Olivier Cardi
email: olivier.cardi@u-paris2.fr.

Romain Restout
email: romain.restout@uclouvain.be.

FISCAL SHOCKS IN A TWO SECTOR OPEN ECONOMY *

Keywords: Non-traded Goods, Fiscal Shocks, Investment, Current Account. JEL Classification: F41, E62, E22, F32

We use a two-sector neoclassical open economy model with traded and non-traded goods to investigate both the aggregate and the sectoral effects of temporary fiscal shocks. One central finding is that both sectoral capital intensities and labor supply elasticity matter in determining the response of key economic variables. In particular, the model can produce a drop in investment and in the current account, in line with empirical evidence, only if the traded sector is more capital intensive than the non-traded sector, and labor is supplied elastically. Irrespective of sectoral capital intensities, a fiscal shock raises the relative size of the non-traded sector substantially in the short-run.

Additionally, allowing for the markup to depend on the number of competitors, the two-sector model can produce the real exchange rate depreciation found in the data.

Finally, markup variations triggered by firm entry modify substantially the response of the real wage and the sectoral composition of GDP in the short-run.

Introduction

There has recently been a revival of interest among policy makers in the fiscal policy tool.

The fiscal transmission mechanism has also attracted considerable attention in the academic literature. A number of papers have explored the ability of quantitative business cycle models, both of the neoclassical and of the new Keynesian variety, to account for the data, see Burnside, see e.g. [START_REF] Craig | Fiscal Shocks and their Consequences[END_REF] and Gali, Lopez-Salido and Valles [2007], respectively. However, most of the analyses have been confined to closed economy models and to one-sector frameworks. In the present paper we take up the following question instead: to what extent can an open economy version of the two-sector neoclassical model account for the time-series evidence on fiscal policy transmission mechanism?

Assuming that government spending is predetermined relative to the other variables included in the vector autoregression (VAR) model, as suggested by [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF], [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF] establish a first set of main findings: an exogenous increase in government spending raises output, and lowers both investment and the current account. 1

The second set of main findings relates to the labor market. [START_REF] Perotti | Search of the Transmission Mechanism of Fiscal Policy[END_REF] documents an increase in hours worked and in the real wage. 2 The third empirical fact relates to the impact of fiscal shocks on the sectoral composition of output. Estimates by Bénétrix and Lane [2010] reveal that a boost to government spending benefits disproportionately the non-traded sector. The fourth empirical fact relates to the shift in the relative price of home goods. [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF] and [START_REF] Enders | How do Fiscal and Technology Shocks affect Real Exchange Rates? New Evidence for the United States[END_REF] find that government spending yields a real exchange rate depreciation. 3 To address these empirical evidence, we use an open economy with a traded and a non-traded sector. Our neoclassical framework builds on [START_REF] Turnovsky | Investment in a Two-Sector Dependent Economy[END_REF] and [START_REF] Coto-Martinez | Profits, Markups and Entry: Fiscal Policy in an Open Economy[END_REF]. Like Coto-Martinez and Dixon, we allow for the nontraded sector to be imperfectly competitive. Our work differs from that of [START_REF] Turnovsky | Investment in a Two-Sector Dependent Economy[END_REF] and [START_REF] Coto-Martinez | Profits, Markups and Entry: Fiscal Policy in an Open Economy[END_REF] in one major respect. 4 They consider the 1 Such findings are consistent with the conclusions reached by [START_REF] Corsetti | Twin Deficits: Squaring Theory, Evidence and Common Sense[END_REF], [START_REF] Beetsma | The Effects of Public Spending Shocks on Trade Balances and Budget Deficits in the European Union[END_REF], and [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF].

2 While [START_REF] Perotti | Search of the Transmission Mechanism of Fiscal Policy[END_REF] conclusions are in line with those of [START_REF] Rotemberg | Oligopolistic Pricing and the Effects of Aggregate Demand on Economic Activity[END_REF] and [START_REF] Pappa | The Effects of Fiscal Shocks on Employment and the Real Wage[END_REF] for the U.S., [START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF] finds that hours worked increase but real wages can rise or decline on impact, depending on the period considered. Yet, in both cases, the real wage exceed its initial level after two years. 3 The sample of countries considered by [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF], [START_REF] Perotti | Search of the Transmission Mechanism of Fiscal Policy[END_REF], [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF], comprises four countries: the U.S., the U.K., Canada and Australia. In [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF], the period runs from 1980:1 to 2007:4, in [START_REF] Perotti | Search of the Transmission Mechanism of Fiscal Policy[END_REF] from 1954:1 to 2003:1 for the U.S., and in [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF] from 1980:1 to 2006:4. Bénétrix and Lane [2010] consider a panel of eleven member countries of the euro area over the period . All these papers adopt the identification procedure of fiscal shocks developed by [START_REF] Blanchard | An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output[END_REF]. 4 Turnovsky and Sen [1995] investigate the effects of permanent government spending shocks by assuming fixed labor supply. Coto-Martinez and Dixon [2003] introduce an elastic labor supply but restrict their analysis to the effects of a permanent rise in public spending by assuming that the traded sector is more effects of permanent fiscal shocks while we examine the impact of temporary fiscal shocks of different degrees of persistence. Beyond the fact that considering a transitory increase in public spending allows us to address the VAR evidence, the effects of temporary fiscal shocks can be different to those of a permanent shock. 5

One attractive feature of a two-sector model with tradable and non tradable goods is to cover both the closed economy and the open economy dimensions of contemporary industrialized countries. In particular, the empirical evidence shows that the non-tradable content of GDP and employment is substantial, at around two-thirds. 6 From an analytical point of view, as in a closed economy model, capital accumulation clears the home good market, see e.g., [START_REF] Baxter | Fiscal Policy in General Equilibrium[END_REF]. As in a small open economy, external borrowing allows households to smooth consumption intertemporally. A second key feature of our framework is that we can investigate the sectoral effects of fiscal shocks. Such a sectoral decomposition of output is pivotal to understanding the fiscal transmission mechanism in an open economy. In particular, such a model enables us to connect sectoral output responses to the trade balance adjustment. Third, we are able to address the depreciation in the real exchange rate which has recently been documented in the empirical literature.

Beyond the relevancy of a two-sector model for investigating the fiscal transmission mechanism, such a framework can accommodate most of the empirical evidence mentioned above, albeit under certain conditions. By contrast, the open-economy version of [START_REF] Baxter | Fiscal Policy in General Equilibrium[END_REF] model fails to account for the first set of observations, particularly for the simultaneous decline of investment and the current account in response to an exogenous and temporary increase in government spending, see e.g., [START_REF] Karayalçin | Temporary and Permanent Government Spending in a Small Open Economy[END_REF]. 7 As stressed in the classic paper by [START_REF] Baxter | Fiscal Policy in General Equilibrium[END_REF], a representative household responds to the higher tax burden (which we assume to be lump-sum) by lowering consumption and increasing labor supply. This raises the return on capital and triggers a rise in investment, which, in turn, drives the current account into deficit. Furthermore, as the marginal product of labor falls dramatically, the real wage fails to exceed its initial value during the transition.

One prominent feature of the time series of government spending is that its non tradable content is substantial, at around 90%. 8 We therefore concentrate on the effects of a rise in public purchases of non-traded goods. We find that a two-sector model with traded capital intensive. Additionally, neither [START_REF] Turnovsky | Investment in a Two-Sector Dependent Economy[END_REF] nor [START_REF] Coto-Martinez | Profits, Markups and Entry: Fiscal Policy in an Open Economy[END_REF] solve the model numerically. 5 The reason behind this result is that after a temporary fiscal shock, consumption falls much less than after a permanent fiscal shock due to consumption smoothing behavior. Hence, if the traded sector is more capital intensive, an excess demand (rather than excess supply) arises in the non-traded good market so that investment is crowded out rather than being crowded in as long as the shock is transitory. 6 Non tradable proportions are given in Table 3 (see Appendix A).

7 Karaylalçin [1999] analyzes the effects of permanent and temporary fiscal shocks by using an open economy version of the [START_REF] Baxter | Fiscal Policy in General Equilibrium[END_REF] model. Regardless of its persistence, a fiscal expansion triggers an investment boom and a current account deficit. 8 The non-tradable content of government spending is reported in Table 3 for thirteen OECD countries.

and non-traded goods can accommodate the two first sets of empirical findings, with the exception of the rising real wage, as long as the traded sector is more capital intensive than the non-traded sector. The explanation is intuitive. Following a fiscal expansion, agents cut real expenditure and raise labor supply. In contrast to a small open economy model, investment clears the home goods (or non-traded goods) market. Assuming that the traded sector is more capital intensive, an excess demand arises in the non-traded goods market which triggers a drop in investment. In addition, according to Rybczynski's theorem, higher labor supply produces a fall in traded output which in turn lowers net exports and thereby drives the current account into deficit. Assuming that the non-traded sector is more capital intensive, the real exchange rate appreciates which shifts resources towards the non-traded sector so that investment is crowded in while the current account enters in deficit as a result of the fall in traded output.

We also estimate numerically the sectoral effects of fiscal shocks to address the third empirical fact outlined above. Regardless of sectoral capital intensities, a temporary fiscal shock benefits the non-traded sector substantially in the short-run, in line with the empirical evidence reported by Bénétrix and Lane [2010]. Furthermore, our numerical results show that, in the long run, GDP growth is mostly driven by expansion in the traded output.

The steady-state rise in traded output is necessary to compensate for the short-run current account deficits.

Keeping the markup fixed, the predictions of the two-sector model run counter to two of the stylized facts outlined above: the real wage does not rise and the real exchange rate does not depreciate, irrespective of whether the traded sector is more or less capital intensive than the non-traded sector. To address the real exchange rate depreciation and the increase in the real wage following government spending shocks, we follow Jaimovich and Floetotto [2008] in allowing for the markup to be endogenous. Considering that only a limited number of intermediate good producers operate in the non-traded sector, the priceelasticity of demand and thereby the markup faced by each firm depends on the number of competitors. 9 As the rise in government spending is expected to boost non-traded output, a fiscal shock triggers the entry of new firms. Hence, the markup falls, regardless of sectoral capital intensities. If the traded sector is more capital intensive, the real exchange rate must depreciate so that the return on domestic capital equalizes the return on foreign bonds. By exerting a positive influence on the wage rate and triggering a depreciation in the real exchange rate, the decline in the markup can boost the real wage, although only under certain circumstances. More precisely, the cumulative response of the real wage rate two years after the fiscal shock becomes positive only if the fiscal shock is either short-lived or long-lived. 10 If the non-traded sector is more capital intensive, the real exchange must appreciate to equalize the return on domestic and foreign assets. As a consequence, the real wage falls dramatically and remains below its original level over the transition towards the steady-state.

