Cross-border spill-overs from fiscal stimulus in a monetary union

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Economic Modelling journal homepage: www.elsevier.com/locate/econmod

Cross-border spill-overs from fiscal stimulus in a monetary union ⁎

Ruthira Naraidooa, Eric Schalingb, , Mewael F. Tesfaselassiec a b c

Department of Economics, University of Pretoria, South Africa Wits Business School (University of the Witwatersrand) and VU University, Amsterdam, The Netherlands Kiel Institute for the World Economy, Kiellinie 66, 24105 Kiel, Germany

A R T I C L E I N F O

A BS T RAC T

JEL classification: E62 F42 F45

We analyse domestic and cross-border effects of fiscal policy in a two-region business cycle model of a monetary union. Without relying on debt consolidation via spending reversals along the lines of Corsetti, Meier and Mueller (2010) and Corsetti and Mueller (2014) we show that a fiscal expansion by the core economies of the euro area is associated with crowding in of both core and periphery consumption. Interestingly, cross-border spill-over effects are larger the larger the share of credit constrained households in the periphery.

Keywords: Fiscal policy New-Keynesian model Open economy Monetary union Rule-of-thumb consumers Habit persistence

1. Introduction Following the Eurozone and Greek Sovereign debt crises there have been several policy recommendations by prominent academic economists such as Paul Krugman that the core economies in the Eurozone— especially Germany—should engage in a fiscal expansion to boost economic growth in Europe: “Germany wants to run surpluses and wants everyone else to run surpluses. Germany's tight fiscal policy directly contributes to weakness of overall European demand, and its deficit hawkery is an important reason why other European countries that have low borrowing costs are still pursuing austerity”.1 This has also been a prominent theme in the media, for example The Economist of September the 3rd 2016 says: “Within the euro area, the struggling Mediterranean economies need faster rates of GDP growth to bring down unemployment and stabilise government debt. Germanys enormous surpluses mean that its households are buying less from other countries than they ought to. That hurts the growth prospects of the periphery, and raises the risk of a politically induced break-up”. These calls for actions are backed by empirical studies by e.g. Beetsma et al. (2005), Auerbach and Gorodnichenko (2012) and Corsetti and Mueller (2014) that fiscal expansions tend to be locomotive policies' in the sense that they positively impact both domestic and foreign activity; that is, that they have positive spill-over effects.

⁎

1

In spite of empirical evidence supporting ‘crowding in’ of output of both instigating and recipient countries, typically modern macroeconomic frameworks such as the real business cycle model and the new Keynesian model have a hard time reproducing the stylized fiscal facts. A key reason is that these models feature infinitely-lived Ricardian households, whose consumption decisions at any point in time are based on an intertemporal budget constraint. Ceteris paribus, an increase in government spending lowers the present value of aftertax income, thus generating a negative wealth effect that induces a cut in consumption. Negative spill-over effects of fiscal expansions on foreign output are also typical results in two-country DSGE environments such as Corsetti and Pesenti (2001), unless special fiscal scenario assumptions are made. Here notable studies are Corsetti et al. (2010) and Corsetti and Mueller (2014), who assume that the fiscal expansion is followed by a spending reversal (an exogenous, debt-financed increase in government spending implies a spending reversal after some time, that is, a decline of government spending below trend after the initial increase), sometimes referred to as debt consolidation. In this paper we study fiscal expansions in a two-region version of the new Keynesian model of a monetary union. Here one region is seen as representing the core economies of the Eurozone (including Germany), whilst the other region stands for the periphery. Without relying on debt consolidation via spending reversals along the lines of

Corresponding author. E-mail addresses: [email protected] (R. Naraidoo), [email protected] (E. Schaling), [email protected] (M.F. Tesfaselassie). See Krugman's blog for the New York Times http://krugman.blogs.nytimes.com/2016/08/26/germanys-drag/.

http://dx.doi.org/10.1016/j.econmod.2017.05.010 Received 15 December 2016; Received in revised form 3 April 2017; Accepted 14 May 2017 0264-9993/ © 2017 Elsevier B.V. All rights reserved.

Please cite this article as: Schaling, E., Economic Modelling (2017), http://dx.doi.org/10.1016/j.econmod.2017.05.010

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financial imperfections. They highlight the central importance of policy frameworks, notably the medium-term debt consolidation regime. Domestic and foreign crowding in of consumption is a result of their analysis in the case in which a temporary debt-financed increase in government spending gives rise to higher future taxes along with some reduction in spending over time. The anticipated spending reversal not only strengthens the domestic stimulus effect but also enhances positive cross-border spill-over effects. According to our reading of the literature spending reversals work to counter the above mentioned crowding-out effects of RBC models where higher government expenditure lowers the present value of after-tax income, thus generating a negative wealth effect that induces a cut in consumption. Corsetti and Mueller (2014) (CM) consider the case for fiscal coordination by providing new evidence on the cross-border effects of discretionary fiscal measures. They use a vector auto regression model as well as quantitative two-country business cycle model. They find that large positive spill-over effects cannot be ruled out. The latter are importantly driven by the presence of a budget rule allowing for a systematic response of taxes and government spending to public debt or debt consolidation in short. More specific, an exogenous, debtfinanced increase in government spending implies a spending reversal after some time, that is, a decline of government spending below trend after the initial increase. For a monetary union, Blanchard et al. (2016) show that a fiscal expansion by the core economies of the euro area would have a large and positive impact on periphery GDP assuming that policy rates remain low for a prolonged period. Under their preferred model specification, an expansion of core government spending equal to one percent of euro area GDP would boost periphery GDP by over 1 percent in a liquidity trap lasting three years, nearly half as large as the effect on core GDP. Our contribution builds on the canonical two-country new Keynesian model by Clarida et al. (2002) (CGG).3 We extend their model with fiscal policy, ROT households and habit persistence in consumption. Contrary to CGG—who focus on the case of flexible exchange rates—we analyse the case of a monetary union. Without relying on debt consolidation or spending reversals along the lines of CMM and CM, we show that a fiscal expansion by the core economies is associated with crowding in of both core and periphery consumption. These effects are stronger when the share of ROT households in the periphery is larger.

