20.7
	Skewness	0.1	0.6	0.2	-0.4 0.3	0.1	0.5	0.2	0.5	0.5	-0.4	0.2	-1.0	0.2	0.4	0.6	0.4	1.3
	Kurtosis	1.5	3.3	2.4	2.5	1.7	1.3	2.0	1.2	1.9	1.8	2.0	1.9	2.8	1.3	1.7	2.5	1.3	3.2
	Jarque-Bera	7.4	5.6	2.4	2.8	6.7	9.0	6.4	10.7	7.3	9.7	6.0	4.4	15.9	10.7	9.4	6.6	14.1	60.0
	Probability	0.02 0.06	0.30 0.25 0.03 0.01 0.04 0.00	0.03	0.01	0.05	0.11 0.00	0.00	0.01 0.04 0.00	0.00
	Observations 78	95	118	78	78	78	83	78	81	95	90	83	95	83	95	95	98	214
								Table 4.C. Unit Root Tests Results
							GDP in level						GDP growth rate
					ADF test statistic			PP test statistic			ADF test statistic		PP test statistic
				t-Statistic	Prob.*	Adj. t-Stat	Prob.*	t-Statistic	Prob.*	Adj. t-Stat	Prob.*
	AUSTRIA			0.2565	0.9755	0.1309	0.9674	-6.0462	0.0000	-14.6192	0.0000
	BELGIUM			-0.0176	0.9551	0.0951	0.9647	-8.8412	0.0000	-8.8459	0.0000
	CANADA			1.2132	0.9982	1.3062	0.9987	-9.9102	0.0000	-10.0397	0.0000
	DENMARK			0.1751	0.9705	0.1018	0.9652	-13.9734	0.0000	-14.0792	0.0000
	FINLAND			-0.4258	0.9011	-0.4393	0.8987	-5.4589	0.0000	-15.1845	0.0000
	FRANCE			-0.9383	0.7745	-0.8584	0.7998	-10.6825	0.0000	-18.6270	0.0000
	GERMANY			-0.2277	0.9315	-0.2759	0.9249	-12.9975	0.0000	-13.2900	0.0000
	GREECE			-1.8730	0.3446	-1.9270	0.3194	-5.0038	0.0000	-14.8132	0.0000
	IRELAND			4.3334	1.0000	3.6556	1.0000	-6.3815	0.0000	-16.4083	0.0000
	ITALY			3.0219	0.9994	3.2846	0.9998	-6.8989	0.0000	-9.8068	0.0000
	JAPAN			4.4270	1.0000	4.1450	1.0000	-4.8786	0.0001	-11.7076	0.0000
	NETHERLAND		0.2495	0.9751	0.1247	0.9669	-16.6916	0.0000	-16.5688	0.0000
	NORWAY			0.3101	0.9784	0.2740	0.9765	-17.2703	0.0000	-17.0500	0.0000
	PORTUGAL			-1.3390	0.6114	-1.3711	0.5960	-5.8511	0.0000	-11.6654	0.0000
	SPAIN			-0.0987	0.9469	-0.2549	0.9278	-4.1685	0.0009	-12.1406	0.0000
	SWEDEN			1.2149	0.9982	1.6841	0.9996	-10.0465	0.0000	-16.4551	0.0000
	UK			0.5707	0.9887	0.9282	0.9958	-8.0347	0.0000	-13.0782	0.0000
	USA			1.6819	0.9996	2.0992	0.9999	-10.5931	0.0000	-10.9155	0.0000

Table 5 .C. Lag length criteria selection

 5

	AUSTRIA

Table 5 .C. (Continued): Lag length criteria selection

 5

	IRELAND

Table 6 .C. Gross External Debt Position: Foreign Currency and Domestic Currency Denominated Debt, as of September 30, 2019 US Dollars in Millions

 6 The currency composition is unallocated for debt in Direct Investment and Trade credit and advances of the General Government.

	Foreign Currency

*

  model calculating growth-maximizing of the government size. The Scully model formulae follow a form similar to the Cobb-Douglas framework, linking the current output to the first lagged government flows of expenditure and the first lag of output. Furthermore, assuming that the government budget is balanced and, with the government budget constraint equalizing government expenditure flows to the taxes represented as a share of the output, this leads to the following model: 𝑌 𝑖𝑡 = 𝛽 0 (𝜏𝑌 𝑖𝑡-1 ) 𝛽 1 [(1 -𝜏)𝑌 𝑖𝑡-1 ] 𝛽 2 , with 𝑌 as output, 𝜏 as the lump sum tax rate, and 𝑡 as the time period. This model is used to derive an optimal government size (equivalent to optimal taxation rate, as the balanced budget constrained is assumed) represented by the taxation rate as 𝜏 =

	𝛽 2
	𝛽 1 +𝛽 2

  = (1 -𝛿 𝑔,𝑡 )𝐾 𝑔,𝑡 + 𝐺 𝑡+1 .

	Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential
	public debt
	Dividing the equation of public capital by the first lagged output and assuming as negligible the
	public capital depreciation rate, we obtain:
							∆𝐾 𝑔,𝑡 𝑌 𝑡	= -	𝛿 𝑔,𝑡-1 𝑌 𝑡	+	𝐺 𝑡 𝑌 𝑡	≅	𝐺 𝑡 𝑌 𝑡	= 𝑔	(22)
	where 𝑔 is government expenditure, representing the dimension size of the institutions (the
	state/government size). From Equation (23), we have 𝐾 𝑔,𝑡 =	𝛼(1-𝜀𝜃) 𝜌 𝑘 𝑔	𝑌 𝑡 , which yields:
							𝐾 𝑔,𝑡 =	𝛼(1-𝜀𝜃) 𝜌 𝑘 𝑔	𝑌 𝑡	(23)
	Considering (28), Equation (27) is now written as	∆𝐾 𝑔,𝑡 𝑌 𝑡	=	𝛼(1-𝜀𝜃) 𝜌 𝑘 𝑔	.	𝑌 𝑡 𝑌 𝑡	=	𝐺 𝑌	= 𝑔.
	As	𝑌 𝑡 𝑌 𝑡	=	𝑌 𝑡 𝑌 𝑡-1	𝑌 𝑡-1 𝑌 𝑡	=	𝛾 1+𝛾
								218

  Table 2 for elasticities and Figure B.3 for simulated public investment flows).