Closely related to our paper is the study by [START_REF] Ramey | Costly Capital Reallocation and the Effects of Government Spending[END_REF] who simulate a two-sector neoclassical model with costly capital reallocation. In a similar spirit, we achieve a better understanding of aggregate effects of fiscal shocks by investigating sectoral effects.

In contrast to our study, they consider a closed economy so that they do not address the behavior of the current account or the real exchange rate. In addition, they do not discuss the role of sectoral capital intensities. Finally, whereas Ramey and Shapiro analyze the implications of costly capital mobility, we rather conduct a sensitivity analysis with respect to the duration of the fiscal shock and the elasticity of labor supply, considering a traded sector alternatively more or less capital intensive than the non-traded sector, and contrasting the case of a fixed markup with that of an endogenous markup.

The remainder of this paper is organized as follows. Section 2 outlines the specification of a two-sector model with traded and non-traded goods. Section 3 provides an analytical exploration of the short-run and long-run effects of fiscal shocks. In section 4, we report the results of our numerical simulations and discuss the sectoral effects of a temporary fiscal expansion. Section 5 explores the case of an endogenous markup quantitatively, focusing on the reactions of the real exchange rate and the real wage. In Section 6, we summarize our main results and present our conclusions.

The Framework

We consider a small open economy that is populated by a constant number of identical households and firms that have perfect foresight and live forever. 11 The country is small in terms of both world goods and capital markets, and faces a given world interest rate, r . A perfectly competitive sector produces a traded good denoted by the superscript T that can be exported and consumed domestically. An imperfectly competitive sector produces a nontraded good denoted by the superscript N which is devoted to physical capital accumulation and domestic consumption. 12 The traded good is chosen as the numeraire. 13 scenario, the fiscal shock lasts 16 quarters, in line with estimates by [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF] for the U.S. [START_REF] Ramey | Identifying Government Spending Shocks: It's All in the Timing[END_REF] also find that a fiscal shock lasts 4 years. 11 More details on the model as well as the derivations of the results which are stated below are provided in an Appendix which is available from the authors on request.

12 As stressed by [START_REF] Turnovsky | Investment in a Two-Sector Dependent Economy[END_REF], allowing for traded capital investment would not affect the results (qualitatively). Furthermore, like [START_REF] Burstein | Investment Prices and Exchange Rates: Some Basic Facts[END_REF], we find that the non tradable content of investment accounts for the lion's share of total investment expenditure (averaging to 60%). 13 The price of the traded good is determined on the world market and exogenously given for the small open economy.

Households

At each instant the representative agent consumes traded goods and non-traded goods denoted by C T and C N , respectively, which are aggregated by a constant elasticity of substitution function:

C C T , C N = ϕ 1 φ C T φ-1 φ + (1 -ϕ) 1 φ C N φ-1 φ φ φ-1 , ( 1
)
where ϕ is the weight attached to the traded good in the overall consumption bundle (0 < ϕ < 1) and φ is the intratemporal elasticity of substitution (φ > 0).

The agent is endowed with a unit of time and supplies a fraction L(t) of this unit as labor, while the remainder, l ≡ 1 -L, is consumed as leisure. At any instant of time, households derive utility from their consumption and experience disutility from working.

Households decide on consumption and worked hours by maximizing lifetime utility:

U = ∞ 0 1 1 -1 σ C C(t) 1-1 σ C -γ 1 1 + 1 σ L L(t) 1+ 1 σ L e -βt dt, ( 2
)
where β is the consumer's discount rate, σ C > 0 is the intertemporal elasticity of substitution for consumption, and σ L > 0 is the Frisch elasticity of labor supply.

Factor income is derived by supplying labor L at a wage rate W , and capital K at a rental rate r K . In addition, households accumulate internationally traded bonds, B(t), that yield net interest rate earnings of r B(t). Denoting lump-sum taxes by Z, the households' flow budget constraint can be written as:

Ḃ(t) = r B(t) + r K (t)K(t) + W (t)L(t) -Z -P C (P (t)) C(t) -P (t)I(t), (3)
where P C is the consumption price index which is a function of the relative price of nontraded goods P . The last two terms represent households' expenditure which includes purchases of consumption goods and investment expenditure P I. Aggregate investment gives rise to overall capital accumulation according to the dynamic equation

K(t) = I(t) -δ K K(t), ( 4
)
where we assume that physical capital depreciates at rate δ K . In the rest of this paper, the time-argument is suppressed to increase clarity.

Denoting the co-state variable associated with eq. ( 3) by λ the first-order conditions characterizing the representative household's optimal plans are:

C = (P C λ) σ C , (5a) L = λ γ L W σ L , ( 5b
) λ = λ (β -r ) , (5c) r K P -δ K + Ṗ P = r , ( 5d

Firms

Both the traded and non-traded sectors use physical capital, K T and K N , and labor, L T and L N , according to constant returns to scale production functions,

Y T = F K T , L T
and Y N = H K N , L N , which are assumed to have the usual neoclassical properties of positive and diminishing marginal products. Both sectors face two cost components: a capital rental cost equal to r K , and a labor cost equal to the wage rate W . The traded sector is assumed to be perfectly competitive. As described in more details below, the non-traded sector contains a large number of industries and each industry is comprised of differentiated monopolistically competitive intermediate firms. 14 The final non-traded output, Y N , is produced in a competitive retail sector with a constant-returns-to-scale production which aggregates a continuum measure one of sectoral non-traded goods. 15 We denote the elasticity of substitution between any two different sectoral goods by ω > 0. In each sector, there are N > 1 firms producing differentiated goods that are aggregated into a sectoral non-traded good. The elasticity of substitution between any two varieties within a sector is denoted by > 0, and we assume that this is higher than the elasticity of substitution across sectors, i.e. > ω (see e.g., Jaimovich and Floetotto [2008]). Within each sector, there is monopolistic competition; each firm that produces one variety is a price setter. Output X i,j of firm i in sector j is produced using capital and labor, i.e. X i,j = H (K i,j , L i,j ). Each firm chooses capital and labor by equaliz-14 This assumption relies upon observed empirical facts. The markups in the traded sector we estimated for a sample of 13 OECD economies average to 1.2 with small dispersion across countries whereas for the non-traded sector, the markups average to 1.4 with large dispersion across countries. Additionally, assuming that the traded sector is imperfectly competitive would not affect qualitatively the results, as long as the markup is fixed. Estimates of the markups charged by the traded sector are available on request while estimates for the non-traded sector are reported in Table 3.

ing markup-adjusted marginal products to the marginal cost of inputs, i. e. H K /µ = r K , and H L /µ = W , where µ is the markup over the marginal costs. At a symmetric equilibrium, non-traded output is equal to Y N = N X = H K N , L N . We assume that there are a large number of firms within each sector, so that each single intermediate producer is small relative to the economy. In this set up each producer in a sector faces the same price elasticity of demand, . Hence, the producer of a variety charges a constant markup

µ = e e-1
, where e is the price-elasticity of demand. Because the number of competitors is large, e is equal to . In section 5, we relax this assumption and assume instead that a finite number of firms operate within each sector producing non-tradable varieties. 16 Whether the markup is fixed or endogenous, we assume instantaneous entry, which implies that the zero profit condition holds at each instant of time.

Denoting by k i ≡ K i /L i the capital-labor ratio for sector i = T, N , enables us to express the production functions in intensive form, i.e. f k T ≡ F K T , L T /L T and h k N ≡ H K N , L N /L N . Production functions are supposed to take a Cobb-Douglas form: f k T = k T θ T , and h k N = k N θ N , where θ T and θ N represent the capital income share in output in the traded and non-traded sectors respectively. Since inputs can move freely between the two sectors, marginal products in the traded and the non-traded sector equalize:

θ T k T θ T -1 = P µ θ N k N θ N -1 ≡ r K , (6a) 1 -θ T k T θ T = P µ 1 -θ N k N θ N ≡ W. ( 6b
)
These static efficiency conditions state that the sectoral marginal products must equal the labor cost W and capital rental rate r K .

Government

The final agent in the economy is the government which finances government expenditure by raising lump-sum taxes Z in accordance with the balanced condition: 17

G T + P G N = Z. ( 7
)
Public spending consists of purchases of traded goods, G T , and non-traded goods, G N . As the data suggests that government expenditure tends to be mainly on non-traded goods, we concentrate on the effects of an increase in G N . 18

16 As stressed by [START_REF] Yang | Monopolistic Competifion and Optimum Product Diversity: Comment[END_REF], departing from the usual assumption made by [START_REF] Dixit | Monopolistic Competition and Optimum Product Diversity[END_REF] implies that the price elasticity of demand becomes an increasing function of the number of firms and that the markup is endogenous. 17 Government spending on traded goods G T is considered for calibration purpose. The effects of a permanent and temporary fiscal expansion on G T are explored in the Appendix, available on request. 18 The data summarized in Table 3 reveal that the non-tradable content of government spending averages about 90%.

Short-Run Static Solutions

System (6a)-(6b) can be solved for sector capital intensity ratios: k T = k T (P ) and k N = k N (P ). Using the fact that W ≡ θ T k T θ T -1 , the wage rate also depends on P , i.e.

W = W (P ), with W P ≷ 0. An increase in the relative price P raises or lowers W depending on whether the traded sector is more or less capital intensive than the non-traded sector.

Plugging sectoral capital-labor ratios into the resource constraints and production functions leads to short-term static solutions for sectoral output: Y T = Y T (K, L, P ) and

Y N = Y N (K, L, P ).
According to the Rybczynski effect, a rise in K raises the output of the sector which is more capital intensive, while a rise in L raises the output of the sector which is more labor intensive. An increase in the relative price of non tradables exerts opposite effects on sectoral outputs by shifting resources away from the traded sector towards the non-traded output.

