Agnès Bénassy-Quéré

Guillaume Roussellet
email: guillaume.roussellet@ensae.fr

Gunther Capelle-Blancard

Fiscal Sustainability in the Presence of Systemic Banks: the Case of EU Countries *

Keywords: H21, H23, J41 Fiscal sustainability, tax gap, systemic banking risk, off-balance sheet liabilities

. We then introduce two alternative measures of implicit off-balance sheet liabilities related to the risk of a systemic bank crisis. The first one relies of microeconomic data at the bank level. The second one relies on econometric estimations of the probability and the cost of a systemic banking crisis, based on historical data. The former approach provides an upper evaluation of the fiscal cost of systemic banking crises, whereas the latter one provides a lower one. Hence we believe that the combined use of these two methodologies helps to gauge the range of fiscal risk.

Nous proposons une première tentative pour prendre en compte les engagements hors-bilan de l'Etat liés lassurance implicite apportée aux banques systémiques, pour les 27 pays de lUnion européenne. Tout dabord, nous calculons des écarts de fiscalité (tax gaps) à la [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF] et [START_REF] Blanchard | La soutenabilité de la politique budgétaire : nouvelles réponses à une question ancienne[END_REF]. Nous introduisons alors deux mesures alternatives des engagements implicites hors-bilan liés au risque de crise bancaire systémique. La première mesure repose sur des données microéconomiques au niveau des banques. La seconde sappuie sur des estimations macro-économétriques de la probabilité et du coût dune crise bancaire systémique, à partir de données historiques. La première approche procure une mesure haute du risque hors-bilan tandis que la seconde offre une mesure basse. JEL: H21, H23, J41. Mots-clés: soutenabilité budgétaire, écart fiscal, risqué bancaire systémique, engagements horsbilan.

Introduction

In the wake of the 2007-09 global crisis, advanced economies suffered dramatic deteriorations of their fiscal balances, due to bank bailouts, fiscal stimulus packages and the action of automatic stabilizers. In the Euro area, this deterioration triggered a severe sovereign debt crisis. Still, prior to the crisis, a number of European countries such as Ireland and Spain had been praised for fiscal discipline. The brutal change of status from best to worst in class has questioned traditional analyses of fiscal sustainability. The Stability and Growth Pact (SGP) has been revamped to account for excess leverage in the private sector and cumulated losses in competitiveness. In times of a financial crisis, the government may find it necessary to bail out the so-called Systemically Important Financial Institutions (SIFIs), whose failure would put the whole financing system at risk. As theoretized by [START_REF] Acharya | A Pyrrhic Victory? Bank Bailouts and Sovereign Credit Risk[END_REF], bank bailouts in turn lead to an increase in taxes and/or a dilution of existing sovereign debt. In both cases, there are negative feedback effects on the banking sector through lower growth and collateral damage. Hence there is a strong interplay between bank and sovereign solvency.

To our knowledge, though, there has been little attempt to measure the implications of off-balance sheet liabilities related to SIFIs within a consistent analysis of government sustainability. One exception is the European Commission (2011) that, based on a model of bank default combined with data from Bankscope and a standard statistical model of credit risk, simulates the probability that fiscal sustainability is put at risk. The task is however extremely difficult given the lack of clarity surrounding the definition of SIFIs, and the fragility of any evaluation of the fiscal cost in case of a bail out. Last but not least, the probability of a systemic banking crisis is difficult to evaluate.

This paper provides an attempt to include off-balance sheet, implicit insurance to SIFIs into a consistent assessment of fiscal sustainability, for the 27 countries of the European Union. We successively consider a micro and a macroeconomic approach. The microeconomic approach relies on the stress tests released by the European Banking Authority (EBA) in July 2011 for 90 "systemic" banks. Alternatively, we use a measure of bank capital shortage in the event of a financial crisis provided by the Volatility Laboratory of New York University. As for the macroeconomic approach, it is based on historical data on the fiscal cost of systemic banking crises. In both cases, we incorporate implicit liabilities related to a banking crisis to a standard calculation of tax gaps à la [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF] and [START_REF] Blanchard | La soutenabilité de la politique budgétaire : nouvelles réponses à une question ancienne[END_REF]. Contrasting with European Commission (2011), we are not interested in the probability that the tax gap exceeds a certain threshold but on the impact of implicit liabilities on the tax gap itself. More importantly, we consider the banking risk as a repeated risk, whereas European Commission (2011) focuses on stochastic shocks at one point of time.

Depending on the measure of the costs (either micro or macro) and on the data source, we find contrasted impact of the banking risk on the tax gap of the different countries under review, ranging from a few tenths of percentage points (macro-base approach for "old" member states) to several percentage points (micro-based, EBA approach). In between, the micro-based (V-Lab) approach suggests that systemic banking risk could raise tax gaps by around one percentage point.

The remainder of the paper is organized as follows. In Section 2, we present the concept of fiscal sustainability and its operationalization through the tax gap, with an application to EU countries. Section 3 discusses the measurement of contingent liabilities related to SIFIs and proposes a first, micro-based correction of the tax gaps. In Section 4, we develop a macro-based approach of contingent liabilities related to SIFIs and propose an alternative, macro-based correction of the tax gaps, relying on two, complementary sets of econometric estimations. Section 5 concludes.

Tax sustainability gaps

Fiscal sustainability refers to the ability of current or projected fiscal policy to be run infinitely given the macroeconomic path of a country. The literature has followed two main avenues to operationalize this concept. First, it has used econometric techniques and especially cointegration to determine whether past fiscal policies can be considered sustainable (see [START_REF] Hamilton | On the limitations of government borrowing: A framework for empirical testing[END_REF]). The second approach intends to assess fiscal sustainability forward, based on fiscal and growth projections and on the debt accumulation process. Because it relates to the possibility of future events -systemic banking crises -our approach needs to lie within the second strand of the literature. Here we rely on [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF] and [START_REF] Blanchard | La soutenabilité de la politique budgétaire : nouvelles réponses à une question ancienne[END_REF] to measure the distance to fiscal sustainability through the tax gap, i.e. the difference between the constant tax rate that would ensure debt sustainability, and the current tax rate. In this section, we present how the tax gaps are calculated. In the next sections, we will adjust the methodology to take into account the fiscal risk related to the banking sector.

Methodology

Denoting by b t the gross public debt-to-GDP ratio at the end of period t, and s u the ratio of primary balance to GDP during period u, the inter-temporal budget constraint of the government writes:

b t e -(r-γ)t = b 0 - t 0 s u e -(r-γ)u du (1)
where b 0 is the debt-to-GDP ratio at the end of the initial period, r is the nominal interest rate and γ is the nominal growth rate. Equation (1) states that the present value of b t at time 0 is equal to the current value of the debt minus the sum of all present values of primary surpluses from time 0 to time t. Considering the standard case where r > γ, debt sustainability involves both sides of the equation to converge to zero when t goes to infinity:

1 lim t→+∞ b t e -(r-γ)t = 0 ⇔ b 0 = ∞ 0 s u e -(r-γ)u du (2)
The left hand-side condition is the transversality condition.2 It states that the debtto-GDP ratio should grow at a slower pace than the gap between the interest rate and the GDP growth rate. The second condition states that the interest payments on the current debt should be fully covered by future primary surpluses. A sustainability indicator can then be derived from this second condition through decomposing the primary surplus as follows: s t = τ t -g t with τ t the tax rate (total tax pressure) and g t the primary spending of the government (in percent of GDP). Considering r and γ as exogeneous, the sustainable tax rate τ * is the constant tax rate that ensures debt sustainability, given projected expenditures:

τ * = (r -γ) b 0 + ∞ 0 g u e -(r-γ)u du (3)
τ * can be compared to the current tax rate τ to assess fiscal sustainability. For instance, τ * > τ implies that the current policy cannot be run forever: either spending will need to be cut, or the tax rate will have to be raised.

One important limitation of this approach is the assumption of exogenous interest and growth rates. For instance, [START_REF] Bohn | The sustainability of budget deficits in a stochastic economy[END_REF] argues that future government revenues and expenditures should not be discounted by a fixed interest rate on government (safe) bonds, but rather by the variable intertemporal marginal rate of substitution, that may be correlated with fiscal variables. However he confesses that such approach is difficult to carry out in practice. More worrisome, the interest rate may be endogenous to the assessment about sustainability. Consider a country where τ < τ * , i.e. the debt is found non-sustainable. Then, international investors will ask for higher interest rates to compensate for the sovereign risk. In turn, this will raise the sustainable tax rate τ * and make the debt even less sustainable. Symmetrically, a country where τ > τ * will enjoy a lower interest rate, hence τ * will fall and make the debt even safer. Hence, assuming a constant interest rate tends to under-estimate tax gaps in absolute value, and it can also miss multiple equilibria when the tax gap is close to zero. 3Assuming an exogenous growth rate raises similar difficulties. Consider a country where τ < τ * . In this country, a fiscal adjustment needs to be implemented to ensure debt sustainability. The problem is that this adjustment will likely depress the level of nominal GDP, hence raise by itself the level of τ * and make the debt even less sustainable. Conversely, a finding of τ > τ * would suggest the existence of some fiscal space to stimulate GDP, which would endogenously reduce τ * . However, if the Keynesian multiplier is close to zero in the long run, this reasonning only applies in the short term: at sufficiently long horizon, GDP growth can be assumed independent from fiscal policy.