Table 3 . The effects of elasticity changes on the potential public debt limit

 3

		D			D15		D30	D15-D30	D-D30
		Mean Median	Mean Median	Mean Median Mean Median Mean Median
	Australia	99.3	96.2	98.3	95.2	96.9	93.9	1.3	1.4	2.3	2.4
	Austria	300.7	303.0	301.1	303.3	300.2	302.6	0.9	0.7	0.6	0.4
	Belgium	111.4	114.3	111.7	114.5	111.0	114.0	0.7	0.4	0.4	0.2
	Canada	138.9	132.3	139.4	132.8	138.5	132.0	0.9	0.9	0.3	0.3
	Denmark	233.3	237.7	233.0	237.5	232.7	237.2	0.3	0.2	0.6	0.4
	France	131.1	125.8	130.9	125.7	130.4	125.4	0.4	0.3	0.7	0.4
	Germany	130.9	140.6	132.6	141.8	132.0	141.4	0.6	0.4	-1.1	-0.8
	Greece	90.1	82.9	84.5	80.7	82.6	79.8	1.9	0.9	7.6	3.1
	Ireland	163.5	167.3	177.9	176.2	175.1	174.8	2.8	1.4	-11.6	-7.5
	Italy	143.3	136.8	145.0	137.5	144.0	137.1	1.0	0.4	-0.7	-0.3
	Japan	-591.1	-592.7	-585.1	-589.2	-582.8	-587.8	-2.3	-1.4	-8.2	-5.0
	Netherlands	178.9	181.5	178.9	181.5	178.3	181.1	0.6	0.4	0.6	0.4
	New Zealand	101.7	100.8	101.0	100.4	100.4	100.0	0.6	0.4	1.3	0.8
	Norway	150.5	154.8	152.4	156.8	151.3	155.6	1.2	1.2	-0.8	-0.8
	Portugal	209.8	209.8	210.2	210.1	208.5	208.8	1.8	1.3	1.4	1.0
	Spain	105.1	105.7	105.4	105.8	104.6	105.2	0.8	0.6	0.6	0.4
	Sweden	170.3	170.5	171.7	171.2	171.2	171.0	0.5	0.2	-0.9	-0.4
	Switzerland	254.7	259.6	254.8	259.6	253.4	258.9	1.4	0.8	1.3	0.7
	United Kingdom	98.1	101.6	98.9	102.4	98.5	102.0	0.4	0.4	-0.4	-0.4
	United States	187.4	194.9	187.5	194.9	186.7	194.0	0.8	0.9	0.7	0.9

Table 4 . Real long-term interest rates and real economic growth differential for selected countries

 4

		Long Term Interest Rates (% per	GDP Growth rate	Gap [interest rate-
		annum)		(%)			growth]
	Sample: 1960-2015	Mean	Median	Mean	Median	Mean	Median
	France	7.3	6.7	2.9	2.4	4.5	4.3
	United States	6.3	6.1	3.1	3.3	3.2	2.8
	United Kingdom	7.8	7.5	2.4	2.6	5.4	4.9
	Canada	7.0	6.8	3.2	3.1	3.8	3.7
	Sample: 1960-1984	Mean	Median	Mean	Median	Mean	Median
	France	9.4	8.6	4.2	4.5	5.2	4.0
	United States	7.3	6.8	3.6	4.5	3.7	2.4
	United Kingdom	9.7	8.8	2.5	2.7	7.2	6.1
	Canada	8.3	7.6	4.2	4.0	4.1	3.5
	Sample: 1985-2015	Mean	Median	Mean	Median	Mean	Median
	France	5.6	4.9	1.8	2.0	3.8	2.9
	United States	5.5	5.3	2.7	2.7	2.8	2.5
	United Kingdom	6.2	5.1	2.3	2.5	3.9	2.5
	Canada	6.0	5.5	2.4	2.6	3.5	2.9

Table 5 . Simulated effect of differences between long-term interest rates and economic growth

 5

	Simulating potential debt over the period 1960-2015, using constant elasticity of public capital = 0.30
		France	United States	United Kingdom	Canada
	Mean	137.4	194.7	100.5	145.1
	Median	126.2	194.6	106.6	134.3
	Maximum	212.1	279.7	123.7	213.0
	Minimum	88.8	127.4	59.9	102.9
	Scenario 1: simulating potential debt using interest rates and growth of the period 1960-1984
		France	United States	United Kingdom	Canada
	Mean	122.2	172.2	77.6	137.1
	Median	112.3	172.1	82.3	126.9
	Maximum	188.6	247.3	95.5	201.2
	Minimum	79.0	112.6	46.3	97.2
	Scenario 2: simulating potential debt using interest rates and growth of the period 1985-2015
	1985-2015	France	United States	United Kingdom	Canada
	Mean	156.0	220.1	134.7	154.4
	Median	143.2	220.0	142.9	142.8
	Maximum	240.7	316.1	165.8	226.5
	Minimum	100.8	144.0	80.3	109.5
			Scenario 2 -Scenario 1
	1985-2015	France	United States	United Kingdom	Canada
	Mean	33.7	47.9	57.1	17.3
	Median	31.0	47.9	60.5	16.0
	Maximum	52.0	68.8	70.2	25.3
	Minimum	21.8	31.4	34.0	12.2

Simulated potential debt sensitivity to the differential of interest rates and economic growth for selected countries