By substituting first W = W (P ), eqs. ( 5a)-(5b) can be solved for consumption and labor supply as follows: C = C λ, P with Cλ < 0, C P < 0, and L = L λ, P with Lλ > 0 and L P ≷ 0. A rise in the shadow value of wealth induces agents to cut their real expenditure and to supply more labor. By raising the consumption price index, an appreciation in the relative price of non tradables drives down consumption. Finally, depending on whether k T ≷ k N , a rise in P stimulates or depresses labor supply by raising or lowering W .

Macroeconomic Dynamics

The adjustment of the open economy towards the steady-state is described by a dynamic system which comprises two equations. First, the dynamic equation for the relative price of non-traded goods (5d) equalizes the return on domestic capital and traded bonds r .

Second, the accumulation equation for physical capital clears the non-traded goods market along the transitional path. This can be written as:

K = Y N (K, L, P ) µ -C N λ, P -G N -δ K K. ( 8
)
Dynamic equations (5d) and ( 8) form a separate subsystem in P and K. Inserting short-run static solutions, linearizing these two equations around the steady-state, and denoting the long-term values with a tilde, we obtain in a matrix form:

  K Ṗ   =   Y N K µ -δ K Y N P µ -C N P 0 Y T K P     K(t) - K P (t) - P   (9)
The determinant of the linearized 2 × 2 matrix is unambiguously negative and the trace is equal to r . 19 Hence, the equilibrium yields a unique one-dimensional stable saddle-path, irrespective of the relative sizes of the sectoral capital-labor ratios. Denoting the negative 19 See the Appendix for further details.

eigenvalue by ν 1 and the positive eigenvalue by ν 2 , the general solutions for K and P are

K(t) -K = B 1 e ν 1 t + B 2 e ν 2 t , P (t) -P = ω 1 2 B 1 e ν 1 t + ω 2 2 B 2 e ν 2 t , ( 10
)
where B 1 and B 2 are constants to be determined and ω i 2 is the eigenvector associated with the eigenvalue ν i (with i = 1, 2). Two features of the two-sector economy's equilibrium dynamics deserve special attention. First, as long as the markup is fixed, if k T > k N , the temporal path for the relative price remains flat for the no-arbitrage condition (5d) to be fulfilled. Hence, in this case, ω 1 2 = 0. If capital intensities are reversed, then ω 1 2 < 0. As a consequence, the relative price exhibits transitional dynamics; P and K move in opposite directions. Second, after a permanent fiscal shock, to ultimately approach the steady-state ( K, P ) and to satisfy the transversality condition lim t→∞ P (t)K(t)e -r t = 0, it is necessary to set the arbitrary constant B 2 equal to zero. When the expansionary policy is only transitorily implemented (i.e. the fiscal shock only lasts for T periods), two periods have to be considered, namely a first period (labelled period 1) over which the temporary policy is in effect, and a second period (labelled period 2) after the policy has been removed. While the small country converges towards its new long run equilibrium over period 2, i. e. B 2 must be set to zero, the economy follows unstable paths over period 1. These are described by eqs. (10).

Substituting eqs. ( 8) and ( 7) into eq. ( 3), we obtain the dynamic equation for the current account (denoted by CA ≡ Ḃ):

Ḃ = r B + Y T (K, L, P ) -C T λ, P -G T , ( 11
)
where Y T -C T -G T correspond to net exports. Eq. ( 11) states that the current account is equal to the balance of trade denoted by N X plus interest receipts on outstanding assets.

Linearizing [START_REF]The French "Earned Income Supplement" (RSA) and back-to-work incentives Denis Anne, Yannick L'Horty 11-2[END_REF] around the steady-state and substituting (10), the general solution for the stock of foreign assets is given by: 20

B(t) = B + B 0 -B -Φ 1 B 1 -Φ 2 B 2 e r t + Φ 1 B 1 e ν 1 t + Φ 2 B 2 e ν 2 t . ( 12
)
When the disturbance is temporary, we must take into account that assets (i.e. domestic capital and foreign bonds) have been accumulated (or decumulated) over the period 1.

The time path for net foreign assets is described by eq. ( 12) during this unstable period.

As stocks of assets are modified over period 1 (i.e. (0, T )), we have to take new initial conditions (i.e. B T and K T ) into account when the fiscal policy is removed.

21 20 If k T > k N , then Φ 1 = -P < 0 and Φ 2 = P ν 1 1 + ω 2 2 P ν 1 σ C CN -σ L Lk T (ν 1 + δ k ) . If k N > k T , then Φ 1 = P ν 2 1 + ω 1 2 P ν 2 σ C CN -σ L Lk T (ν 2 + δ K )
and Φ 2 = -P . 21 Following a permanent budget policy, the economy moves along a stable path; hence, the trajectory for B(t) is obtained by invoking the transversality condition limt→∞ λB(t)e -r t = 0 which implies that B2 = 0.

Steady-State

We will now discuss the salient features of the steady-state. Setting Ṗ = 0 into eq. ( 5d), we obtain the equality between the rate of return on domestic capital income and the exogenous world interest rate, i.e.

h k k N P µ -δ K = r . ( 13
)
This equality determines the steady-state value of the relative price of non-tradables, i.e.

P . Hence, the long-run level of P remains unaffected by a rise in government spending, as long as the markup is fixed.

Setting K = 0 into eq. ( 8) yields the market-clearing condition for the non-traded good:

Y N K, L, P , µ = C N λ, P + Ĩ + G N , ( 14
)
where Ĩ = δ K K.

Setting Ḃ = 0 into eq. ( 11) leads to the market-clearing condition for the traded good:

Y T K, L, P = -r B + C T λ, P + G T . ( 15
)
For the country to remain ultimately solvent, we have to impose one single and overall intertemporal budget constraint: 22

B 0 -B = Φ 1 K 0 -K . ( 16
)
where Φ 1 < 0 describes the effect of capital accumulation on the the external asset position and K 0 and B 0 are the initial conditions. 23 The four equations ( 13)-( 16) jointly determine P , K, B and λ.

Temporary Fiscal Expansion: An Analytical Exploration

In this section, we explore analytically the macroeconomic effects of a temporary fiscal expansion, emphasizing how traded and non-traded goods modify the propagation mechanism. 24 Suppose that at time t = 0, the government raises public spending on the nontraded good and at time T it removes the expansionary budget policy. 25 The higher T ,

22 Substituting first the short-run solutions, then linearizing the dynamic equation of the internationally traded bonds [START_REF]The French "Earned Income Supplement" (RSA) and back-to-work incentives Denis Anne, Yannick L'Horty 11-2[END_REF] in the neighborhood of the steady-state, substituting the solutions for K(t) and P (t) and finally invoking the transversality condition, we obtain the linearized version of the nation's intertemporal budget constraint (16).

23 Since for all parameterizations, Φ 1 is always negative, we assume Φ 1 < 0 from now thereon. Hence, capital accumulation deteriorates the current account along the transitional path. 24 As the shocks identified in the VAR literature are transitory, we focus the theoretical analysis on temporary increases in government spending. 25 We assume further that all agents perfectly understand at the outset the temporary nature of the policy change. Hence, at time T , there is no new information and thereby no jump in the marginal utility of wealth at this date.

the stronger the persistence of the shock. For ease of computation, we first consider the labor supply to be inelastically supplied; only in this case are we able to derive analytical expressions for the impact effects of a temporary fiscal expansion, regardless of sectoral capital intensities.26 At the end of this section, we discuss the implications of elastic labor supply, when analytical expressions can be derived only if k T > k N .27

The Case of Inelastic labor Supply

We investigate both the impact and long-run effects of a temporary rise in G N by assuming that the labor supply is fixed. In particular, we provide analytical expressions of impact effects on key economic variables, namely investment and the current account.

Impact Effects

Let fist consider the situation when the traded sector is more capital intensive than the non-traded sector. Since taxes must be raised to balance the budget, the subsequent fall in the real disposable income induces agents to lower their consumption. Because the reduction in real expenditure is spread over the two goods, the fall in consumption of the non-traded good is not large enough to compensate for the rise in public spending G N .

Hence, an excess demand arises in the non-traded good market which produces a drop in investment (see eq. ( 8)). Formally, the initial reaction of investment is given by

dI(0) dG N = α C 1 -e -r T -1 < 0, ( 17
)
where α C is the non tradable content of consumption. The first term on the RHS of (17) reflects the positive effect of the drop in C N on capital accumulation. As shown by the second term on the RHS, the rise in G N withdraws resources from investment. Since

α C 1 -e -r
T is smaller than one, a rise in G N unambiguously crowds-out investment on impact. If public spending is raised over a short period (i.e. if T is small), agents reduce their real expenditure by a small amount because the tax burden is low. Consequently, the excess of demand in the non-traded good market increases, which drives down further investment.

The adjustment of the current account is described by the market-clearing condition for the traded good, i.e. eq [START_REF]The French "Earned Income Supplement" (RSA) and back-to-work incentives Denis Anne, Yannick L'Horty 11-2[END_REF]. Since consumption in the traded good falls, net exports increase which yields a current account surplus as the stock of traded bonds is initially predetermined. After tedious computations, it can be shown that the initial reaction of the current account is given by:

dCA(0) dG N = P (1 -α C ) 1 -e -r T > 0. ( 18
)
where 1 -α C is the tradable content of consumption. The current account surplus increases with the length of the shock T as consumption in the traded good C T falls by a larger amount.

If the traded sector is more capital intensive than the non-traded sector, sectoral outputs remain unaffected as the relative price P is unchanged and the capital stock is predetermined.

The responses of investment and the current account change dramatically when the capital intensities are reversed. The reason is that now, the relative price of non tradables appreciates on impact as a result of the excess of demand in the non-traded good market.

The increase in P influences sectoral outputs by shifting resources from the traded sector towards the non-traded sector. Since Y N now expands, the response of investment becomes ambiguous as resources are devoted to capital accumulation. More formally, the reaction of investment is given by:

dI(0) dG N = ν 2 -ν 1 ν 2 1 -e -ν 2 T + σ C CN λ ν 1 ν 2 d λ dG N -1, (19)
where d λ

dG N = α C λ σ C CN 1 - Ψ 1 -α C Ψ   1 -e -ν 2 T - e -r T -e -ν 2 T 1 -Ψ   > 0, with 0 < Ψ ≡ -r ν 2 2 CN P σ C ω 1 2 < 1.
The first term on the RHS of eq. ( 19) reflects the positive influence on investment of the initial appreciation in the relative price of non tradables. This term is positive and increasing with T . As shown by the second term on the RHS, the wealth effect reflected by a rise in the marginal utility of wealth λ, now exerts a negative impact on capital accumulation. The reason is that the drop in real disposable income induces agents to reduce C N which in turn moderates the excess of demand in the nontraded good market and thereby the appreciation in P . The last term on the RHS of eq. ( 19) reflects the rise in G N that withdraws resources from physical capital accumulation.

