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Finance and Economics Discussion Series: 2012-71 Screen Reader version ^♣

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

Anna Lipinska¹, Leopold von Thadden²

This version: August 31, 2012

Keywords: Fiscal regimes, monetary policy, currency union

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 financial markets are perfectly integrated. In contrast to the existing literature, we find that short-run 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.

JEL Classification: E61, E63, F42.

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 specific countries. The share of indirect taxes in total taxation (including social security contributions) 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.³ 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.⁴

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 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).⁵ In other words, under incomplete financial integration the fiscal devaluation hypothesis has no bite.

The model, which is similar to (Benigno, 2004), (Duarte & 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 union-wide variables. By contrast, fiscal policy is country-specific, and government expenditures and interest 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 & Uribe, 2007) and (Leith & 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 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).

Within this broad set-up, we assume that the `home' country changes its long-run fiscal priorities and decides once and for all, at unchanged government expenditures, to permanently increase its consumption tax. In line with the fiscal devaluation hypothesis, the additional consumption tax revenues are 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.

As already stressed, our analysis suggests, in general, that the (in-)effectiveness of the fiscal devaluation hypothesis depends significantly on the degree of financial integration between the two countries. 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.⁶ 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 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.

Our paper is related to a recent paper by (Farhi et al., 2012) who establish a number of exact equivalence 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 & Krugman, 1990), (Calmfors, 1998) and recently (de Mooij & 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, explores the quantitative relevance of the fiscal devaluation channel under the assumption 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 & Sutherland, 2004), (Beetsma & Jensen, 2005), (Ferrero, 2009), and (Gali & Monacelli, 2008). In particular, the beggar-thy-neighbour-type output effects of the fiscal devaluation hypothesis would be counteracted in (cooperative or non-cooperative) optimal policy settings in which both countries are allowed to choose optimal actions. In line with our positive approach, (Roeger & in't Veld, 2006) and (European Commission, 2008), using a richer model structure, assess quantitatively the effects of unilateral tax shifts 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 open-economy dimension of unilateral tax shifts under alternative asset market assumptions. More closely related to our monetary union set-up, (Duarte & 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).⁷ (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.

Our paper is structured as follows. Section 2 summarises the model. Section 3 presents the benchmark 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 & 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 structurally identical, but we allow for differences in size. The description of the model economy, unless explicitly needed, is kept short since most of the assumed New Keynesian open economy features are standard (see, in particular, (Obstfeld & Rogoff, 1996)). We treat in the following the home country as the representative one to avoid duplication of notation whenever possible.

2.1 Consumers

The monetary union consists of a measure one of consumers of which $\left[ 0,n\right)$ belong to the home country and $\left[ n,1\right]$ to the foreign country. Each of the two countries produces a composite tradeable good. The two composite goods consist of differentiated home tradeable goods, indexed on the interval $\left[ 0,n\right) ,$ and foreign tradeable goods, indexed on the interval $\left[ n,1\right] ,$ respectively. Hence, the parameter 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 $C_{t}$ and $L_{t}$ denote private consumption and the labour supply of the representative home consumer in period As of period this consumer maximises the following utility function

$\displaystyle \max E_{0}\left\{ \sum\limits_{t=0}^{\infty}\beta^{t}\left[ U\left( C_{t}\right) -V\left( L_{t}\right) \right] \right\} ,%$

(1)

where $E_{0}$ denotes the expectation conditional on the information set at date

, $\beta$ is the intertemporal discount factor (with $0<\beta<1)$ and

and

denote the flow utilities from consumption and labour, assumed to be additively separable.⁸ The home consumption index $C_{t},$ made up of home tradeable goods ( $C_{H,t}$ ) and foreign tradeable goods ( $C_{F,t}$ ), is given by

$\displaystyle C_{t}=\left[ \nu^{\frac{1}{\phi}}C_{H,t}^{\frac{\phi-1}{\phi}}+(1-\nu )^{\frac{1}{\phi}}C_{F,t}^{\frac{\phi-1}{\phi}}\right] ^{\frac{\phi}{\phi-1}% },$

where $\phi>0$ denotes the elasticity of substitution between home and foreign goods and $\nu$ represents the share of home goods in the basket of home consumers if the prices of $C_{H,t}$ and $C_{F,t}$ are equal. Moreover, let $\nu=1-(1-n)\lambda,$ where $\lambda\in(0,1]$ denotes the degree of openness of the home country. Similarly we write the consumption bundle of the representative foreign consumer as

