On the (In)effectiveness of Fiscal Devaluations in a Monetary Union

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. On the (In)effectiveness of Fiscal Devaluations in a Monetary Union Anna Lipinska and Leopold von Thadden 2012-71 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

On the (In)effectiveness of Fiscal Devaluations in a Monetary Union∗ Anna Lipin´ska†, Leopold von Thadden‡ This version: August 31, 2012 Abstract This paper explores the fiscal devaluation hypothesis in a model of a monetary union characterised by national fiscal policies and supranational monetary policy. We show that a unilateral tax shift towards indirect taxes in one of the countries produces small but non-negligible long run effects on output and consumption within and between the two countries only when international financialmarketsareperfectlyintegrated. Incontrasttotheexistingliterature, wefindthatshortrun effects are not always amplified by nominal wage rigidities. We document also how short-run effects of the tax shift depend on the choice of the inflation index stabilized by the central bank and on whether the tax shift is anticipated. Keywords: Fiscal regimes, Monetary policy, Currency union JEL classification numbers: E61, E63, F42. ∗Comments on an early draft by Kosuke Aoki, Bianca De Paoli, Philipp Harms, Jan IntVeld, Christophe Kamps, Werner Roeger, Jean-Pierre Vidal and seminar participants at the Royal Economic Society Meeting 2009 (University of Surrey), the European Economic Association Meeting 2009 (Barcelona), the European Central Bank, DG ECFIN (Brussels), the University of Aachen and the Brussels Tax Forum 2012 are gratefully acknowledged. This draft is an extended and largely improved version of the ECB Working Paper no. 1097: Monetary and Fiscal Policy Aspects of Indirect Tax Changes in a Monetary Union. †Federal Reserve Board, Monetary Affairs, United States; e-mail: Anna.Lipinska@frb.gov. ‡EuropeanCentralBank,DivisionMonetaryPolicyStrategy(currentlyonleave)andUniversityofMainz,Germany. e-mail: thadden@uni-mainz.de. Theviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyreflect those of the Federal Reserve Board or the European Central Bank.

1 Introduction It is well-known that the structures of taxation differ significantly between European countries. One important source of cross-country differences is the importance of indirect taxes in the tax systems of specificcountries. Theshareofindirecttaxesintotaltaxation(includingsocialsecuritycontributions) stands for the European Union as a whole at about 35%. Yet, the dispersion of this share across countries is substantial, ranging from about 50% in Bulgaria and Cyprus to about 30% in Belgium, Germany, and the Czech Republic.1 Differences in taxation structures are of particular relevance for countries belonging to the euro area which share an irrevocably fixed nominal exchange rate, a feature which makes it elusive to affect the competitiveness of economies through nominal exchange rate adjustments. This feature is at the heart of ongoing debates of whether those euro area countries which need to improve their competitiveness may mimic the effects of the devaluation of the exchange rate through an appropriate use of fiscal instruments, in particular, by rebalancing the tax structure away from direct (production-based) taxes towards indirect (consumption-based) taxes.2 This argument (which is commonly labelled as the ‘fiscal devaluation hypothesis’) relies largely on the idea that in an open economy context there seems to be scope for balanced-budget tax reforms which shift the tax incidence towards ‘immobile’ consumers and at the same time, through lower direct taxes (or social security contributions), make tradeable production more competitive. Motivated by this observation, our paper explores quantitatively the relevance of the fiscal devaluation hypothesis in a two-country model of a monetary union with endogenously derived terms of trade. Our main finding is that the long-run effects of such a tax shift on output and consumption within and between the two countries depend significantly on the degree of financial integration between the two countries. Moreover, short-run dynamics are shown to depend on the choice of the inflation index stabilised by the central bank, on whether the tax shift is anticipated or not, and on the degree of nominal wage stickiness. Quantitatively, the calibrated model version indicates that only in the case of complete financial integration there is scope for small but non-negligible long-run spillovers between 1Thenumbersrefertotheyear2006andaretakenfromthedetaileddescriptionofEuropeantaxationstructuresfrom across-countryperspectivepublishedinEuropeanCommission(2008). Notwithstandingthisvariationacrosscountries, indirect taxes have become the main source of tax revenues in the EU (amounting in 2006 to 13.9% of GDP), followed bydirecttaxes(13.5%ofGDP)andsocialsecuritycontributions(12.5%ofGDP).Sincetheonsetofthefinancialcrisis theroleofindirecttaxesasthemainrevenuesourceintheEUhasfurtherincreased(seeEuropeanCommission(2012)). 2In recent years a number of euro area countries have decided to give indirect taxes (relative to taxes on labour), at least at the margin, a more prominent role in their tax systems. A prominent example is the substantial increase in German VAT by 3pp in 2007 which was partly offset by reduced contributions to the unemployment insurance scheme. More recently, France has embarked on a similar agenda under the label of a ‘social VAT’. For a broad discussion of recentpolicyinitiativesandproposalsthatadvocateashiftoftaxsystemstowardsindirecttaxes,bothattheEuropean level and within individual member countries, see European Commission (2006), European Commission (2008). 1

countries. Under incomplete financial integration spillovers are negligible such that the quantitative effects of the tax shift are similar to a closed economy (which we characterise as a limiting case of our general set-up).3 In other words, under incomplete financial integration the fiscal devaluation hypothesis has no bite. The model, which is similar to Benigno (2004), Duarte and Wolman (2008), and Ferrero (2009), is kept deliberately small in order to allow for a transparent discussion of a broad range of monetary and fiscal policy aspects which emerge if one member country of a monetary union unilaterally shifts its tax structure from direct towards indirect taxes. Key features of the model are as follows. To allow for non-trivial price-setting decisions of firms, production in both countries is characterised by Dixit-Stiglitz-type monopolistic competition. Monetary policy has a meaningful stabilisation role because of nominal price rigidities, in line with New Keynesian tradition (see Woodford (2003)). Moreover, monetary policy is supranational and follows a Taylor-type feedback rule, targeting unionwidevariables. Bycontrast, fiscalpolicyiscountry-specific, andgovernmentexpendituresandinterest payments on outstanding government debt can be financed through a linear (and non-discriminating) consumption tax or a linear tax on labour income (with labour being the only factor of production). Fiscal policymakers follow feedback rules which anchor the economies at country-specific target levels of government debt, similar to Leeper (1991), Schmitt-Grohe and Uribe (2007) and Leith and von Thadden (2008). Each country is specialised in the production of a composite tradeable good which is consumed in both countries. Firms set identical producer prices in both countries and the terms of trade (i.e. the producer price ratio between the two composite tradeable goods) depend in general equilibrium, inter alia, on the structure of taxes and government expenditures in the two countries. The two countries may be of different relative size, measured in terms of the share of goods produced in a country, holding constant the total number of goods produced in the monetary union. Finally, we assumethatthemonetaryunioncanbecharacterisedbythreedistinctdegreesoffinancialintegration. Inparticular,weassumethathouseholdsineachcountryhaveaccesstostate-contingentrisklessbonds (complete markets) or have access to non state-contingent bonds (incomplete markets) or have no access at all to international bonds (financial autarky). Within this broad set-up, we assume that the ‘home’ country changes its long-run fiscal priorities and decidesonceandforall, atunchangedgovernmentexpenditures, topermanentlyincreaseitsconsumption tax. In line with the fiscal devaluation hypothesis, the additional consumption tax revenues are 3As argued below, our model is too stylised to address closed-economy aspects in detail. Nevertheless, the closedeconomyversionoffersanimportantbenchmarkforthediscussionoftheopeneconomyaspectswhicharecentralforthe assessment of the fiscal devaluation hypothesis. 2

used to reduce the labour tax such that the home country’s long-run level of real government debt stays unchanged, consistent with the target level. The ‘foreign’ country does not have actively any intention to change its taxes and government spending levels, but, to keep its own level of real debt on target, it reacts passively by adjusting its labour tax. In sum, the consumption tax changes only in the home country, while labour taxes adjust endogenously in both countries. Asalreadystressed,ouranalysissuggests,ingeneral,thatthe(in-)effectivenessofthefiscaldevaluation hypothesisdependssignificantlyonthedegreeoffinancialintegrationbetweenthetwocountries. From a more detailed perspective, four findings are worth summarising. First, long-run outcomes depend strongly on the degree of financial integration, since the wealth effects associated with the shift in the tax structure tend to be very different, depending on whether financial markets are complete or not. As a result, under complete markets the increase of home output is about four times larger than under incomplete markets. At the same time, because of risk sharing, complete markets ensure a significant decline of home consumption, while foreign consumption increases. Under incomplete markets, in the absence of risk sharing, consumption patterns are markedly different: home consumption increases mildly, in line with the dampened increase in home output, while foreign consumption and output are virtually unaffected. Second, our analysis indicates that the strength of the terms of trade channel on home variables decreases in the relative size of the home country. In other words, as the home country becomes small, this strengthens the effects of the fiscal devaluation channel on home consumption and output levels, indicating that under Dixit-Stiglitz monopolistic competition the price setting power of a country does not vanish as a country becomes small. Third, from a short-run perspective, all effects (within and between countries) are shown to depend on whether i) the central bank’s objective is specified in terms of pre-tax or after-tax consumer price inflation, ii) the tax shift is anticipated by the private sector or not, and iii) the degree of nominal wage stickiness.4 For the particular combination of an inflation objective in terms of pre-tax consumer prices, a non-anticipated tax shift, and flexible nominal wages our analysis reveals that the central bank may not face any aggregate (pre-tax) inflationary pressure (because of offsetting deflationary and inflationary impact effects in the home and foreign country, respectively) such that union-wide monetary policy remains neutral with respect to the fiscal reform in the home country. However, departures from these particular assumptions lead to less symmetric constellations in which the feedback of union-wide monetary policy matters for the pattern of short-run dynamics in both countries. Fourth, relative to a world 4For a detailed discussion of aspects related to the appropriate inflation indices stabilised by central banks, see, for example, Camba-Mendez (2003). In the particular context of our tax shift experiment one may find it suggestive to think of pre-tax inflation as ‘core inflation’, while after-tax inflation corresponds to ‘headline’ inflation. 3

with flexible nominal wages, the short-run effects of sticky nominal wages depend crucially on the degree of financial integration. In particular, we establish the novel finding that sticky wages amplify the effects of the tax shift in the short run only when the degree of financial integration is not perfect. OurpaperisrelatedtoarecentpaperbyFarhietal.(2012)whoestablishanumberofexactequivalence results between nominal exchange rate devaluations and fiscal devaluations. Farhi et al. (2012) show that the particular combinations of the fiscal instruments which replicate the real allocations attained under a nominal exchange rate devaluation depend sensitively on features like alternative pricing assumptions and the degree of asset market incompleteness. The focus of our paper is somewhat different as we study under what assumptions, if at all, the fiscal reform undertaken by a member country of a monetary union can lead to quantitatively relevant effects. Thus, our interest lies more in evaluating the possible success of a fiscal devaluation under a number of well-defined assumptions (while we take for granted in all cases the proximity to a corresponding nominal devaluation stressed by Farhi et al. (2012)). Given this focus, our paper can be used to see why the long-run effectiveness of the fiscal devaluation channel is subject to a number of well-known caveats. In particular, several authors, including Feldstein and Krugman (1990), Calmfors (1998) and recently de Mooij and Keen (2012), argue that an across-the-board increase in consumption taxes (which do not discriminate between domestic and imported consumption goods and are rebated on exports), accompanied by a balanced-budget cut in labour taxes, tends to have no long-run effects on trade patterns if changes in domestic goods and factor prices undo the effects of the tax changes. Similarly, studies in the spirit of Poterba et al. (1986) stress that short-run effects of a fiscal devaluation that are driven by nominal rigidities will disappear in the long run (i.e. under flexible prices). These results hold for the special case of a small open economy which acts as a price-taker in international output markets. Our paper, by contrast, exploresthe quantitativerelevanceof thefiscaldevaluationchannel under theassumption that the terms of trade are endogenous (i.e. they react to changes in the tax structure). It is worth stressing that our analysis is exclusively concerned with positive implications of fiscal reforms undertaken in the home country. Hence, we do not address strategic aspects of optimal monetary and fiscal policies in monetary unions, as explored, for example, by Lombardo and Sutherland (2004), Beetsma and Jensen (2005), Ferrero (2009), and Gali and Monacelli (2008). In particular, the beggar-thy-neighbour-typeoutputeffectsofthefiscaldevaluationhypothesiswouldbecounteractedin (cooperative or non-cooperative) optimal policy settings in which both countries are allowed to choose optimal actions. In line with our positive approach, Roeger and in’t Veld (2006) and European Commission (2008), using a richer model structure, assess quantitatively the effects of unilateral tax shifts 4