Hence, investment may now respond positively to a fiscal shock as a result of the initial rise in P .

Whereas the relative price appreciation of non-traded goods exerts a positive impact on investment by raising non-traded output, it drives down net exports by depressing traded output on impact, due to the shift of resources towards the non-traded sector. Regardless of the length of the fiscal shock, we find that the current account unambiguously deteriorates after an increase in G N :

dCA(0) dG N = -P e -r T -e -ν 2 T -ν 1 Φ 1 (1 -α C ) ν 2 1 -α C Ψ 1 -e -ν 2 T + α C 1 -α C e -r T -e -ν 2 T < 0. ( 20
)
where

Φ 1 = -P 1 + 1 ν 2 CN P σ C ω 1 2 < 0.
When k N > k T , the initial rise in the relative price of non tradables causes a shifting of labor away from the traded to the non-traded sector. Hence, Y N rises in the short-run while Y T falls on impact.

Long-Run Effects

A temporary increase in government spending has permanent or long-run effects, because the model features the zero-root property. 28 Since government spending reverts back to its initial level at time T , in the long-run (i.e. in the steady-state) changes are only driven by the change in the equilibrium value of the marginal utility of wealth. Confronted with a fall in their disposable income, agents are induced to permanently lower their real consumption. As consumption in the non-traded sector is reduced, non-traded output is decreased as well in the long-run, regardless of sectoral capital intensities. Hence, labor shifts from the non-traded to the traded sector, and traded output expands in the long-run.

The reason is that the small open economy decumulates traded bonds as a result of the investment boom once the fiscal shock ends. To service the debt accumulated over the transition, the economy must run a trade balance surplus in the long-run, which is achieved through a drop in C T and a rise in Y T .

As labor is fixed, the long-run adjustment of GDP is driven by capital accumulation which depends on sectoral capital intensities. Since Y N declines in the long-run to meet lower demand, capital falls or rises depending on whether the non-traded sector is more or less capital intensive, and so GDP decreases or increases. 29

The Case of Elastic Labor Supply

We now clarify the role of labor supply in the transmission of fiscal policy.

Impact Effects

Let us first assume that the traded sector is more capital intensive than the non-traded sector. Following the drop in their disposable income, agents always cut their real expenditure but also supply more labor. According to Rybczynski's theorem, a rise in labor supply raises the output of the sector which is more labor intensive.

The labor supply channel now makes the responses of investment and the current account ambiguous by affecting sectoral outputs. More precisely, the rise in non-traded output implies that higher public spending G N may crowd in or crowd out capital investment.

Formally, the initial reaction of investment should now be rewritten as:

dI(0) dG N = -   1 + 1 -e -r T σ L Lk T P ν 1 -σ C P CN σ C P C C + σ L W L   ≶ 0. ( 21
)
Setting σ L = 0 in eq. ( 21) yields eq. ( 17). As long as σ L > 0, the sign of eq. ( 21) 28 Technically, this follows from the assumption that β = r , which requires the joint determination of the transition and the steady-state.

29 Formal expressions are derived by setting σL = 0 into (23).

is no longer clear-cut. The more responsive the labor supply, the larger the increase in employment on impact, and thereby the less likely it is that investment is crowded out by public spending.

Turning to the initial response of the current account, we obtain after computation:

dCA(0) dG N = P 1 -e -r T   1 + σ L Lk T P ν 1 -σ C P CN σ C P C C + σ L W L   ≷ 0. ( 22
)
By depressing traded output, the increase in labor now makes a deterioration in the current account possible. The higher the elasticity of labor supply σ L , the more likely an initial drop in the current account.

When k N > k T , the initial change in labor supply is the result of two opposite forces:

the wealth effect which induces agents to supply more labor and the appreciation in the relative price of non tradable goods that counteracts this effect by driving down the wage rate. Hence, employment may increase or decrease on impact. As will become clear in Section 4, the elasticity σ L plays a crucial role in driving the initial reaction of labor supply, and thereby the change in GDP on impact. For clarity, let us assume that agents supply more labor. Higher employment exerts a negative impact on non-traded output and a positive influence on traded output. 30 Hence, the increase in L makes a drop in investment more likely as resources are shifted towards the traded sector. However, the relative price of non-tradables exerts a positive impact on investment. Finally, the initial current account reaction is no longer clear cut as net exports may fall or increase on impact.

More precisely, while a higher labor supply boosts traded output, the appreciation of the real exchange rate exerts a negative impact on Y T . To sum up, if the relative price channel predominates, investment is crowded in while the current account falls into deficit.

Long-Run Effects

The conclusions established in the case of an inelastic labor supply hold in the long run, with the exception of the steady-state changes in physical capital and GDP. Regardless of sectoral capital intensities, it is found that the open economy accumulates physical capital as long as the labor supply is elastic enough. Using the fact that the steady-state capital stock can be expressed as a function of the marginal utility of wealth and government spending G N , and remembering than in the long-run, G N remains unchanged, the long-run adjustment of physical capital is given by: 31

d K dG N = Kλ d λ dG N = - 1 λν 1 σ C CN -σ L Lk T ν 1 d λ dG N > 0, k T > k N , (23a) d K dG N = Kλ d λ dG N = - 1 λν 2 σ C CN -σ L Lk T ν 2 d λ dG N ≷ 0, k N > k T , ( 23b
)
30 We were unable to obtain analytical results for k N > k T . Yet, as shown numerically, the analytical results for an inelastic labor supply hold.

31 Solving ( 13)-( 15) for P , K and B yields:

P = constant, K = K λ, G N and B = B λ, G N .

Temporary Fiscal Expansion: A Quantitative Exploration

In this section, we analyze the effects of a temporary rise in government spending quantitatively. For this purpose we solve the model numerically. We therefore discuss parameter values first, before turning to the long-and short-term effects of the fiscal shock

Baseline Parametrization

We start by describing the calibration of consumption-side parameters that we use as a baseline. The world interest rate which is equal to the subjective time discount rate β is set to 1%. One period of time corresponds to a quarter. The elasticity of substitution between traded and non-traded goods φ is set to 1.5 (see e.g. Cashin and Mc Dermott [2003]). An additional critical parameter is ϕ which is set to 0.5 in the baseline calibration to target a non tradable content in total consumption expenditure (i.e., α C ) of 45%, in line with our empirical evidence. 32 The intertemporal elasticity of substitution for consumption σ C is set to 0.5 because empirical evidence overwhelmingly suggest values smaller than one. 33 One critical parameter is the intertemporal elasticity of substitution for labor supply σ L . In our baseline parametrization, we set σ L = 0.5, in line with evidence reported by [START_REF] Domeij | The Labor-Supply Elasticity and Borrowing Constraints: Why Estimates are Biased[END_REF].

We now describe the calibration of production-side parameters. We assume that physical capital depreciates at a rate δ K = 1.5% to target an investment-GDP ratio of 20%. The shares of sectoral capital income in output take two different values depending on whether the traded sector is more or less capital intensive than the non-traded sector. In line with our estimates, if k T > k N , θ T and θ N are set to 0.4 and 0.3, respectively. 34 Alternatively, 32 Table 3 shows the non tradable content of GDP components for thirteen OECD countries. 33 Consumption expenditure is 55% of GDP for our baseline calibration.

34 Table 3 gives the values of θ j (j = T, N ) for thirteen OECD countries. The values of θ T and θ N we have chosen correspond roughly to the averages for countries with k T > k N . For these values, the non tradable content of GDP and labor are 63% and 66%, respectively. When k N > k T , we can use reverse but symmetric values for θ N so that the size of k T -k N remains unchanged. For θ T = 0.3 and θ N = 0.4, the when k N > k T , we choose θ T = 0.3 and θ N = 0.4. Setting the elasticity of substitution between sectoral goods ω to 1 and the elasticity of substitution between varieties, to 4 yields a markup charged by the non-traded sector of 1.35, which is close to our estimates (see Table 3).

We set G N and G T so as to yield a non-tradable share of government spending of 90%, and government spending as a share of GDP of 20%. 35 We consider three different scenarios for the duration of the fiscal shock: a short-lived (T = 8), a medium-lived (T = 16), and a long-lived (T = 32) fiscal shock. As the baseline scenario, we take the medium-lived fiscal shock, i.e. a shock that lasts 16 quarters. In this case, the cumulative increase in government spending corresponds approximately to the cumulative increase in US government spending six years after an exogenous spending shock by one percentage point of GDP according to the estimates reported by [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF]. For T = 16, we also conduct a sensitivity analysis with respect to the elasticity of labor supply (i.e. we set σ L to 0.1 and 1).

Long-Run Effects

Panel A of Table 1 gives the numerical results for the long-run effects of a temporary fiscal expansion. In the baseline scenario, agents cut real expenditure by 0.07% of GDP while non tradable content of GDP and labor are 69% and 65%, respectively.

35 Close to the average of the values reported in Table 3, the ratios G T /Y T and G N /Y N are 6% and 28% in the baseline calibration.

Short-Run Effects

We now turn to the short-run effects of the fiscal expansion. We take the medium-lived spending shock as our baseline scenario, but we also refer to short-lived and long-lived fiscal shocks, as the length of fiscal stimulus may vary across countries. Panels B and C of Table 1 show the results for this situation, as well as for a number of alternative scenarios. While Before analyzing in the detail the role of sectoral reallocation in shaping the short-run dynamics in response to a temporary increase in government spending, we should mention the set of empirical evidence established by [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF]. It is found that in all the countries in their sample, an exogenous increase in government spending raises output, and induces a simultaneous decline of investment and the current account. In the following, we discuss the predictions of our model for the behavior of these variables when k T > k N and when k N > k T .

While employment and thereby GDP increase in all the scenarios where k T > k N , labor supply and output increase slightly or decrease when the capital intensities are reversed.

The reason is that when k T > k N , agents are induced to supply more labor as a result of the wealth effect. By contrast, when k N > k T , the appreciation of the real exchange rate drives down the wage rate which in turn counteracts the wealth effect. Interestingly, we find that employment and thereby GDP falls on impact if σ L is raised from 0.5 to 1. The reason is that for a given change in the shadow value of wealth, the relative price must appreciate more as a result of the larger labor outflow. Hence, the consecutive decrease in W is large enough to induce agents to supply less labor, which reduces GDP by 0.05% on impact.