Corsetti et al. (2010) and Corsetti and Mueller (2014) we show that fiscal expansion by the core economies of the euro area is associated with crowding in of both core and periphery consumption. Interestingly, cross-border spill-over effects are larger the larger the share of credit constrained households in the periphery The remainder of this paper is organized as follows. Section 2 outlines related literature. In Section 3 we present the model—derive private sector behavior and discuss fiscal policy. In Section 4 we present the equilibrium of the two economies and derive the linearized version of the model. In Section 5 we show our main results while in Section 6 we conduct a number of sensitivity analyses. Section 7 concludes and suggests avenues for further research.

2. Related literature There is a large literature regarding the effects of fiscal policy on consumption and output in DSGE models. Starting with the closed economy RBC model it is well-known that contrary to the empirical evidence and the textbook IS-LM model a fiscal expansion leads to crowding out of consumption. The reason is that the RBC model features infinitely-lived Ricardian households, whose consumption decisions at any point in time are based on an intertemporal budget constraint. Ceteris paribus, an increase in government spending lowers the present value of after-tax income, thus generating a negative wealth effect that induces a cut in consumption. This effect is also present in the standard new Keynesian model. In order to generate more plausible positive effects of government expenditure on consumption and output Gali et al. (2007) (GLV) introduce rule-of-thumb (ROT) consumers in a closed economy setting who do not borrow or save; instead, they are assumed to consume their current income fully. They show that the interaction of the latter with sticky prices and deficit financing can account for the existing evidence on the effects of government spending.2 In a critique on GLV, Furlanetto and Seneca (2009) state that their results rely on an empirically implausible high degree of price stickiness and too large a share of ROT households in total consumers. Instead, they introduce real rigidities in the form of habit persistence in consumption. This assumption has—amongst others—also been used by Smets and Wouters (2007). More specific, they are then able to reproduce the same consumption multiplier as GLV under only two and a half quarters of price stickiness, instead of four, and only 30 per cent of constrained agents instead of 50 per cent. According to Leeper et al. (2015) so far no consensus has emerged in the empirical literature on the dynamic impacts of government spending on macroeconomic aggregates. There are starkly different conclusions from similar models and data (see e.g. Coenen et al. (2012) versus Cogan et al. (2010)). They call this the fiscal multiplier morass. They attempt to clear up the morass for the US by using Bayesian prior and posterior analysis of a monetary DSGE model, extended to include fiscal details and two distinct monetary-fiscal policy regimes, to quantify government spending multipliers. They get the following results regarding the transmission mechanisms that underlie government spending multipliers. Posterior mean estimates of short-run output multipliers are comparable across regimes but much larger after 10 years under passive money/active fiscal than under active money/passive fiscal. There has also been work on the international spill-over effects of fiscal policy on consumption and output. For example, using a twocountry business cycle model Corsetti et al. (2010) (CMM) find that consumption spill-over effects are affected by a range of features, including trade elasticities, the size and openness of economies, and

3. The model There is a monetary union composed of two regions, the core and the periphery economy, and labeled H and F respectively. The mass of Eurozone population is normalized to one. Region H and F households lie, respectively, on the interval [0, 1 − γ ] and [1 − γ , 1], where 0 < γ < 1. Each region has a final good and intermediate goods producing sectors. There are the same number of final good producing firms in each region as there are households. Final good producers are perfectly competitive and use as production inputs a continuum of differentiated intermediate goods, whose mass is normalized to 1. The intermediate goods sector is subject to Calvo-type nominal price rigidity. Moreover, we allow for the presence of rule-of-thumb (ROT) households, who make up a fraction λ of all households in each region and do not have access to capital markets and therefore consume their current labor income net of lump-sum taxes. The rest of the households (“optimizing” or “Ricardian”) can trade internationally a full set of state-contingent Arrow-Debreu securities. Moreover, we allow for consumption habit formation. As is shown in Furlanetto and Seneca

2 An alternative rationale for a positive effect of government spending on consumption is the presence of non-separable preferences in utility. See for example Tesfaselassie (2013) and the references therein.

3 Among others, Schaling and Tesfaselassie (2015) use the CGG model to study the performance of simple monetary policy rules in the presence of trend growth.

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whose gross nominal yield is Rt. Then taking expectations of Eq. (7) and rearranging gives the familiar Euler equation

(2009), who consider the case of a closed economy, habit persistence helps generate consumption crowd-in of government spending without the need to assume an implausibly high share of ROT households. For future reference variables with superscripts “o” and “r” refer to optimizing and ROT households, respectively. Moreover variables with an asterisk correspond to the foreign economy. Following CGG we assume CPI-based PPP so that PC*, t = PC , t = PW , t , where PW , t denotes union wide CPI. Let πW , t be the common inflation rate and rt the common nominal interest rate in the union. There are two differences vis-a-vis the flexible exchange rate case. First, the single monetary policy rule is given by rt = φπ πW , t . Second, the real rate rt − Et πW , t +1 appears in both home and foreign consumption Euler equations.

⎛ ⎛ C o − h C o ⎞σ ⎞ o t −1 1 = βRt Et ⎜⎜ ⎜ to ΠC−1, t +1⎟⎟ , o⎟ ⎝ ⎝ Ct +1 − ho Ct ⎠ ⎠

= Et Qt , t +1 is the price of the discount bond. where Rule of thumb households. As the ROT household do not save or borrow consumption is determined by current period income net of taxes Ctr = W͠ t Ntr − Ttr .