Table 6 . Simulated potential debt following the 2009-2012 crisis

 6

	Sample: 2009-2012 Actual Potential1 Gap1 Potential2 Gap2 Potential3 Gap3
	Switzerland	48.4	255	206.6	283.8	235.4	131.8	83.4
	Austria	71.9	179.8	107.8	133.2	61.3	112.1	40.2
	Sweden	39.5	138.2	98.7	121.9	82.4	148.8	109.3
	Denmark	41.6	119.4	77.8	100.9	59.3	126.8	85.2
	Australia	20.3	84.4	64.2	95.6	75.4	126.6	106.4
	Norway	43.5	107	63.4	86.1	42.6	111.7	68.2
	New Zealand	30.2	87.9	57.8	91.1	60.9	153.1	123
	Netherlands	62.8	107.8	45.1	126.7	64	110.8	48.1
	United States	91.5	132	40.5	149.2	57.7	132	40.5
	Ireland	84.5	111.8	27.3	310.1	225.6	141	56.5
	Canada	80.8	104.2	23.4	110.8	30	122.5	41.7
	France	81.2	90.9	9.7	103.1	21.9	124.7	43.4
	Germany	76.8	85.2	8.4	102	25.2	95.8	19
	Portugal	96.8	102.5	5.7	70.5	-26.3	86.8	-10
	Spain	62.4	58.9	-3.5	59.5	-2.9	92.7	30.3
	United Kingdom	73.2	62.7	-10.5	84	10.8	103.4	30.3
	Belgium	96.5	76	-20.5	84.3	-12.2	98.3	1.8
	Italy	117.2	60.9	-56.3	41.1	-76.1	63	-54.2
	Greece	144.2	1.5	-142.7	1.1	-143.1	2.1	-142
	Japan	215.5	-432.1	-647.5	876.5	661	185	-30.4

Note: Countries are filtered, according to the column Gap1, from high values to lower values.

Fiscal Space as reported in Ostrey et al. (2015) Distance to debt limit (Gap1 from table 6)

	Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential
	public debt
	0				50			100	150	200	250
	Switzerland Austria Sweden Denmark Australia Norway New Zealand Netherlands United States Ireland Canada France Germany Portugal Spain United Kingdom Belgium Italy Greece Japan	0 0 0 0 0 0 0 0 0	9.7 8.4 5.7	27.3 23.4	45.1 40.5	64.2 63.4 57.8 58.8	77.8	107.8 98.7 105.5 116.9 115.2 124.3 132.6	156.6 158.1 165.1 149.8 167.9	202 206.6 188.8 195.7 214.5 228.1	248
								246

  If we adjust the potential debt to consider such a fact (let us reduce potential government expenditure for all countries by an extra 20% of their actual taxes), 127 the potential public debt is significantly reduced, on average, for example, to 35% over the period 1960-2015, 72% in Germany, 21% in Italy, 50% in Ireland, 38% in Spain, 62% in Canada and 115% in the USA. Without considering this fact, averages are higher and are, respectively, 131% in France and Germany, 143% in Italy, 163% in Ireland, 105% in Spain, 139% in Canada and 187% in the United States. Some other countries, such as the United Kingdom, saw potential debt significantly reduced to very low levels.

	Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential
	public debt
	247

). Government investment was around 3.5%. Hence, a deficit of approximately 11 points of GDP was not compensated by taxes (around 20% of additional taxes are needed to finance such needs).

Table A .1. Summary and features of the models of public debt and fiscal policy

 A

	Authors	Type	Main Features	Main hypotheses	Results
			-Two periods of infinite long-life agents
	Diamond (1965)	OLG	living for 2: working in the 1 st and retiring in the 2 nd . -Study the impact of domestic/foreign
			debt on the interest rate and utility level.

Table A .3. Descriptive statistics Public investment (Public Gross Capital Formation) as percent of GDP

 A

	Sample: 1960 2015	AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR NZL PRT	SPA	SWE	USA
	Mean	2.3	4.7	3.4	3.6	3.7	6.3	4.8	3.6	3.5	3.2	4.5	3.6	8.3	4.7	3.6	4.5	4.3	3.9	5.0	4.5
	Median	2.2	4.4	2.9	3.5	3.7	4.6	4.5	3.2	3.1	2.8	4.6	3.5	8.8	4.1	3.5	4.6	4.4	3.9	4.7	4.2
	Maximum	3.5	6.9	6.4	4.9	4.6	14.0	6.6	6.6	6.1	5.5	6.7	5.0	11.9	8.0	4.8	6.7	6.1	5.7	7.6	7.1
	Minimum	1.7	2.5	2.4	2.8	2.2	3.3	3.7	1.6	1.9	1.9	2.1	2.5	4.2	3.3	2.6	2.4	2.4	2.5	3.9	3.4
	Std. Dev.	0.4	1.5	1.1	0.6	0.5	3.4	0.7	1.4	1.4	1.1	1.2	0.6	2.3	1.4	0.5	0.9	0.9	0.7	1.1	1.0
	Skewness	1.0	0.1	1.3	0.4	-0.6	0.9	0.9	0.7	0.4	0.8	-0.1	0.5	-0.5	1.0	0.4	-0.5	-0.3	0.3	1.0	1.4
	Kurtosis	3.7	1.5	3.4	1.9	3.7	2.2	2.9	2.1	1.7	2.3	2.0	2.8	2.2	2.6	3.1	3.0	2.5	3.2	3.0	3.8
	Jarque-Bera	10.7	5.5	15.6	4.5	4.0	8.7	7.6	5.9	5.8	6.6	2.5	2.8	3.7	10.3	1.6	2.1	1.3	1.1	8.7	19.9
	Probability	0.0	0.1	0.0	0.1	0.1	0.0	0.0	0.1	0.1	0.0	0.3	0.3	0.2	0.0	0.5	0.4	0.5	0.6	0.0	0.0

Private investment (Private Gross Capital Formation) as percent of GDP

		AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR NZL PRT	SPA	SWE	USA
	Mean	14.9	22.2	23.7	16.3	21.9	16.8	18.9	16.4	17.8	13.2	25.1 22.5	17.9	18.1	19.3	11.7 21.0 20.1	17.5	14.3
	Median	14.3	22.4	23.9	16.0	22.0	17.1	18.9	16.4	17.4	13.4	24.5 21.7	18.0	18.0	19.6	11.3 21.0 19.5	17.5	13.8
	Maximum	22.2	24.3	30.0	20.8	24.2	23.9	21.9	21.4	21.5	19.0	34.2 31.0	22.9	22.1	27.0	15.2 27.6 28.4	21.0	17.9
	Minimum	11.1	19.1	16.2	12.7	17.2	10.7	16.9	13.1	16.0	6.7	16.5 17.3	12.4	15.3	12.8	8.8	14.9 14.9	13.3	11.1
	Std. Dev.	3.0	1.5	3.1	2.1	1.6	3.5	1.2	1.9	1.5	2.6	3.9	3.4	2.3	1.6	3.5	1.8	3.0	3.5	1.7	1.9
	Skewness	0.9	-0.4	-0.5	0.5	-0.9	0.2	0.4	0.4	0.9	-0.4	0.3	0.9	0.1	0.4	0.0	0.4	0.0	0.8	-0.3	0.4
	Kurtosis	2.7	2.0	3.3	2.4	3.7	1.9	2.8	2.9	2.7	3.1	2.7	3.0	3.0	2.7	2.3	2.2	2.8	3.0	2.8	2.1
	Jarque-Bera	7.5	3.8	2.4	2.9	9.0	3.0	1.3	1.7	6.9	1.5	0.9	7.8	0.0	1.5	1.2	3.2	0.2	5.2	1.0	3.5
	Probability	0.0	0.2	0.3	0.2	0.0	0.2	0.5	0.4	0.0	0.5	0.6	0.0	1.0	0.5	0.6	0.2	0.9	0.1	0.6	0.2