In the model, the initial reaction of investment is ambiguous as long as labor supply is elastic. Numerically, we find that its short-run response depends heavily on sectoral capital intensities. On impact, an increase in G N crowds out investment only if the traded sector is more capital intensive. While non-traded output expands as a result of the increase in labor supply, the rise in public spending G N produces an excess of demand which must be eliminated by a drop in investment. As shown in the seventh line of panel B of Table 1, the less elastic labor supply is, the larger the crowding-out effect of investment. By contrast, if the non-traded sector is more capital intensive, the increase in G N triggers an appreciation in the relative price of non tradables P which stimulates Y N and thereby investment, in all scenarios. The cumulative responses reported in the third line of panel C of Table 1 show that a fiscal expansion crowds in investment by about 3.22% of initial GDP on impact if

k N > k T ,

Transitional Adjustment

We now discuss the dynamic effects which are depicted in Figures 1, starting with the adjustment of labor which is displayed in the third line. The dashed-dotted line shows the results for a weakly responsive labor supply (i.e. σ L = 0.1), while the dotted line shows the results for a highly elastic labor supply (i.e. σ L = 1). If the traded sector is more capital intensive, the temporal path for L is flat as the relative price P remains unaffected. When k N > k T , the dynamics for L no longer degenerate as a result of the depreciation in the real exchange rate (after its initial appreciation) along the transitional path. The consequent increase in the wage rate W induces agents to supply more labor during the transitional period.

The transitional path of investment is also quite distinct, depending on whether the traded sector is more or less capital intensive than the non-traded sector. Along the transitional path, capital accumulation clears the non-traded good market. When k T > k N , the size of the crowding-out of investment reduces over time, but when k T > k N , investment decreases monotonically as the depreciation in the relative price P lowers non-traded output.

After about 2 years, the investment flow becomes negative and the open economy decumulates physical capital until the fiscal policy is removed. At time T , government spending G N 36 As shown in the fifth line of panel C in Table 1, the cumulative response of GDP at a two-year horizon is negative in two scenarios when k T > k N : when σL is low and when the fiscal shock is short-lived. In these two scenarios, the response of labor supply is limited, Y N rises less, and the excess demand in the non-traded good market becomes larger, which in turn produces a larger decline in investment.

reverts back to its initial level which releases resources for capital accumulation. Regardless of sectoral capital intensities, investment is crowded in.

The temporal path for GDP is driven by the adjustments in both labor and capital. In the case k T > k N , the dynamics for GDP are the mirror image of capital accumulation: the slowdown in GDP growth as government spending is raised originates from the crowding out of investment. By contrast, when k N > k T , the temporal path of output is humpshaped: GDP growth first increases as labor supply rises, and then slows down as a result of the decline in investment which starts after about two years. At the time the fiscal policy is removed, the economy experiences an investment boom which boosts GDP in both cases. While in a one-sector model, the response of output increases with labor supply responsiveness (as stressed by [START_REF] Baxter | Fiscal Policy in General Equilibrium[END_REF]), this is not the case when we consider a two-sector model. Considering that k T > k N and raising σ L from 0.5 to 1 increases the cumulative GDP response from 0.32 to 0.55. By contrast, when k N > k T , the reaction of GDP decreases from 0.69 to 0.58, as a result of the drop in the wage rate which depresses labor supply.

Regardless of sectoral capital intensities, the current account stays in deficit while government spending is raised. In the case k T > k N , the decumulation of physical capital drives down traded output, which in turn amplifies the current account deficit along the transitional path. If the sectoral capital intensities are reversed, the depreciation in the relative price of non tradables moderates the decrease in Y T and thereby the worsening in the foreign asset position. Yet, in the latter case, the current account deficit at an horizon of two years is almost three times larger, as shown in the fourth line of panel C of Table 1.

Sectoral Decomposition of the Effects of Fiscal Shocks

The sectoral decomposition of the effects of fiscal shocks sheds light on the propagation mechanism in an open economy. The impact and cumulative responses of sectoral outputs are summarized in the last two lines of panels B and C of Table 1, respectively. Interestingly, the sectoral outputs change in opposite directions, both on impact and along the transitional path. In the benchmark scenario, assuming that k T > k N , agents raises the labor supply by 0.12% which induces a shift of employment towards the more labor intensive sector. As a result, non-traded output increases by 0.32% of GDP while traded output declines by 0.24% of GDP. If sectoral capital intensities are reversed, the appreciation in the relative price of non-tradables is large enough to more than offset the Rybczynski effect which boosts nontraded output by 1% of initial GDP while the traded sector experiences a decline by the same amount. Hence, GDP remains unchanged on impact in the case k N > k T . Interestingly, raising σ L amplifies the dispersion of sectoral output responses as agents supply less labor.

The fifth line of Figure 1

Taking the Model to the Data

Since time-series evidence on the effects of fiscal shocks, in particular on key variables like investment, current account, and GDP, is now available, we decided to compare our model's predictions withe the empirical results.

Three notable papers have estimated the effects of fiscal shocks on the trade balance:

Beetsma, Giuludori and Klassen [2008], [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF], [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF]. While the first paper includes only GDP and trade variables in its VAR model, the other two also include components of GDP such as investment. All these papers use the Blanchard-Perotti identification scheme that assumes that government spending is predetermined within the quarter relative to the other variables included in the VAR model. Yet, they differ in their sample of countries: [START_REF] Beetsma | The Effects of Public Spending Shocks on Trade Balances and Budget Deficits in the European Union[END_REF] consider fourteen European Union countries and use a panel vector auto-regression approach; [START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF] and [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF] estimate the effects of fiscal shocks for four countries:

Canada, Australia, the UK and the US. All three papers find that an exogenous increase in government spending raises output and lowers the current account. Additionally, Cardi and Müller and Monacelli and Perotti report a substantial decline in investment following a fiscal expansion. The ability of our model to predict such empirical facts is mixed, as it relies upon sectoral capital intensities.

A rise in government spending crowds out investment only if the traded sector is more capital intensive than the non-traded sector. The reason is that when k N > k T , the relative price of non-tradables appreciates on impact, which produces a reallocation of resources towards the non-traded sector so that investment is crowded in on impact, irrespective of the shock's duration or the elasticity of labor supply. It is worthwhile noting that a one-sector small open economy model (see e.g., [START_REF] Karayalçin | Temporary and Permanent Government Spending in a Small Open Economy[END_REF]) cannot produce a drop in investment after a fiscal shock because the increased labor supply raises the marginal product of capital which leads to more investment.

We find that the current account deteriorates in all our model scenarios, in line with empirical evidence. In the model, the short-run worsening in the foreign asset position originates from the drop in the traded output caused by the labor shift towards the nontraded sector. When k T > k N , the fall in Y T is triggered by the Rybczynski effect. If sectoral capital intensities are reversed, the real exchange rate appreciation produces the decline in Y T .

Empirical studies generally find that a fiscal expansion tends to raise output. Our model produces a significant increase in GDP on impact in the benchmark scenario if k T > k N since the real wage does not decrease in this case. If k N > k T , output is almost unaffected.

Yet, in this case, the cumulative response of GDP at an horizon of two years becomes substantial across all scenarios, as shown in the fifth line of panel C of Table 1.

It is interesting to compare our results when 2007, Cardi and[START_REF] Cardi | Habit Formation and Fiscal Transmission in Open Economies[END_REF] find that cumulative impulse responses after two years range between 0.3 and 1.1 for output, between -0.1 and -1.1 for investment, and -0.1 and -1.8 for the current account. While our model overpredicts both the crowding out of investment and the current account deficit, it predicts pretty well the GDP response, falling in the range of VAR evidence.

k T > k N (panel C of
Finally, since our model predicts the sectoral impact of fiscal shocks, it is interesting to compare our results with empirical data in this area. Only a few previous studies have estimated the effects of a boost to government spending on sectoral outputs. Among these, Bénétrix and Lane [2010] find that fiscal spending shocks generate a shift in the sectoral composition of output as public purchases disproportionately benefit the non-traded sector.

This finding is in line with our numerical results reported in the two last lines of panel B of Table 1. Regardless of sectoral capital intensities and across all the scenarios, a rise in government spending boosts non-traded output, more so if the non-traded sector is more capital intensive.

---------------------

< Please insert Table 1 about here > --------------------- --------------------- < Please insert Figure 1 about here > ---------------------
5 Temporary Fiscal Expansion: The Case of Endogenous

Markup

Several papers have stressed that the variation in the number of competitors and the consecutive change in the markup provides an important magnification mechanism, see e.g., Jaimovich and, Floetotto [2008], [START_REF] Wu | Endogenous markups and the effects of income taxation: Theory and evidence from OECD countries[END_REF], [START_REF] Zhang | Estimating the Effects of the Fiscal Policy in OECD Countries[END_REF], all of whom consider one-sector models. We therefore decide to revisit quantitatively the effects of temporary fiscal shocks by allowing for the markup to be endogenous. Since the long-run effects remain almost unchanged compared to those the case of fixed markup, we will not discuss them further. Rather, we will concentrate on how an endogenous markup modifies the short-run adjustment of key variables and influences the sectoral composition of GDP.

Before analyzing in detail the role of sectoral reallocation in shaping the short-run dynamics in response to a temporary increase in government spending, we recall the conclusions of empirical studies. [START_REF] Perotti | Search of the Transmission Mechanism of Fiscal Policy[END_REF] finds that the real wage responds positively to a fiscal shock. Estimates by [START_REF] Monacelli | Fiscal Policy, the Real Exchange Rate and Traded Goods[END_REF] show that the real exchange rate depreciates in the U.S., Australia, the U.K. and Canada, while [START_REF] Enders | How do Fiscal and Technology Shocks affect Real Exchange Rates? New Evidence for the United States[END_REF] confirm this finding for the U.S. As shown in section 4, a two-sector model can produce the positive impact on output and the simultaneous drop in investment and the current account after a fiscal shock as long as the traded sector is more capital intensive than the non-traded sector. However, it fails to produce the real exchange rate depreciation or the rise in the real wage. Since markup variations affect the relative price P and the wage rate W , we decide to investigate whether the predictive power of the two-sector model would improve if the markup were endogenous.