Here we stick to the literature in assuming exogenous interest rates and growth rates. We however examine the role of r -γ in our results and perform some robustness exercises (see Section 3.2). 4Calculating sustainable tax rates as defined above would require projections of public spending at an infinite horizon. To make the concept operational, [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF] and [START_REF] Blanchard | La soutenabilité de la politique budgétaire : nouvelles réponses à une question ancienne[END_REF] propose the following finite-horizon equivalent of τ * :

τ * T = (r -γ) 1 -e -(r-γ)T -1 T 0 g u e -(r-γ)u du + b 0 ( 4
)
where T is the time horizon (1, 5 or 40 years in [START_REF] Blanchard | La soutenabilité de la politique budgétaire : nouvelles réponses à une question ancienne[END_REF]). The equivalent in discrete time is:

τ * T = r -γ 1 + r -γ 1 - 1 (1 + r -γ) T -1 T u=1 1 1 + r -γ u-1 g u + b 0 (5)
It can be checked that lim

T →+∞ τ * T = τ * , i.
e. the finite-horizon indicator converges to the infinite one when T goes to infinity. The tax gap at horizon T is then the difference between the sustainable tax level τ * T and the present tax level τ t . A positive tax gap means that either expenditures need to be reduced or taxes need to be raised to meet the sustainability condition.

The intuition of Equation ( 5) can be grasped by assuming constant public spending in percentage of GDP over the entire T period (g u = g T = cst for u = 1 to T ). Equation (5) then boils down to:

τ * T = g T + r -γ 1 + r -γ b 0 (6)
The sustainable tax rate is the one that covers both primary expenditures and the share of interest payments that is not absorbed by GDP growth, so that the public debt ratio stays constant. In a dynamic framework where government expenditures vary over time, the debt ratio is not constant but it tends to fall back to its initial level. Hence, such approach is intrinsically conservative, since the initial level of debt may not be optimal. The European Commission (European Commission ( 2009)) has developed a variant of above calculations aiming at measuring the fiscal consolidation that would be necessary to bring the debt-to-GDP ratio to 60 percent in 2060 (S1), and another one that would just stabilise the debt ratio while accounting for ageing cost even beyond 2060 (S2). 5In the following, we calculate tax gaps at the 1, 4 and 50-year horizon, successively. Following [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF], we neglect the discount factor 1/(1 + r -γ) for the oneyear and the four-year horizons. For these two horizons, the time path of g u is then irrelevant and the sustainable tax gap is recovered simply as:

τ * T = ḡT + r -γ 1 + r -γ b 0 (7)
where ḡT denotes average expenditures over the T -year horizon (T = 1, 4). At the 50-year horizon, the discount factor can no longer be neglected and we apply Equation (5).

Tax sustainability gaps: an application to EU countries

To calculate tax gaps at the 1, 4 and 50-year horizons for year 2011, we rely on various publications of the European Commission in the Autumn of 2011, and use Maastricht definitions of deficits and debts. The sources and assumptions are detailed in Appendix A. For the 50-year horizon, we successively consider two scenarios: in the first, "on the fly" scenario, public expenditures excluding interest payments and age-related spending are supposed to stay constant in percentage of GDP from 2015 to 2060. In the second, "adjustment" scenario, public spending excluding interest payments are assumed constant over the same period, hence the rise in age-related expenditures is compensated by spending cuts in other areas.

The results are reported in Table 1, together with r -γ gaps at the corresponding horizons. The table also reports the end-2010 debt ratio and the tax gaps obtained by the European Commission ("S2" tax gap that stabilizes the debt ratio, see European Commission (2010)) and by the IMF (based on debt ratios that would not exceed 60 percent of GDP at the 2020 horizon, see International Monetary Fund (2011)). In the last column of the table, we report the aggregate tax gap for the Euro area, which would be the appropriate measure of fiscal sustainability in the event of a "fiscal union". At the one-year horizon, tax gaps are positive in 18 countries (meaning that the fiscal situation is unsustainable) and negative or close to zero in the remainder. They exceed 5 percent of GDP in Greece, Ireland, Portugal, Slovenia, Spain and the United Kingdom. The UK suffers from a large primary deficit in 2011 (-6.3 percent of GDP6 ) but it enjoys an interest rate that is close to its growth rate. The other countries of this group suffer from both primary deficits and a positive gap between the interest rate and the growth rate. At the other end of the spectrum, Hungary posts a large, negative tax gap resulting from a very large primary surplus (7.5 percent of GDP in 2011 according to autumn 2011's forecasts). In between, some countries (Finland, Italy) display a positive tax gap despite primary surpluses: their tax gaps result from their interest rates exceeding their growth rates.

At the four-year horizon, tax gaps are generally lower (the unweighed average is -0.4 percent of GDP, against 2.3 percent at the one-year horizon).This results both from optimistic fiscal prospects (those reported in Convergence/Stability reports) and from tighter gaps between interest rates and growth rates. This is especially striking for the six countries with large one-year tax gaps mentioned above. At the four-year horizons, their tax gaps are all below 4 percent, and in all but Greece and Ireland, they are below 3 percent (the tax gap even turns negative in the UK). Tax gaps in the other countries are either negative or less than 1.2 percent of GDP, with the exception of the Czech Republic (+3.3 percent).

At the fifty-year horizon, the interest rate is assumed to exceed the growth rate in all countries. Additionally, ageing-related expenditures are now taken into account. In the "on-the-fly" scenario, most tax gaps are back to positive territory. Interestingly, the group of countries with tax gaps above 4 percent includes Luxembourg, Malta and Slovakia. Spain is also part of this group, but Greece and Ireland are below 4 percent (3.8 and 2.5, respectively), the UK is balanced and Portugal and Slovenia display negative tax gaps. Unsurprisingly, the "adjustment" scenario reduces the tax gaps at the 50-year horizon. The majority of them become negative.

The comparison with EC and IMF calculations is not easy since both the concepts of tax gaps and the underlying assumptions (e.g. about interest and growth rates) differ. Our one-year ahead tax gaps are highly correlated (more than 75 percent) with both EC and IMF tax gaps. The correlations drop to around 50 percent for the 4-year horizon and the 50-year "on-the-fly" one. It further drops to 22-29 percent for the 50-year "adjustment" scenario, which makes sense since neither the EC nor the IMF assume further reforms to tackle ageing-related spending. On the whole, we consider our calculations meaningful enough to proceed to the next step of the analysis, which consists in incorporating the implicit liabilities related to SIFIs into our tax gaps, concentrating on the 4-year horizon.7

Contingent liabilities related to SIFIs

From end 2007 to end 2010, the Irish government debt-to-GDP ratio jumped from 25 to 96 percent, and Ireland experienced a deep sovereign debt crisis. Still, before the crisis, this country had displayed fiscal balance and not raised any sustainability concern. 8 The reason for this sudden change has to do with the collapse of the Irish banking sector and the decision to bail it out to avoid a major financial crisis. This experience suggests that off-balance sheet liabilities related to the banking sector should be included in fiscal sustainability assessments.9 In this section, we intend to clarify the notion of contingent liability, before trying to incorporate it into our calculations of tax gaps.

Contingent liabilities: concept and measurement

Following [START_REF] Polackova | Contingent liabilities: A threat to fiscal policy[END_REF] and [START_REF] Polackova | Contingent government liabilities: A hidden fiscal risk[END_REF], four types of government liabilities can be distinguished depending on whether they are explicit or implicit, direct or contingent. Explicit liabilities are enacted by a law or a contract, whereas implicit liabilities do not rely on any formal commitment but relate to a kind of moral (or unavoidable) obligation. In turn, direct liabilities will almost surely have to be honored in a predictable way, whereas the payment of contingent liabilities is conditional on the occurrence of a specific event outside the control of the debtor (see also [START_REF] Cebotari | Contingent Liabilities: Issues and Practice[END_REF]).