Government capital stock in billions of 2011 constant US Dollars (ppp)

	KG	AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR NZL PRT	SPA	SWE	USA
	Mean	163	188	157	464	174	221	1237	980	1490	100	54	904	3622	376	94	62	118	525	221
	Median	147	209	192	435	178	228	1233	1025	1671	80	50	907	3779	382	85	66	102	460	232
	Maximum	364	237	235	870	275	261	1921	1254	1777	216	124	1386 5991	553	198	105	219 1056	314	10889
	Minimum	54	88	44	184	49	132	463	536	726	29	13	376	716	178	26	28	40	168	91
	Std. Dev.	82	48	66	189	74	34	459	182	333	61	34	319	1904	103	51	20	59	281	66
	Skewness	0.76	-0.77 -0.55 0.46 -0.25 -1.17 -0.12 -1.04	-1.11	0.74 0.81 -0.05 -0.19 -0.16 0.39	0.16 0.42 0.53 -0.51	0.37
	Kurtosis	2.82	2.11	1.68	2.31	1.73	3.50	1.75	3.23	2.76	2.18 2.57	1.75	1.52	2.34	1.95	2.42 1.76 2.02	2.12	1.96
	Jarque-Bera	5.41	7.38	6.96	3.08	4.32	13.4	3.76	10.17 11.68 6.69 6.56	3.67	5.45	1.26	3.97	1.02 5.20 4.86	4.24	3.85
	Probability	0.07	0.02	0.03	0.21	0.12	0.00	0.15	0.01	0.00	0.04 0.04	0.16	0.07	0.53	0.14	0.60 0.07 0.09	0.12	0.15

Table A .3. (continued): Descriptive statistics Private capital stock in billions of 2011 constant US Dollars (ppp)

 A

	KP	AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR	NZL	PRT	SPA	SWE	USA
	Mean	710	534	721	1326	709	282	3036	2597	4560	294	205	3639	5034	895	353	103	380	1781	487	12793
	Median	636	533	687	1315	731	266	3227	2718	4670	293	180	3879	5163	905	395	98	364	1608	502	12126
	Maximum	1575	748	992	2420	909	469	4331	3670	5742	491	433	4686	7997	1275	515	168	585	3298	669	22156
	Minimum	234	243	359	434	374	115	1144	1113	2402	118	54	1839	941	383	155	48	161	649	254	4427
	Std. Dev.	375	164	189	596	158	114	1027	844	1046	113	122	868	2622	276	105	34	136	849	115	5845
	Skewness	0.70	-0.21 -0.19	0.16	-0.57	0.26	-0.45	-0.33	-0.52	0.12	0.69 -0.64	-0.26	-0.29 -0.46 0.36	0.04	0.47	-0.36	0.28
	Kurtosis	2.51	1.74	2.01	1.88	2.17	1.73	1.91	1.63	2.02	1.81	2.27	2.11	1.50	1.94	2.00	2.14	1.71	1.94	2.18	1.77
	Jarque-Bera	5.16	4.15	2.63	3.16	4.64	4.36	4.64	5.41	4.76	3.46	5.63	5.73	5.87	3.42	4.30	2.94	3.89	4.72	2.77	4.24
	Probability	0.08	0.13	0.27	0.21	0.10	0.11	0.10	0.07	0.09	0.18	0.06	0.06	0.05	0.18	0.12	0.23	0.14	0.09	0.25	0.12

GDP in billions of 2011 constant US Dollars (ppp)

  Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential public debt 257

		AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR	NZL	PRT	SPA	SWE	USA
	Mean	519	233	290	850	292	174	1588	1514	2339	212	100	1495	2945	481	188	86	179	908	261	9258
	Median	461	218	278	831	283	169	1565	1459	2260	207	66	1595	3186	437	179	76	174	839	252	8579
	Maximum	1074	381	465	1538	454	246	2503	2538	3618	365	286	2192	4568	789	335	157	289	1590	446	16940
	Minimum	165	85	111	275	139	87	540	696	973	57	23	501	575	177	60	38	49	241	112	3212
	Std. Dev.	269	93	108	380	86	50	608	570	803	83	74	532	1331	195	88	34	80	412	94	4272
	Skewness	0.54	0.10	0.06	0.25	0.22	-0.02 -0.07	0.30	-0.07 -0.06 0.78 -0.41	-0.36	0.18	0.19	0.59 -0.08	0.21	0.36	0.31
	Kurtosis	2.08	1.77	1.83	1.86	2.11	1.65	1.79	1.75	1.72	2.29	2.20	1.83	1.67	1.73	1.67	2.11	1.60	1.81	2.02	1.72
	Jarque-Bera	4.72	3.61	3.25	3.61	2.32	3.88	3.47	4.52	3.84	1.20	7.17	4.76	5.33	4.07	4.48	5.09	4.62	3.68	3.43	4.70
	Probability	0.09	0.16	0.20	0.16	0.31	0.14	0.18	0.10	0.15	0.55	0.03	0.09	0.07	0.13	0.11	0.08	0.10	0.16	0.18	0.10
								Working age population (15-65) in millions
		AUS	AUT	BEL	CAN	CHE	DNK	FRA	GBR	GER	GRC	IRL	ITA	JPN	NLD	NOR	NZL	PRT	SPA	SWE	USA
	Mean	10.88	5.12	6.56	17.95	4.51	3.39	36.96 37.33 52.68	6.55	2.26 37.08 79.11	9.70	2.74	2.20	6.33	25.47	5.52	162.00
	Median	10.91	5.17	6.67	18.25	4.50	3.44	38.24 37.28 53.51	6.61	2.12 38.35 81.06 10.15	2.71	2.15	6.51	25.45	5.43	161.00
	Maximum	15.79	5.79	7.31	24.32	5.57	3.64	42.13 41.87 55.88	7.42	3.11 39.04 87.13 11.15	3.41	3.00	7.07	31.76	6.18	212.00
	Minimum	6.29	4.59	5.90	10.49	3.50	2.94	29.09 34.11 48.84	5.47	1.64 32.85 59.31	7.01	2.26	1.39	5.34	19.62	4.93	109.00
	Std. Dev.	2.78	0.41	0.41	4.19	0.55	0.21	3.96	2.31	2.61	0.73	0.50	2.05	7.59	1.32	0.32	0.48	0.61	3.90	0.35	31.69
	Skewness	0.05	0.00	0.03	-0.21	0.15	-0.52 -0.39	0.57	-0.30 -0.17 0.46 -0.69	-0.91	-0.59	0.47	0.06 -0.35	0.13	0.44	0.00
	Kurtosis	1.88	1.52	2.15	1.90	2.07	2.06	1.91	2.19	1.46	1.38	1.88	1.87	2.85	1.95	2.31	1.84	1.59	1.78	2.20	1.82
	Jarque-Bera	2.95	5.14	1.69	3.25	2.23	4.56	4.21	4.52	6.35	6.42	4.95	7.38	7.74	5.85	3.14	3.18	5.82	3.63	3.34	3.23
	Probability	0.23	0.08	0.43	0.20	0.33	0.10	0.12	0.10	0.04	0.04	0.08	0.02	0.02	0.05	0.21	0.20	0.05	0.16	0.19	0.20