$\displaystyle C_{t}^{\ast}=\left[ \nu^{\ast\frac{1}{\phi^{\ast}}}C_{H^{\ast},t}^{\frac {\phi^{\ast}-1}{\phi^{\ast}}}+(1-\nu^{\ast})^{\frac{1}{\phi^{\ast}}}% C_{F^{\ast},t}^{\frac{\phi^{\ast}-1}{\phi^{\ast}}}\right] ^{\frac{\phi^{\ast }}{\phi^{\ast}-1}},$

where $\nu^{\ast}=n\lambda^{\ast}$ relates to the share of home goods in the basket of foreign consumers and $\lambda^{\ast}\in(0,1]$ denotes the degree of openness of the foreign economy. In the benchmark calibration reported below we allow for home bias, i.e. home consumers demand relatively more home goods than foreign consumers and vice versa, implying $\nu>\nu^{\ast}.$ The variables $C_{j}$ and $C_{j^{\ast}}$ (where $j=H,H^{\ast}$ and $j^{\ast }=F,F^{\ast}$ ) are composite goods which bundle together the underlying individual tradeable goods according to

$\displaystyle C_{j,t}=\left[ \left( \frac{1}{n}\right) ^{\frac{1}{\sigma}}\int \limits_{0}^{n}c_{j,t}\left( h\right) ^{\frac{\sigma-1}{\sigma}}dh\right] ^{\frac{\sigma}{\sigma-1}},$ $\displaystyle C_{j^{\ast},t}=\left[ \left( \frac {1}{1-n}\right) ^{\frac{1}{\sigma^{\ast}}}\int\limits_{n}^{1}c_{j^{\ast}% ,t}\left( f\right) ^{\frac{\sigma^{\ast}-1}{\sigma^{\ast}}}df\right] ^{\frac{\sigma^{\ast}}{\sigma^{\ast}-1}},$

where $\sigma>1,$ $\sigma^{\ast}>1$ 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

$\displaystyle P_{t}$	$\displaystyle =\left[ \nu P_{H,t}^{1-\phi}+(1-\nu)P_{F,t}^{1-\phi}\right] ^{\frac{1}{1-\phi}}$	(2)
$\displaystyle P_{t}^{\ast}$	$\displaystyle =\left[ \nu^{\ast}P_{H^{\ast},t}^{1-\phi^{\ast}}% +(1-\nu^{\ast})P_{F^{\ast},t}^{1-\phi^{\ast}}\right] ^{\frac{1}{1-\phi^{\ast }}},%$	(3)

$\displaystyle P_{j,t}=\left[ \left( \frac{1}{n}\right) \int\limits_{0}^{n}p_{j,t}\left( h\right) ^{1-\sigma}dh\right] ^{\frac{1}{1-\sigma}},$ $\displaystyle P_{j^{\ast}% ,t}=\left[ \left( \frac{1}{1-n}\right) \int\limits_{n}^{1}p_{j^{\ast}% ,t}\left( f\right) ^{1-\sigma^{\ast}}df\right] ^{\frac{1}{1-\sigma^{\ast}}% }.$

Firms are assumed to charge identical producer prices in the two countries ( $p_{H,t}\left( h\right) =p_{H^{\ast},t}\left( h\right) \equiv p_{t}(h)$ and $p_{F,t}\left( f\right) =p_{F^{\ast},t}\left( f\right) \equiv p_{t}(f)$ ), i.e. the law of one price holds at the producer price level such that $P_{H,t}=P_{H^{\ast},t}$ and $P_{F,t}=P_{F^{\ast},t}.$ Let the real exchange rate be defined as $RS_{t}=\frac{P_{t}^{\ast}}{P_{t}}.$ Then, in the presence of home bias, purchasing power parity does not hold ( $P_{t}\neq P_{t}^{\ast})$ and the real exchange rate may fluctuate over time. Moreover, we define the terms of trade as $T_{t}=\frac{P_{F,t}}{P_{H,t}}$ .