Only direct, explicit liabilities are recorded in the national accounting system. As discussed above, ageing-related expenditures are off-balance sheet. Except for civil-servant pensions which are explicit, they can be classified direct, implicit liabilities. Examples of contingent liabilities include state guarantees (explicit), public-private partnerships (explicit), compensations for environmental catastrophes (implicit) or the support of ailing banks (implicit).10 Because they are by nature unpredictable, they are more difficult to evaluate ex ante. Still, as argued by [START_REF] Abbey | Fiscal irresponsibility and fiscal illusion[END_REF], there is a temptation for the government to extend generous explicit or implicit guarantees that bear political reward at no cost in the short run.

Different strategies have been proposed in the literature to measure the risk and associated amounts of government contingent liabilities (see [START_REF] Polackova | Contingent liabilities: A threat to fiscal policy[END_REF][START_REF] Polackova | Contingent government liabilities: A hidden fiscal risk[END_REF], [START_REF] Hemming | Public private partnerships, government guarantees and fiscal risk[END_REF], [START_REF] Currie | Risk management of contingent liabilities within a sovereign asset-liability framework[END_REF] for instance).

The European Commission ( 2009) proposes a measure of risk based on composite indicators covering macro-financial risk and short-term rigidities on the top of more traditional fiscal variables. This approach however does not provide an evaluation of the costs incurred by the government under the bad state of nature, neither does it provide a probability. To fully evaluate contingent liabilities, it is necessary to combine probabilities with costs. Two alternative avenues can be followed. The first one is to measure contingent liabilities as the mathematical expectation of the present value of costs (probability of occurrence × cost in occurrence), or as the present value of the "maximum probable loss" (value-at-risk approach, see [START_REF] Currie | The potential role of government debt management offices in monitoring and managing contingent liabilities[END_REF]). Probabilities and losses can be estimated based on historical data. To recover the variance of the costs, one option is to use Monte Carlo simulations (see [START_REF] Hemming | Public private partnerships, government guarantees and fiscal risk[END_REF] for instance). The second approach relies on option prices: a government guarantee can be considered as "put" option (see [START_REF] Merton | An analytic derivation of the cost of deposit insurance and loan guarantees an application of modern option pricing theory[END_REF], [START_REF] Cebotari | Contingent Liabilities: Issues and Practice[END_REF]), so the contingent liability can be recovered based on the price of this option.

Contingent liabilities and fiscal sustainability: a micro-based approach

In this section, we intend to incorporate a micro-based measure of contingent liabilities of European governments related to their SIFIs into the tax gap described in Section 2. To measure contingent liabilities, we rely on the consistent -although debated -stress tests of 90 banks (considered "systemic") in 21 countries released by the European Banking Authority in July 2011 (see European Banking Authority ( 2011)). The scenario of stress includes haircuts (with associated probabilities) on sovereign debts affecting the trading book, a fall in housing prices, a downturn in growth, and a depreciation of the USD (see Appendix 3 of the EBA report). The impact on each bank's balance sheet is then calculated for 2011 and 2012.

We rely on the difference between the consolidated Risk-Weigthed Asset (RWA) of each bank and the value of core tier 1 capital denoted K. For each bank, the implicit exposure of the government is then X = RW A-K, which measures the risk not covered by core capital. 11 We finally sum up all exposures to individual banks at the country level, bank nationality being that of its headquarters.

It should be noted that, by summing up exposures to individual banks, we consider a pessimistic scenario where all systemic banks need simultaneously to be bailed out. Furthermore, the government is assumed to be the only source of recapitalization. Finally, the cost is considered definitive, whereas in some cases it can be at least partially recovered. 12Here we concentrate on the tax gap at the four-year horizon. Consistently, we need to introduce government exposure to systemic banking risk, X, for the next four years (here 2011 to 2014). Given the lack of forward-looking data, we consider X to be a fixed proportion of GDP which we denote by x and calculate for 2011 based on EBA data for costs and European Commission forecasts for GDPs. 13To calculate the expected costs of banking crises over the next four years, we need to combine x with a probability of crisis at each period. We consider the instantaneous probability of a crisis p as a parameter (ranging from 0 to 10%),14 and assume that when a banking crisis appears in a country, it has no chance to appear again during the next three years. We therefore model the probability process as a binomial tree, stopping whenever a crisis occurs. Without discounting future losses,15 we get:

E(cost) = px + p(1 -p)x + p(1 -p) 2 x + p(1 -p) 3 x (8) = px 4 u=1 (1 -p) u-1 (9)
The expected recapitalization costs are finally incorporated into the medium-run tax gap detailed in Section 2. More specifically, we add the annualized expected cost of a crisis to the average spending ratios in Equation (7). To account for the possible mutualization of the banking risk, we also calculate the cost of a banking crisis affecting all the SIFIs of the Euro area simultaneously, and derive the corresponding tax gaps through the same methodology. 16The results are reported in Table 2. The first column (p = 0%) recalls the results obtained without accounting for the exposure of the government to systemic banking crises. The next two columns report the results for an instantaneous probability of five and ten percent, successively. The third column reports the cost of a bailout independently from its probability. Unsurprisingly, the cost of a bailout, relative to GDP, is higher in countries where bank balance sheets are large relative to GDP: the cost exceeds 100 percent of GDP in Cyprus, Spain, Ireland, the Netherlands, Portugal, Sweden and the United Kingdom. In these countries, even a 5 percent instantaneous probability of a banking crisis has a dramatic impact on the tax gap. The latter rises by 13.3 percentage points between he first two columns in Cyprus, 7.7 pp in Spain, 5.6 pp in Ireland, 4.8 pp in the Netherland, 5.8 pp in Portugal, 6.0 pp in Sweden and 5.8 pp in the UK. With a 10 percent instantaneous probability of a crisis, all these countries display tax gaps exceeding 6 percent, and four of them are double-digit. It should be noted also that even in countries with a more limited cost in the case of a crisis, the impact of accounting for a crisis event is significant. For instance, the German tax gap rises by 2.1 pp when accounting for a 5 percent probability of a crisis. The Finish tax gap rises by 1.0 pp although the cost of a bail out would be "only" 20.8% of GDP in this country.

financially-integrated zone such as the Euro area justifies analysing a worst-case scenario of a general SIFI crisis.

13 Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

For the euro area as a whole, the potential cost of a simultaneous SIFI crisis in all Member countries is of the same magnitude as the aggregate sovereign debt of the zone: (80 percent of GDP). This translates into a substantial impact of the inclusion of the banking risk on the aggregate tax gap. For a 5 percent crisis probability, we get a tax gap of 3.8 percent. Hence a mutualization of the risk related to the SIFIs involves a considerable increase in the aggregate tax gap of the Euro area level, which suggests to reduce the cost (through appropriate regulation, supervision, bail-in and bankrupcy procedures) before any mutualization can take place.

As already mentioned in Section 2, one important qualification to tax gap calculations is the assumption of exogenous interest rates and growth rates. On the top of the classical arguments against this hypothesis, it can be argued here that a banking crisis may simultaneously raise the interest rate paid by governments on their debt, and lower the growth rate of the economy. The last column of Table 2 calculates the impact of a one pp increase in the difference between the interest rate and the growth rate (r -γ) on the tax gaps. The calculation is straightforward since at the four-year horizon, this factor impacts on the tax gap separately from public spending and the cost of a banking crisis. Specifically, we can differentiate Equation ( 7) with respect to r -γ. We then get:

dτ * T = b 0 (1 + r -γ) 2 d(r -γ) (10)
The impact of a higher r-γ on tax gaps depends on the initial debt level. It is higher for Greece and Italy than for Luxembourg. The usual range obtained is an additional 0.5-to-1.0 pp tax gap for each pp increase in r -γ. Since a banking crisis can raise r -γ by several percentage points, this calculation further darkens the assessment on fiscal sustainability when the risk related to a banking crisis is accounted for. Equivalently, it raises the case for strict regulations that would reduce the probability and cost of a banking crisis.

To measure the impact of stricter regulation on tax gaps, we perform the following exercise: we assume that all banks adjust by 2014 to the capital requirement ratios of Basel 3. Specifically, we assume that, in all banks where it is below the 6 percent tier 1 requirement, banks increase their capital K so that the ratio K/RW A converges lineary to 6 percent in 2014. We the recalculate (RW A -K)/GDP for each bank, based on the Basel 3 scenario for K and on projected nominal GDP. We ultimately aggregate these ratios at the country level and re-calculate the tax gaps at end-2011. The results are reported in Table 3 for the six countries where initial bank capitalization is below the Basel 3 requirement. Although the Basel 3 scenario reduces the cost of a banking crisis, the impact on the tax gap appears relatively limited.