towards indirect taxation within EMU under imperfect financial integration. The order of magnitude of the long-run output effects is similar to our findings. The role of the terms of trade is less important and, differently from the focus of our paper, these studies do not address in analytical detail the openeconomy dimension of unilateral tax shifts under alternative asset market assumptions. More closely related to our monetary union set-up, Duarte and Wolman (2008) explore the ability of national fiscal policies to reduce inflation differentials with respect to union-wide average inflation. However, the paper focuses on the design of systematic fiscal stabilisation rules in a business cycle context (and not on the effects of lasting changes in tax structures which are the focus of our paper).5 Coenen et al. (2008) use a large scale two-country model to investigate systematic effects of tax reforms for the euro area as a whole, focusing on tax-related labour market distortions in the euro area relative to the US economy. However, the focus is on international spillovers, while, by construction, there is no scope for spillovers between euro area countries. Ourpaperisstructuredasfollows. Section2summarisesthemodel. Section3presentsthebenchmark calibration. Sections 4 and 5 discuss long-run and short-run effects, respectively, of a tax shift in the home country, in line with the fiscal devaluation hypothesis. Section 6 concludes. Technical material as well as various impulse response figures are displayed in the Appendix. 2 The model We consider a small-scale model of a monetary union which consists of two countries, similar to Benigno (2004), Duarte and Wolman (2008), and Ferrero (2009). For convenience we label these two countries as ‘home’ and ‘foreign’. Fiscal policy is country-specific. By contrast, monetary policy is supranational and the common central bank targets union-wide variables. The two economies are structurallyidentical,butweallowfordifferencesinsize. Thedescriptionofthemodeleconomy,unless explicitly needed, is kept short since most of the assumed New Keynesian open economy features are standard (see, in particular, Obstfeld and Rogoff (1996)). We treat in the following the home country as the representative one to avoid duplication of notation whenever possible. 5Canzonerietal.(2004)developamonetaryunionmodelwhichallowsforcountriesofdifferentsizeandasymmetric fiscal positions, in line with stylised features of euro area countries. The paper argues that fiscal shocks, compared with other shocks, are relatively unimportant for the explanation of inflation differentials in the euro area. Differently from our paper, however, the paper does not investigate systematic effects of country-specific changes in fiscal policy. 5

2.1 Consumers Themonetaryunionconsistsofameasureoneofconsumersofwhich[0,n)belongtothehomecountry and [n,1] to the foreign country. Each of the two countries produces a composite tradeable good. The twocompositegoodsconsistofdifferentiatedhometradeablegoods, indexedontheinterval[0,n),and foreign tradeable goods, indexed on the interval [n,1], respectively. Hence, the parameter n measures the size of the home country both in terms of population size and in terms of the share of produced goods. Home and foreign consumers are infinitely lived. In each country, consumers demand a mix of home and foreign produced tradeable goods which enter an aggregate consumption index as described below. Let C and L denote private consumption and the labour supply of the representative home t t consumer in period t. As of period t = 0, this consumer maximises the following utility function (cid:40) ∞ (cid:41) (cid:88) maxE βt[U (C )−V (L )] , (1) 0 t t t=0 where E denotes the expectation conditional on the information set at date t = 0, β is the intertem- 0 poral discount factor (with 0 < β < 1) and U and V denote the flow utilities from consumption and labour, assumed to be additively separable.6 The home consumption index C , made up of home t tradeable goods (C ) and foreign tradeable goods (C ), is given by H,t F,t (cid:20) (cid:21) φ 1 φ−1 1 φ−1 φ−1 C t = νφC H φ ,t +(1−ν)φC F, φ t , where φ > 0 denotes the elasticity of substitution between home and foreign goods and ν represents the share of home goods in the basket of home consumers if the prices of C and C are equal. H,t F,t Moreover, let ν = 1−(1−n)λ, where λ ∈ (0,1] denotes the degree of openness of the home country. Similarly we write the consumption bundle of the representative foreign consumer as C∗ = (cid:20) ν ∗ φ 1 ∗C φ∗ φ − ∗ 1 +(1−ν∗)φ 1 ∗C φ∗ φ − ∗ 1 (cid:21) φ∗ φ − ∗ 1 , t H∗,t F∗,t where ν∗ = nλ∗ relates to the share of home goods in the basket of foreign consumers and λ∗ ∈ (0,1] denotesthedegreeofopennessoftheforeigneconomy. Inthebenchmarkcalibrationreportedbelowwe allow for home bias, i.e. home consumers demand relatively more home goods than foreign consumers 6InordertohaveawelldefinedmaximisationproblemweassumethatU istwicecontinuouslydifferentiable,increasing and concave in C , while V is twice continuously differentiable, increasing and convex in L . For the specific functional t t forms, see Section 2.7.1. 6

and vice versa, implying ν > ν∗. The variables C and C (where j = H,H∗ and j∗ = F,F∗) are j j∗ composite goods which bundle together the underlying individual tradeable goods according to  (cid:18) (cid:19)1 (cid:90) n  σ− σ 1  (cid:18) (cid:19) 1 (cid:90) 1  σ∗ σ − ∗ 1 1 σ σ−1 1 σ∗ σ∗−1 C j,t =  c j,t (h) σ dh , C j∗,t =  c j∗,t (f) σ∗ df , n 1−n 0 n where σ > 1, σ∗ > 1 denote the constant elasticities of substitution between the components in each country. Consistent with these aggregators, the consumption-based price indices in the two countries are given by (cid:104) (cid:105) 1 P = νP1−φ+(1−ν)P1−φ 1−φ (2) t H,t F,t (cid:104) (cid:105) 1 P∗ = ν∗P1−φ∗ +(1−ν∗)P1−φ∗ 1−φ∗ , (3) t H∗,t F∗,t  (cid:18) (cid:19)(cid:90) n  1− 1 σ  (cid:18) (cid:19)(cid:90) 1  1− 1 σ∗ 1 1 P j,t =  p j,t (h)1−σdh , P j∗,t =  p j∗,t (f)1−σ∗ df . n 1−n 0 n Firmsareassumedtochargeidenticalproducerpricesinthetwocountries(p (h) = p (h) ≡ p (h) H,t H∗,t t and p (f) = p (f) ≡ p (f)), i.e. the law of one price holds at the producer price level such that F,t F∗,t t P∗ P H,t = P H∗,t and P F,t = P F∗,t . Let the real exchange rate be defined as RS t = P t t . Then, in the presence of home bias, purchasing power parity does not hold (P (cid:54)= P∗) and the real exchange rate t t may fluctuate over time. Moreover, we define the terms of trade as T = PF,t. t PH,t We assume that the monetary union can be characterised by three distinct degrees of financial integration. In particular, we assume that households in each country have access to state-contingent riskless bonds (complete markets) or have access to non state-contingent bonds (incomplete markets) or have no access at all to international bonds (financial autarky). Apart from that, consumers also hold riskless nominal government bonds. Moreover, consumers own the firms of their own country. In sum, the representative consumer of the home country faces in period t the budget constraint: n (cid:82) Π (h)dh t (cid:0) 1+τC(cid:1) P C +D +B ≤ D + (cid:0) 1−τL(cid:1) W L +0 +R B +R D +P AC , t t t H,t H,t t t H,t t n t−1 H,t−1 t−1 H,t−1 t t (4) where W , τL, and τC denote the nominal wage, the labour tax rate and the consumption tax rate, H,t t t respectively. Π (h) represents the nominal profit of home firm h, while B denotes one–period t H,t−1 home government bonds (purchased in period t−1 and redeemed in period t), measured in per-capita 7

terms. Moreover, R = 1+i denotes the nominal interest factor paid on these bonds in period t, t−1 t−1 respectively.7 D represents holdings of nominal one–period international bonds, possibly state- H,t−1 contingent, purchased in period t−1 and redeemed in period t with the nominal interest rate factor R . In the case of incomplete markets, we follow Schmitt-Grohe and Uribe (2003) and introduce t−1 bond adjustment costs (AC ) in order to guarantee stationarity of the current account (i.e. AC = 0 t t ∀t for complete markets and financial autarky). The adjustment cost is defined by the following expression: χ (cid:18) D (cid:19)2 H,t AC = −d , t H 2 P t where d is the steady-state holding of the bond by the home consumers. The adjustment cost H implies that households in both economies have a strong incentive to return to their initial position and creditors face lower nominal interest rate than debtors. Finally, in the case of financial autarky households do not have access to any international bonds, thus D = 0 ∀t. H,t A similar budget constraint applies for consumers in the foreign country. In both countries consumers face no-Ponzi restrictions. For simplicity, we assume that both economies operate at the cashless limit. In sum, the optimisation problem of the home consumer amounts to choose paths of private consumption (C ), labour supply (L ), international bonds (D ) and government bonds (B ) in t t H,t+1 H,t order to maximise (1) subject to the budget constraint (4), ∀t (cid:62) 0. Thesolutiontothisproblemischaracterisedbyanumberofwell-knownfirst-orderconditions,describing optimal consumer behaviour. The optimal labour supply satisfies the static first-order condition: V (L ) 1−τL W L t = t H,t , (5) U (C ) 1+τC P C t t t where (1−τL)/(1+τC) captures the relevant tax wedge for the labour-consumption trade-off. t t Let G and G denote the (per capita) levels of composite government expenditures in the two H,t F,t countries. As concerns the composition of these goods in terms of individual components, we assume perfect home bias for government expenditures. Combined with the optimal consumption behaviour, this implies that the demand for generic home and foreign tradeable goods can be written as: (cid:20) p (h) (cid:21)−σ (cid:40) (cid:20) P (cid:21)−φ (cid:18) P (cid:19)−φ∗ ν∗(1−n) (cid:41) (cid:20) p (h) (cid:21)−σ y (h) = t H,t νC +G + H,t C∗ = t Y , (6) t P P t H,t P∗ n t P H,t H,t t t H,t 7One could assume, more generally, that home consumers can also hold riskless foreign government bonds B F,t−1 (paying the same nominal equilibrium interest factor R ), and vice versa, as considered by Duarte and Wolman t−1 (2008). Given the supply of government bonds introduced below, this would affect none of our results. 8