Table A .4. Countries sample and their corresponding alpha-3 codes used in all Tables and figures whenever it applies

 A

	Chapter 3. Public debt effects in theory-based models with an empirical assessment of the potential
	public debt
	Country	Country code
	Australia	AUS
	Austria	AUT
	Belgium	BEL
	Canada	CAN
	Switzerland	CHE
	Denmark	DNK
	France	FRA
	Germany	GER
	Greece	GRC
	Ireland	IRL
	Italy	ITA
	Japan	JPN
	Netherlands	NLD
	New Zealand	NZL
	Norway	NOR
	Portugal	PRT
	Spain	SPA
	Sweden	SWE
	United Kingdom	GBR
	United States	USA
	259

[START_REF] Bentour | Government Expenditure Multipliers Under Oil Price Swings[END_REF] a aussi trouvé la sensibilité des multiplicateurs de dépenses aux fluctuations des prix du pétrole pour un nombre de pays de la région MENA. En particulier, ces multiplicateurs sont positifs et très élevés (dépassant la valeur de

2) notamment pour les pays exportateurs de pétrole, pour des périodes de baisse du prix de pétrole, alors qu'ils sont faibles, voire négatifs pour certains pays, en période d'expansions des prix pétroliers.

Exception faite au chapitre 2 qui est restreint à 18 pays en omettant l'Australie et la Nouvelle Zélande suite au manque de données trimestrielles suffisantes pour ces pays.

Cette méthode a été utilisée par[START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF] pour un échantillon différent de pays et une période relativement courte comparée à celle de ce chapitre.

The time sample differs between countries depending on data availability. The United States have the largest dataset (1791-2011) while Ireland has the shortest sample.

Only fewer studies weakly investigated country specific regressions such as in Gomez-Puig and Sosvilla-Rivero (2017) that used time series regressions for 11 eurozone countries between 1961 and 2015 and draw conclusions based on thresholds that vary from a minimum of 21% in France to a maximum of 61% in Belgium.

The example of debt-growth non-linear effect is becoming more used to test new econometric methods. See, for example,[START_REF] Egert | The 90% public debt threshold: the rise and fall of a stylized fact[END_REF],[START_REF] Henderson | Nonparametric Threshold Regression: Estimation and Inference[END_REF] or[START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF].

The difference in countries in terms of institutions, governance, and economic policies, among others, contributes mainly to such endogeneity bias. In general, these variables are difficult to measure, and their effects could be better assessed in a theoretical model (such as endogenous growth model) rather than in a simple non-linear relationship for which the main goal here is to detect a turning point in the link between debt and growth simply from the datagenerating process (DGP).

Other threshold models include a variety of autoregressive time series models with threshold, used particularly in financial applications[START_REF] Chen | A review of threshold time series models in finance[END_REF].

A theoretical generalization of[START_REF] Hansen | Regression Kink with an Unknown Threshold[END_REF] method to panel data appeared recently in[START_REF] Zhang | Panel kink regression with an unknown threshold[END_REF].

The algorithm is presented in the appendix C (algorithm 1).

Our exercise is distinct from[START_REF] Checherita | The impact of high and growing government debt on economic growth: an empirical investigation for the Euro area[END_REF] by adopting a longer span of time as well as different sample of countries and different instrumental variables. For example, these authors use Gross Capital Formation as instrument while it is rejected in our choice. The Pearson's correlations(Table A.3) reveal that this variable is weakly correlated with the explanatory variable.

The algorithm is presented in the appendix C (algorithm 2).

This statistic follows a 𝜒 𝑟-𝑘 2 distribution where 𝑟 is the number of instruments and 𝑘 is the number of estimated parameters (including the constant term).

The GMM instruments are not observed before 1950.

[START_REF] Baum | Debt and growth: New evidence for the euro area[END_REF] tested this effect for the euro area sample by introducing the years 2009-2010 and found a considerable upward effect on the threshold, especially in dynamic panel regression.

The term fixed effects imply that although the intercept may differ across countries, it is time invariant. The fixed effects model allows for heterogeneity or individuality among countries.

+ 𝛿𝑔 𝑡-1 + 𝜀 𝑡 ) estimation for each country using GLS method over 1880-2010 (no observed instruments on this period) and GMM method for 1950-2010. Results, available upon request from the author, are not significant.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 10 20 30 40 50 60 70 -6 -4 -2 0 2 4 Switzerland : 1956-2010 Debt/GDP

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * ** * * * * * * * 50 150 -40 -20 0 20 Greece: 1884-2010 Debt/GDP

* * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * 20 40 60 80

* ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 50 100 150 200

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

See the World of Work Report (2010) for a list of detailed consolidation and austerity measures for advanced countries.