Extending the Model to Endogenous Markup

So far, we adopted the Dixit-Stiglitz assumption according to which the number of competitors is large enough within each sector to yield a fixed price-elasticity of demand. Yet, as emphasized by [START_REF] Yang | Monopolistic Competifion and Optimum Product Diversity: Comment[END_REF], the [START_REF] Dixit | Monopolistic Competition and Optimum Product Diversity[END_REF] assumption is an approximation when the sectoral good is aggregated from a finite number of intermediate goods. Following Jaimovich and Floetotto [2008], we depart from the usual practice by assuming that the number of firms is large enough that the strategic effects can be ignored, but not so large that the effect of entry on the firm's demand curve is minuscule. Consequently, the price elasticity of demand faced by a single firm is no longer constant and equal to the elasticity of substitution between any two varieties, but rather a function of the number of firms N . Taking into account that output of one variety does not affect the general price index P , but does influence the sectoral price level, in a symmetric equilibrium the resulting price elasticity of demand is given by: 37

e (N ) = - ( -ω) N , N ∈ (1, ∞) . ( 24
)
Assuming that > ω, the price elasticity of demand faced by any single firm is an increasing function of the number of firms N within a sector. Henceforth, the markup µ = e e-1

decreases as the number of competitors increases.

In the interest of space, we restrict our attention to the major changes in deriving the macroeconomic equilibrium. First, the zero-profit condition in the intermediate good sector can be solved for the number of firms, i.e. N = N (K, L, P ). Bearing in mind that µ = µ (N ), the equalities of marginal products between sectors (i.e., eqs. ( 6)) imply that capital-labor ratios k j (j = T, N ) are affected by the markup and so by the number of firms, i.e. k j = k j (P, µ). Substituting the capital-labor ratios into θ T k T θ T -1 ≡ W to solve for the wage rate, and into the resource constraints (i.e., eqs. (??)) and the production functions to solve for the sectoral outputs, short-run static solutions become:

W = W (P, µ) , Y T = Y T (K, P, L, µ) , Y N = Y N (K, P, L, µ) , ( 25
)
where

W µ ≶ 0 depending on whether k T ≷ k N , Y T µ > 0 and Y N µ < 0.
To understand this result intuitively, i.e. the impact of markup variations, let us consider that the number of competitors increases so that µ falls. All things being equal, since the ratio P/µ rises, nontraded output Y N increases while traded output Y T falls. Additionally, if k T > k N , a fall in the markup µ raises the capital-labor ratios and thereby the wage rate. As a consequence, Y N rises further and Y T declines more because the increased real wage induces households to raise labor supply which shifts towards the more labor intensive sector. The same logic applies in the case k N > k T but W falls.

Short-Run Effects

We now investigate the short-term effects of fiscal shocks when the markup is endogenous, focusing on the shift in the real exchange rate and the adjustment of the real wage. The latter has been estimated as the ratio of the wage rate to the consumption price index.

Numerical results for impact and cumulative effects are summarized in panels B and C of Table 2. 38 The baseline calibration is identical to that described in section 4.1.

Case k T > k N

We first consider the situation when the traded sector is more capital intensive. As the number of firms, and thereby the markup, adjusts over time, the dynamics for the real exchange rate are restored and driven by the no-arbitrage equation according to which the 37 Details of the derivation can be found in the Appendix. 38 To aid comprehension, panel B of Table 2 also shows the initial reaction of the wage rate W .

return on domestic capital must be equalized with the return on traded bonds:

h k k N [P, µ (N )] µ (N ) + Ṗ P -δ K = r . ( 26
)
The markup µ depends on the number of firms N which drives profits down towards zero in the non-traded sector at each instant of time. Since non-traded output is expected to increase while government spending G N is raised, it creates profit opportunities in that sector. Hence, the number of firms increases over time, which lowers the markup. The subsequent decrease in the return of capital h k /µ triggered by the rise in k N requires a fall in the relative price of non-traded goods. As shown in the second line of panel B of Table 2, P drops on impact across all scenarios, as long as k T > k N . While the initial depreciation in P is fairly small, the first line of panel C reveals that the real exchange rate depreciation becomes substantial at an horizon of two years.

The reaction of the wage rate is the result of two opposite forces: the fall in the markup which raises W and the decline in P that lowers it. As shown in the third line of panel B of Table 2, the wage rate decreases on impact as the relative price channel predominates. The second line of panel C shows that the two-year horizon cumulative response of the real wage is negative for the baseline scenario. Yet, as displayed in Figure 1, the dynamic path for the real wage shows that it increases along the transitional path and exceeds its initial level after about 6 quarters. Only if the fiscal shock is short-lived or long-lived (i.e., G N is raised over 8 or 32 quarters), does the cumulative response of the real wage becomes positive.

After a long-lived fiscal shock, both non-traded output expansion and, as a consequence, firm entry are larger. Hence, the decline in the markup is large enough to produce a positive cumulative response of the real wage. Following a short-lived fiscal shock, the real exchange rate appreciates rapidly after its short-term depreciation, and it has a positive impact on the wage rate.

Let now investigate how the markup variations modify the responses of key economic variables, relative to those obtained with a fixed markup. First, as a result of the initial drop in the wage rate, labor supply increases more moderately. Second, the real exchange rate depreciation induces a shift of resources towards the traded sector. As shown in the two last lines of panel B of Table 2, while non-traded output increases very slightly on impact in the baseline scenario, Y N decreases substantially if the fiscal shock is short-lived (i.e., T = 8) or the labor supply is weakly responsive (i.e., σ L = 0.1), because the wealth effect is smaller or the labor supply reacts less to the wealth effect. As a consequence, investment is crowded out by a larger amount (almost 1% of initial GDP rather than 0.66% when the markup is fixed). Third, as the relative price P depreciates, traded output now expands (instead of declining) in all scenarios, except that of a long-lived fiscal shock. While the initial increase in Y T triggers a small current account surplus on impact, panel C of Table 2 reveals that the external asset position worsens very rapidly and dramatically in the short-run. Fourth, as labor the supply increases less, the cumulative response of GDP summarized in panel C remains smaller than when the markup is fixed.

To summarize, the two-sector model can produce a real exchange rate depreciation but fails to trigger a positive cumulative response of the wage rate for the baseline duration of the fiscal shock, i.e. T = 16.

Case k N > k T
While the two-sector model does a fairly good job of accommodating most of the evidence reported by empirical studies if the traded sector is more capital intensive than the non-traded sector, the predictive power of the two-sector model is weak if sectoral capital intensities are reversed.

When k N > k T , non-traded output is expected to increase sizeably after a temporary increase in G N . The consequent flow of entries triggers a substantial decline in the markup.

The drop in µ now raises the return on domestic capital, which requires a real exchange rate appreciation. This prediction contradicts the empirical evidence. The real exchange rate appreciation, together with the decline in the markup, drive down the wage rate. As the cost of consumption goods increases, the real wage falls substantially. The last line of Figure 1 reveals that the real wage fails to exceed its original value along the transitional path.

The GDP response to a fiscal shock when k N > k T is negative in most of scenarios, due the substantial decline in the real wage which exerts a negative impact on labor supply.

More precisely, L increases only if σ L is low or the fiscal shock is long-lived. Furthermore, the competition channel amplifies the increase in investment. The reason is that, as intermediate good producers in the non-traded sector perceive a more elastic demand, they are induced to produce more. Since Y N increases by a larger amount than in the case of a fixed markup, investment is further crowded in.

Whereas non-traded output expands substantially, traded output falls dramatically across all scenarios as a result of the appreciation in the real exchange rate and the smaller markup. The subsequent decline in net exports drives the current account into a larger deficit than with a fixed markup.

---------------------< Please insert Table 2 about here > ---------------------

Sectoral Effects

We now turn to the sectoral impact of fiscal policy. This will allow us to investigate whether the competition channel amplifies or reduces the heterogeneity in sectoral output responses.

When k T > k N , the competition channel modifies the distribution of the increase in GDP across sectors substantially, as summarized in the two last lines of panel B of Table 2. With a fixed markup, traded output falls in all scenarios, while the fiscal shock boosts non-traded output. But if µ is endogenous, the real exchange rate depreciation is strong enough to boost traded output on impact, as long as the fiscal shock does not last too long.

The reason is that when the fiscal shock is long-lived, the wealth effect is substantial and thereby counteracts the negative impact on L of the decline in W . As a consequence, the labor supply increases substantially and shifts towards the non-traded sector.

With regard to the transitional dynamics, as shown in the sixth line of Figure 1, while the real exchange rate continues to depreciate, the crowding-out of investment together with the rise in labor supply boost Y N but depress Y T . In a nutshell, due to the intersectoral reallocation of resources, the transitional adjustment of Y T is the mirror image of the dynamics of Y N . The results displayed in the two last lines of panel C of Table 2 show that with an endogenous markup, the cumulative responses of traded and non-traded output are -3.84% and 4.05% of initial GDP respectively, while the cumulative responses are -4.11% and 4.42%, respectively, with a fixed markup. Hence, when k T > k N , the decline in µ reduces the heterogeneity in the responses of sectoral outputs. Nevertheless, the fall in traded output remains substantial after two years. Once the fiscal shock ends, non-traded output starts decreasing (as investment is crowded in), while traded output rises. In the long-run, GDP growth is mostly driven by the rise in traded output.

If k N > k T , the patterns of the transitional adjustment of sectoral output remain approximately the same as those found with a fixed markup. Yet, the competition channel amplifies the dispersion of sectoral output responses. More precisely, non-traded output rises by more than 2% of initial GDP (rather than about 1% when the markup is fixed).

In conclusion, regardless of sectoral capital intensities and whether the markup is fixed or not, non-traded output always expands significantly following a temporary increase in public spending. Allowing for the markup to depend on the number of competitors, the numerical analysis reveals that the competition channel moderates or amplifies the responses of sectoral outputs, depending on whether the traded sector is more or less capital intensive than the non-traded sector.