(cid:20) p (f) (cid:21)−σ∗(cid:40) (cid:20) P (cid:21)−φ (1−ν)n (cid:20) P (cid:21)−φ∗ (cid:41) (cid:20) p (f) (cid:21)−σ∗ y (f) = t F,t C + F,t (1−ν∗)C∗+G = t Y , (7) t P P 1−n t P∗ t F,t P F,t F,t t t F,t where Y and Y denote per capita levels of composite home and foreign output, respectively. H,t F,t 2.2 Firms Output markets are subject to monopolistic competition, while labour markets (with labour being the only production input) are perfectively competitive within each of the two countries. Labour is immobile between the two countries. Consider the home country. Let A denote the home level H,t of labour productivity (assumed, for simplicity, to be identical across home sectors). Output of the representative home firm h is produced according to the linear production function: y (h) = A L (h), (8) t H,t t where L (h) denotes the labour input used by firm h. Notice that competitive equilibria (as further t discussedbelow)satisfyL = (cid:0)1(cid:1)(cid:82)n L (h)dh,sincebothworkersandfirmsareofmeasuren.Nominal t n 0 t wages are taken as given by the representative firm such that nominal marginal costs are identical for all home firms, i.e.: W H,t MC = . H,t A H,t The price-setting of firms is in line with Calvo (1983). Each period a fraction (1−α) of firms has the chance to reset prices in an optimal manner, implying that P follows the law of motion: H,t P1−σ = α(P )1−σ +(1−α)(p (h))1−σ, H,t H,t−1 (cid:101)t where p (h) denotes the optimal price chosen by home firms in period t which have the chance to (cid:101)t adjust prices. The optimal price p (h) solves ∀t (cid:62) 0 the maximisation problem: (cid:101)t ∞ (cid:88) maxE (α)sQ [p (h)−MC ]y (h) t t,t+s t H,t+s t:t+s pt(h) s=0 (cid:18) p (h) (cid:19)−σ t subject to y (h) = Y , t:t+s H,t+s P H,t+s wherey (h)denotesthedemandforgoodhattime(t+s),conditionalonkeepingthepricep (h)for t:t+s t s periods fixed at the level chosen at time t. The solution of the maximisation problem is characterised 9

by the first-order condition (cid:16) (cid:17)σ E (cid:80)∞ (αβ)sU (C )MCr PH,t+s Y PH,t+s p (cid:101)t (h) = σ t s=0 C t+s H,t+sPt+s(1+τ t C +s ) H,t+s PH,t , P H,t σ−1 E (cid:80)∞ (αβ)sU (C ) PH,t+s Y (cid:16) PH,t+s (cid:17)σ−1 t s=0 C t+s Pt+s(1+τ t C +s ) H,t+s PH,t where MCr = MC /P , H,t H,t H,t represents real marginal costs in period t, expressed in terms of home producer prices. Notice that under flexible price setting the optimal price in the representative home sector is set according to the well-known static mark-up equation: pFlex(h) σ (cid:101)t = MCr . (9) P σ−1 H,t H,t Analogous expressions can be derived for the foreign country. 2.3 Fiscal policies Thefiscalauthorityinthehomecountryissuesone-periodnominaldebt(B )andtaxeshomelabour H,t income at rate τL and home private consumption expenditures at rate τC, respectively. Revenues are t t spent on homegovernment expenditures G (exhibiting perfect home bias) andinterestpayments on H,t outstanding debt, issued in the previous period.8 Hence, the home country’s flow government budget constraint in nominal terms (and on a per capita basis) is given by: B = R B −s , H,t t−1 H,t−1 H,t with the nominal primary surplus (s ) being defined as: H,t s = τLW L +τCP C −P G . H,t t H,t t t t t H,t H,t 8For simplicity, it is assumed that government expenditures do not enter the preferences of households. Yet, none of our results would change if government expenditures entered preferences in an additively separable manner. 10

To rewrite these two equations in real terms let Rr = R P /P denote the real interest factor H,t−1 t−1 t−1 t and use Br = B /P , sr = s /P and w = W /P , leading to: H,t H,t t H,t H,t t H,t H,t t Br = Rr Br −sr , H,t H,t−1 H,t−1 H,t P sr = τLw L +τCC − H,t G , H,t t H,t t t t P H,t t with analogous equations holding for the foreign country. Notice that the primary surplus depends on three separate fiscal instruments (τL,τC,G ), allowing, in principle, for a large range of fiscal t t H,t scenarios to be studied. 2.3.1 Benchmark specification of fiscal policy We use this broad set-up to explore the effects of permanent and unilateral changes in the home consumptiontaxonhomeandforeignvariablesinanumberofdistinctgeneralequilibriumscenarios. Our benchmarkscenarioexhibitstwoparticularassumptions, inlinewiththefiscaldevaluationhypothesis. First, in response to the change in the home consumption tax by ∆τC both fiscal authorities keep their budgets permanently balanced in real terms, ensuring that the real debt levels in both countries remain constant in all periods, i.e. Br = Br and Br = Br ∀ t. For given target levels of real debt H,t H F,t F this implies that real primary surpluses are given by: sr,BB = (Rr −1)Br and sr,BB = (Rr −1)Br. (10) H,t H,t−1 H F,t F,t−1 F Second, our benchmark assumes that budget balance is achieved by adjustments in labour taxes. In other words, in response to the permanent change in τC by ∆τC, we treat τL and τL∗ as the residual t t instrumentswhichensurethat(10)issatisfied, takingasgivenG andG (whichareheldconstantat H F their steady-state values). These two assumptions imply for τL and τL∗ the following law of motions: t t τLBB = (R H r ,t−1 −1)B H r −(τC +∆τC)C t + P P H t ,tG H and τL∗BB = (R F r ,t−1 −1)B F r −τC∗C t ∗+ P P F t ∗ ,tG F . t w L t w L∗ H,t t F,t t (11) 2.4 Degree of financial integration As stated above, we allow for three different degrees of financial integration. First, in the case of complete asset markets households in both countries have access to state-contingent bonds. This 11

assumption implies that the marginal rates of substitution in consumption are equalised between countries in all states and at all times in nominal terms (after tax) such that the following condition (derived from Euler equations for home and foreign consumers) holds: U (C∗ )P 1+τC U (C )P∗ 1+τC∗ C t+1 t+1 t+1 = C t+1 t+1 t+1. U (C∗) P 1+τC U (C ) P∗ 1+τC∗ C t t t C t t t After choosing appropriately the distribution of initial wealth, one obtains: U (C ) P 1+τC C t = υ t t , (12) U (C∗) P∗1+τC∗ C t t t where the parameter υ > 0 depends on the initial wealth distribution, measured in terms of aftertax consumer prices. This relationship implies that in all states and at all times there is a strong correlation between home and foreign private consumption. In particular, in the absence of home bias and assuming identical consumption tax rates, per capita consumption levels will be equalised in both countries. Second, in the case of incomplete markets households have access to non state-contingent bonds. This assumptionimpliesthatmarginalratesofsubstitutioninconsumptionareequalisedbetweencountries only on average. Intertemporal optimality of bond holdings leads to the following Euler equation for home and foreign consumers: (cid:32) (cid:33) U (C )P (1+τC) βR E C t+1 t t t = 1. (13) t U C (C t )P t+1 (1+τ t C +1 ) 1+χ( D P H t ,t −d H ) Third, in the case of financial autarky households do not have access to any international borrowing. This implies that the value of domestic production has to be equal to the sum of public and private consumption: C = p (Y −G ). (14) t H,t H,t H,t 2.5 Monetary policy Because of nominal price stickiness, there is a stabilisation role for monetary policy. The central bank runs a common monetary policy for the two countries, responding only to aggregate union-wide 12

variables. To this end, the central bank follows a New Keynesian interest rate feedback rule: (cid:32) Y U,t (cid:33)µyu (cid:18) π U,t (cid:19)µπu 1+(cid:101)i t = Yn π (1+i), (15) U,t U where i denotes the steady-state nominal interest rate, while µ and µ denote the feedback coeffiyu πu cients associated with the union-wide output gap (with Y and Yn denoting the current union-wide U,t U,t output level and the natural union-wide output level under flexible prices, respectively) and pre-tax union-wide consumer price inflation (π ) in deviation from the target rate π , normalised to π = 1. U,t U U Moreover, to allow for interest rate smoothing we assume: (1+i t ) = (1+(cid:101)i t )1−κ(1+i t−1 )κ, whereκ ∈ (0,1)capturesthedegreeofinterestratesmoothing. Union-widerealoutputY isobtained U,t from the corresponding values of union-wide nominal output: nP Y +(1−n)P Y = P Y ,, H,t H,t F,t F,t U,t U,t and the deflator P corresponds to the pre-tax union-wide consumer price level (i.e. net of consump- U,t tion taxes), with P = s P +(1−s )P∗, where s = nPC denotes the steady-state share U,t C t C t C nPC+(1−n)P∗C∗ of the home country in union-wide nominal consumption. Because of π = P /P the central U,t U,t U,t−1 bank’s inflation objective in our benchmark specification is based on the index P which measures U,t pre-tax consumer prices. However, this assumption is not without alternatives, as further discussed below in Section 5.2. 2.6 Price levels and real wages: some definitions 2.6.1 Price level definitions This subsection summarises compactly the different price level definitions (and short-cuts) which will be used in the remainder of this paper: (i) P : producer price level of the (composite) home produced good, for short: home producer price H,t level. (ii) P : consumer price level prevailing in the home country net of the home consumption tax, for t short: pre-tax home consumer price level. (iii) P : union-wide consumer price level net of consumption taxes, for short: pre-tax union-wide U,t 13

consumer price level, with P = s P + (1 − s )P∗, s = nPC and the corresponding U,t C t C t C nPC+(1−n)P∗C∗ inflation measure π = P /P . U,t U,t U,t−1 (iv) (1+τC)P : consumer price level prevailing in the home country including home consumption t t taxes, for short: after-tax home consumer price level. (v) PτC : union-wide consumer price level including consumption taxes of both countries, for short: U,t after-tax union-wide consumer price level, with PτC = sτC(1+τC)P +(1−sτC)(1+τC∗)P∗, sτC = U,t C t t C t t C n(1+τC)PC and the corresponding inflation measure πτC = PτC/PτC . n(1+τC)PC+(1−n)(1+τC∗)P∗C∗ U,t U,t U,t−1 2.6.2 Real wage definitions As indicated by the notation introduced above, we consider symmetric equilibria across households and firms. To characterise such equilibria in a compact manner, it is convenient to introduce: W 1−τL W wp = H,t and wc = t H,t , H,t P H,t 1+τC P H,t t t where wp and wc denote the real producer and real consumer wage in the home country, respec- H,t H,t tively. Since the producer real wage is deflated by P it is directly linked to real marginal costs, H,t i.e.: wp MCr = H,t , H,t A H,t implying that wp , wc , and MCr are related to each other according to: H,t H,t H,t 1−τL PH 1−τL PH wc = t t wp = t t A MCr . (16) H,t 1+τC P H,t 1+τC P H,t H,t t t t t 2.7 General equilibrium In general equilibrium, the decisions of households and firms need to be individually optimal and consistent with each other at the aggregate level, taking as given the behaviour of monetary and fiscal policymakers and the evolution of exogenous shock processes. In principle, the model could be used to analyse the effects of a broad range of shocks. However, we focus exclusively on the fiscal experiments mentioned above, i.e. we abstract from productivity shocks (and assume, for simplicity, A = A = 1,∀t (cid:62) 0) and refrain from the specification of any other shock processes. H,t F,t Our analysis of competitive equilibria proceeds in two steps. First, for a given vector of constant policy variables, we solve for the unique symmetric steady-state equilibrium, as discussed in the next subsection. Second, starting out from this initial steady state, we consider a permanent change in 14