We should be cautious when the values of multipliers deducted from fiscal stimulus, for example, are used to draw conclusions and policy advice on fiscal consolidations, and vice versa, as there is no revealed symmetry of effects in the instrument changes: an increase/decrease in expenditure could have an effect that is not necessarily the same in absolute value for a similar decrease/increase in expenditure. Few authors cared about this issue (see Section 2.4).

See, for example, Ramey (2018) for a recent and large literature review.

[START_REF] Parker | On Measuring the Effects of Fiscal Policy in Recessions[END_REF] built on earlier versions ofAuerbach and Gorodnichenko (2012, 2013) (as did some other authors), which are issued, respectively, as NBER working papers in 2010(No. 16311) and 2011 (No. 17447).

Historically, according to Hegeland (1954), the concept of fiscal multiplier goes back at least to the "Tableau Economique" of François[START_REF] Quesnay | Tableau Economique[END_REF], as mentioned by some authors[START_REF] Mustea | How large are fiscal multipliers in the US?[END_REF].

The government spending multiplier for a closed economy under a fixed interest rate is given by: 1/(1 -𝑚𝑝𝑐) with 𝑚𝑝𝑐 the marginal propensity to consume.

The author used a panel of 19 OECD countries over the period 1970-2002 to assess the effects of fiscal policy changes on private consumption during recessions and expansions.

This is explained by the presence of individuals facing binding liquidity constraints in a recession that will consume the additional income generated by the fiscal stimulus.

[START_REF] Blanchard | Public Debt and Low Interest Rates[END_REF] uses the terminology "safe interest rate" to describe, depending on the situation: the risk-adjusted rate of return on capital or the interest rate on nominal bonds (assuming no default).

See http://www.crfb.org/sites/default/files/CRFB_DoNotMischaracterizeBlanchard.pdf.

https://www.nytimes.com/2019/01/09/opinion/melting-snowballs-and-the-winter-of-debt.html.

http://bruegel.org/2019/01/is-public-debt-a-cheap-lunch/ and https://www.stern.nyu.edu/experience-stern/facultyresearch/true-cost-public-debt.

Before the financial crisis of 2008, researchers studying the constraint of the zero interest rate policy were inspired by the real situation of the Japanese economy, where the interest rate has nearly touched zero since 1995, accompanied by anaemic economic growth[START_REF] Eggertsson | The Zero Bound on Interest Rates and Optimal Monetary Policy[END_REF].

[START_REF] Farhi | Fiscal Devaluations[END_REF] show that both a uniform increase in import tariff and export subsidy, and a VAT tax increase and uniform payroll tax reduction, can play a role equivalent to exchange rate devaluation (which is mentioned as fiscal devaluation). However, when these policies are anticipated by economic agents, they need to be supported by consumption tax reduction and income tax increases.

For example,[START_REF] Correia | Unconventional Fiscal Policy at the Zero Bound[END_REF] use a standard new Keynesian model to assess the fiscal policy when the conventional monetary policy is constrained by the ZLB nominal interest rate. They show that tax policy (distortionary taxes) can deliver similar expected benefits to the monetary policy (being constrained in this case).

[START_REF] Woodford | Simple Analytics of the Government Expenditure Multiplier[END_REF] reviews the benchmark of the neoclassical models, assuming perfect flexibility of prices and wages, leading generally to spending multipliers of less than 1. The author also inferred cases under which the new Keynesian DSGE models could lead to spending multipliers greater than, equal to or below unity.

[START_REF] Farhi | Fiscal Multipliers: Liquidity Traps and Currency Unions[END_REF] distinguish between local fiscal multipliers due to local government spending only and the overall fiscal multipliers, which consider in the model not only local government transfers but also the possibility of transfers from other countries or regions in the currency area (for example, in the US, federal military spending allocated to each state is financed by the federal budget). This may explain, in part, the difference between the Unites States' relatively fast recovery compared to the eurozone countries, as these fiscal transfers are almost absent between eurozone countries. The allocated federal budget is roughly 1% in the eurozone, while it is around 20% in the United States[START_REF] Feyrer | How Much Would US Style Fiscal Integration Buffer European Unemployment and Income Shocks? (A Comparative Empirical Analysis)[END_REF].

In addition, a section of Chapter 3 (in the literature review) also summarizes the critiques of the neoclassical models (overlapping generation models and infinitely lived agents), as well as the new Keynesian models (DSGE models).

STVAR stands for smooth transition vector autoregressive, which uses a regime-switching model.

[START_REF] Nickel | Fiscal stimulus in times of high debt: reconsidering multipliers and twin deficits[END_REF] consider fiscal position in assessing fiscal multipliers by incorporating debt ratio as an interaction term in the panel VAR, which is indicated as interacted panel VAR (IPVAR).

For example, the distinction should be made between positive expenditure shocks (fiscal stimulus) and negative shocks (austerity measures). The outcome of the fiscal policy is different under the two scenarios and depends on the economic environment and countries' economic fundamentals.

The lag order adopted is 1, which is confirmed in the results section by the appropriate tests discussed in the general methodology.

Contrary to our bi-variate case, the[START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF] is a tri-variate SVAR linking three variables: tax revenue, government expenditure and GDP.

[START_REF] Bentour | Do developing countries benefit from foreign direct investments? An analysis of some Arab and Asian countries[END_REF] use this approach to deduce foreign direct investment return from estimated elasticities of the Cobb-Douglas production function.

Other authors used formulae without mentioning any normalization with reference to the volatility of the fiscal instrument (𝜎 𝑔 )[START_REF] Ilzetzki | How big (small?) are fiscal multipliers?[END_REF][START_REF] Priftis | Sources of borrowing and fiscal multipliers[END_REF].

Although the Cholesky impact is higher, the multiplier is reduced by, in particular, the second component of the adjusted parameter used as pass-through to fiscal multipliers in Table2.A. Indeed, government consumption volatility is higher (exceeding 2) for this country in the period of estimation.

6 8 10 12 14 16 18 20 Response of LGE to Shock2

See, for example, De la Croix and Michel (2010) and[START_REF] Weil | Overlapping Generations: The First Jubilee[END_REF] for a large literature review.