As in Gali et al. (2007) and Furlanetto and Seneca (2009) the labor market has a continuum of differentiated labor types z ∈ [0, 1]. Aggregate employment Nt is a Dixit-Stiglitz composite of all labor ε ⎛ 1 ε −1 ⎞ ε −1 types: Nt = ⎜∫ Nz, tε dz⎟ . The corresponding demand for labor type z ⎠ ⎝ 0 is given by

Cjt

Let be the consumption index of domestic household j where j = r , o defined over a home produced good CHj , t and an imported good CFj , t (1)

⎛ W͠ z, t ⎞−ε Nz, t = ⎜ ⎟ Nt . ⎝ W͠ t ⎠

where the respective prices of the Home and Foreign produced goods are denoted by PH , t and PF , t F,t. Here γ represents the share of foreign (imported) goods in the domestic consumption basket, and is therefore a natural measure of the degree of openness. As γ goes to 0, the home (core) economy becomes closed. Let PC , t be the consumption price index. From consumption expenditure minimization we have

ϕ ⎤ ⎡ W͠ N ⎡ W͠ N Nz1+ N1+ ϕ ⎤ z, t z, t ,t ⎥ + (1 − λ ) ⎢ z, t oz, t − z, t ⎥ . − λ⎢ r ⎢⎣ U ′(Cz, t ) 1 + ϕ ⎥⎦ 1 + ϕ ⎥⎦ ⎣⎢ U ′(Cz, t )

(2)

where St ≡ PF , t / PH , t is the terms of trade and k ≡ (1 − γ )(1− γ ) γ γ . Household j's optimal consumption allocation across home and imported goods for a given level of Cjt gives the demand equations

CHj , t = (1 − γ )

CFj , t

PC , t j Ct PH , t

PC , t j =γ Ct . PF , t

(3)

⎛ λ 1 − λ⎞ ͠ ε . + ⎜ ⎟ Wt = MRSto ⎠ ε−1 ⎝ MRStr

(4)

j ) Ntϕ , j ∈ {o , r}. where MRSt j = (Ct j − hj Ct −1 A symmetric set of conditions holds for the representative Ricardian and ROT household in the periphery region. Risk sharing. Given the assumption of symmetric preferences across home and foreign households, PC*, t = PC , t . Then full risk sharing across home and foreign Ricardian households and the assumed utility function imply6

(5)

j

where Ct is aggregate consumption within household group j, ho controls the degree of habit formation in consumption and σ , ϕ > 0 .4 Ricardian households. The representative home Ricardian household's budget constraint is

PC , t Cto + Et (Qt , t +1 Dt +1) = Wt Nto + Dt − PC , t Tto + Γt .

* Cto − ho Cto−1 = Cto * − ho Cto−1

(6)

As in CGG the production side has two sectors: (i) a perfectly competitive final goods sector and (ii) a monopolistically competitive intermediate goods sector. Final goods sector. The final good Yt is a Dixit-Stiglitz composite of a continuum of intermediate goods over the unit interval (expressed in per capita) 5 As noted by Gali et al. (2007) the index z is dropped from W͠ t and Nt since all unions face a symmetric optimization problem. Given the wage firms choose employment and workers readily fulfill employment demand. It follows that, given identical productivity both ROT and Ricardian households work identical hours. 6 Under a symmetric initial steady state, which is a standard assumption in the literature, consumption is equalized across home and foreign Ricardian households. Note, however, that in the presence of ROT consumers, who can not insure against consumption risks, home and foreign aggregate consumption levels are not equal.

(7)

where ΠC , t +1 ≡ PC , t +1/ PC , t is consumer price inflation. We assume the presence of a risk-free one-period discount bond 4

(13)

3.3. Firms

Here, β is the subjective discount factor, Dt+1 is the nominal (random) payoff in period t + 1 of the portfolio purchased at t, with Qt , t +1 the corresponding stochastic discount factor, Wt is the market nominal wage, Tot is real lump-sum tax and Γt is profit income from the ownership of intermediate goods firms. The first order condition with respect to the intertemporal allocation of consumption leads to

⎛ ⎛ C o − h C o ⎞σ ⎞ o t −1 Qt , t +1 = β ⎜⎜ ⎜ to ΠC−1, t +1⎟⎟ , o⎟ ⎝ ⎝ Ct +1 − ho Ct ⎠ ⎠

(12)

σ

j

(Ct j − ho Ct −1)1− σ − 1 (N j )1+ ϕ − t , 1−σ 1+ϕ

(11)

which is a weighted average of the ROT and Ricardian households' wage income (in utility terms) net of the disutility from work. As shown by Gali et al. (2007), the optimal wage rate fulfills the first-order condition5

Household utility takes the same form as in CGG

U (Ct j , Nt j ) =

(10)

where ε > 1 is the elasticity of substitution between the differentiated labor types. The fraction of ROT and Ricardian households is uniformly distributed across labor types and the wage of each labor type is set by a labor union, with an objective function

PC , t = k −1PH1−, tγ PFγ , t = k −1PH , t Stγ ,

(9)

3.2. Wage setting

3.1. Households

Ct j = (CHj , t )1− γ (CFj , t )γ ,

(8)

Rt−1

Note that when σ = 1 (5) reduces to the log-separable utility as in GLV.