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 the budget constraint:

$\displaystyle \left( 1+\tau_{t}^{C}\right) P_{t}C_{t}+D_{H,t}+B_{H,t}\leq D_{t}+\left( 1-\tau_{t}^{L}\right) W_{H,t}L_{t}+\frac{\int\limits_{0}^{n}\Pi_{t}(h)dh}% {n}+R_{t-1}B_{H,t-1}+R_{t-1}D_{H,t-1}+P_{t}AC_{t},%$

(4)

where $W_{H,t},$ $\tau_{t}^{L}$ , and $\tau_{t}^{C}$ denote the nominal wage, the labour tax rate and the consumption tax rate, respectively. $\Pi_{t}% (h)$ represents the nominal profit of home firm

, while $B_{H,t-1}%$ denotes one-period home government bonds (purchased in period

and redeemed in period

measured in per-capita terms. Moreover, $R_{t-1}=1+i_{t-1}$ denotes the nominal interest factor paid on these bonds in period

, respectively.⁹ $D_{H,t-1}$ represents holdings of nominal one-period international bonds, possibly state-contingent, purchased in period

and redeemed in period

with the nominal interest rate factor $R_{t-1}$ . In the case of incomplete markets, we follow (Schmitt-Grohe & Uribe, 2003) and introduce bond adjustment costs ( $AC_{t}$ ) in order to guarantee stationarity of the current account (i.e. $AC_{t}=0$ $\forall{t}$ for complete markets and financial autarky). The adjustment cost is defined by the following expression:

$\displaystyle AC_{t}=\frac{\chi}{2}\left( \frac{D_{H,t}}{P_{t}}-{\overline{d}_{H}}\right) ^{2},$

where ${\overline{d}_{H}}$ is the steady-state holding of the bond by the home consumers. The adjustment cost 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 $D_{H,t}=0$ $\forall{t}$ .

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 ( $C_{t}$ ), labour supply ( $L_{t}$ ), international bonds ( $D_{H,t+1}$ ) and government bonds ( $B_{H,t}$ ) in order to maximise (1) subject to the budget constraint (4), $\forall t\geqslant0$ .

The solution to this problem is characterised by a number of well-known first-order conditions, describing optimal consumer behaviour. The optimal labour supply satisfies the static first-order condition:

$\displaystyle \frac{V_{L}(L_{t})}{U_{C}(C_{t})}=\frac{1-\tau_{t}^{L}}{1+\tau_{t}^{C}}% \frac{W_{H,t}}{P_{t}},%$

(5)

where $(1-\tau_{t}^{L})/(1+\tau_{t}^{C})$ captures the relevant tax wedge for the labour-consumption trade-off.

Let $G_{H,t}$ and $G_{F,t}$ denote the (per capita) levels of composite government expenditures in the two 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:

$\displaystyle y_{t}(h)=\left[ \frac{p_{t}(h)}{P_{H,t}}\right] ^{-\sigma}\left\{ \left[ \frac{P_{H,t}}{P_{t}}\right] ^{-\phi}\nu C_{t}+G_{H,t}+\left( \frac{P_{H,t}% }{P_{t}^{\ast}}\right) ^{-\phi^{\ast}}\frac{\nu^{\ast}(1-n)}{n}C_{t}^{\ast }\right\} =\left[ \frac{p_{t}(h)}{P_{H,t}}\right] ^{-\sigma}Y_{H,t}, %$

(6)

$\displaystyle y_{t}(f)=\left[ \frac{p_{t}(f)}{P_{F,t}}\right] ^{-\sigma^{\ast}}\left\{ \left[ \frac{P_{F,t}}{P_{t}}\right] ^{-\phi}\frac{(1-\nu)n}{1-n}% C_{t}+\left[ \frac{P_{F,t}}{P_{t}^{\ast}}\right] ^{-\phi^{\ast}}(1-\nu ^{\ast})C_{t}^{\ast}+G_{F,t}\right\} =\left[ \frac{p_{t}(f)}{P_{F,t}% }\right] ^{-\sigma^{\ast}}Y_{F,t},%$

(7)

where $Y_{H,t}$ and $Y_{F,t}$ denote per capita levels of composite home and foreign output, respectively.