[START_REF] Buiter | Death, Birth, Productivity Growth and Debt Neutrality[END_REF] defines Ricardian equivalence by stating that: "There is debt neutrality if, given a program for public expenditure on current goods and services over time, the real equilibrium of the economy is not affected by a change in the pattern over time of lump-sum taxes. If there is debt neutrality, for instance, the substitution of borrowing today for lump-sum taxation today…does not affect the current and future behavior of private consumption and capital formation."

A non-exhaustive list includes among these worksGreiner and Semmler (1999, 2000),Ghosh and Mourmouras (2004a, 2004b),[START_REF] Bräuninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF],[START_REF] Greiner | An endogenous growth model with public capital and sustainable government debt[END_REF][START_REF] Greiner | Public debt in a basic endogenous growth model[END_REF][START_REF] Greiner | Public Debt, Productive Public Spending and Endogenous Growth[END_REF][START_REF] Greiner | Human capital formation and public debt: growth and welfare effects of three different deficit policies[END_REF],[START_REF] Futagami | Debt policy rule, productive government spending, and multiple growth paths[END_REF],[START_REF] Yakita | Sustainability of public debt, public capital formation, and endogenous growth in an overlapping generations setting[END_REF],[START_REF] Minea | Debt policy rule, productive government spending, and multiple growth paths: A note[END_REF] and[START_REF] Maebayashi | Dynamic analysis of reductions in public debt in an endogenous growth model with public capital[END_REF].

The model assumes mainly a constant population of identical individuals with the same time horizon, acting as consumers, workers and voters. Individuals differ only by their preferences for public goods, supplied by the government and financed by means of distortionary taxes on labor. The government is elected democratically and is chosen among two political parties, each maximizing the utility function of its electorate. Disagreements between the governments are viewed as differences about social welfare.

"A social planner: 1) do[es] not face elections; thus, she is reappointed with probability 1 in each period, 2) her preferences are a weighted average of the preferences of the citizens"[START_REF] Alesina | A positive theory of fiscal deficits and government debt[END_REF].

For example,[START_REF] Galí | Understanding the effects of Government Spending on Consumption[END_REF] use a new Keynesian model to empirically test government spending effects on consumption, involving rule-of-thumb agents that only have access to contemporaneous labour income for consumption, and Ricardian agents that can smooth consumption by accumulating capital.

Government consumption posts and public investments are defined by the system of national accounts(SNA, 1993 and SNA, 2008) and the classification of expenditure by functions of the government, are categorized by the OECD classification (COFOG).

[START_REF] Kmenta | On Estimation of the CES Production Function[END_REF] shows that estimating these flexible forms is not really difficult, except that they require [a] large number of observations because there have more parameters to estimate than in the Cobb-Douglas. Furthermore, an omitted variable problem may also be present. The omitted variable problem results in biased and inconsistent OLS parameter estimates"[START_REF] Bentour | Do developing countries benefit from foreign direct investments? An analysis of some Arab and Asian countries[END_REF].

The time in all our equations is labelled by the subscripted lowercase letter "𝑡" and could be omitted in case no confusion arises.

"Seigniorage is government revenue resultant from the emission and maintenance of the stock of currency in circulation"[START_REF] Terra | Principles of International Finance and Open Economy Macroeconomics: Theories, Applications and Policies[END_REF]. "The government resources constraint establishes that the change in government debt should be equal to the interest payment on the existing debt added to the resources necessary to supply public goods, minus the seigniorage revenue"[START_REF] Terra | Principles of International Finance and Open Economy Macroeconomics: Theories, Applications and Policies[END_REF].

Generally, money-creation revenue accounts for less than 2% of GDP[START_REF] Haslag | Money creation, reserve requirements, and seigniorage[END_REF].

Data distribution is relatively heterogenous between countries, where some variables are normally distributed for some countries and others are not, as shown by Jarque-Berra, Skewness and Kurtosis for this data in Table A.3 (Appendix A).

The results of this exercise for all countries are reproduced in FigureB.6 in the appendix.

Remerciements

 Prob. Stat. Prob. Stat.Prob. Breusch-Pagan LM 1362.7 0.000 474.0 0.000 855.2 0.000 539.0 0.000 671.4 0.000 Pesaran scaled LM 60.2 0.000 14.6 0.000 34.1 0.000 17.9 0.000 24.7 0.000 Bias-corrected scaled LM 60.0 0.000 14.1 0.000 33.8 0.000 17.4 0.000 23.9 0.000 Pesaran CD 32.3 0.000 15.9 0.000 23.6 0.000 17.2 0.000 22.2 0.000 Residual Cross-Section Dependence Test for the 10 Euro countries sample Degrees of freedom = 45 1950-2008 1950-1970 1971-2008 1971-1990 1991- African countries (Mid-1980s-2009

Mixed

Most of Africa had favourable pre-crisis macroeconomic standings. Thus, much of the region was able to deliver well-timed, domestic demand and supplyside focused countercyclical stimuli that promoted a better business environment. However, due to their lack of resources, they should look internationally for support to coordinate and establish a long-term mutually-beneficial outcome. Ndikumana, el al. (2010) 41 countries Positive Even with short supply of national resources, African nations enacted a variety of well-timed and targeted policies. Some nations were successful in stimulating domestic demand while offsetting declining exports and supporting local businesses. World Bank (2010b) 18 countries Positive Most Middle Eastern nations improved their near and long-term outlooks. Others, such as Egypt and Tunisia, spent stimulus money on infrastructure and support for SMEs to create new jobs. Unlike the public sector, the private sector has received less support and it is uncertain whether this sector will continue to recover when Saudi Arabia's 400 billion dollar stimulus package expires in 5 years.

Empirical evidence

Considering all the previous elements and discussions, this section augments the productive sector by two additional endogenized inputs representing the government and human capital sectors. The public sector is included through its dimension size of only productive investments (gross capital formation flows and stocks).

The set of countries studied is composed of 20 advanced countries (the same sample as considered in the first chapter), most of which are parts of the European Union, of which 12 adhere to the European Monetary Union, while the rest of the countries generally adopt a floating exchange rate system. These countries are, respectively: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Greece, Ireland, Italy, Japan, The Netherlands, Norway, New Zealand, Portugal, Spain, Sweden, Switzerland, the United Kingdom and the United States of America.