Contingent liabilities and fiscal sustainability: an alternative microbased approach

Obviously, the figures obtained in the previous section are very large due to extreme assumptions concerning the amount of the bail-out in the case of a systemic bank crisis (indeed, we implicitly assume that the value of the RWA collapses to zero). Another approach is to rely on [START_REF] Acharya | Measuring Systemic Risk[END_REF] and VLAB (2011) who propose a measure of how much capital would a bank need in the case of a financial crisis. Their methodology proceeds in two steps. First, they estimate the long run marginal expected shortfall in percent (LRM ES), in the case of a 40% decline in market returns, which they consider the threshold of a financial crisis.17 Second, they calculate the capital shortage in case of a financial crisis, SRISK, depending on existing bank liabilities:

SRISK = k D + (1 -LRM ES)E -(1 -LRM ES)E (11)
where k represents the prudential standard ratio, taken as the capital ratio of the safest banks during the 2007-08 crisis (k = 8%), D is the nominal debt of the bank and E is its nominal equity. The first term in Equation ( 11) represents the needed level of capital as a function of total liability; the second one represents the effective level of capital given the fall in the equity price. SRISK is available for 100 global financial institutions on the website of the Volatility Laboratory of New York University (V-Lab). 18 Here we use a selection of 55 European banks considered as "systemic" according to the European Banking Agency. 19 We use the last figure of SRISK in 2011, in USD million, and convert it into EUR bn by applying a 1.2939 exchange rate. We then follow the same methodology as in the previous section: for each country, we sum up available measures of SRISK, across the different banks of a country, divide this sum by GDP and use this ratio as x in Equation ( 8). The results are reported in Table 4. The last column reports the bank coverage per country. For two countries (Luxembourg and Slovenia), our V-Lab data does not include any bank. For two other countries (Germany, Spain), the coverage is relatively limited.20 For 12 countries, however, Table 4 can directly be compared with Table 2 since they cover the same banks at the same date.

Not surprisingly given the methodology, the costs reported in Table 4 are much lower than those of Table 2. They pick at 32 percent of GDP for Cyprus, instead of 287 percent in Table 2. 21 Consistently, the impact of the banking risk on the tax gaps is much reduced. For a 5 percent risk, the tax gap increases by 1 pp or more in four countries: Cyprus, Sweden, the UK and France. It increases by 0.9 pp in the Netherlands despite the calculation accounting for only half of the systemic banks. These figures are not negligible. For a 10 percent crisis probability, the tax gap is increased by another percentage point, approximately. Like in the previous case, the tax gap can be further widened by an increase in r -γ in the event of a banking crisis. The amounts are the same, so they are not reported here. 224 Contingent liabilities and fiscal sustainability: a macro-based approach One limitation of the micro-based analysis of contingent liabilities is that it relies on a specific assessment of banking risks, based on the EBA or V-Lab methodology for a specific year, hence it lacks generality. Additionally, the micro-based approach should be considered a pessimistic scenario where all the SIFIs of a country need simultaneously to be bailed out by the government, with no recovery of the costs incurred in the later years. Another way of assessing fiscal sustainability is to rely on historical data on banking crises. Here we rely on two databases covering a large number of countries ,158 observations between 1977 and 2007. 23 On this sample, the unconditional probability of a systemic banking crisis is 2.78 percent (60 events out of 2,158 observations). The average, fiscal cost of systemic banking crises is 14.29 percent of GDP.

As a first step, we can plug the unconditional probability of a crisis, p = 2.78 percent, and the average cost in case of a crisis, x = 14.29 percent of GDP in the methodology of the previous section to recover tax gaps at the four-year horizon. The results are reported in the second column of Table 9. The impact of accounting for banking crises on the tax gap is found relatively limited -the maximum is 2.6 pp in Luxembourg. The problem here is that each country is assumed to bear the same costs in the event of a banking crisis. Additionally, although no longer ad hoc (as in the previous case), the instantaneous probability of a crisis is assumed to be the same for all countries, which is a strong assumption. Both the probability and the cost may depend on certain characteristics of the countries such as growth, inflation, the exchange-rate regime or the development of the financial sector. In the following, we calculate conditional probabilities and costs based on an econometric estimation over our sample of crisis events.

Systemic banking crisis: econometric methodology

To explain both the probability of a systemic banking crisis and the fiscal cost in the event of a crisis, we rely on three groups of explanatory variables covering macroeconomic shocks, macrofinancial shocks and institutionnal factors, that all have been highlighted by the existing literature (see [START_REF] Detragiache | Cross-Country Empirical Studies of Systemic Bank Distress: A Survey[END_REF]; Demirguc-Kunt & [START_REF] Demirguc-Kunt | The determinants of banking crises : evidence from industrial and developing countries[END_REF][START_REF] Demirguc-Kunt | Monitoring banking sector fragility : a multivariate logit approach with an application to the 1996-97 banking crises[END_REF], [START_REF] Caprio | Macro Financial Determinants of the Great Financial Crisis: Implications for Financial Regulation[END_REF][START_REF] Hardy | Determinants and leading indicators of banking crises: Further evidence[END_REF][START_REF] Hardy | Determinants and leading indicators of banking crises: Further evidence[END_REF]). Unfortunately, due to data limitations, we were obliged to drop most financial

The retained variables are listed in Table 5. 24 We were also obliged to reduce our whole sample of countries to only 73 countries (see the list in Appendix B).

The level of GDP per capita (in US dollar) is used as an indicator of development, the M2/GDP ratio is a standard indicator of financial development, the short-term real interest rate refers to the refinancing cost of the banks, and the accumulation of foreign-exchange reserves can be viewed as a protection against at least currency crises. We also add real GDP (or real GDP per capita) growth as a measure of the pre-crisis outlook. Note that all ratios and rates are expressed in percent of GDP or percentage points.

The currency-crisis dummy intends to catch the possibility of twin crises, that can be more costly than plain banking crises. We introduce seven geographic dummies based on World Bank and United Nations classifications to correct for the heterogeneity of the sample. 25 A contagion dummy tries to take stock of the correlation of crises within a geographic area.

Because our fiscal cost database includes censored data, the most natural econometric approach is a tobit model with a binomial selection equation modeling the probability of a crisis outbreak. Although we are only interested in the outbreak itself, we cannot 24 The following variables were also tried: terms-of-trade variation, deposit interest rate (nominal and real), exchangerate variation, inflation (GDP deflator), net lending/net borrowing to GDP, debt to GDP, private consumption to GDP, growth rate of real imports, current-account balance in percent of GDP, equity-price index, domestic claims to private sector in percent of GDP, growth of domestic credit, liquid reserves to total bank assets, total claims to broad money, foreign claims to broad money, growth of domestic claims to private sector in percent of GDP, private credit by deposit money banks in percent of GDP, private credit by deposit money banks and other financial institutions in percent of GDP, growth of foreign total liabilities in percent of GDP, growth of total reserves minus gold, banks capital to assets, growth of population, M3 to GDP, net foreign assets to GDP, over or undervaluation of local currency (PPP conversion factor to market exchange rate ratio), income-level dummies.

25 Country dummies or fixed effects are not appropriate here due to the limited number of crisis events over our sample.

18 Documents de Travail du Centre d'Economie de la Sorbonne -2012.77 treat the years of continuation of the crisis as normal data. We therefore drop the corresponding rows of the sample until the crisis is over. Endogeneity is the second problem to solve: Demirguc-Kunt & [START_REF] Demirguc-Kunt | The determinants of banking crises : evidence from industrial and developing countries[END_REF][START_REF] Demirguc-Kunt | Monitoring banking sector fragility : a multivariate logit approach with an application to the 1996-97 banking crises[END_REF]; Detragiache & Demirguc-Kunt ( 2005) use a logit model with contemporaneous regressors. This methodology is problematic as the independent variables may be affected by the banking crisis. To avoid this issue, we lag all explanatory variables by one period. Preliminary estimations of a tobit model showed insignificant correlation between the residuals of the selection equation and those of the outcome equation. We concluded the selection bias to be negligible and therefore decided to estimate the probability and the cost of banking crises separately through multinomial logit and OLS estimations, respectively.26

Estimation results: probability of a crisis

The first step is to estimate a binomial model where the dependent variable is a dummy for the crisis event. We assume logistic residuals and thus perform a binomial logit estimation. The results are reported in Table 6. The (lagged) real growth of GDP per capita always has significant, negative impact on the probability of the outbreak of a banking crisis. As reported in Table 7, a 1-pp increase in the growth rate reduces the probability of a crisis by approximately 6 percent. In Column (5), the growth of GDP per capita is replaced by the growth of GDP. The latter variable also has significant, negative, although more limited impact on the probability of a crisis. Foreign-exchange reserves too have a significant, negative impact on the probability of a crisis: a high reserve-to-GDP ratio tends to protect countries against the occurrence of a banking crisis. The lack of macrofinancial data does not allow us to further explore the channels of this relationship. Conversely, our contagion dummy does not appear significant, neither do our two measures of (financial) development (M2-to-GDP ratio and level of GDP per capita). Only the short-run real refinancing cost of banks has, the positive, expected impact on the probability of a crisis.