τC by ∆τC and discuss in separate sections long- and short-run responses of the model economy to this change. The long-run analysis compares the new and the initial steady state from a comparative statics perspective, while the short-run analysis addresses properties of the transitory dynamics, using a log-linearised version of the model (which is summarised in the Appendix C). 2.7.1 Steady states Let variables without time index denote steady-state values. For simple tractability, we consider from now onwards the specific functional forms U (C) = 1 C1−ρ and V (L) = 1 L1+η, with ρ > 0 1−ρ 1+η and η > 0 denoting the inverse of the intertemporal elasticity of substitution in consumption and of the Frisch elasticity of labour supply, respectively. Notice that (9) implies MCr = σ−1. Moreover, H σ p(h) p(f) β = 1/(1 + i) = 1/(1 + r) because of π = 1. By symmetry, = = 1. Finally, we define U PH PF PH ≡ p and PF ≡ p . P H P∗ F Then, using (8) and (16), the steady-state counterparts of (2), (3), (12) or (14)9, (5), (6) and (7) for both countries can be compactly summarised as the following system of nine equations in the nine unknowns Y , Y , C, C∗, p , p , τL, τL∗,RS, taking as given constant values of the fiscal variables H F H F Br , Br, τC, τC∗, G , G : H F H F ν∗(1−n) Y = p−φνC +G +p−φ∗ RSφ∗ C∗ (17) H H H H n (1−ν)n Y = (p RS)−φ C +G +(p )−φ∗ (1−ν∗)C∗ (18) F F F F 1−n 1−τL σ−1 (Y )η = C−ρ p (19) H 1+τC σ H 1−τL∗ σ∗−1 (Y )η∗ = (C∗)−ρ∗ p (20) F 1+τC∗ σ∗ F 1 = νp1−φ+(1−ν)(p RS)1−φ (21) H F 1 = ν∗(p RS−1)1−φ∗ +(1−ν∗)p1−φ∗ (22) H F (cid:20) (cid:21) β β σ−1 Br = sr = τL p Y +τCC −p G (23) H 1−β H 1−β σ H H H H β β (cid:20) σ∗−1 (cid:21) Br = sr = τL∗ p Y +τC∗C∗−p G (24) F 1−β F 1−β σ∗ F F F F C−ρ 1+τC = υRS−1 orC = p (Y −G ) (25) (C∗)−ρ∗ 1+τC∗ H H H Below we solve numerically a calibrated version of this system for the nine unknowns, and, using 9Depending on the degree of financial integration. 15

these numbers, it is straightforward to back out the steady-state values of the remaining endogenous variables. In particular, the steady-state terms of trade can be calculated from T = RSp /p . F H 3 Calibration of the benchmark monetary union with countries of equal size and symmetric home bias This section summarises our benchmark calibration which considers a monetary union in which the two countries are assumed to have equal size (n = 0.5) and a symmetric home bias because of λ = 0.5. We calibrate the model using aggregate euro area data, with a quarterly frequency. Both countries are characterised by identical structural parameters (as summarised in Table 1), which are chosen in line with related literature. The intertemporal elasticity of substitution is set to 0.5 (i.e. ρ = 2), as in Stockman and Tesar (1995). The labour supply elasticity is chosen to be 0.4 (i.e. η = 2.5), striking a balance between micro data evidence and macro aspects, in line with the DSGE literature concerned with the euro area (e.g. Smets and Wouters (2003), Altissimo et al. (2011), Coenen et al. (2010), Christiano et al. (2005)). The discount factor equals β = 0.99, implying an annual interest rate of around four percent. As in Rotemberg and Woodford (1997) and Altissimo et al. (2011), the elasticity of substitution between differentiated goods within countries is assumed to be σ = 7.88, consistent with a steady-state markup of 15%. The elasticity of substitution between home and foreign goods is set as φ = 1.5 (as in Altissimo et al. (2011) and Chari et al. (2002)). Since this intratemporal elasticity of substitution is higher than the intertemporal elasticity of substitution (i.e. φ > 1), home and foreign goods are substitutes in the preferences of agents. Like Duarte and Wolman ρ (2008), the degree of openness in both countries equals λ = 0.5, implying an import share of 25% in the consumption basket. The Calvo parameter, which fixes the share of firms that cannot change prices every quarter, is assumed to be α = 0.85, implying that the average duration between price adjustments is 11 months. This value is somewhat higher than the estimated values found in micro studies for euro area countries, but in line with the values chosen by Smets and Wouters (2003) and Coenen et al. (2010). The portfolio cost adjustment parameter, χ, is set to 0.001 which corresponds to an average annual interest rate premium of 0.405%, in line with Schmitt-Grohe and Uribe (2003). Moreover, we assume that the steady-state value of bond holdings is zero, i.e. d = 0. H 16

Table 1: Structural parameters Size of the (home) country n 0.5 Inverse of the intertemporal elasticity of substitution ρ 2 Inverse of the labour supply elasticity η 2.5 Discount factor β 0.99 Elasticity of substitution between goods within countries σ 7.88 Elasticity of substitution between home and foreign goods φ 1.5 Degree of openness λ 0.5 Degree of nominal price stickiness α 0.85 Portfolio cost adjustment χ 0.001 Table 2 summarises the fiscal policy values which were used to calibrate the initial steady state, assumed to be identical for both countries. The consumption and labour tax rates as well as the debt-output ratio have been set at values which are roughly in line with average euro area data (see Table 6 in the Appendix A) and consistent with related literature. Notice that the assumed value of the debt-output ratio corresponds to a value of 66% in annualised terms, while the government expenditure share is residually determined by the steady-state government budget constraint.10 Table 2: Fiscal characteristics of the initial steady state Consumption tax rate τC = τC∗ 0.15 Labour tax rate τL = τL∗ 0.30 Share of government expenditures in output d = GH = d = GF 0.33 GH YH GF YF Debt-output ratio b = BH = b = BF 2.64 H PHYH F PFYF Table 3 summarises the parameter values used for the monetary policy rule. Following the DSGE literature concerned with the euro area, the rule is characterised by a large smoothing parameter, i.e. the coefficient on the lagged interest rate is set equal to κ = 0.95. Moreover, the benchmark response coefficient to inflation is set equal to µ = 2, while we assume that monetary policy does not respond πu to output fluctuations (µ = 0).11 Notice that the benchmark balanced-budget rule (11) does not yu require any additional fiscal parameter. 10A more detailed matching of all aspects of fiscal data would require a richer specification of government activities which is beyond the scope of this paper. In particular, our model does not allow for public transfers and investment, implyingthattheresiduallydeterminedshareofgovernmentexpendituresistoohighcomparedwiththedata. Moreover, the labour tax rate is too low if one looks at the combined numbers for labour taxes and social contribution rates (as reported, for example, in Coenen et al. (2010)). For numerical choices similar to ours in small scale DSGE models, see Ferrero (2009) and Canzoneri et al. (2004). 11For a discussion of this assumption, see Section 5.1. 17

Table 3: Parameters of monetary policy rule Response parameter of monetary policy to union output gap µ 0 yu Response parameter of monetary policy to union inflation µ 2 πu Smoothing parameter κ 0.95 4 Long-run effects of a permanent shift in the tax structure of the home country from direct towards indirect taxes This section focuses on long-run effects of a permanent shift in the tax structure of a union member country under different degrees of financial integration, abstracting from the transitory dynamics induced by the short-run monetary and fiscal feedbacks. Specifically, to address the fiscal devaluation hypothesis, it is assumed that the home country permanently increases its consumption tax by 1 pp from15%to16%(i.e. ∆τC = 0.01)andusestheadditionalrevenuestofinanceapermanentcutinthe labour tax rate such that the home country’s long-run level of real government debt stays unchanged, holding constant government expenditures. The foreign country does not have actively any intention to change its tax structure, but, to keep its own level of real debt on target, it reacts passively by adjusting its labour tax rate at unchanged government expenditures. In sum, the consumption tax changes only in the home country, while labour taxes adjust endogenously in both countries, in line with (11). Table 4 summarises the long-run effects for key real variables of the two countries. The table covers thebenchmark‘monetaryunionwithcountriesofequalsizeandsymmetrichomebias’(assummarised in Section 3), but also a number of alternative monetary unions specifications. These specifications differ from the benchmark, ceteris paribus, in terms of i) the size of the two countries (captured by n) and ii) the strength of the home bias (captured by λ), while otherwise the calibration is identical to Section 3. To allow for variation along these two dimensions facilitates the identification of the core general equilibrium channels which are of relevance for the benchmark monetary union. All these specifications have in common that the driving force behind the shift in the tax structure of the home country from direct towards indirect taxes is the following clear-cut difference between the two considered tax instruments: The home consumption tax affects the entire consumption of the home country, irrespective of whether the consumption goods have been produced at home or in the foreign country. By contrast, the home labour tax affects the entire production of the home country, 18

irrespective of whether the produced output is sold at home or in the foreign country. Hence, the change in the tax structure of the home country from direct to indirect taxes tends to favour home production relative to home consumption. Since the terms of trade are endogenously determined, this feature has significant implications for the two countries in our model. However, to establish a clear reference point, we discuss first the degenerate case of a monetary union which consists only of the home economy, i.e. by considering n → 1 our discussion starts out from a closed economy scenario. 4.1 Closed economy For the special case of a closed economy (column 1 in Table 4), the two taxes have very similar steady-state effects under the particular assumptions of our set-up, in which labour is the only input for production and all tax schedules are linear. This finding can be readily reconciled with wellknown channels as summarised, for example, in Layard et al. (1996), Bovenberg (2006), and European Commission(2008). Specifically,inorderforarevenue-neutralshiftfromlabourtaxestoindirecttaxes tobeabletoincreaseoutputandemploymentitiscrucialthatthisshiftreducestheeffectivetaxburden on labour. Given our simplifying assumption of linear tax schedules, this in turn requires that the shareofnon-labourincome(related,inparticular,tonon-indexedunemploymentbenefitsandpensions as well as capital income) is sufficiently large.12 However, under our modelling assumptions (which abstract from unemployment, life-cycle behaviour and capital accumulation) the only alternatives to labour income are pure profit income and interest income on predetermined bond holdings, and both of these items are quantitatively small. Because of these features, there is, by construction, little scope for significant real effects of the considered change in the tax structure. Under our calibration, a permanent increase of the consumption tax by 1 pp from 15% to 16% leads to a decline in the labour tax by 0.76 pp from 30% to 29.24%. The implied increase in output (which is proportional to employment) and consumption by 0.05% indicates that under our modelling assumptions in the special scenario of a closed economy the consumption tax is just slightly less distortionary than the labour tax. 12In this spirit, benefits from redirecting the tax structure towards consumption taxes are substantially larger in fullfledged dynamic settings with capital accumulation. In such environments, consumption taxes act implicitly as efficient taxes on the inelastically supplied, predetermined capital stock, as discussed and quantitatively explored in Atkinson and Stiglitz (1972), Cooley and Hansen (1992), Mendoza and Tesar (1998), and Coleman (2000). 19