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⎛ Yt = ⎜ ⎝

∫0

1

Yt ( f )

ξ ξ −1 ⎞ ξ −1 ξ df ⎟ ,

⎠

The home government budget constraint in nominal terms is given by PC , t Tt + Btn = PH , t Gt + Rt −1 Btn−1, where Bnt denotes nominal bond issuance in period t and Tt = λTtr + (1 − λ ) Tto . Using the definition Bt ≡ Btn / PC , t , where Bt denotes bond issuance in terms of CPI-based consumption

(14)

where an intermediate good is indexed by f and ξ is the elasticity of substitution between any two differentiated goods. Cost minimization by final goods firms, for a given level of Yt, gives the demand for each good

PC , t Tt + PC , t Bt = PH , t Gt + Rt −1 PC , t −1 Bt −1

Dividing through by PC , t and slightly manipulating the right hand side terms gives

⎛ PH , t ( f ) ⎞−ξ Yt ( f ) = ⎜ ⎟ Yt , ⎝ PH , t ⎠

(15)

PH , t R B Gt + t −1 t −1 PC , t ΠC , t Rt −1 Bt −1 −γ = kSt Gt + ΠC , t

Tt + Bt =

where PH , t is given by

⎛ PH , t = ⎜ ⎝

∫0

1

1

⎞ 1− ξ PH , t ( f )1− ξ df ⎟ . ⎠

MCt = k −1Stγ W͠ t .

Note that according to Eq. (23) a decrease in the terms of trade (which implies PH , t rises relative to PC , t ), at any given level of government spending Gt, necessitates an increase in current period taxes Tt or bond issuance (a deficit) Bt. At the same time, it necessitates a decrease in foreign taxes or bond issuance, given foreign government spending, as

(17)

Tt* + Bt* = kSt1− γ Gt +

While intermediate goods firms set prices, output is demand determined according to Eq. (15), which in turn pins down labor demand. Pricing decisions are subject to Calvo-type price staggering so that in any given period a fraction θ of firms cannot reset their prices optimally. It follows that for each firm f in period t, its nominal price PH , t ( f ) is set such that PH , t ( f ) = PH0 , t if set optimally and PH , t ( f ) = PH , t −1 ( f ) otherwise. When firm f gets a chance to reset its price it does so in order to maximizes the expected lifetime profit

i =0

⎛ kS −γ G ⎞ fg Tt = G e ⎜ t e t ⎟ + fb Bt −1 ⎝ G ⎠

(18)

4. Equilibrium and linearization Goods market clearing in the home and foreign economies implies8

(1 − γ ) Yt = (1 − γ )[(1 − λ ) CHo , t + λCHr , t ] + γ [(1 − λ ) CHo *, t + λCHr *, t ] (26)

+ (1 − γ ) Gt

(19)

γYt* = (1 − γ )[(1 − λ ) CFo, t + λCFr , t ] + γ [(1 − λ ) CFo,*t + λCFr *, t ] + γGt* (27) Combining the final goods demand (3) and its foreign counterpart with Eq. (26), and remembering that the government spends on the home good only, yields Home aggregate demand

1

(20)

PC , t ((1 − γ ) Ct + γCt*) + Gt PH , t = κ −1Stγ ((1 − γ ) Ct + γCt*) + Gt

Yt =

It is straightforward to derive a symmetric set of equations for the periphery. 3.4. Fiscal policy

λ ) Cto

λCtr

(28)

λ ) Cto *

+ and Ct* = (1 − where Ct = (1 − + ond equality follows from Eq. (2). Likewise Foreign aggregate demand is given by

For simplicity we assume that the home (core) government buys only domestic output. As is standard in the literature, government spending is assumed to be exogenous. That is, debt consolidation via spending reversals, along the lines of Corsetti et al. (2010) and Corsetti and Mueller (2014), does not play a role in our analysis. To be specific, government spending Gt follows an AR(1) process

Gt = (1 − ρ) G + ρGt −1 + εt

(25)

where fg , fb > 0 . In this case, a balanced budget is where fg = 1.

where μp is steady state price markup and PH0 , t / PH , t is the optimal relative price. Price staggering among firms implies that the price level (16) can be rewritten as

PH , t = ((1 − θ )(PH0 , t )1− ξ + θPH1−, tξ−1) 1− ξ .

(24)

implying A balanced Home economy budget is where Tt = Bt=0 for all t. That is, tax revenue in terms of the CPI-based consumption bundle is equal to government spending in terms of the CPI-based consumption bundle. Let G e ≡ kS −γG . The domestic fiscal policy rule involves Tt responding to kSt−γ Gt and Bt−1 (see Corsetti et al. (2010) for a similar approach).

where the term (PH0 , t − PH , t + i MCt + i ) Yt + i ( f ) is nominal profit and θi reflects the probability that the chosen price PH0 , t still holds in period t + i . Optimal price setting gives

⎛ PH , t + i ⎞ξ (1 + μ p ) Et ∑ θ iQt , t + i Yt + i MCt + i ⎜ ⎟ ⎝ PH , t ⎠ = , ⎛ PH , t + i ⎞ξ −1 Et ∑ θ iQt , t + i Yt + i ⎜ ⎟ ⎝ PH , t ⎠

Rt −1 Bt*−1 ΠC*, t

kSt−γ Gt

∞

Et ∑ θ iQt , t + i (PH0 , t − PH , t + i MCt + i ) Yt + i ( f ),

PH , t

(23)

(16)

Intermediate goods sector. A typical firm f in the intermediate goods sector has a linear production technology Yt ( f ) = Nt ( f ). It follows that the firm's marginal cost (expressed in terms of domestic output) is MCt = Wt / PH , t , which is a function of aggregate variables only.7 For future reference it can be rewritten as

PH0 , t

(22)

Yt* = κ −1St−(1− γ ) ((1 − γ ) Ct + γCt*) + Gt*

λCtr *

and the sec-

(29)

Note that Eqs. (28) and (29) imply that the terms of trade can be written as

St =

(21)

Yt − Gt Yt* − Gt*

(30)

where 0 < ρ < 1, G is steady state government spending and εt is a zero mean i.i.d shock to government spending. 7

8 Here total domestic output is equal to the per capita domestic output Yt times the size of the domestic economy 1 − γ . The same holds for total domestic demand and total foreign demand and analogously for goods market clearing in the foreign economy.

Unlike CGG but following GLV we set τ = 0 .