Table 6 andTable 7 (which reports the odd ratios) show the significant, negative and large impact of the "Other EU countries" dummy. It should be reminded at this stage that the 2007-09 crisis is not included in the sample. Although less systematically, the "Other OECD" and "Sub-Saharan Africa" dummies also bear significant, negative coefficients: other things equal, the probability of a crisis is lower in these regions than in South-East Asia -our benchmark in the estimation.

Estimation results: cost of a crisis

As already mentioned, we do not find any convincing evidence of a relationship between the selection equation (occurrence of a crisis) and the cost of a crisis. We therefore proceed to standard, OLS estimations of the logarithm of the cost of crisis. The results are reported in Table 8. Both the lagged growth rate of GDP per capita and the lagged value of foreign-exchange reserves (as a proportion of GDP) have a significant, positive impact on the fiscal cost of a crisis. It should be reminded here that the regression is performed only on crisis events: although high growth and high foreign-exchange reserves reduce the probability of a crisis (see Table 6), once the crisis hits, these two variables tend to increase the cost of a crisis. A possible interpretation is that higher growth in the previous period may be related to a credit-based, bubble boom. As for foreign-exchange reserves, they are included in our measure of the cost of a crisis: more reserves allow the government to bear a higher cost.

Like for the logit regression, neither the level of GDP per capita nor the M2-to-GDP ratio have a significant impact on the cost of a crisis. Now, though, the currencycrisis dummy has a positive, significant impact on the fiscal cost of the banking crisis: whenever there is a currency crisis, the cost of the banking crisis rises by 0.6 percent. This can be explained by the currency mismatch between the asset side and the liability side of the banking sector, with more debts than assets in foreign currencies.

Implications for debt sustainability

We can now combine the logit and the OLS estimations to get the conditional expectation of fiscal costs related to the possible occurrence of a systemic banking crisis. For each year from 2011 to 2014, we calculate the probability of an outbreak of a banking crisis and the cost of such an event, for each country depending on the values of the explanatory variables of the logit and OLS models, successively. We then multiply the probabilities with the costs to obtain the mathematical expected cost. Assuming, again, that if the crisis hits at time t, there will not be any other outbreak of a crisis during the next three years, we have:

E(cost i,t ) = xi,t pi,t + xi,t+1 pi,t+1 (1 -pi,t ) (12) + xi,t+2 pi,t+2 (1 -pi,t+1 )(1 -pi,t ) + xi,t+3 pi,t+3 (1 -pi,t+2 )(1 -pi,t+1 )(1 -pi,t )
where xi,t is the conditional estimation of the crisis cost for country i at time t, and pi,t is the conditional probability of a crisis. These two conditional estimates are calculated for t = 2011 to 2014, based on the following assumptions:

• Growth of GDP per capita: IMF projections of September 2011 (World Economic Outlook);

• Foreign-exchange reserve ratio set at its end-2010 level;

• Two alternative scenarios depending on whether there is a currency crisis or not.

The expected cost of a banking crisis is ultimately incorporated into the tax gap of Section 2. The results are reported in Table 9. The first column (p = 0) recalls the tax gap obtained without accounting for banking crises. The second column (px) shows the tax gaps with the unconditional probability and the unconditional cost. The next two columns (p i xi ) report the tax gaps when following the methodology just described, assuming no currency crisis ("No CC") and the occurrence of a currency crisis ("CC"), successively. For the sake of interpretation, we then report the conditional probability pi and cost xi for each country in turn, averaged over 2011-14. In the last column pi x i , we use the conditional probabilities given by the logit model but rely on the micro-based evaluation of the costs in case of a crisis of Section 3.

Not surprisingly, the average estimated costs obtained from the macro-based approach are much lower and less diverse than those obtained from the micro-based (EBA) approach: from 6 to 59 percent of GDP, compared to 9 to 287 percent of GDP when relying on EBA figures. The orders of magnitude are closer to the micro-based (V-Lab) approach. Nonetheless, those countries displaying high crisis costs according to the micro-based approach (Cyprus, the Netherlands, Sweden, the UK) do not display high cost according to the macro-based approach. A first, major reason for these discrepancies is that here we no longer assume that, in the event of a crisis, all the SIFIs of a country will have to be bailed out. Secondly, our database includes a minority of banking crises in advanced economies where the banking sector represents a large share of the economy. Thirdly, due to data limitations, we were unable to include proxies of financial vulnerability in our macro-based approach, concentrating on macro variables.

One major advantage of the macro-based approach is that it attributes a conditional probability to the possibility of a crisis. On average over 2011-14, these probabilities range from 0.5 percent in Denmark to 11.0 percent in Cyprus. This range validates ex post the different probabilities studied in the micro-based approach. Interestingly, though, those countries with higher probabilities of crisis (Cyprus, Slovakia) would suffer relatively limited costs in the event of a crisis (less than 10 percent of GDP). Conversely, in Hungary and Romania, the probability of a crisis is limited but the cost in the case of a crisis is relatively high. On the whole, the combined effect of probabilities and macro-based costs is found very limited, except in new member states where the the cost in the case of a crisis is found much higher than in the other member states.

It is then tempting to combine our estimated crisis probabilities to the costs recovered from the micro (EBA) approach. 27 Accounting for the banking risk now raises the tax gap by at most one percentage point. A major exception is Cyprus, with a tax gap rising from 1.6-2.2 percent of GDP (macro-based approach) to 27.9 percent. Interestingly, the tax gaps obtained from unconditional probabilities and risks (second column of Table 9) are found in-between the pure macro-based approach (with conditional probabilities and costs) and the hybrid, micro-macro approach (macro-based, conditional probabilities with micro-based costs). Again, Cyprus is the exception.

Conclusion

We have proposed an attempt to include the contingent liabilities arising from SIFIs into a standard, tax-gap assessment of fiscal sustainability. To do so, we have followed two alternative routes. The first one relies on microeconomic data at the bank level either collected and released by the European Banking Authority in the occasion of its second wave of stress tests (July 2011), or calculated by the Volatility Laboratory of New York University. The second one relies on econometric estimations of the probability and the cost of a systemic banking crisis, based on historical data gathered by and [START_REF] Laeven | Systemic Banking Crises: A New Database[END_REF], 2010) and [START_REF] Reinhart | From Financial Crash to Debt Crisis[END_REF]. The former approach provides an upper measure of the fiscal cost of systemic banking crises since it assumes that in the event of a crisis, all SIFIs would need to be bailed out by the government. In turn, the latter approach provides an lower evaluation of the fiscal cost as it relies on historical data involving a limited number of countries where the banking sector represents a large share of the economy, and it tends to neglect financial fragilities. Hence we believe that the combined use of these two methodologies helps to measure the range of fiscal risk.

Depending on the measure of the costs (either micro or macro) and on the data source, we find contrasted impact of the banking risk on the tax gap of the different countries under review, ranging from a few tenths of percentage points (macro-base approach for "old" member states) to several percentage points (micro-based, EBA approach). In-between, the micro-based (V-Lab) approach suggests that systemic banking risk could raise tax gaps by around one percentage point. Importantly, each percentage point increase in the gap between the inteest rate and the growth rate that would follow a banking crisis raises the tax gap by 0.5 to 1 percent of GDP.

Our work cannot easily be compared with the inclusion of age-related implicit and explicit liabilities. In the case of ageing, the cost is relatively limited but the probability is close to unity. In the case of a systemic banking crisis, the probability is limited but the cost can be very high. This suggests to complement our expected-cost analysis with a value-at-risk analysis. However, it is already difficult to estimate the probability of a systemic banking crisis based on a limited number of events. Recovering the whole distribution of costs in order to perform a value-at-risk analysis cannot be envisaged. The solution then would be to perform stress tests, e.g. to calculate the impact of the worst-case scenario on the tax gap, with a unitary probability. However, given the amounts involved (even in the macro-based case), tax gaps would no longer provide any information on fiscal sustainability. Rather, this approach would point to the needs to avoid any implicit government insurance granted to SIFIs, except maybe after the building up of a dedicated fund financed through the SIFIs themselves and/or restricting such insurance to part of banking activities.

More generally, our work illustrates the limits of stress testing. In the case of a very detrimental scenario, fiscal sustainability can be at risk whatever the initial surplus; or a bank can go bankrupt whatever its initial ratio of core capital. The orders of magnitude suggest to search for ways to circumvent the sustainability issue in case of a catastrophic event through reducing the probability and the cost of the catastrophic event itself.