Table 4: Permanent shift in the home tax structure - complete markets, % changes Closed economy Monetary union benchmark Home bias − no home bias (λ = 1) home bias (λ = 0.5) Country size n = 1 n = 0.75 n = 0.5 n = 0.1 n = 0.5 Change in τC in pp 1 1 1 1 1 Change in τL in pp −0.76 −0.75 −0.73 −0.71 −0.74 Terms of trade − 0.21 0.21 0.21 0.38 Home consumption 0.04 −0.07 −0.19 −0.38 −0.14 Home output 0.05 0.12 0.18 0.29 0.15 Home consumer real wage 0.21 0.13 0.06 −0.06 0.08 Foreign consumption − 0.36 0.25 0.06 0.20 Foreign output − −0.20 −0.13 −0.03 −0.11 Foreign consumer real wage − 0.21 0.13 0.02 0.11 Home loss −0.01 0.16 0.33 0.61 0.27 Foreign loss − −0.52 −0.35 −0.07 −0.28 Home and Foreign losses are in % of the initial steady state consumption. 4.2 Monetary union with countries of equal size (no home bias) In a monetary union of two equally sized countries with no home bias (column 3 in Table 4), the shift in the tax structure of the home country towards indirect taxation has more significant effects on real variables, affecting both countries. Importantly, both the sign and the size of spillovers in a monetary union depend on the assumed degree of financial integration. In that respect, our results are in line with Baxter and Crucini (1995), whofindthattheextentoffinancialintegrationiscentraltotheinternationaltransmissionmechanism of persistent shocks. In particular, the wealth effects associated with the shift in the tax structure tend to be very different, depending on whether financial markets are complete or not. First, we address the transmission mechanism of the tax shift under complete markets. Under this assumption, both home and foreign consumers own risky claims to home and foreign output. The shift in the tax structure of the home country lowers the tax burden on home production. As a result there is an increase in home production (and, hence, also home labour supply). Because of risk sharing the proceeds of the additional home production are not reserved for home consumers. Foreign consumers, through risk sharing, experience a positive wealth effect, inducing an increase in foreign consumption and a decline in foreign output. By contrast, the home country experiences a negative wealth effect, and the increase in home output is accompanied by a fall in home consumption, leading to a welfare loss of the home country. Moreover, home terms of trade depreciate significantly. This 20

channel supports the reallocation of output from the foreign to the home country. In sum, risk sharing resulting from perfect financial integration drives a certain wedge between consumption and production in the two countries. In absolute terms, the effects are small, but not negligible, as evidenced by the terms of trade increase by 0.21%. This terms of trade effect (which is at the heart of the fiscal devaluation hypothesis) ensures that home output increases by 0.18% (which is about four times the effect of the closed economy), while home consumption decreases by 0.19% (i.e. the risk sharing effect dominates the consumption increase reported for the closed economy). Moreover, with foreign output decreasing by 0.13% and foreign consumption increasing by 0.25%, the risk sharing generates limited, but non-negligible spillovers. Second, we analyse the transmission mechanism under incomplete markets. In such a situation, home consumers are the sole owners of risky claims to their output. Since the tax shift is assumed to be permanent foreign consumers have no ability to support higher consumption via borrowing.13 This implies that consumption is essentially determined by the output response in either country. As summarised in Table 5 the wealth effect in the home country is of opposite sign, ensuring that under incomplete markets all endogenous variables differ significantly from the complete markets case. In particular, homeconsumptionincreasesasaresultofthepositivewealtheffect. Itisworthnotingthat thestrengthofthiswealtheffectdependsonthepermanentcharacterofthetaxshift.14 Moreover, the increase in home output is significantly dampened (reflecting that home labour supply is subject to oppositeeffectsfromthewealthchannelandthesignificantriseinthehomewagerate). Thesechanges inhomevariablesareaccompaniedbyasmalltermsoftradeincrease,supportinganincreaseinforeign consumptionandadecreaseinforeignoutput. Quantitatively, however, theeffectsonforeignvariables are very small, implying that under incomplete markets, in the absence of risk sharing, spillovers are negligible. Hence, our model predicts that under incomplete markets the quantitative effects of the permanent tax shift are very similar to the one in the closed economy (compare column 1 in Table 4 and column 2 in Table 5). Notice that according to Farhi et al. (2012) our tax shift experiment is equivalent to a nominal exchange rate devaluation only when markets are incomplete, ie exactly when this policy is not effective.15 13This implies that in the case of permanent shocks reactions under incomplete markets are equivalent to those in financial autarky. 14Ifthetaxshiftwastemporarythenforeignconsumerscouldengageinborrowingandthusinsurethemselvesagainst the tax shift. 15Under complete markets, Farhi et al. (2012) achieve the exact equivalence between a nominal devaluation and a devaluation through fiscal instruments by a simultaneous reduction in the labour tax and an increase in the VAT tax which has to be accompanied by a decrease in the consumption tax and an increase in the income tax. 21

Table 5: Permanent shift in the home tax structure - complete markets vs incomplete markets Complete markets Financial autarky Change in τC in pp 1 1 Change in τL in pp −0.73 −0.76 Terms of trade 0.21 0.04 Home consumption −0.19 0.03 Home output 0.18 0.05 Home consumer real wage 0.07 0.20 Foreign consumption 0.24 0.01 Foreign output −0.13 −0.01 Foreign consumer real wage 0.15 0.02 Home loss 0.33 0.01 Foreign loss −0.35 −0.02 Comparison for the symmetric no home bias case. 4.3 Monetary unions with countries of different size (no home bias) Theresultsestablishedsofarcanbegeneralisedifonelooksatmonetaryunionsconsistingofcountries of different size (and no home bias). It is worth stressing that under incomplete markets the effects of the tax shift are virtually unaffected by the relative size of the home country (see Table 7 in Appendix B). Hence, in this subsection we restrict our attention to the complete markets case. Columns 2 and 4 in Table 4 report results for a ‘large’ home country (n = 0.75) and a ‘small’ home country (n = 0.1). Notice that the long-run change in the terms of trade is independent of the size of the two countries. Moreover, it is straightforward to verify that all the other long-run effects discussed so far are a monotonic function of the size of the two countries. Hence, the reasoning given so far can be extended to two more general and symmetric conclusions. As concerns the home country, the magnitude of the terms of trade related effects on production, consumption and the real consumer wage decreases in the size of the home country, i.e. the leverage of a change in the home tax structure on home variables is largest in the case of a small home country. In other words, this finding indicates that under Dixit-Stiglitz-type monopolistic competition the price setting power of a country does not vanish as the country becomes small, differing thereby from the textbook case of a small open economy, as discussed in Feldstein and Krugman (1990). Similarly, as concerns the foreign country, the magnitude of the terms of trade related effects on production, consumption and the real consumer wagedecreasesinthesizeoftheforeigncountry, i.e. theleverageofachangeinthehometaxstructure on foreign variables is largest in the case of a small foreign country. These numerical findings reflect a robust pattern of our model economy. To substantiate this claim, it 22

is instructive to analyse key equations which come from a first-order approximation of the equilibrium conditionsofthemodel. AsderivedinAppendixC.3,onecanshowthatinthecaseofcompletemarkets changes in the terms of trade do not directly depend on changes in consumption taxes. Instead, they are entirely driven by changes in labour tax rates:16 1 T(cid:98)t = 1+ηφ(d +d ) (wL∗ τ (cid:98)t L∗−wLτ (cid:98)t L). (26) C C∗ Becauseoftheassumptionofconstantproductivitylevels, thehomerealproducerwagestaysconstant in the long run. By contrast, the home real consumer wage varies, depending on the changes in the two tax rates as well as in the terms of trade: ωp = 0, (cid:98)H,t ω (cid:98)H c ,t = −(1−n)T(cid:98)t −wCτ (cid:98)t C −wLτ (cid:98)t L. While the change in the tax structure has a priori an ambiguous effect on the home real consumer wage, Table 4 shows that for the special case of a closed economy the net effect is positive. As one moves from this limiting scenario to ‘proper’ monetary unions, the terms of trade effect becomes increasingly important for the home real consumer wage, and home consumers are most strongly hurt in the case of a small home economy (i.e. n being small). Extending this reasoning, the long-run effects for home consumption and output can also be decomposed into changes in the two tax rates and the terms of trade, i.e.: C(cid:98)t = −(1−n) 1 η + (d ηφ + (d d C + ) d + C∗ ρ ) T(cid:98)t − η(d 1+ +d η ρ d C ) ∗ +ρ wCτ (cid:98)t C − η(d + 1 d )+ρ wLτ (cid:98)t L (27) C C∗ C C∗ C C∗ φ(d +d ) C C∗ Y(cid:98)H,t = (1−n)(ρφ−1) T(cid:98)t (28) ηφ(d +d )+ρφ C C∗ d d +d − C wCτC − C C∗ wLτL. η(d +d )+ρ (cid:98)t η(d +d )+ρ (cid:98)t C C∗ C C∗ Equations (27) and (28) reveal that the terms of trade effects on C(cid:98)t and Y(cid:98)H,t are largest in the case of a small home economy. Moreover, the partial effects of T(cid:98), τ (cid:98)t C, and τ (cid:98)t L on home consumption have the same sign structure as established for the home real consumer wage. By contrast, the effect of 16The following equations use wC = 1+ τC τC , wL = 1− τL τL , wC∗ = 1+ τC τC ∗ ∗ , wL∗ = 1− τL τL ∗ ∗ , d C = Y n H C, d C∗ = (1− Y n F )C∗ . 23

T(cid:98) on home output is of opposite sign (i.e. positive) whenever ρφ > 1, in line with our calibration. Hence, home output increases in the terms of trade if home and foreign goods are substitutes in the preferences of agents, as discussed in Corsetti and Pesenti (2001) and Tille (2001).17 It should be stressed once more that these results heavily depend on the assumption of market completeness. In the case of incomplete markets one can show that the terms of trade depend not only on labour taxes but also on consumption taxes: T(cid:98)t = γ fa (wL∗ τ (cid:98)t L∗−wLτ (cid:98)t L−wCτ (cid:98)t C), (29) where γ is defined in the Appendix C.3. As a result, under incomplete markets the implied change fa in the terms of trade is much smaller than in the case of complete markets. This is in line with the opposite wealth effects under complete and incomplete markets. 4.4 Benchmark monetary union with countries of equal size and symmetric home bias Buildingontheseinsightsitisstraightforwardtoseehowtheresultschangeifoneconsidersamonetary union with countries of equal size and symmetric home bias in consumption patterns, in line with the calibration in Section 3. Since under incomplete markets the effects of the tax shift are virtually unaffected by the existence of a home bias of a country (see Table 7 in Appendix B) we summarise only the complete markets case. As one can infer from the last column in Table 4, the assumption of home bias implies that the real exchange rate is no longer constant over time. Compared with column 3, this feature dampens the long-run effects on home consumption and home output as well as the spillover effects on foreign consumption and foreign output. In other words, the assumption of home bias ensures that both economies are less exposed to the terms of trade related effects of the considered change in the tax structure of the home economy. Quantitatively, however, this dampening effect is negligible, i.e. the increase in home output (by 0.15%) and foreign consumption (by 0.20%) as well as the decrease in 17Evidently,C(cid:98)t andY(cid:98)H,t canbeentirelyexpressedasafunctionoftax-relatedtermsifoneuses(26)in(27)and(28), asshownintheAppendixC.3. However,tounderstandthespecialroleplayedbythetermsoftrade,(27)and(28)offer more intuitive representations. Moreover, corresponding patterns can be established for the long-run effects on foreign variables. In particular, the foreign real consumer wage can be decomposed as follows: ω (cid:98)F c ,t =nT(cid:98)t −wC∗ τ (cid:98)t C∗ −wL∗ τ (cid:98)t L∗ , implying that the terms-of-trade effect on the foreign real consumer wage is of opposite sign (i.e. positive), and it can be shown that the terms-of-trade effects on foreign consumption and foreign output are also of opposite sign. 24