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Next, linearizing the exogenous government spending, given by Eq. (21), leads to

Aggregate domestic production function under price rigidity is given by

gt = ρgt −1 + et ,

(31)

Nt = Vt Yt , 1

where et = (εt − ε )/ Y . Likewise, linearizing the government budget constraint (23) and rearranging gives the debt dynamics

with Vt ≡ ∫ (PH , t ( f )/ PH , t )−ξ df being the domestic price dispersion in the 0 intermediate goods sector. In steady state we impose symmetry across Ricardian and ROT households (C r = C o = C , C r * = C o * = C *) and assume government debt is zero. The governments use lump-sum transfers to achieve the symmetric steady state, implying that steady state taxes may differ across Ricardian and ROT consumers. Moreover in steady state the two regions are symmetric in per capita terms so that C = C * and N = N * and trade is balanced. This is a common assumption (see, e.g., Corsetti, Meier and Mueller 2010). In what follows we linearize the model around a zero inflation steady state. Small letters denote percentage deviations from steady states with the exception that bt ≡ (Bt − B )/ Y , tt ≡ (Tt − T )/ Y and gt ≡ (Gt − G )/ Y . For simplicity we assume ttr = tto = tt .9 Consumption of Ricardian households is given by

cto

bt = β −1bt −1 − tt + k (gt − γg γst ),

rt = φπ πW , t

πW , t = (1 − γ ) πH , t + γπF*, t

5. Main results Similar to a closed economy setting (e.g., Gali et al. (2007) and Furlanetto and Seneca (2009)), government spending on domestic output raises domestic demand and thus output.11 Because of nominal price rigidity, the rise in domestic output demand increases domestic employment demand and the real wage. The resulting rise in aggregate wage income raises aggregate consumption if the share of ROT consumers in the population is large enough. The presence of consumption habit persistence strengthens the rise in aggregate consumption since it dampens the fall in Ricardian household's consumption triggered by the negative wealth effect of higher lumpsum taxes accompanying higher government spending. What are the cross-border output and consumption spillover effects? Given the terms of trade, foreign output rises as domestic households increase not only domestic but also imported goods consumption. However, the rise in the domestic real wage increases domestic marginal cost and therefore the domestic price level PH , t . The former raises domestic and union-wide inflation and the latter lowers the terms of trade. The monetary authority raises the nominal interest rate in response to higher union-wide inflation, raising the real rate of interest, which in turn induce all Ricardian households to reduce current consumption. Thus the reaction of monetary policy dampens the rise in foreign consumption and output. However, the decrease in the terms of trade induces both domestic and foreign households to increase their demand for the foreign good and reduce the demand for the domestic good (expenditure switching effect). This raises foreign output, and under nominal price rigidity, foreign employment demand and the real wage. The rise in wage income leads to higher foreign aggregate consumption. Moreover, a decrease in the terms of trade leads to (given real foreign taxes and government spending on foreign goods) a foreign government surplus, as nominal tax revenues rise by more than does nominal government expenditure. The effects identified above are partial equilibrium effects. The terms of trade has general equilibrium effects because (i) a change in domestic relative to foreign consumption

(34)

(1 − λ ) (1 − h )σ σ 1 − h λ (1 − h )σ + (1 r− λ)(1 − h )σ . o o r

χr = and χo = From the risk sharing condition (13) we have

(35)

Consumption and hours aggregation yields

ct = λctr + (1 − λ ) cto ,

(36)

whereas the aggregated production function and home aggregate demand are

yt = nt ,

(37)

yt = (1 − γg )((1 − γ ) ct + γct* + γst ) + gt ,

(38)

The terms of trade is

st = (1 − γg )−1 [( yt − gt ) − ( yt* − gt*)],

(39)

Note that as in Blanchard et al. (2016) the terms of trade does not depend on monetary union monetary policy. Combining the optimal relative price and the price level leads to a new Keynesian Phillips curve relating domestic inflation to the domestic real marginal cost

πH , t = βEt πH , t +1 + δmct ,

(40)

where from Eq. (17) the marginal cost is given by ∼ + γs , mct = w t t

(41)

(46)

is the union-wide inflation rate. As remarked by Corsetti et al. (2010), the Taylor-type rule (45) provides a simple and familiar way to account for the role of monetary policy in the transmission of government spending shocks.10

(33)

*, cto − ho cto−1 = cto * − ho cto−1

(45)

where φπ > 0 and

(32)

λ (1 − h )σ σ 1 − h λ (1 − h )σ + (1 −o λ)(1 − h )σ r o r

(44)

where tt ≡ (Tt − T )/ Y , bt ≡ (Bt − B )/ Y , gt ≡ (Gt − G )/ Y . Moreover, linearization of Foreign economy equations follow analogously (see the Appendix). Finally, abstracting from the zero lower bound (ZLB), the monetary policy rule for the monetary union is given by

In a zero steady state inflation the aggregate production function is given by Y=N and optimal price setting implies MC = 1/(1 + μ p ). Moreover, from Eq. (17) MC = W͠ S γ / k . It follows that W͠ = kS −γ /[(1 + μ p )]. Imposing symmetry in prices in steady state so that S=1 implies W͠ = k /(1 + μ p ). Then the consumption of ROT households is

where γc ≡ C / Y . Wage setting follows ∼ = χ (c r − h c r ) + χ (c o − h c o ) + ϕn w t r t −1 o t −1 t r t o t

(43)

whereas linearizing the domestic fiscal rule (25) leads to

tt = fg k (gt − γg γst ) + fb bt−1,

ho 1 1 − ho = cto−1 + Et cto+1 − (rt − Et πH , t +1 − γEt Δst +1), 1 + ho 1 + ho σ (1 + ho )

∼ + n ) − γ −1 t r ctr = γc−1 W͠ (w t t c t

(42)

10 Note that as in Blanchard et al. (2016) monetary policy only affects the core and periphery through its effects on the monetary union as a whole, but does not influence the terms of trade, or the implied differences between the responses of periphery and core variables. 11 Veld (2013) calls this demand spillover.