Ageing Report also provides average growth rates from 2010 to 2060. Like for the 1-year and 4-year horizons, we also rely on the end-2010 debt ratio and the projected receipt ratio for 2011 taken from EC's forecasts of Autumn 2011. Finally, we follow the European Commission (Sustainability Report 2009 ) in assuming a real interest rate of 3 percent from 2015 to 2060.

7

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

Table 1 :

 1 Gap between the sustainability tax rate and the observed, implicit tax rate in 2011, in percent

	Country	Tax gap	Tax gap		Tax gaps
		1 year	r -γ	4 years	r -γ	50 years	50 years	r -γ	b 2010	IMF 2011 EC 2010
			(1 year)		(4 years) On the fly Adjustment (50 years)		10 years	(S2)
	AT	-0.1	-1.4	0.2	-0.2	2.2	0.5	1.3	71.8	3.4	4.6
	BE	-0.6	-1.0	-0.5	-0.2	2.4	-0.4	1.2	96.2	2.8	6.5
	BG	1.2	-3.1	0.4	-2.1	1.8	-0.7	1.1	16.3	1.0	2.8
	CY	4.6	0.5	1.1	-0.8	3.9	0.4	0.2	61.5	n/a	12.5
	CZ	3.1	1.2	3.3	-0.4	2.8	1.7	1.2	37.6	3.4	9.8
	DK	3.0	1.9	0.8	0.8	-3.0	-0.3	1.3	43.7	2.0	-1.4
	EE	-1.5	-8.4	-1.5	-3.0	-6.0	-4.1	0.9	6.7	-3.9	1.2
	FI	-1.5	-3.2	-2.2	-1.7	1.6	-1.0	1.3	48.3	1.1	4.3
	FR	3.5	0.4	0.2	-0.5	1.2	0.2	1.2	82.3	6.3	1.0
	DE	-1.7	-0.7	-2.4	0.4	-0.4	-2.3	1.8	83.2	2.3	4.5
	EL	15.0	8.5	3.9	3.7	3.8	-2.4	1.2	144.9	15.5	20.3
	HU	-6.6	1.2	-11.7	-0.3	-12.3	-13.0	1.3	81.3	1.9	-1.3
	IE	10.2	3.7	3.8	1.7	2.5	-0.8	0.6	94.9	12.0	14.8
	IT	1.7	2.3	-0.5	1.3	-0.4	-0.8	1.6	118.4	3.1	2.6
	LV	0.6	-4.1	-1.8	-1.1	-4.4	-5.3	1.2	44.7	2.5	9.0
	LT	1.4	-4.8	1.3	-1.9	-2.4	-1.0	1.2	38.0	4.9	10.4
	LU	-0.1	-1.0	-3.2	-3.4	5.0	-3.0	0.3	19.1	n/a	12.7
	MT	-0.1	0.1	-0.7	0.1	4.1	-1.1	1.3	69.0	n/a	6.4
	NL	2.3	-0.1	0.1	0.7	5.3	0.0	1.5	62.9	4.4	8.5
	PL	1.7	-1.9	0.0	-1.5	-0.6	-0.1	1.3	54.9	6.9	5.6
	PT	6.2	4.9	1.1	3.4	-1.3	-2.4	1.2	93.3	9.6	8.9
	RO	2.9	-0.7	1.1	-2.5	3.2	1.5	1.0	31.0	4.3	9.7
	SK	3.4	-2.3	-0.7	-2.3	5.5	-1.3	1.0	41.0	6.6	8.5
	SI	5.2	3.5	0.2	0.9	-1.9	-1.8	1.4	38.8	4.0	12.2
	ES	5.3	1.3	2.3	0.3	4.7	1.2	1.1	61.0	8.3	15.3
	SE	-3.0	-3.4	-4.3	-1.9	-5.9	-4.4	1.1	39.7	-0.5	0.5
	UK	6.5	0.3	-2.0	-1.1	0.0	-2.4	0.9	79.9	9.1	13.5
	EA	1.8	0.6	0.1	0.5	1.8	-0.3	1.4	85.4	n/a	n/a

Notes: "one-the-fly": constant non-ageing expenditures in percent of GDP; "adjustment": adjusted non-ageing expenditures; b 2010 : debt ratio at end-2010; r -γ: average value of r -γ at the corresponding horizon. IMF 2011: debt-to-GDP ratio back to 60 percent for countries above this figure in 2012; debt ratio stabilized at its end-2012 ratio for the other countries (Fiscal Monitor 2011). EC 2010: debt ratio stabilized at an infinite horizon (Public Finances in EMU 2010 ). n/a: non-available. EA: Euro area at 17. Source: Author's calculations based on European Commission data.

Table 2 :

 2 Four-year tax gaps with exposure to banking crises, micro-based, EBA approach

		Tax gap with micro-based	Micro-based cost	Impact of a 1 pp
		crisis costs, in percent		increase in r -γ
	p = 0%	p = 5%	p = 10%	x i (% of GDP)	on tax gaps (in pp)
	AT	0.2	3.8	6.9	77.9	+0.7
	BE	-0.5	2.4	4.9	63.2	+1.0
	CY	1.1	14.4	25.7	287.0	+0.6
	DE	-2.4	-0.3	1.5	44.7	+0.8
	DK	0.8	5.1	8.9	94.5	+0.4
	EL	3.9	7.9	11.4	87.8	+1.3
	ES	2.3	10.0	16.7	167.5	+0.6
	FI	-2.2	-1.2	-0.4	20.8	+0.5
	FR	0.2	4.5	8.0	90.7	+0.8
	HU	-11.7	-10.5	-9.6	24.2	+0.8
	IE	3.8	9.4	14.1	119.3	+0.9
	IT	-0.5	2.5	5.1	64.6	+1.2
	LU	-3.2	-1.9	-0.8	28.4	+0.2
	MT	-0.7	1.5	3.5	48.9	+0.7
	NL	0.1	4.9	9.0	103.0	+0.6
	PL	0.0	0.4	0.8	8.8	+0.6
	PT	1.1	6.9	11.9	125.6	+0.9
	SE	-4.3	1.7	6.8	129.1	+0.4
	SI	0.2	2.7	4.9	54.8	+0.4
	UK	-2.0	3.8	8.7	125.1	+0.8
	EA	0.1	3.8	7.0	80.4	+0.8
	Note: EA: Euro area at 17.

Source: Author's calculations based on EBA data.

Table 3 :

 3 Four-year tax gaps with exposure to banking crises, micro-based, EBA approach, Basel 3 scenario

		Tax gap with micro-based	Crisis cost
		crisis costs, in percent	in 2014 *
		p = 0%	p = 5%	p = 10%	x i (% of GDP)
	DE Baseline	-2.4	-0.3	1.5	44.7
	DE Basel 3	-2.4	-0.4	1.3	39.7
	ES Baseline	2.3	10.0	16.7	167.5
	ES Basel 3	2.3	9.5	15.8	144.4
	IE Baseline	3.8	9.4	14.1	119.3
	IE Basel 3	3.8	9.0	13.5	103.9
	IT Baseline	-0.5	2.5	5.1	64.6
	IT Basel 3	-0.5	2.3	4.8	57.0
	PT Baseline	1.1	6.9	11.9	125.6
	PT Basel 3	1.1	6.8	11.7	120.0
	SI Baseline	0.2	2.7	4.9	54.8
	SI Basel 3	0.2	2.5	4.5	46.4

* Constant crisis cost ratio (baseline) or reclining crisis cost from 2011 to 2014 (Basel 3). Source: Author's calculations based on EBA data.

Table 4 :

 4 Four-year tax gaps with exposure to banking crises, micro-based, V-Lab approach

		Tax gap with micro-based	Micro-based cost
		crisis costs, in percent
		p = 0%	p = 5%	p = 10%	x i (% of GDP)	Bank coverage (%)
	AT	0.2	0.6	1.0	9.7	100
	BE	-0.5	0.2	0.8	16.1	100
	CY	1.1	2.6	3.8	32.1	100
	DE	-2.4	-1.9	-1.5	9.8	25
	DK	0.8	1.4	2.0	14.6	75
	EL	3.9	4.4	4.9	11.5	100
	ES	2.3	2.9	3.5	14.3	32
	FI	-2.2	-2.1	-2.1	1.3	100
	FR	0.2	1.2	2.0	20.0	75
	HU	-11.7	-11.6	-11.6	1.4	100
	IE	3.8	4.3	4.7	10.4	100
	IT	-0.5	0.0	0.4	10.0	100
	LU	-3.2	-3.2	-3.2	na	0
	MT	-0.7	-0.7	-0.7	0.7	100
	NL	0.1	1.0	1.7	18.1	50
	PL	0.0	0.0	0.0	-0.2	100
	PT	1.1	1.5	1.9	9.6	75
	SE	-4.3	-3.1	-2.1	25.1	100
	SI	0.2	0.2	0.2	na	0
	UK	-2.0	-0.8	0.3	26.9	100