Conclusion

In this paper we have shown that the open economy version of the two-sector neoclassical model with traded and non-traded goods can account for the empirical evidence on the effects of fiscal shocks, but only if the traded sector is more capital intensive than the nontraded sector. In particular, a robust conclusion emerging from empirical papers is that government spending tends to crowd out both investment and the current account. Considering both traded and non-traded goods enables the model to account for this finding, whereas the standard one-sector small open-economy framework cannot. In addition, by enabling the markup to depend negatively on the number of competitors, the model can generate a counter-cyclical markup which is pivotal to producing the real exchange rate depreciation which has recently been documented in the empirical literature. The subsequent decline in the consumption price index and the positive impact of the lower markup on the wage rate produces an increase in the real wage, although only if the fiscal shock is shortor long-lived, not if it holds for a medium term.

In addition to the ability of the two-sector economy model to provide a better understanding of the fiscal transmission mechanism in an open economy, it delivers interesting insights into the sectoral effects of fiscal shocks. The numerical analysis reveals that the relative size of the non-traded sector increases substantially in the short-run, in line with the evidence reported by Bénétrix and Lane [2010]. Our numerical results also show that in the long-run, the relative size of the traded sector increases to service the debt accumulated in the short-run. Hence, GDP growth is mostly driven by the rise in traded output in the long-run. Along the transitional path, in all scenarios, the outputs of the two sectors move in opposite direction. More precisely, traded output can either fall or rise during the transition period when government spending is raised, depending on whether the traded sector is more or less capital intensive than the non-traded sector.

The duration of the fiscal shock plays also a pivotal role in driving the responses of both aggregate and sectoral variables. In all the scenarios, both labor supply and GDP increase more when the fiscal expansion is implemented over a long rather than a short period. The multiplier can exceed one only in this case, while the dispersion of responses of sectoral outputs is amplified.

In conclusion, we must stress a number of caveats. If the non-traded sector is assumed to be the more capital intensive sector, the model fails to match the evidence along a number of dimensions. Notably, in this case, the two-sector model fails to account for the crowding-out of investment which is one of the most consistent responses to a fiscal shock documented in the empirical literature. Additionally, if the traded sector is more capital intensive than the non-traded sector, the model cannot produce a positive cumulative response of the real wage in the baseline scenario. Finally, due to our assumption of perfect mobility across sectors, traded and non-traded output vary in opposite direction while evidence by Bénétrix and Lane [2010] mostly predict that sectoral outputs co-vary. Further analysis of these issues has to be left for future research.

Fixed Markup

Endogenous Markup The proportion of government spending on the traded and non-traded good (i.e., G T /Y T and G N /Y N ) are shown in the sixth and seventh column of Table 3. They average to 7% and 32%, respectively.

k T > k N k N > k T k T > k N k N > k T
Markups in the non-traded sector were estimated at the industry level in each country and aggregated as follows to construct the markup: µ = 6 j=1 ω j µ j where ω j is the nominal value-added weight of industry j in the non-traded sector. Estimates of µ j were obtained by applying the methodology developed by [START_REF] Roeger | Can Imperfect Competition Explain the Difference between Primal and Dual Productivity Measures? Estimates for U.S. Manufacturing[END_REF]. The testable equation is:

y j,t = β j x j,t + ε j,t , ( 27
)
where the dependent variable y j,t is the Solow residual -percentage change in output less the percentage change in inputs (each input is weighted by the corresponding income share in output) -and x j,t is the output growth minus capital growth. [2008c]). To tackle the potential endogeneity of the regressor and the heteroskedasticity and autocorrelation of the error term when estimating (27), we use the correction of Newey and West [1993]. 41 According to the estimates given in the last column of

  ) plus the appropriate transversality conditions. In an open economy model with a representative agent having perfect foresight, a constant rate of time preference and perfect access to world capital markets, we impose β = r in order to generate an interior solution. This standard assumption made in the literature implies that the marginal utility of wealth, λ, will undergo a discrete jump when individuals receive new information and must remain constant over time from thereon, i.e. λ = λ. The homogeneity of C(.) allows a two-stage consumption decision: in the first stage, consumption is determined, and the intratemporal allocation between traded and nontraded goods is decided at the second stage. Applying Shephard's lemma gives C T = (1 -α C ) P C C and P C N = α C P C C, with α C being the share of non-traded goods in the consumption expenditure.

  they raise labor supply by 0.13% as a result of the decrease in real disposable income. The open economy accumulates physical capital in the long-run, regardless of sectoral capital intensities. This is because when k T > k N , the increase in employment produces an excess of supply in the non-traded good market which calls for a long-run increase in capital that yields a shift of labor towards the more capital intensive sector. This in turn raises traded output and thereby net exports which allows the external debt accumulated in the shortrun to be serviced. If the capital intensities are reversed, the long-run rise in labor drives down non-traded output. To clear the market, capital must be raised. Interestingly, while GDP increases in all scenarios, the rise in G N always benefits the traded sector in the long-run, irrespective of sectoral capital intensities. More precisely, remembering that the relative price P remains unaffected by the fiscal shock in the long-run, traded output, i.e.Y T = L T f k T ( P ) ,is only driven by employment L T . As the open economy must run a trade balance surplus in the long-run, traded output and thereby labor in that sector must increase. With regard to non-traded output, Y N decreases in all scenarios if k N > k T since the open country experiences sizeable current account deficits in the short-run that require significant long-run improvement in the balance of trade.

  panel B gives the response on impact, panel C displays the cumulative responses over the first two years (i.e. eight quarters) after the shock. The transitional paths of key variables under the baseline scenario are displayed in Figures 1. The responses of GDP, investment and current account are expressed in percentage of the initial steady-state output, while the real exchange rate is given as the percentage deviation from the initial steady state. Horizontal axes measure quarters. When the reaction of the variable is sensitive to the elasticity of labor supply, we compare the baseline scenario (solid line) to alternative scenarios. The dashed-dotted line gives the results for a low labor supply elasticity (i.e. σ L = 0.1), while the dotted line shows those for a high labor supply elasticity (i.e. σ L = 1).

  depicts the transitional paths of sectoral outputs expressed as percentage deviations from the initial steady-state values scaled by the initial GDP. The solid line depicts the transitional path for traded output while the dotted line shows the dynamics for Y N . Along the transitional path, sectoral outputs vary in opposite directions as a result of the reallocation of inputs across sectors. When k T > k N , capital decumulation produces a fall in traded output while non-traded output expands. Whereas sectoral outputs diverge in this configuration, Y T and Y N converge when k N > k T . More precisely, the relative price depreciation raises traded output whereas the fall in P drives down nontraded output. Finally, as shown in the two last lines of panel A of Table1, long-run GDP growth is driven by traded output growth. The rise in traded output is required in the long-run to produce an improvement in the balance of trade, regardless of sectoral capital intensities.

Figure 1 :

 1 Figure 1: Effect of government spending shocks. Notes: variables are measured in percentage points of output, with the exception of employment, the real exchange rate and real wage which are scaled by their initial steady-state values.

-

  of government spending on good j in output of sector j; θ j is the share of capital income in output of sector j = T, N ; µ is the markup charged by the non-traded sector. to firm-provided training in France: Evidence on mobility and wages Arnaud Chéron, Bénédicte Rouland, François-Charles Wolff 10-11. Taxation of early retirement windows and delaying retirement:

  Kλ represents the partial derivative of the steady-state capital stock w.r.t. the shadow value of wealth λ, ν 1 < 0 and ν 2 > 0 are the stable and unstable roots, and d λ/dG N > 0 reflects the wealth effect. If k T > k N , capital stock and labor supply are positively correlated in the long-run, and a temporary fiscal expansion crowds in investment in the long run. With the reversal of capital intensities, K and L move together only if σ CCN -σ L Lk T ν 2 < 0. More precisely, if the labor supply is elastic enough, higher employment triggers a drop in non-traded output to such an extent that capital stock must increase to clear the non-traded good market. As we shall see in the next section, K increases in all scenarios, even if σ L is small.

See the Appendix for further details.

where

  while investment is crowded out by 3.16% if k T > k N . The investment boom when k N > k T triggers a positive cumulative response of output, as summarized in the fifth line of panel C in Table1. By contrast, the decline in investment when k T > k N implies a smaller cumulative response of GDP, across all scenarios.36 As shown in the eight line of panel B of Table1, the open economy experiences a current account deficit, regardless of sectoral capital intensities. When k T > k

N

, a larger labor supply induces a shift of labor towards the non-traded sector, and the subsequent decrease in traded output drives down net exports. When the capital intensities are reversed, the appreciation in the real exchange rate more than offsets the positive effect of the labor inflow on Y T . As a consequence, traded output falls which yields a current account deficit.

Table 2

 2

) with the numbers documented in empirical studies. By estimating a VAR model on quarterly time-series data for the U.S., Australia, the U.K, and Canada, covering the period 1980-

Table 1 :

 1 Quantitative Effects of a Temporary Fiscal Expansion (in %): The Case of a Fixed Markup

  We consider a temporary rise in G N which raises total government spending by one percentage point of GDP. Impact and steady-state deviations are scaled by initial GDP, exception with the real exchange rate, wage rate, labor, and capital which are scaled by their initial steady-state values. A short-lived, medium-lived and long-lived shock lasts 8, 16, 32 quarters respectively.

	-1.01	1.07		0.51	-1.79	5.23	-12.76	1.33	-7.11	8.45
	0.80	0.79		0.31	-1.08	-0.94	-7.62	0.13	-4.02	4.15
		1.12		0.41	-1.44	3.70	-12.34	0.58	-7.49	8.07
		0.88		0.38	-1.35	2.43	-10.36	0.50	-6.17	6.67
		1.00		0.42	-1.47	3.22	-11.53	0.69	-6.70	7.39
		0.59		0.00	0.00	-1.74	-4.28	1.00	-4.73	5.73
		0.16		0.00	0.00	-3.95	-3.70	-0.07	-3.75	3.69
		0.41		0.00	0.00	-2.75	-4.32	0.55	-4.39	4.94
		0.11		0.00	0.00	-4.04	-3.02	-0.18	-3.50	3.32
		0.32		0.00	0.00	-3.16	-3.91	0.32	-4.11	4.42
		Non traded output, dY N (0)	C.Cumulative Response	RER, dP	Real wage, dW/P C	Investment, dI	Current account, dCA	GDP, dY	Traded output, dY T	Non traded output, dY N	Notes: Notes:

Table 2 :

 2 Quantitative Effects of a Temporary Fiscal Expansion (in %): The Case of an Endogenous Markup

  We consider a temporary rise in G N which raises total government spending by one percentage point of GDP. Impact and steady-state deviations are scaled by initial GDP, exception with the real exchange rate, wage rate, labor, and capital which are scaled by their initial steady-state values. A short-lived, medium-lived and long-lived shock lasts 8, 16, 32 quarters respectively. Forestry, Fishing, and Hunting; Mining, Manufacturing, and Construction; Transport and Communications. The sectors treated as non-traded are: Government Public Services; Defense; Public Order and Safety; Education; Health; Social Security and Welfare; Housing and Community Amenities; Recreation Cultural and Community Affairs. The non tradable component of government spending shown in the fifth column of Table 3 averages to 90%.