9

GLV implicitly assume that tto = ttr = tt (see equation (C.6) of their appendix) but this does not necessarily imply Tto = Ttr . It only implies Tto − T o = Ttr − T r . In the paragraph following their Eq. (27) they say that Tr and To are appropriately chosen such that Cr = Co = C .

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foreign consumption price index (PC*, t ) rises more than the price of the foreign good (PF , t ). Since foreign government spending is at its steady state, foreign taxes need to fall so as to ensure a balanced budget. Moreover, a decrease in the terms of trade leads to (given real foreign taxes and government spending on foreign goods) foreign government surplus, as nominal government expenditure falls relative to nominal tax revenues.13 As pointed out above habit persistence plays a key role in generating positive cross-border spillovers. In order to underscore this point, Fig. 3 compares the impulse responses of selected home and foreign aggregate variables under the baseline calibration to those under no habit persistence in consumption (i.e., ho=0). The solid line shows the baseline case with ho=0.85 while the dashed line shows the case with ho=0. The main result here is that in the absence of habit persistence in consumption there are negative cross-border consumption spillovers and output spillovers are much weaker than the baseline case. For instance, whereas foreign consumption rises by about 0.2 percent under the baseline case it falls by about 0.45 percent in the absence of habit persistence. The intuition for this result is that in the absence of habit persistence Ricardian households cut their consumption more strongly given the negative wealth effect implied by the rise in government spending. How do our results compare with those of the literature? As can be seen from Fig. 1 in our baseline calibration periphery output and consumption rise on impact by 0.6 and 0.2 percent respectively. Blanchard et al. (2016) find that spillovers from core to periphery in the Euro area are that periphery output and consumption rise by up to 1 and 0.6 percent, respectively, depending on the presence of a liquidity trap and a recession. Thus, there domestic and spillover effects are larger than ours although our result holds that the former are larger than the latter. In Corsetti et al. (2010)—whose model unlike ours features capital accumulation and flexible exchange rates—spillovers from the US to rest of the OECD indicate that foreign output and consumption rise by about 0.15 and 0.05 percent, respectively. Thus, there spillovers are much smaller than ours. Similar results were obtained by Corsetti and Mueller (2014) regarding international spillovers of fiscal policy from the US to the Euro area and the UK. We stress that their setup also features capital goods and flexible exchange rates which makes results somewhat difficult to compare with ours. Perhaps what can be said is that qualitative results in the theoretical literature are robust with respect to the exchange rate regime and the presence of investment. Regarding the empirical literature (which is truly data based unlike calibrated theoretical DSGE models), in the empirical part of Corsetti and Mueller (2014) it is reported that an increase in US government spending by one percent of US GDP raises output by about 0.5 percent in the Euro area and 1 percent in the UK. Finally, using a VAR model of the EU Beetsma et al. (2005) find that a public spending shock of 1 percent of GDP in Germany raises GDP in the rest of the EU by 0.23 percent over two years. So, here the magnitude of the spillover is in line with ours.

affects domestic relative to foreign aggregate demand, output and thus the terms of trade. (ii) deficits and surpluses affect future taxes and thus consumption and aggregate demand. As is standard in the business cycle literature, the model is calibrated to a quarterly frequency. Some of the parameter values are within ranges that are commonly used in the literature: the subjective discount factor β is set to 0.99, the risk aversion parameter σ is set to one, which is consistent with balanced growth. We set ϕ, the inverse of the Frisch elasticity of labor supply, to one as in Gali (2008).12 As in Erceg and Linde (2013) we set the region size parameter γ to 1/3, reflecting the relative share of euro area periphery GDP in total euro area GDP. Following Furlanetto and Seneca (2009) we set the consumption smoothing parameter ho to 0.85. As in Corsetti et al. (2010) the share of ROT consumers in both countries (λ and λ*) is set to 1/3 while the ratio of government spending to domestic output in steady state is set to 0.2. The tax rule parameters fb and fg are set, respectively, to 0.33 and 0.1 (Gali et al. (2007) and Furlanetto and Seneca (2009)). We also illustrate the effect of a larger share of foreign ROT consumers so as to capture the notion that financing constraints in the euro area periphery (the foreign economy in the model) were much tighter since the onset of the global financial crisis as well as the euro area sovereign debt crisis. Finally, in line with Corsetti et al. (2010) the Calvo parameter θ is set to 0.75, the elasticity of substitution among differentiated goods and labor services, ξ and ϵ, are set to 11, implying a steady state markup of 1.1, and the monetary policy parameter φπ is set to 1.5. Fig. 1 shows impulse responses of home and foreign aggregate variables to an exogenous expansion in home government expenditure. The immediate result of this expansion of demand is an increase in domestic output. The latter increases domestic employment and the real wage (not shown). The increase in the home real wage increases consumption of ROT households, whilst the consumption of home and foreign Ricardian households drops because of the familiar crowding out (wealth) effect. In line with closed economy models (e.g., Gali et al. (2007) and Furlanetto and Seneca (2009)) the former effect dominates leading to an increase in aggregate home consumption. In our open economy setup an increase in aggregate home consumption leads to higher import demand and therefore higher foreign output. Higher home and foreign real wages imply that domestic and foreign marginal costs and hence inflation rates rise. Home inflation rises faster than foreign inflation which leads to a decrease in the terms of trade. The latter is associated with a deterioration of the domestic trade balance, which is associated with a positive spillover on foreign demand and hence higher foreign output. The implied increased demand for foreign labour raises foreign real wages which leads to a positive spillover effect on consumption driven by foreign ROT consumers. Fig. 2 shows the impulse responses of taxes and government deficits under the baseline calibration. After an initial increase, government spending (shown by the dashed line) decreases monotonically towards its steady-state level. This is in contrast to the spending reversal analysed in Corsetti et al. (2010) and Corsetti and Mueller (2014), in which government spending rises above its steady-state initially but then undershoots its steady-steady level before eventually returning to its steady-state. In our case, both taxes and deficits rise initially but follow different dynamics—deficits fall smoothly while taxes follow a humpshaped response. The continued rise in taxes reflects the stabilizing role of taxes—they respond to government debt. Moreover, given that the foreign government follows a balanced budget, foreign taxes decline initially, though by much lower than the rise in domestic taxes. As remarked above a balanced budget for the foreign economy is where PC*, t Tt* = PF , t G*, G* = γg Y *. The decline in the terms of trade (lower St) means that the