home consumption (by 0.14%) and foreign output (by 0.11%) are only marginally smaller than in the absence of home bias. 5 Short-run effects of a permanent shift in the tax structure of the home country from direct towards indirect taxes Reflecting the assumption of nominal rigidities, the model implies that monetary policy is non-neutral in the short run. Importantly, since monetary policy reacts to union-wide developments there is scope for short-run interactions between the two countries which go beyond the long-run spillovers identified inSection4. Tocharacterisecorefeaturesoftheshort-rundynamicsinatractablemanner,thisSection proceeds as follows. Section 5.1 summarises the short-run dynamics of the benchmark specification introduced above under complete and incomplete markets. We report then, as a robustness exercise, how these dynamics change under three distinct experiments, each relaxing a different characteristic feature of the benchmark. Section 5.2 considers short-run dynamics which result from the use of a different target index of monetary policy, holding the other features of the Taylor rule constant. In particular, Section 5.2 discusses how the benchmark results of Section 5.1 change if monetary policy targets after-tax (i.e. ‘headline’) rather than pre-tax (i.e. ‘core’) union-wide consumer price inflation. Section 5.3 discusses how the benchmark results of Section 5.1 change if the change in the tax structure is no longer modelled as a genuine surprise, but rather as a policy which is announced aheadandthereforeanticipatedbytheprivatesector. Finally, Section5.4assumesthatnominalwages are no longer flexible but sticky in the short run. 5.1 Benchmark monetary union with countries of equal size and symmetric home bias This subsection complements Subsection 4.4 and summarises main characteristics of the transitional dynamics triggered by the unilateral shift in the tax structure of the home economy. It is worth noting at the outset that, as concerns the different cases of financial integration, the only substantial difference can be seen in the response of home and foreign consumption (see Figures 1- 3), in line with the long-run findings discussed in the previous section. For the other endogenous variables, like outputandthetermsoftrade,theimpulseresponsesarequalitativelyofsimilarshape,notwithstanding their quantitative differences. In all cases, short-run adjustments leave core union-wide CPI inflation dynamicsunaffected. Thisimpliesthatthehomecountrycanimplementitsreformofthetaxstructure 25

without triggering a reaction of the common monetary policy. As to be inferred from Figures 1- 3, the logic underlying this result can be summarised as follows.18 Irrespective of the degree of financial integration,nominalpricestickinessensuresthatthetermsoftradeincreaserelativelyslowlyovertime before reaching the new long-run level after about 20 quarters. Corresponding to this slow change in the terms of trade, on impact home output increases less than in the long run while foreign output is higher in the short run than in the long run. The short-run response of home consumer real wages is smaller than in the long run. This implies that producer real wages (which are equal to the real marginal cost) will decline on impact. With the dynamics of home producer prices being driven by the New-Keynesian Phillips curve: π (cid:98)H,t = k H M(cid:100)C r H,t +βE t π (cid:98)H,t+1 with: M(cid:100)C r H,t = w (cid:98)H p ,t , thisimpliesthatthechangeinthetaxstructureexertsonimpactadeflationaryeffectonhomeproducer prices. This deflationary effect is very small, i.e. π drops on impact by about 5 basis points in (cid:98)H,t the case of complete markets and 1 basis point in the case of incomplete markets. In any case, this deflationary effect is inconsequential for core union-wide inflation dynamics since it is offset by an equally sized inflationary effect on foreign producer prices.19 This latter effect reflects that short-run dynamics in the foreign country are the mirror image of developments in the home country. In sum, these features generate inflationary dynamics of foreign producer prices which offset the deflationary dynamics of home producer prices. To see this point in greater clarity, notice that core union-wide CPI inflation dynamics are approximately given by: π = s π +(1−s )π∗, (cid:98)U,t C(cid:98)t C (cid:98)t with the country-specific elements being given by: π = νπ +(1−ν)π , (cid:98)t (cid:98)H,t (cid:98)F,t π∗ = ν∗π +(1−ν∗)π . (cid:98)t (cid:98)H,t (cid:98)F,t 18TheimpulseresponsesinFigures1−3arebasedonafirst-orderapproximationoftheeconomydevelopedinSection 2. The approximate long-run levels in Figures 1-3 are virtually identical to the exact values reported in column 5 in Table 4, i.e. the approximation error is negligible. 19Foreign real producer wages increase on impact in line with higher foreign consumer real wages. 26

Our benchmark calibration of n = λ = 0.5 implies ν = 0.75 and ν∗ = 0.25, while s = 0.5. Hence, C π = 0.5π +0.5π , implying that deflationary and inflationary producer price effects of equal size (cid:98)U,t (cid:98)H,t (cid:98)F,t in the two countries exactly offset each other in terms of core union-wide CPI inflation. Because of this symmetric feature the nominal interest rate remains unchanged during the transition period. In other words, the union-wide monetary policy remains entirely ‘neutral’ with respect to the unilateral change in the tax structure of the home country. Notice, however, that headline union-wide CPI inflation does reflect the increase in consumption taxes of the home country. With the tax change being modelled as a genuine surprise, with producer prices being largely predetermined, and with monetary policy being unresponsive, the pass-through into headline consumer prices is on impact virtually complete, i.e. headline union-wide CPI inflation increases on impact by close to 50 basis points, in line with the weight of 50% in πUcarried by the home country.20 (cid:98)t Two points are worth emphasising. First, the offsetting effects of core national inflation developments on union wide inflation also hold for monetary unions composed of countries of different size: If the home country (where the consumption tax increase takes place) is, for example, the smaller one of the two countries, the impact on home inflation will be relatively stronger, while the impact on inflation of the foreign (and larger) country will be weaker. As a result of these counteracting effects, core union-wide inflation will not change. However if the countries differ with respect to their openness thisreasoningneedstomodified. Forexample, ifthehomecountryischaracterisedbyastrongerhome bias the deflationary effect in the home economy will outweigh the inflationary effect in the foreign economy. Consequently, core union wide inflation will decrease. Second, for the benchmark monetary uniontheunion-wideoutputgap(i.e. thedifferencebetweenunion-wideoutputlevelsunderstickyand flexible prices) is zero. Because of this feature, the assumption of µ = 0 in (15) is inconsequential, yu provided the countries satisfy the symmetric features of the benchmark specification. 5.2 Different targets of monetary policy This subsection shifts focus and switches to a genuine aspect of monetary policy which affects the short-run dynamics. Specifically, we illustrate that the short-run response of key endogenous variables like consumption, output and inflation depends sensitively on whether the monetary policy reaction specifies the consumer price inflation objective net of indirect taxes or not. To this end, Figures 4 and 6 compare the findings from the benchmark specification, as discussed in Section 5.1, with an 20This reasoning would require modifications if the assumption of Calvo-style price-setting would be replaced by state-dependent pricing, as discussed, for example, in Dotsey et al. (1999). 27

alternative specification (dashed lines) in which, everything else being equal, the after-tax union-wide CPI inflation rate πτC replaces π in the monetary feedback rule (15). This change in the target U,t U,t variable has a number of interesting implications. First, the alternative specification shows that, in principle, the degree and the timing of the pass-through of the tax increase into consumer prices dependsontheindexwhichunderliestheinflationobjective. Bythiswemeanthat, ifmonetarypolicy reacts to πτC, both the pre-tax and the after-tax inflation rates will be lower during the transition U,t than in the benchmark specification.21 Quantitatively, however, with the tax change being modelled as a genuine surprise and with producer prices being largely predetermined, this relative decline in bothinflationmeasuresisinsignificant. Second, thechangeinτC pushesafter-taxunionwideinflation above the target level of inflation and the interest rate reaction of monetary policy introduces for the transitional dynamics a certain stabilisation trade-off, i.e. consumption and output, both in the home and the foreign country, are uniformly lower than in the benchmark specification. Specifically, with monetary policy being no longer neutral with respect to the tax change in the home country, this finding implies that indirect negative spillovers for the foreign country emerge which are triggered by thereactionofmonetarypolicytounion-widevariables. Moreover,underthetwoassumptionsofi)the tax change being modelled as a genuine surprise and ii) producer prices being largely predetermined, Figure 4 indicates that gains in terms of lower inflation are rather costly in terms of output and consumption sacrifices during the transitional dynamics. However, it should be emphasised that the model does not capture a number of other margins which would influence the assessment of this tradeoff from a comprehensive welfare perspective. In particular, during the entire transitional dynamics the assumption of rational expectations firmly anchors inflation expectations and constrains wage settlements in a stabilising manner. Hence, within our analysis there is no scope for so–called ‘secondround’ effects of inflation which typically concern central banks. 5.3 Anticipated versus unanticipated policy changes Another key feature which shapes the short-run dynamics relates to the fact that fiscal policy changes of the discussed type are typically not genuine surprises to the private sector when they become implemented. To ignore implementation lags associated with fiscal policymaking in rational expectation models has quantitatively important implications, as shown by Yang (2005) and Leeper et al. (2008). To confirm the importance of this aspect in our context, this subsection compares the benchmark 21Recall from above that this difference does not affect the long-run incidence of the fiscal experiment. This feature can also be seen in Figures 4 and 6 in which eventually the impulse responses of all variables converge against the same levels under the two specifications. 28

results (of an unanticipated change in the tax structure) with an alternative scenario in which the change in the tax structure is credibly announced and correctly anticipated four quarters ahead. The ex ante announcement of the policy change affects the transitory dynamics in a sizable manner, as depicted in Figures 5 and 7 (dashed lines). Three features are worth pointing out. First and most importantly, home consumption increases immediately (i.e. at the time of the announcement of the future policy change) in anticipation of higher consumption taxes in the future. This upward jump in home consumption is sizable (i.e. about 0.2 percent of the steady-state value for the complete markets case and 0.4 for the incomplete markets case) and exerts on impact a significant demand stimulus which pulls up both home output and home producer prices. However, reflecting the presence of intertemporal substitution effects these movements are reversed in the future, i.e. once the tax change has been implemented home consumption, home output and home producer price inflation are all lower than in the benchmark scenario. Second, the initial demand stimulus in the home country spills over into the foreign country, leading on impact, relative to the benchmark scenario, to an increase in foreign output and foreign producer price inflation, while foreign consumption on impact increases by less (in line with a smaller increase in terms of trade).22 Third, the inflationary stimulus in the two countries implies that on impact pre-tax union-wide CPI inflation also rises. This feature has the interesting implication that nominal interest rate increases on impact. In other words, due to the anticipation effects of private consumers, monetary policy reacts even before the announced fiscal change has been implemented. 5.4 Sticky wages Finally, a crucial factor that should be taken into account in the analysis of the potential effects of the fiscal devaluation hypothesis is the flexibility of the labour market. Several papers, among others Calmfors (1998) and de Mooij and Keen (2012), argue that a shift from direct to indirect taxes can be effective in the short run provided that nominal wages are sticky. According to these papers, if nominal wages are sticky in the short run then a decline in labour taxes will result in smaller labour costs and a reduction in export prices. If nominal wages were flexible, then a decline in labour taxes would be counteracted by an increase in nominal wages. So the tax shift would not be effective. Moreover, this reasoning implies that there are no long-run effects of the tax shift as an adjustment of nominal wages would eliminate any benefits of lower labour taxes. However, this analysis is based on 22In the case of incomplete markets foreign consumption actually decreases on impact due to limited risk sharing. 29

a partial equilibrium analysis of a small open economy which faces exogenously given terms of trade. In order to test the validity of the above reasoning in our model we now assume that nominal wages are sticky `a la Calvo (for details, see the specific equations in the Appendix C.4).23 In our benchmark model with complete markets we obtain, in fact, that the effects of the tax shift are dampened if nominal wages are sticky in the short run. Why is that? Recall that in the short run the home real consumer wage actually declines in the benchmark scenario (see Figure 8). If nominal wages are sticky such decline does not occur, and this feature dampens the increase in home output and in the home terms of trade. As a result, home consumption will decline by less under sticky wages. The impact of sticky wages is notably different when the degree of financial integration is not perfect. In such a situation home real consumer wages increase in the short run when wages are flexible (see Figure 9). If wages are sticky the rise in home real consumer wages will be smaller, and this feature leads to a stronger depreciation of the terms of trade and thus higher home output and higher home consumption (which is determined by home output). Foreign consumers will also benefit from the fact that wages are sticky as both foreign output and foreign consumption will increase. In sum, the results presented in this subsection indicate that the impact of nominal sticky wages depends crucially on the degree of financial integration. We find that sticky wages amplify the effects of the tax shift in the short run only when the degree of financial integration is not perfect. This finding extends the existing literature. 6 Conclusion This paper considers a two-country model of a monetary union to discuss monetary and fiscal interactions between member countries of a monetary union in response to a unilateral ‘fiscal devaluation reform’ in one of the countries. The paper studies conditions under which such a policy, which implies a shift in the tax structure from direct to indirect taxes, is effective both in the short run and long run. We find that the long-run effects depend significantly on the degree of financial integration between the two countries. Short-run effects can be greatly influenced by the conduct of union-wide monetary policy, a possible anticipation of the fiscal reform and, finally, the flexibility of the labour market. Quantitatively, our analysis indicates that, unless there is complete financial integration between member countries, spillovers are negligible such that the quantitative effects of the tax shift are similar to a closed economy. 23Forsimplicity,weassumethatinbothcountriesthedegreeofwagestickinessandofpricestickinessareidenticalto each other. 30