Source: Author's calculations based on V-Lab data. na: non-available.

from 1977 to 2007:

[START_REF] Reinhart | From Financial Crash to Debt Crisis[END_REF]

for the frequency of banking crises, and

[START_REF] Laeven | Systemic Banking Crises: A New Database[END_REF], 2010)

for their fiscal cost. The definition of a systemic bank crisis is detailed in Appendix B. Among the 124 crises identified by Laeven and Valencia, we eliminate those not included in

[START_REF] Reinhart | From Financial Crash to Debt Crisis[END_REF]

's database, which leaves us with 60 systemic crises involving 51 different countries from 1977 to 2007. This database of systemic banking crises is then inserted into the wide database of

[START_REF] Reinhart | From Financial Crash to Debt Crisis[END_REF]

to get a set of 2

Table 5 :

 5 Variables used in the econometric analysis

	Variable name Description	Source	number of obs
	bank	Dummy for banking crisis: 1 for the outbreak of a	Leaven Valencia (2010)	2158
		systemic banking crisis, 0 otherwise
	cost	Gross fiscal cost of a systemic banking crisis. Re-	Leaven Valencia (2010)	60
		ported at the beginning of the crisis
	gdp g	Real GDP growth	IMF IFS and World Bank	1996
			databases
	gdppc g	Real growth of GDP per capita	IMF IFS and World Bank	1996
			databases
	rir	Short term real interest rate: discount rate minus	IMF IFS and World Bank	1696
		GDP deflator change. Central bank interest rate	databases
		when missing
	currency	Dummy for currency crisis	Reinhart Rogoff (2010)	1653
	contagion	Contagion dummy: 1 if there is a banking crisis in		2158
		the same region (see below), 0 otherwise
	gdppc usd	GDP per capita in USD	World Bank database	1977
	M2 GDP	Ratio of M2 in percent of GDP	WB database	1609
	foreign exch	Ratio of foreign exchange reserves to GDP	IMF IFS line 1d	1884
	geog	Regional dummies: (1) East Asia and Pacific, (2)	World Bank database	2158
		Eastern Europe and Central Asia, (3) Latin Amer-
		ica and the Caribbean, (4) Middle East, North
		Africa and South Asia, (5) Sub-Saharan Africa,
		(6) Western, Northern and Southern Europe, (7)
		Other high income

Table 6 :

 6 Logit estimation results: probability of a crisis

	Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	gdppc g	-0.058**	-0.054*	-0.058**	-0.058**		-0.062*	-0.077**
		(0.026)	(0.028)	(0.027)	(0.026)		(0.036)	(0.033)
	foreign exch	-0.046**	-0.045**	-0.046**	-0.046**	-0.047**	-0.029*	-0.046**
		(0.018)	(0.018)	(0.020)	(0.019)	(0.019)	(0.016)	(0.019)
	contagion		0.329
			(0.298)
	M2 GDP			-0.003
				(0.005)
	gdppc usd				-0.011
					(0.024)
	gdp g					-0.047*
						(0.024)
	currency						0.263
							(0.379)
	rir							0.001**
								(0.001)
	East. EU & CA	0.093	-0.008	0.070	0.043	0.038	0.025	-0.013
		(0.457)	(0.455)	(0.485)	(0.472)	(0.461)	(0.556)	(0.462)
	LAC	-0.385	-0.525	-0.525	-0.434	-0.317	-0.355	-0.729
		(0.425)	(0.406)	(0.464)	(0.448)	(0.414)	(0.443)	(0.472)
	MENA	-0.360	-0.310	-0.423	-0.388	-0.317	-0.453	-0.726
		(0.609)	(0.618)	(0.615)	(0.610)	(0.617)	(0.796)	(0.677)
	SSA	-1.155**	-1.198**	-1.285**	-1.226**	-1.059*	-1.433*	-1.366**
		(0.545)	(0.539)	(0.554)	(0.566)	(0.549)	(0.750)	(0.541)
	Other EU	-1.843*** -1.881***	-1.731**	-1.726*** -1.869*** -2.068*** -2.149***
		(0.522)	(0.523)	(0.682)	(0.607)	(0.521)	(0.621)	(0.568)
	Other OECD	-2.298**	-2.209**	-2.333**	-2.166**	-2.286**	-2.129**	-2.215**
		(1.053)	(1.063)	(1.054)	(1.045)	(1.052)	(1.065)	(1.057)
	cons	-2.279*** -2.388*** -2.045*** -2.199*** -2.248*** -2.518*** -2.062***
		(0.358)	(0.401)	(0.455)	(0.407)	(0.362)	(0.431)	(0.364)

Table 8 :

 8 OLS estimation results: cost of a crisis

		(1)	(2)	(3)	(4)	(5)	(6)
	gdppc g	0.055*	0.056*	0.068**	0.046	0.058*	0.109***
		(0.030)	(0.030)	(0.032)	(0.032)	(0.030)	(0.036)
	foreign exch	0.053*	0.052*	0.055*	0.044	0.049*	0.063**
		(0.027)	(0.027)	(0.028)	(0.027)	(0.027)	(0.029)
	gdppc usd		-0.003
			(0.018)
	M2 GDP			0.001
				(0.004)
	rir				0.010
					(0.008)
	contagion					0.410
						(0.264)
	currency						0.589*
							(0.323)
	cons	1.769*** 1.789*** 1.667*** 1.764*** 1.566*** 1.323***
		(0.237)	(0.265)	(0.283)	(0.243)	(0.268)	(0.282)
	Number of obs.	54	54	51	45	54	41
	Adjusted R 2	0.138	0.121	0.155	0.139	0.161	0.298
	Fisher p-value	0.0086	0.0238	0.0121	0.0274	0.0081	0.0010
	Source: own calculations.

Table 9 :

 9 Four-year tax gaps in percent: a synthesis

	Country		Tax gap with macro-based	Average over 2011-14	Tax gap with micro-based
			costs (% of GDP)		proba (%) cost (% of GDP)	costs (% of GDP)
		p = 0	px	pi xi , No CC	pi xi , CC	pi	xi , No CC	pi x i
	AT	0.2	0.6	0.3	0.3	1.2	7.7	1.1
	BE	-0.5	-0.2	-0.5	-0.4	1.2	7.2	0.2
	BG	0.4	0.8	1.7	2.7	2.3	58.7	n/a
	CY	1.1	1.5	1.6	2.1	11.0	5.9	27.9
	CZ	3.3	3.7	4.3	5.1	4.1	25.5	n/a
	DK	0.8	1.1	0.9	1.0	0.5	33.5	1.2
	EE	-1.5	-1.1	-1.4	-1.3	0.6	21.0	n/a
	FI	-2.2	-1.8	-2.1	-2.0	1.1	8.4	-1.9
	FR	0.2	0.6	0.3	0.4	1.3	7.0	1.4
	DE	-2.4	-2.0	-2.3	-2.2	1.2	8.0	-1.9
	EL	3.9	4.3	3.9	4.0	1.8	4.5	5.4
	HU	-11.7	-11.3	-10.4	-9.6	2.3	56.3	-11.1
	IE	3.8	4.2	3.9	4.0	1.4	6.0	5.5
	IT	-0.5	-0.1	-0.4	-0.4	1.3	6.5	0.3
	LV	-1.8	-1.4	-0.6	0.4	2.5	53.3	n/a
	LT	1.3	1.7	2.3	3.1	3.9	28.3	n/a
	LU	-3.2	-2.8	-3.1	-3.1	1.3	6.8	-2.9
	MT	-0.7	-0.4	-0.6	-0.6	1.1	8.6	-0.2
	NL	0.1	0.5	0.2	0.2	1.28	6.8	1.4
	PL	0.0	0.4	1.0	1.6	3.79	28.5	0.3
	PT	1.1	1.5	1.2	1.2	1.47	5.7	2.9
	RO	1.1	1.5	2.4	3.1	3.12	44.3	n/a
	SK	-0.7	-0.3	-0.1	0.5	8.77	8.4	n/a
	SI	0.2	0.5	0.2	0.3	1.21	7.4	0.8
	ES	2.3	2.7	2.4	2.4	1.34	6.4	4.5
	SE	-4.3	-3.9	-4.2	-4.1	0.73	15.1	-3.4
	UK	-2.0	-1.7	-1.9	-1.9	1.23	7.2	-0.5
	CC=Currency crisis; n/a: non available.
	Source: own calculations.

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When r < γ, an ever-rising primary deficit is consistent with the debt ratio not rising infinitely. Following Blanchard, we exclude this dynamic inefficiency case and assume r > γ.