6. Further sensitivity analysis In this section we undertake further sensitivity analysis with respect to key model parameters. Share of ROT Consumers. An important question is whether the shares of liquidity-constrained households in the periphery and core countries matter for the magnitude of the spillover effects. Fig. 4 shows impulse responses of selected home and foreign aggregate variables to an expansion in home government expenditure under alternative values of λ*. The solid line shows the baseline case (λ* = 1/3), the 13 Note that the foreign country has a balanced budget (the idea is the periphery government cannot borrow gt* = 0 ). From the tax rule one can see that when fg=1 and given gt* = 0 , tt* changes one-for-one with the CPI-based government spending kγg (1 − γ ) st . As can be seen in the figure foreign taxes decline since the terms of trade st declines (it costs less to maintain the steady state level of foreign government spending).

12 By contrast, Corsetti et al. (2010) choose ϕ = 2 while Corsetti and Mueller (2014) choose ϕ = 3. Our choice is more conservative, as we find that cross-border spillover effects are quantitatively much larger under these alternative values of ϕ. Those results are available upon request.

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Fig. 1. Impulse responses to a positive domestic government spending shock under the baseline calibration.

Fig. 2. Impulse responses of taxes and government deficits to a positive domestic government spending shock under the baseline calibration.

By similar reasoning, the lower (higher) is the share of ROT consumers in the Core the smaller (higher) is the domestic consumption crowding-in and thus the smaller (larger) are the spillover effects (see top left panel of Fig. 5). But note that the baseline value of 1/3 for λ is likely to underestimate the general tightening of credit constraints since the financial crisis. Our conjecture is that during the sovereign debt crisis, stricter credit conditions meant that the share of credit constrained households had risen in general, more so in the periphery. The Fiscal Policy Rule. Recent empirical and theoretical evidence has suggested that the size of fiscal multipliers may be time varying being notably higher in bad times and lower in good times (see Blanchard et al. (2016)). We perform sensitivity analyses on the parameters fg and fb (the periphery government has a balanced budget as it cannot borrow) in the fiscal policy rule. The top middle and right panels of Fig. 5 show that cross-border spillovers are smaller on impact, the larger is fg; it is larger the larger is fb. The reason is that a stronger response to government spending dampens the rise on impact

dashed line shows the case with a higher fraction of foreign ROT consumers (λ* = 0.5) and the dash-dotted line shows the case with a lower fraction of foreign ROT consumers (λ* = 0.2 ). As pointed out above a larger share of foreign ROT consumers is meant to capture the notion that financing constraints in the euro area periphery (the foreign economy in the model) were much tighter since the onset of the global financial crisis. The main result here is that the spillover effects on foreign output and consumption are larger (smaller) when the fraction of foreign ROT is higher (smaller). For instance, on impact foreign consumption rises by about 0.2 percent under the baseline calibration while it rises by about 0.5 percent under λ* = 0.5 and by less than 0.1 percent under λ* = 0.2 . The intuition for this result is that a larger share of the rise in foreign wage income ends up boosting foreign consumption and output, as ROT consumers consume all their income. Note also that the effects of the shock on domestic output are amplified, while those on the terms of trade and the trade balance are dampened the higher is λ*. 7

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Fig. 3. Impulse responses to a positive domestic government spending shock (baseline vs no habit persistence).

Fig. 4. Impulse responses to a positive domestic government spending shock. The effect of larger λ*.

Size of the Core. In the baseline calibration, the size of the periphery is 1/3, this implies that the core economies represent a larger part of the euro area than the periphery. A share of 2/3 for the core implicitly includes Germany, France, the Netherlands, Belgium, Austria, Finland

of ROT consumption, implying weaker cross-border spillovers. By contrast, since taxes respond to past debt levels, a larger response coefficient does not affect taxes on impact but implies expectation of a stronger rise in future taxes.

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Fig. 5. The impact effect of government spending on periphery output (solid line) and consumption (dashed line); sensitivity to key parameters.

We find that a core fiscal expansion is a locomotive policy as it increases both home and foreign output and consumption. These results are in line with empirical evidence supporting crowding in of output of both instigating and recipient countries. Accordingly, fiscal policy seems an effective tool for boosting economic activity in the Eurozone.14 A domestic fiscal expansion increases core output which results in higher employment, inflation and real wages. The latter increases consumption of rule of thumb households and—if there is a critical mass of those—aggregate consumption. Higher core consumption combined with a decrease in the terms of trade leads to higher import demand, a domestic trade deficit, and therefore higher output in the periphery. Foreign aggregate consumption also increases as higher foreign output pushes up the demand for labour, real wages and thereby consumption of foreign rule of thumb consumers. The effect on foreign consumption is larger, the larger the share of credit constrained consumers in the periphery. We think that latter scenario is plausible as financing constraints in the periphery have tightened since the onset of the global financial crisis. Our model has abstracted from a number of features that would seem to be useful extensions for future research. First, the model does not include capital which is arguably an important omission.15 Although our framework does not require spending reversals or debt consolidation to capture the fiscal facts it would be interesting to see how inclusion of the latter would affect our results. Further, we abstract from liquidity traps which may amplify domestic and cross-border effects. Finally, it would be interesting to investigate whether our results are robust to the exchange rate regime and study fiscal policy transmission under flexible exchange rates and an exchange rate peg.