Toobtainclearanalyticalfindingsthepapermakesanumberofsimplifyingassumptions. Inparticular, redistribution effects within countries are negligible, and government expenditures play no interesting role. Similarly, the model counterfactually imposes linear tax schedules for direct and indirect taxes. Extensions of the model in these directions are left fur future work. Finally, the analysis takes a strictly positive perspective to discuss implications of unilateral fiscal reforms. Not least because of the beggar-thy-neighbour nature of output effects associated with such reforms, it seems worthwhile to re-investigate the issue at hand in future work in an optimal policy framework which allows for strategic behaviour of policymakers in both countries. 31

A Calibration Table 6: Characteristics of euro area countries Consumption tax rate Labour tax rate Debt to GDP ratio Euro Area 19.46 39.17 69.06 Austria 21.53 40.58 64.82 Belgium 21.64 43.5 106.45 Finland 28.25 43.49 45.53 France 21.03 41.82 60.65 Germany 18.46 40.09 62.07 Greece 18.21 37.96 105.52 Ireland 25.74 27.48 41.66 Italy 17.29 43.24 110.16 Luxembourg 22.76 29.23 6.77 Netherlands 24.08 31.94 57.15 Portugal 19.66 28.08 57.53 Spain 15.66 28.89 54.7 Note: AllthedataaretakenfromEurostat(sourcefolders: EconomyandFinance,AnnualGovernment Finance Statistics). Data on consumption and labour tax rates are implicit tax rates by economic function. The values shown are averages (in %) over the period 1996 - 2006. 32

B Financial autarky - long-run effects Table 7: Permanent shift in the home tax structure - incomplete markets, % changes Closed economy Monetary union benchmark Home bias − no home bias (λ = 1) home bias (λ = 0.5) Country size n = 1 n = 0.75 n = 0.5 n = 0.1 n = 0.5 Change in τC in pp 1 1 1 1 1 Change in τL in pp −0.76 −0.76 −0.76 −0.76 −0.76 Terms of trade − 0.04 0.04 0.04 0.03 Home consumption 0.04 0.04 0.03 0.02 0.04 Home output 0.05 0.05 0.05 0.06 0.05 Home consumer real wage 0.21 0.21 0.20 0.18 0.21 Foreign consumption − 0.02 0.01 0.00 0.01 Foreign output − −0.01 −0.00 −0.00 −0.00 Foreign consumer real wage − 0.03 0.02 0.00 0.01 Home loss −0.01 −0.00 0.01 0.02 −0.00 Foreign loss − −0.03 −0.02 −0.00 −0.01 Home and Foreign losses are in % of the initial steady state consumption. C Log-linearization around the steady state This Appendix summarises the log-linearisation of the model around the steady state summarised in Section 2 for both the flexible price economy and the sticky price economy. Let key steady-state ratios be defined as follows: G G H F d = , d = GH GF Y Y H F C 1−nC∗ d = ν , d = ν∗ CH C∗H Y n Y H H n C C∗ d = (1−ν) , d = (1−ν∗) CF C∗F 1−nY Y F F τC τL wC = ,wL = 1+τC 1−τL τC∗ τL∗ wC∗ = ,wL∗ = 1+τC∗ 1−τL∗ 33

C.1 The flexible price economy Real consumer wage: ωc = p −wCτC −wLτL (cid:98)H,t (cid:98)H,t (cid:98)t (cid:98)t ωc = p −wC∗τC∗−wL∗τL∗, (cid:98)F,t (cid:98)F,t (cid:98)t (cid:98)t with: p (cid:98)H,t = −(1−ν)T(cid:98)t and p (cid:98)F,t = ν∗T(cid:98)t . Labour supply: ω (cid:98)H c ,t = ηY(cid:98)H,t +ρC(cid:98)t ω (cid:98)F c ,t = ηY(cid:98)F,t +ρC(cid:98) t ∗ Market clearing: Y(cid:98)H,t = d CH (C(cid:99)t +φ(1−ν)T(cid:98)t )+d C∗H (C(cid:98) t ∗+φ(1−ν∗)T(cid:98)t )+d GH G(cid:98)H,t Y(cid:98)F,t = d CF (C(cid:99)t −φνT(cid:98)t )+d C∗F (C(cid:98) t ∗−φν∗T(cid:98)t )+d GF G(cid:98)F,t Euler conditions: R(cid:98) H r ,t +wC(cid:0) τ (cid:98)t C −τ (cid:98)t C +1 (cid:1) = ρ(E t C(cid:98)t+1 −C(cid:98)t ) R(cid:98) F r ,t +wC∗(cid:0) τ (cid:98)t C∗−τ (cid:98)t C + ∗ 1 (cid:1) = ρ(E t C(cid:98) t ∗ +1 −C(cid:98) t ∗), with: R(cid:98) H r ,t = R(cid:98)t −π (cid:98)t+1 and R(cid:98) F r ,t = R(cid:98)t −π (cid:98)t ∗ +1 In case of bond economy: R(cid:98) H r ,t −χB(cid:98) H u, , r t +wC(cid:0) τ (cid:98)t C −τ (cid:98)t C +1 (cid:1) = ρ(E t C(cid:98)t+1 −C(cid:98)t ) R(cid:98) F r ,t −χ∗B(cid:98) F u, , r t +wC∗(cid:0) τ (cid:98)t C∗−τ (cid:98)t C + ∗ 1 (cid:1) = ρ(E t C(cid:98) t ∗ +1 −C(cid:98) t ∗). 34

Market clearing condition for the international bond: nB(cid:98) u,r +(1−n)RSB(cid:98) u,r = 0. H,t F,t Relationship between real exchange rate and terms of trade: R(cid:99)S t = (ν −ν∗)T(cid:98)t Fiscal policy (flow budget constraint): 1 (cid:16) (cid:17) B(cid:98) r = B(cid:98) r +R(cid:98) r H,t β H,t−1 H,t−1 sr (cid:18) τLp Y (σ−1) τCC p G (cid:19) − B H r H σ H sr (τ (cid:98)t L+ω (cid:98)H p ,t +p (cid:98)H,t +Y(cid:98)H,t )+ sr (τ (cid:98)t C +C(cid:98)t )− H sr H (p (cid:98)H,t +G(cid:98)H,t ) H H H H 1 (cid:16) (cid:17) B(cid:98) r = B(cid:98) r +R(cid:98) r F,t β F,t−1 F,t−1 sr (cid:18) τL∗p Y (σ−1) τC∗C∗ p G (cid:19) − B F r F σ F sr (τ (cid:98)t L∗+ω (cid:98)F p ,t +p (cid:98)F,t +Y(cid:98)F,t )+ sr (τ (cid:98)t C∗+C(cid:98) t ∗)− F sr F (p (cid:98)F,t +G(cid:98)F,t ) F F F F Balanced-budget rule (G(cid:98)H,t = G(cid:98)F,t = 0) 1 (cid:16) (cid:17) B(cid:98) r +R(cid:98) r β H,t−1 H,t−1 sr (cid:18) τLp Y (σ−1) τCC p G (cid:19) = B H r H σ H sr (τ (cid:98)t L+ω (cid:98)H p ,t +p (cid:98)H,t +Y(cid:98)H,t )+ sr (τ (cid:98)t C +C(cid:98)t )− H sr H (p (cid:98)H,t +G(cid:98)H,t ) H H H H 1 (cid:16) (cid:17) B(cid:98) r +R(cid:98) r β F,t−1 F,t−1 sr (cid:18) τL∗p Y (σ−1) τC∗C∗ p G (cid:19) = B F r F σ F sr (τ (cid:98)t L∗+ω (cid:98)F p ,t +p (cid:98)F,t +Y(cid:98)F,t )+ sr (τ (cid:98)t C∗+C(cid:98) t ∗)− F sr F (p (cid:98)F,t +G(cid:98)F,t ) F F F F Asset markets: 1) Complete markets: C(cid:98) t ∗ = C(cid:98)t − ρ 1 R(cid:99)S t + ρ 1 (cid:0) wCτ (cid:98)t C −wC∗τ (cid:98)t C∗(cid:1) 2) Financial autarky: C(cid:98)t = (n−1)T(cid:98)t +d Y h Y(cid:99)Ht . 35

3) Bond economy: 1 1 p Y p G C(cid:99)t + C B(cid:98) H u, , r t − βC B(cid:98) H u, , r t−1 = H C H (p (cid:98)H,t +Y(cid:98)H,t )− H C H (p (cid:98)H,t +G(cid:98)H,t ). C.2 The sticky price economy Theequationsforthelaboursupply,marketclearing,completeassetmarkets,theEulerconditions,the relationship between the real exchange rate and the terms of trade, and the fiscal policy specifications are identical with the flexible price economy. In addition, we use: New Keynesian Phillips-curve: π (cid:98)H,t = k H (ω (cid:98)H c ,t +wCτ (cid:98)t C +wLτ (cid:98)t L+(1−ν)T(cid:98)t )+βE t π (cid:98)H,t+1 π (cid:98)F,t = k F (ω (cid:98)F c ,t +wC∗τ (cid:98)t C∗+wL∗τ (cid:98)t L∗−ν∗T(cid:98)t )+βE t π (cid:98)F,t+1 Monetary policy rule: R(cid:98)t = µ yu (1−κ)Y(cid:98) t U −1 +µ πu (1−κ)π (cid:98)t U −1 +κR(cid:98)t−1 πU = s π +(1−s )π∗ (cid:98)t C(cid:98)t C (cid:98)t Y(cid:98) t U = ((1−s C )ν∗−s Y +s C ν)T(cid:98)t +s Y Y(cid:98)H,t +(1−s Y )Y(cid:98)F,t where s = nPHYH. Y PUYU After-tax union-wide CPI inflation rate (used in Section 5.3): πτC = sτC (1+τC)π +(1−sτC )(1+τC∗)π∗+sτC (1+τC)w (cid:0) τC −τC (cid:1) +(1−sτC )(1+τC∗)w∗ (cid:0) τC∗−τC∗(cid:1) (cid:98)U,t C t C (cid:98)t C C (cid:98)t (cid:98)t−1 C C (cid:98)t (cid:98)t−1 Relationships between inflation rates and terms of trade: π = νπ +(1−ν)π (cid:98)t (cid:98)H,t (cid:98)F,t π∗ = ν∗π +(1−ν∗)π (cid:98)t (cid:98)H,t (cid:98)F,t T(cid:98)t = π (cid:98)F,t −π (cid:98)H,t +T(cid:98)t−1 C.3 Equations used in Section 4 To derive equation (26), let τ (cid:98)t C∗ = 0, G(cid:98)H,t = G(cid:98)F,t = 0. Moreover, assuming there exists no home bias (λ = λ∗ = 1), this implies ν = ν∗ = n and R(cid:99)S t = 0. Combining the equations for real consumer wages, 36