		-0.13	0.23	0.16	0.20	0.24	-0.03		-0.14	0.09	-0.33	-0.38	0.06	-1.06	1.31	-2.36	0.04	-2.41	2.45	3.49		0.35	-1.73	6.06	-13.60	1.41	-13.54	14.96
		-0.04	0.07	0.04	0.06	0.07	-0.01		-0.04	0.05	-0.22	-0.24	-0.04	-1.14	0.63	-1.76	-0.03	-1.78	1.75	2.48		0.22	-1.06	-0.05	-8.52	0.22	-8.28	8.52
		-0.05	0.17	0.13	0.15	0.15	0.00		-0.06	0.07	-0.28	-0.32	-0.11	-1.21	1.23	-2.44	-0.07	-2.46	2.38	3.39		0.26	-1.40	5.01	-13.69	0.68	-13.31	14.00
		-0.12	0.04	0.01	0.03	0.09	-0.06		-0.13	0.07	-0.25	-0.29	0.02	-1.04	0.82	-1.86	0.01	-1.91	1.93	2.75		0.28	-1.32	3.22	-11.15	0.58	-11.16	11.75
		-0.07	0.13	0.09	0.11	0.13	-0.02		-0.08	0.07	-0.28	-0.32	-0.02	-1.13	1.06	-2.19	-0.01	-2.21	2.20	3.13		0.29	-1.44	4.28	-12.60	0.78	-12.36	13.15
		-0.13	0.22	0.28	0.24	0.23	0.00		-0.12	-0.01	-0.02	-0.01	0.21	-0.74	-0.49	-0.25	0.14	-0.33	0.46	0.71		-0.13	0.05	-1.81	-4.23	0.97	-4.70	5.65
		-0.04	0.06	0.08	0.07	0.07	0.00		-0.03	-0.01	-0.05	-0.05	0.03	-0.98	-1.22	0.24	0.02	0.22	-0.20	-0.30		-0.09	0.04	-3.78	-3.87	-0.09	-3.95	3.84
		-0.04	0.15	0.19	0.16	0.14	0.02		-0.04	-0.01	-0.05	-0.05	0.09	-0.93	-1.07	0.14	0.06	0.11	-0.05	-0.07		-0.13	-0.05	-3.27	-3.94	0.39	-4.05	4.43
		-0.12	0.04	0.07	0.05	0.09	-0.04		-0.12	-0.01	-0.05	-0.04	0.04	-0.89	-1.14	0.25	0.03	0.18	-0.16	-0.24		-0.09	-0.08	-4.48	-2.67	-0.23	-3.17	2.92
		-0.07	0.12	0.15	0.13	0.13	0.00		-0.07	-0.01	-0.04	-0.04	0.09	-0.90	-0.99	0.09	0.06	0.05	0.01	0.02		-0.11	-0.04	-3.55	-3.61	0.23	-3.84	4.05
	A.Long-Term	Consumption, d C	Labor, d L	Capital, d K	GDP, d Ỹ	Traded output, d Ỹ T	Non traded output, d Ỹ N	B.Impact	Consumption, dC(0)	RER, dP (0)	Wage, dW (0)	Real wage, dW (0)/PC (0)	Labor, dL(0)	Savings, dS(0)	Investment, dI(0)	Current Account, dCA(0)	GDP, dY (0)	Traded output, dY T (0)	Non traded output, dY N (0)	Number of firms, dN (0)	C.Cumulative Response	RER, dP	Real wage, dW/P C	Investment, dI	Current account, dCA	GDP, dY	Traded output, dY T	Non traded output, dY N	Notes: Notes:

  40 Estimate of µ j is equal to 1/(1 -βj ). Variables required to apply the Roeger's method are the following: gross output (at basic current prices), compensation of employees, intermediate inputs at current purchasers prices, and capital services (volume) indices. All these variables are compiled from the EU KLEMS database (Source: EU KLEMS[2007]), with the exception of the user cost of capital r t . No sector-specific information was available to construct r t ; hence, the capital user cost is calculated as r t (≡ r j,t ) = p I (i -π GDP + δ K ), with p I the deflator for business non residential investment, i the long-term nominal interest rate, π GDP the GDP deflator based inflation rate; the rate of depreciation δ K is set to 5%; p I , i and π GDP were taken from the OECD Annual National Accounts database (Source OECD

  Table 3, the markup charged by the non-traded sector averages to 1.39.

40

Formally, yt = ∆ (pj,tYj,t) -αL,t∆ (wj,tLj,t) -αM,t∆ (mj,tMj,t) -(1 -αL,t -αM,t) ∆ (rtKj,t) and xj,t = ∆ (pj,tYj,t) -∆ (rtKj,t). We denote by αi,t for i = L, M, K the share of a generic input (labor, material and capital) on total output, ∆ (pj,tYj,t) the nominal output growth in industry j, ∆ (wj,tLj,t) the nominal labor cost growth, ∆ (m j,t M j,t ) the growth in nominal intermediate input costs and ∆ (r t K j,t ) the nominal capital cost growth.

41 Countries estimates for each μj are not reported here to save space, but are available on request.

Table 3 :

 3 Data to Calibrate the Two-Sector Model

	Capital Share Markup	θ T θ N µ	0.28 0.32 1.42	0.33 0.35 1.34	0.22 0.33 1.45	0.32 0.32 1.40	0.27 0.30 1.32	0.22 0.35 1.35	0.30 0.28 1.37	0.42 0.39 1.60	0.37 0.29 1.51	0.41 0.33 1.32	0.35 0.26 1.33	0.30 0.30 1.31	0.36 0.32 1.43
	/Y j	G T /Y T	0.07	0.09	0.06	0.07	0.09	0.06	0.05	0.06	n.a.	0.08	0.05	0.09	0.06
	Non tradable Share G j	Output Labor Consumption Investment Gov. spending G N /Y N	0.65 0.60 0.44 0.59 0.90 0.28	0.67 0.65 0.44 n.d. 0.85 0.30	0.64 0.61 0.44 0.54 0.91 0.30	0.70 0.67 0.43 0.58 0.93 0.40	0.58 0.57 0.44 0.63 0.84 0.34	0.69 0.64 0.40 0.61 0.93 0.33	0.62 0.66 0.52 0.52 0.93 0.33	0.63 0.56 0.36 0.59 0.91 0.29	0.64 0.61 0.39 0.63 n.a. n.a.	0.67 0.69 0.45 0.64 0.91 0.34	0.61 0.59 0.50 0.63 0.90 0.25	0.65 0.67 0.51 0.47 0.90 0.43	0.68 0.72 0.49 0.59 0.90 0.22
	Countries		AUT	BEL	DEU	DNK	FIN	FRA	GBR	ITA	JPN	NLD	SPA	SWE	USA	Notes: G j

[START_REF] Coto-Martinez | Profits, Markups and Entry: Fiscal Policy in an Open Economy[END_REF] consider the case of a fixed markup rather than an endogenous markup.

A long-lived and a short-lived fiscal shock last 32 quarters and 8 quarters, respectively. In the baseline

This setup builds on Jaimovich and Floetotto's[2008] model. Details of its derivation are therefore relegated to the Appendix, which is available on request.

To derive formal solutions after a temporary fiscal shock, we applied the procedure developed by Schubert and[START_REF] Schubert | The Dynamics of Temporary Policies in a Small Open Economy[END_REF]

.27 In deriving formal solutions after temporary fiscal shocks, without loss of generality, we assume that the non-traded sector is perfectly competitive so that the markup is one, and that the rate of depreciation of physical capital is zero. In the numerical analysis, we relax these two assumptions.

* Romain Restout wishes to express his gratitude to the Belgian Federal Government for its financial support (Grant PAI P6/07 on "Economic Policy and Finance in the Global Economy: Equilibrium Analysis and Social Evaluation").

A Data

In this Appendix, we describe how we split output, labor and GDP components into a traded sector and a non-traded sector. Table 3 shows the non-tradable content of GDP, employment, consumption, gross fixed capital formation and government spending. Table 3 also shows the share of government spending on the traded and non-traded good in the sectoral output, the shares of capital income in output in both sectors, and the markup charged by the non-traded sector for 13 OECD countries. The choice of these countries has been dictated by data availability. For the countries of our sample, the period runs from 1970 to 2004. 39 For output and employment, we used the methodology proposed by De [START_REF] Gregorio | International Evidence on Tradables and Nontradables Inflation[END_REF], who treat Agriculture, Hunting, Forestry and Fishing, Mining and Quarrying, Total The non-tradable share of consumption shown in the third column of Table 3 averages to 45%, in line with the share reported by [START_REF] Alan | Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements[END_REF].

With regard to investment, we follow the methodology proposed by [START_REF] Burstein | Investment Prices and Exchange Rates: Some Basic Facts[END_REF] who treat Housing and Other Construction as non-tradable investment and Products of agriculture, forestry, fisheries and aquaculture, Metal products and machinery, Transport Equipment as tradable investment expenditure (Source: OECD Input-Output database [2008a]). Non tradable share of investment shown in the fourth column of Table 3 averages to 60%, in line with estimates provided by [START_REF] Burstein | Investment Prices and Exchange Rates: Some Basic Facts[END_REF].

Sectoral government expenditure data were obtained from the Government Finance Statistics Yearbook (Source: IMF [2007]) and the OECD General Government Accounts database (Source: OECD [2008b]). Adopting [START_REF] Morshed | Sectoral Adjustment Costs and Real Exchange Rate Dynamics in a Two-Sector Dependent Economy[END_REF] methodology, the following four sectors were treated as traded: Fuel and Energy; Agriculture, 39 The exception is consumption expenditure. Data start in 1976for Austria, in 1995for Belgium, in 1975 for Finland, in 1991 for Germany, in 1987 for Netherlands, in 1995 for Spain and in 1993 for Sweden. Data end in 2004 for all countries except Japan (1999) and the U.S. (2000).

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