and Ireland in the core EMU countries. However, it can be argued that not all of these countries have fiscal space. Hence, we report results based on a smaller core, i.e. considering values of γ up to 2/3. The lower left panel of Fig. 5 shows that there is still crowding-in but it is smaller compared to the baseline. Monetary Policy Rule. We also consider the case of a more or less hawkish central bank. As can be seen from the lower middle panel of Fig. 5, the spillover effects are larger the less hawkish is the central bank—as interest rates are raised less aggressively real interest rates go up by less, thereby increasing the spillover. The Degree of Nominal Rigidity. An important parameter which affects the rise in inflation - and hence the response of the central bank—is the degree of nominal rigidity. The higher is the degree of nominal rigidity the flatter is the domestic Phillips curve—i.e., the less sensitive is inflation to aggregate demand. On the one hand, the smaller is the rise in domestic inflation in response to government spending the smaller is the decline in the terms of trade and thus the smaller the spillover effects. On the other hand, the smaller is the rise in domestic inflation the smaller is the rise in the nominal and real interest rate. Moreover, the less aggressive is monetary policy the less the real interest rate rises to a given rise in inflation. In both of these cases, a given rise in government spending raises output and consumption by more and leads to larger spillover effects. As can be seen from the lower right panel of Fig. 5, the latter effect dominates so that the spillover effects rise with the degree of nominal rigidity. 7. Concluding remarks We have analysed the domestic and spillover effects of a fiscal expansion in a two-region new Keynesian model of a monetary union.

14 However, it is not clear whether Germany would really accept to increase its public spending and lose competitiveness in order to stimulate the Euro area economy given the euro area constraints. 15 For an analysis of fiscal consolidations and spillovers in the Euro area based on a model that includes investment see Veld (2013).

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Appendix Foreign economy aggregate relationships

1 * + Et cto+1 *) (ho cto−1 1 + ho 1 − ho − (rt − Et πF , t +1 + (1 − γ ) Et Δst +1) σ (1 + ho )

ct*o =

(47)

∼* + n *r ) − γ −1 t * ct*r = q−1 (w t t c t

(48)

σ ∼* = * ) + ϕnto * (cto * − ho cto−1 w t 1 − ho

(49)

σ * ) + ϕntr * (ctr * − hr ctr−1 1 − hr

(50)

∼* = w t

ct* = λct*r + (1 − λ ) ct*o nt* =

λnt*r

+ (1 −

(51)

λ ) nt*o

(52)

πF , t = βEt πF , t +1 + δmct*

(53)

∼* − (1 − γ ) s mct* = w t t

(54)

yt* = nt*

(55)

bt* =

β −1bt*−1

− tt* + k (gt* + (1 − γ ) γg st )

(56)

* tt* = fg k (gt* + γg (1 − γ ) st ) + fb bt−1

(57)

gt* = ρg gt*−1 + eg*, t

(58)

In the limiting case of ho = hr = 0 , the system of linearized equations can be simplified to give the analog of GLV Eq. (38)

ct = Et ct +1 − σ∼−1 (φπ πW , t − Et πH , t +1) + Θs Et (st +1 − st ) − Θn Et (nt +1 − nt ) + Θτ fg (Et (gt +1 − gt ) − γg γEt (st +1 − st )) + Θτ fb (bt − bt −1)

(59)

ct* = Et ct*+1 − σ∼−1 (φπ πW , t − Et πF , t +1) − Θs* Et (st +1 − st ) − Θn Et (nt*+1 − nt*) + Θτ fg γg (1 − γ ) Et (st +1 − st ) + Θτ fb (bt* − bt*−1)

(60)

nt = (1 − γg )((1 − γ ) ct + γct* + γst ) + gt

(61)

nt* = (1 − γg )((1 − γ ) ct + γct* − (1 − γ ) st )

(62)

πH , t = βEt πH , t +1 + δ (σct + ϕnt + γst )

(63)

bt =

(β −1

− fb ) bt −1 + (1 − fg ) k (gt − γg γst )

(64)

πF , t = βEt πF , t +1 + δ (σct* + ϕnt* − (1 − γ ) st )

(65)

bt* = (β −1 − fb ) bt*−1 + (1 − fg ) k ((1 − γ ) γg st )

(66)

gt = ρg gt −1 + eg, t

(67)

πW , t = (1 − γ ) πH , t + γπF , t

(68)

where

σ∼−1 Θs Θn Θτ

≡ ≡ ≡ ≡

(1 − λ )(qϕ + σ ) σ −1Γ , σ∼−1γ , λ (1 + ϕ) ϕΓ , λqϕΓ / γc,

and Γ ≡ (qϕ + σ − σλ (1 + ϕ))−1. Note that for σ∼−1 to be positive we require Γ > 0 implying λ < (σ + qϕ)/(σ (1 + ϕ)).

a Rise in Core Fiscal Spending Help the Periphery?. NBER Macroeconomics Annual, Volume 31 (eds.: Martin Eichenbaum and Jonathan A. Parker), University of Chicago Press. Clarida, R., Gali, J., Gertler, M., 2002. A simple framework for international monetary policy analysis. J. Monet. Econ. 49, 879–904. Coenen, G., Erceg, C., Freedman, C., Furceri, D., Kumhof, M., Lalonde, R., Laxton, D., Linde, J., Mourougane, A., Muir, D., Mursula, S., de Resende, C., Roberts, J., Roeger, W., Snudden, S., Trabandt, M., in't Veld, J., 2012. Effects of fiscal stimulus in

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