labour supplies and complete asset markets yields 1 (cid:104) (cid:105) Y(cid:98)H,t = η −(1−n)T(cid:98)t −wCτ (cid:98)t C −wLτ (cid:98)t L−ρC(cid:98)t 1 (cid:104) (cid:105) Y(cid:98)F,t = η nT(cid:98)t −wL∗τ (cid:98)t L∗−ρC(cid:98)t −wCτ (cid:98)t C Combining the equations for market clearing and complete asset markets yields (cid:18) (cid:19) 1 Y(cid:98)H,t = d CH (C(cid:99)t +φ(1−n)T(cid:98)t )+d C∗H C(cid:98)t + ρ wCτ (cid:98)t C +φ(1−n)T(cid:98)t (cid:18) (cid:19) 1 Y(cid:98)F,t = d CF (C(cid:99)t −φnT(cid:98)t )+d C∗F C(cid:98)t + ρ wCτ (cid:98)t C −φnT(cid:98)t Since the two economies are assumed to be structurally identical and calibrated at the same initial fiscal positions, output levels per capita must also be identical, implying d = d ≡ d and CH CF C d C∗H = d C∗F ≡ d C∗ .Then, by combining the two pairs of equations and substituting out for i) Y(cid:98)H,t and Y(cid:98)F,t and ii) C(cid:98)t one can solve for T(cid:98)t , leading to 1 T(cid:98)t = 1+ηφ(d +d ) (wL∗τ (cid:98)t L∗−wLτ (cid:98)t L) C C∗ which is equation (26) in the main text. Using this expression in the above derived expressions for C(cid:99)t and Y(cid:98)H,t , one readily verifies C(cid:99)t = − η(d 1+ + d d C∗ η ρ )+ρ wCτ (cid:98)t C −n η(d + 1 d )+ρ wLτ (cid:98)t L−(1−n) η(d + 1 d )+ρ wL∗τ (cid:98)t L∗ C C∗ C C∗ C C∗ (cid:20) (cid:20) (cid:21) (cid:21) 1 ηd ηφ(d +d ) Y(cid:98)H,t = η − η(d +d C )+ρ wCτ (cid:98)t C + nθ− 1+ηφ( C d + C d ∗ ) wLτ (cid:98)t L+(1−n)θwL∗τ (cid:98)t L∗ C C∗ C C∗ with 1 1 θ = − 1+ η (d +d ) 1+ηφ(d +d ) ρ C C∗ C C∗ and θ > 0 if φρ > 1. Moreover, one can also verify that the equations (27) and (28), in which T(cid:98)t has not yet been substituted out, are equivalent to these expressions for C(cid:99)t and Y(cid:98)H,t . Similarly, one can derive equivalent equations for the case of financial autarky. In particular, the coefficient γ in equation (29) is equal to γ = 1 . fa fa (ρφ−ρ+1)+(φ−1)ηdC+ηd C∗(φ+n(1−φ)) 37

C.4 Sticky wages in Section 5.4 We assume that in the short run nominal wages are sticky `a la Calvo in both countries. The degree of wage stickiness is assumed to be the same in both countries. Below we present the derivation of the optimal wage setting and of wage inflation for the home economy. We assume that workers in each country are monopolistic suppliers of their own types of labour. As a result, they have market power and they are able to set their own wage. Demand for a particular worker j can be derived from the minimization problem of firms and is given by: (cid:18) w (j) (cid:19)−σw t L (j) = L , (30) t t w t where σ is the elasticity of demand for differentiated labour, w is the economy-wide real wage w and L is the economy-wide labour. Note that the total labour supply by worker j is given by t (cid:82)n L (j) = L (i)di, where L (i) is the amount of labour supplied by worker j to firm i. t 0 t,j t,j We follow Erceg et al. (2000) and assume that in each period only a fraction (1−α ) of households w can change their wages optimally. We assume that α = α (i.e. the degree of wage stickiness is equal w to the degree of price stickiness). The problem for a worker j who is able to reset his or her wage is to choose a wage w(j) so as to maximize: ∞ (cid:88) maxE βtαt (U w (j)−V )L (j). (31) t0 w C,t0+t t L(j),t0+t t0+t t=t0 The associated aggregate wage index is given by: W t 1−σw = α w W t 1 − − 1 σw +(1−α w )W(cid:102) t 1−σw, (32) where W(cid:102) is the nominal wage that will be set by all workers who are able to reset their wages and W is the economy-wide nominal wage. In order to derive the wage inflation equation we combine the first-order condition of the above maximization problem and the aggregate wage index and log-linearize them around the steady state. The wage inflation equation is given by: (1−α )(1−βα ) π (cid:98)w,t = (1+ w σ η)α w (ηY(cid:98)H,t +ρC(cid:98)t −w (cid:98)H c ,t )+βπ (cid:98)w,t+1 . (33) w w 38

D Short-run analysis Figure 1: Short-run effects of the tax shift - complete markets Terms of trade 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % Output 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 0 10 20 .s.s morf .ved % Consumption 0.3 0.2 0.1 0 −0.1 −0.2 0 10 20 home foreign .s.s morf .ved % home foreign Real consumer wage 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 0 10 20 .s.s morf .ved % Producer inflation 0.05 home 0 foreign −0.05 0 10 20 .s.s morf .ved % Union−wide inflation 0.7 home foreign 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % core headline Figure 2: Short-run effects of the tax shift - comparison of different asset markets Terms of trade 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % Home output 0.2 0.15 0.1 0.05 0 −0.05 0 10 20 .s.s morf .ved % Home consumption 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 10 20 .s.s morf .ved % Home real consumer wage 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 10 20 .s.s morf .ved % Foreign output 0.2 0 −0.2 0.2 0 −0.2 0 10 20 .s.s morf .ved % Foreign consumption 0.25 0.2 0.15 0.1 0.05 0 0 10 20 .s.s morf .ved % complete markets incomplete markets financial autarky 39

Figure 3: Short-run effects of the tax shift - incomplete markets Terms of trade 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 10 20 .s.s morf .ved % Output 0.05 0.04 0.03 0.02 0.01 0 −0.01 0 10 20 .s.s morf .ved % Consumption 0.06 0.05 0.04 0.03 0.02 0.01 0 0 10 20 home foreign .s.s morf .ved % home foreign Real consumer wage 0.25 0.2 0.15 0.1 0.05 0 0 10 20 .s.s morf .ved % Producer inflation 0.005 home 0 foreign −0.005 0 10 20 .s.s morf .ved % Union−wide inflation 0.7 home foreign 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % core headline Figure 4: Short-run effects of the tax shift - target of monetary policy (complete markets) Core union−wide inflation 0 −0.01 −0.02 −0.03 −0.04 −0.05 −0.06 0 10 20 .s.s morf .ved % Home output 0.2 0.1 0 −0.1 −0.2 0 10 20 .s.s morf .ved % Home consumption −0.15 −0.2 −0.25 −0.3 −0.35 −0.4 −0.45 0 10 20 .s.s morf .ved % Headline union−wide inflation 0.5 0.4 0.3 0.2 0.1 0 −0.1 0 10 20 .s.s morf .ved % Foreign output 0.1 0.05 0 −0.05 −0.1 −0.15 0 10 20 .s.s morf .ved % Foreign consumption 0.25 0.2 0.15 0.1 0.05 0 −0.05 0 10 20 .s.s morf .ved % core CPI targeting headline CPI targeting 40

Figure 5: Short-run effects of the tax shift - anticipation of fiscal policy (complete markets) Core union−wide inflation 0.05 0.04 0.03 0.02 0.01 0 −0.01 0 10 20 .s.s morf .ved % Home output 0.3 0.25 0.2 0.15 0.1 0.05 0 −0.05 0 10 20 .s.s morf .ved % Home consumption 0.3 0.2 0.1 0 −0.1 −0.2 0 10 20 .s.s morf .ved % Home producer inflation 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 −0.05 0 10 20 .s.s morf .ved % Foreign output 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 10 20 .s.s morf .ved % Foreign consumption Foreign producer inflation 0.24 0.06 0.23 0.05 0.22 0.04 0.21 0.03 0.2 0.02 0.19 0.18 0.01 0.17 0 0 10 20 0 10 20 .s.s morf .ved % Terms of trade 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % unanticipated fiscal reform anticipated fiscal reform Figure 6: Short-run effects of the tax shift - target of monetary policy (incomplete markets) Core union−wide inflation 0 −0.01 −0.02 −0.03 −0.04 −0.05 −0.06 0 10 20 .s.s morf .ved % Home output 0.05 0 −0.05 −0.1 −0.15 0 10 20 .s.s morf .ved % Home consumption 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 0 10 20 .s.s morf .ved % Headline union−wide inflation 0.5 0.4 0.3 0.2 0.1 0 −0.1 0 10 20 .s.s morf .ved % Foreign output 0.05 0 −0.05 −0.1 −0.15 −0.2 0 10 20 .s.s morf .ved % Foreign consumption 0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 0 10 20 .s.s morf .ved % core CPI targeting headline CPI targeting 41

Figure 7: Short-run effects of the tax shift - anticipation of fiscal policy (incomplete markets) Core union−wide inflation 0.05 0.04 0.03 0.02 0.01 0 −0.01 0 10 20 .s.s morf .ved % Home output 0.2 0.15 0.1 0.05 0 −0.05 0 10 20 .s.s morf .ved % Home consumption 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 0 10 20 .s.s morf .ved % Home producer inflation 0.08 0.06 0.04 0.02 0 −0.02 −0.04 0 10 20 .s.s morf .ved % Foreign output 0.1 0.08 0.06 0.04 0.02 0 −0.02 0 10 20 .s.s morf .ved % Foreign consumption Foreign producer inflation 0.015 0.02 0.01 0.015 0.005 0 0.01 −0.005 0.005 −0.01 0 −0.015 0 10 20 0 10 .s.s morf .ved % Terms of trade 0.1 0.05 0 −0.05 −0.1 0 10 20 unanticipated fiscal reform anticipated fiscal reform Figure 8: Short-run effects of the tax shift - sticky wages (complete markets) Core union−wide inflation 0.005 0 −0.005 −0.01 −0.015 0 10 20 .s.s morf .ved % Home output 0.2 0.15 0.1 0.05 0 −0.05 0 10 20 .s.s morf .ved % Home consumption −0.08 −0.1 −0.12 −0.14 −0.16 −0.18 0 10 20 .s.s morf .ved % Home real consumer wage 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 10 20 .s.s morf .ved % Foreign output 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 10 20 .s.s morf .ved % Foreign consumption Foreign real consumer wage 0.3 0.28 0.6 0.5 0.26 0.4 0.24 0.3 0.22 0.2 0.2 0.1 0.18 0 0 10 20 0 10 20 .s.s morf .ved % Terms of trade 0.5 0.4 0.3 0.2 0.1 0 0 10 20 .s.s morf .ved % flexible wages sticky wages 42

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