Data for the accumulated private and public capital stocks is drawn from the IMF database, 113 for which the data is made available for 170 countries. The data range covers the period 1965-2015, and the database was last updated in January 2017. Either public or private stocks are constructed according to the inventory method following the equation:

where 𝐾 𝑥,𝑖𝑡 is the stock of capital (𝑥 = {𝑝𝑢𝑏𝑙𝑖𝑐; 𝑝𝑟𝑖𝑣𝑎𝑡𝑒}), 𝛿 𝑥,𝑖𝑡 is the corresponding depreciation rate and 𝐼 𝑥,𝑖𝑡 is the investment flows (gross capital formation for the sector x).

To construct the time series of the stocks using the perpetual inventory stock equation (32), assumptions made about the initial values of stock and data on investment flows are described fully in the IMF (2015). 114 Tables A.2 and A.3 in Appendix A give a summary of the data coverage, sources, description of the variables and the corresponding descriptive statistics.

Other variables such as labour and population are drawn from World Development Indicators of the World Bank database, 115 while the human capital is from the Barro and Lee website, displaying educational attainment and average years of schooling for a large set of countries and a wide range of time periods. 116 The human capital data is produced by an interval of five years from 1950 to 2010 (i.e. 1950; 1955; 1960; …; 2005 and 2010), which we extrapolated by simply moving averages to fill the gaps between the extremities of the five-year intervals. The whole methodology and the sources used to produce such data are fully explained in [START_REF] Barro | International comparisons of educational attainment[END_REF] and revised in [START_REF] Barro | A new data set of educational attainment in the world, 1950-2010[END_REF].

Estimation of the Cobb-Douglas production function

The Cobb-Douglas production function encompassing human capital is modified and loglinearized to take the form of the following specification:

where 𝑌 𝑡 is the output, 𝐾 𝑔,𝑡 represents the stock of public capital and 𝐾 𝑝,𝑡 the private capital stock, and 𝐿 𝑡 is the labour, adjusted for human capital by average years of schooling ℎ 𝑡 . The private capital stock and the labour variables ensure constant returns to scale. C is a constant term and 𝜖 𝑡 is the error terms assumed to behave independently and identically distributed.

We produce estimations of the previous specification using public capital stock in Table 1, over two periods of data history: the period 1960-2015; and the sub-period 1960-2007, which excludes the economic financial crisis and its subsequent impacts. Table 1 shows the estimated elasticities for all the variables of Equation ( 33), along with their statistical significance. Overall, the estimations have a high significant coefficient for all countries, with high adjusted R-squared going beyond 95% for all countries and a high Fisher (F-test) global significance. 117 The country results show that 15 out of 20 countries have significant public capital stock elastities for the two periods, with one negative significant elasticty for Greece in the first period and three negative elasticities for Austria, Greece and Japan in the second period. Over the two periods, Australia, Denmark and New Zealand have non-significant public capital elasticties. The average of accepted postive elasticties is around 0.32 and 0.36 for the two periods, respectively, and this average drops, when taking into account negative accepted elastitcities to 0.30 and 0.25, respectively, over the two periods. Higher elastictities (over 0.5) are recorded for the two periods, respectively, by Ireland (1.04 and 1.14), followed by Germany (0.59 and 0.51) and Sweden (0.57 and 0.51). Menawhile, many countries have elasticities ranging between 0.15 (the United States) and 0.25 (Canada and Belgium, for example), except France, which showed a lower accepted eslasticy value of around 0.07. Figure 2 summarizes the significant elasticities for government 117 The Durbin-Watson statistics are also low for all estimations, which indicates the presumption of a cointegration relationship in the data. However, in designing the rest of the simulations for the public debt potential, our model is intended to consider only the long-term effects (classical effects), while the short-term effects (Keynesian effects) are examined in Chapter 2, which links the effects of the public deficit financed by government bonds to fiscal policy effects via the multiplier effect (the Keynesian multiplier). Therefore, cointegration and error correction model formulations are not considered here, where we limit ourselves to long-term estimations. Besides, considering such formulations will completely modify the form of the Cobb-Douglas production function, which is theory grounded rather than ad hoc compilations, and complicate obtaining the overall elasticity effects. For estimations of Equation ( 33), using government capital flows instead of government capital stock, Table 2 shows that 16 out of 20 countries have significant government investment elastities for the period 1960-2015, with one negative elasticty recorded for Greece, and 17 countries for the period of 1960-2007, with two negative significant elasticties shown for Greece and Germany in this period. The average of accepted positive elasticities is around 0.24 and 0.26 for the two respective periods, while it is reduced to around 0.21 and 0.19 over the two periods, respectively, when accounting for negative accepted elasticties (Greece for the two periods, and Germany for the period 1960-2007).

By country, higher elasticities of between 0.30 and 0.50 are recorded for Sweden, Norway, Ireland,

The Netherlands and Italy. Belgium and New Zealand's elasticities are, respectively, negative and non-significant and positive non-accepted for the two periods of estimations. The values of positive elasticities range between:

-Relatively low values of around 5% to 15% recorded for four countries, namely, Australia, Austria, Canada, Denmark, France, Germany and Japan;

-Medium values of around 15% to 25% obtained for countries such as Switzerland, the United Kingdom, Portugal, Spain and the United States;

-Relatively high values of public capital elasticities shown for Ireland, Italy, The Netherlands, Norway and Sweden. OECD Countries, 1960[START_REF] Hulten | Total Factor Productivity: A Short Biography[END_REF].

Information sources

Information on public and private investment and GDP comes from three main sources: the OECD Analytical Database (August 2016 version) for OECD countries, and a combination of the National Accounts of the Penn World Tables (PWT, version 9.0) and the IMF World Economic Outlook (WEO, April 2016 ) for non-OECD countries. Information on country income groupings used in depreciation rates' assumptions is from the World Bank World Development Indicators.

Additional notes

Note that all data series (public investment and capital stock, private investment and capital stock, GDP, etc.) are expressed in billions of constant 2011 international dollars (purchasing power parity adjusted), using the corresponding component-specific deflators from OECD, PWT, and WB databases mentioned above.

Source of the above part of this

Human capital

Measured by average years of schooling of population [15,64] from Barro-Lee dataset (www.barrolee.com)