Also labeled actuarial sustainability or no Ponzi game condition. 4 Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

Multiple equilibria appear because the debt is found sustainable whenever it is believed sustainable, hence the interest rate is low; it is unsustainable whenever it is believed so, hence the interest rate is high.

It should be noted that, by substracting nominal growth from the nominal interest rate, we exclude the possibility that intertemporal sustainability is achieved through an inflation tax. In the following, both nominal variables will be replaced by real ones, consistent with the Fisher effect.

Both the

percent ratio and the objective of a stabilization of the debt ratio are ad hoc. The calculation of an optimal debt ratio is difficult and surely beyond the scope of this paper.6 Documents de Travail du Centre d'Economie de laSorbonne -2012.77

see EC's forecasts of Autumn 2011. 9 Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

It should be reminded here that the aim of the paper is less to asses the fiscal sustainability of individual Member states than to evaluate the impact of accounting for banking risks in such assessment. The 4-year horizon appears the most meaningful for this task: on the one hand, the one-year horizon corresponds to immediate fiscal adjustment, which is completely out of reach for many governments and even not advisable; on the other hand, the assumptions made to include the fiscal risk related to SIFIs cannot be applied to the 50-year horizon.

See, e.g., European Commission, Public Finances in EMU, 2007: "[...] in 11 countries -Belgium, Bulgaria, Denmark, Estonia, Ireland, Spain, Cyprus, the Netherlands, Austria, Finland and Sweden -the current fiscal position would be consistent with sustainable public finances if there was no impact of ageing on public finances" (p. 58).

Another route is to avoid bank liabilities spreading to the public sector, by setting strict rules of bail-in (such as the possibility to convert bonds into equity), so that banks are no longer bailed out. We come back to this issue in the conclusion of the paper.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

Note that the cost incurred in the case of a bank crisis is partly explicit, e.g. deposit insurance schemes.

We use the full static balance sheet assumption here. Like European Commission (2011), we assume that bank losses are first absorbed by core capital. However, the European Commission uses an in-house model of bank default probability, whereas we directly use the EBA estimation of RWAs. We have checked that RWA never exceeds the total of the bank's assets.

In the case of Sweden in the 1990s, for instance, the final cost for the taxpayer was negligible, see[START_REF] Laeven | Systemic Banking Crises: A New Database[END_REF].

In the end of the section, we present a different scenario for x.

This range matches the estimations obtained in Section 4.

Discounting future losses affects marginally the results at the four-year horizon, see[START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF].

It can be argued that risk sharing brings no benefit if the risk is correlated across the Member states, hence if the crisis hits all Member states simultaneously. However a mutualization of crisis costs may be necessary since the costs are unevenly distributed across Member states. As a matter of fact, such mutualization of bank recapitalization costs did take place in the Euro area during the 2009-2012 crisis. Then, the fact that banking crises are higly correlated in a 12 Documents de Travail du Centre d'Economie de laSorbonne -2012.77

Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

They do so by extrapolating the equity losses estimated for a 2% decline in market returns.

vlab.stern.nyu.edu.

We are grateful to Rob Capellini for making the data available to us. Unfortunately, not all 90 EBA's systemic banks are covered by V-Lab.

For these two countries, the EBA provides data for an especially large number of banks: 12 for Germany and 25 for Spain.

Interestingly, though, the correlation between X and SRISK over the 55 bank sample is 89 percent. Hence the ranking of the risks is similar.

Additionally, due to incomplete coverage, we do not report any result for the Euro area.

We exclude the 2007-09 banking crisis from the sample because the final (five-year ahead) cost cannot be assessed by the writing of this paper (see below).

A panel data, random or fixed-effect, logit estimation with simulated maximum likelihood and conditional logit models was also tried. The maximum likelihood estimations did not converge and the small number of countries experiencing a crisis reduced the sample to less than 700 rows. We also tried skewed logit regression and a log linear model specification, which are supposed to be more adapted to rare events, but the functional forms were rejected. 20 Documents de Travail du Centre d'Economie de laSorbonne -2012.77

Here we select the EBA approach rather than the V-Lab one due to its extended coverage.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

including non-tax receipts that are here considered a perfect substitute for tax receipts.

The calculation of the implicit interest rate only relies on convergence and stability reports but the updated debt ratio is used as the starting point of the snowball calculations. Likewise, the updated tax ratio is only used to compare the sustainable tax ratio to the observed one.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.77

Our measure of gross cost includes interest payments on the debts incurred by the government to tackle the crisis. However we consider of second order the additional interest payments related to the additional level of debt, which allows us to include the cost of banking crises directly as primary expenditures in our tax-gap calculations. Conversely, the gross fiscal cost excludes the cost of guarantees that have not been paid.30Documents de Travail du Centre d'Economie de laSorbonne -2012.77

The odds ratio provides the multiplicative effect of each variable on the probability of a crisis. For instance, example, a 1 pp increase in the growth rate of GDP per capita multiplies the base probability by 0.926: the probability is reduced by 8% approximately. Source: own calculations.

Appendix A: Data sources for tax gaps

We use Maastricht definitions of fiscal deficits and debts. Accordingly, general government debt is defined as the total of gross debts at face value, at the end of the current year. Unlike national accounts, Maastricht accounting consolidates the debts of the various government sub-sectors. Note that currency and deposits are included as liabilities of the central banks, but equity and derivatives are excluded from the Maastricht definition of government debt. However, the streams of interest payments related to derivatives are included in the measure of the deficit. The government debt variation then is the sum of net borrowing by the general government and of the net purchase of financial assets. It is adjusted for the variation of non-Maastricht liabilities, capital gains or losses and miscellaneous items.

• For the 1-year horizon, we rely on EC's Economic Forecasts of the Autumn 2011.

From this source we directly take the gross debt-to-GDP ratios at end 2010 and the primary balance in 2011. 28 Based on interest expenditure in 2011 and the debt ratio at end 2010, we recover the implicit interest rate on the debt (interest payments in 2011/debt at end 2010). We also use real GDP growth and GDPdeflator growth in 2011.

• For the 4-year horizon, we use Convergence and Stability reports available in 2011.

The reports provide fiscal and economic projections prepared by each Member state within the Stability and growth pact procedure. From these reports we recover projected deficits, growth and inflation rates for years 2011 to 2014. Like in the previous case, we recover the implicit interest rate on the debt by dividing projected interest expenditures of year t by the debt level at the end of t -1. For consistency, we do not mix these data with more recent EC forecasts, except for the end-2010 debt ratio and the 2011 government receipt ratio that are taken from Autumn 2011 forecasts. 29 Note that Convergence and Stability reports are biased in an optimistic way since they are designed to comply with the budget balance requirement of the SGP in the medium term.

• For the 50-year horizon, we rely on the same data as above up to 2014, and on interpolations from Public Finances in EMU 2009 and the Ageing Report 2009 (baseline scenario) for 2015-2060. These two reports provide public spending ratios (including ageing-related expenditures) on a decade-by-decade basis, and the

Appendix B: Econometric analysis -definitions and sample

We concentrate on systemic banking crises defined by Laeven and Valencia as "Significant signs of financial distress in the banking system [...], and significant banking policy intervention measures in response to significant losses in the banking system" [START_REF] Laeven | Resolution of Banking Crises: The Good, the Bad, and the Ugly[END_REF], p. 6). These authors further quantify these events in the following way: "we consider a sufficient condition for a crisis episode to be deemed systemic when either a country's banking system exhibits significant losses resulting in a share of nonperforming loans above 20% or bank closures of at least 20% of the banking assets, or fiscal restructuring costs of the banking sector are sufficiently high exceeding 5% of GDP" [START_REF] Laeven | Resolution of Banking Crises: The Good, the Bad, and the Ugly[END_REF], pp. 6-7). They identify 124 episodes of such crises. The end of a crisis is defined as "the year before two conditions hold: real GDP growth and real credit growth are positive for at least two consecutive years". They also truncate crisis duration at 5 years to "keep the rule simple" [START_REF] Laeven | Resolution of Banking Crises: The Good, the Bad, and the Ugly[END_REF], p. 10).

The fiscal cost of systemic banking crises is taken from Laeven and Valencia (see the methodology in [START_REF] Andrews | Managing Systemic Banking Crises[END_REF] and Honohan & Laeven (2005)). We use the gross fiscal cost in percent of GDP, which is defined as: "the outlays of the government and central bank in terms of bond issuance and disbursement from the treasury for liquidity support, payout of guarantees on deposits, costs of recapitalization and purchase of non performing loans" (p. 4 of [START_REF] Andrews | Managing Systemic Banking Crises[END_REF]) from the outbreak of the crisis to five years later. Instead of the gross cost, we could have taken the cost net of asset sales and debt repayments by recapitalized entities. However, we would then have departed substantially from our micro-based approach that focuses on gross costs.