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 $A_{H,t}$ denote the home level of labour productivity (assumed, for simplicity, to be identical across home sectors). Output of the representative home firm is produced according to the linear production function:

$\displaystyle y_{t}(h)=A_{H,t}L_{t}(h),%$

(8)

where $L_{t}(h)$ denotes the labour input used by firm

. Notice that competitive equilibria (as further discussed below) satisfy $L_{t}=\left( \frac{1}{n}\right) \int_{0}^{n}L_{t}\left( h\right) dh,$ since both workers and firms are of measure

Nominal wages are taken as given by the representative firm such that nominal marginal costs are identical for all home firms, i.e.:

$\displaystyle MC_{H,t}=\frac{W_{H,t}}{A_{H,t}}.$

The price-setting of firms is in line with (Calvo, 1983). Each period a fraction $(1-\alpha)$ of firms has the chance to reset prices in an optimal manner, implying that $P_{H,t}$ follows the law of motion:

$\displaystyle P_{H,t}^{1-\sigma}=\alpha(P_{H,t-1})^{1-\sigma}+(1-\alpha)(\widetilde{p}% _{t}(h))^{1-\sigma},$

where $\widetilde{p}_{t}(h)$ denotes the optimal price chosen by home firms in period

which have the chance to adjust prices. The optimal price $\widetilde{p}_{t}(h)$ solves $\forall t\geqslant0$ the maximisation problem:

$\displaystyle \max\limits_{p_{t}(h)}E_{t}\sum_{s=0}^{\infty}(\alpha)^{s}Q_{t,t+s}\left[ p_{t}(h)-MC_{H,t+s}\right] y_{t:t+s}(h)$
subject to $\displaystyle y_{t:t+s}(h)=\left( \frac{p_{t}(h)}{P_{H,t+s}}\right) ^{-\sigma}Y_{H,t+s},$

where $y_{t:t+s}(h)$ denotes the demand for good

at time

conditional on keeping the price $p_{t}(h)$ for

periods fixed at the level chosen at time

The solution of the maximisation problem is characterised by the first-order condition

$\displaystyle \frac{\widetilde{p}_{t}(h)}{P_{H,t}}=\frac{\sigma}{\sigma-1}\frac{E_{t}% \sum_{s=0}^{\infty}\left( \alpha\beta\right) ^{s}U_{C}(C_{t+s}% )MC_{H,t+s}^{r}\frac{P_{H,t+s}}{P_{t+s}(1+\tau_{t+s}^{C})}Y_{H,t+s}\left( \frac{P_{H,t+s}}{P_{H,t}}\right) ^{\sigma}}{E_{t}\sum_{s=0}^{\infty}\left( \alpha\beta\right) ^{s}U_{C}(C_{t+s})\frac{P_{H,t+s}}{P_{t+s}(1+\tau _{t+s}^{C})}Y_{H,t+s}\left( \frac{P_{H,t+s}}{P_{H,t}}\right) ^{\sigma-1}},$

where

$\displaystyle MC_{H,t}^{r}=MC_{H,t}/P_{H,t},$

represents real marginal costs in period

, 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:

$\displaystyle \frac{\widetilde{p}_{t}^{Flex}(h)}{P_{H,t}}=\frac{\sigma}{\sigma-1}% MC_{H,t}^{r}.%$

(9)

Analogous expressions can be derived for the foreign country.

2.3 Fiscal policies

The fiscal authority in the home country issues one-period nominal debt ( $B_{H,t})$ and taxes home labour income at rate $\tau_{t}^{L}$ and home private consumption expenditures at rate $\tau_{t}^{C},$ respectively. Revenues are spent on home government expenditures $G_{H,t}$ (exhibiting perfect home bias) and interest payments on outstanding debt, issued in the previous period.¹⁰ Hence, the home country's flow government budget constraint in nominal terms (and on a per capita basis) is given by:

$\displaystyle B_{H,t}=R_{t-1}B_{H,t-1}-s_{H,t},$

with the nominal primary surplus ( $s_{H,t})$ being defined as:

$\displaystyle s_{H,t}=\tau_{t}^{L}W_{H,t}L_{t}+\tau_{t}^{C}P_{t}C_{t}-P_{H,t}G_{H,t}.$

To rewrite these two equations in real terms let $R_{H,t-1}^{r}=R_{t-1}% P_{t-1}/P_{t}$ denote the real interest factor and use $B_{H,t}^{r}% =B_{H,t}/P_{t},$ $s_{H,t}^{r}=s_{H,t}/P_{t}$ and $w_{H,t}=W_{H,t}/P_{t},$ leading to:

$\displaystyle B_{H,t}^{r}$	$\displaystyle =R_{H,t-1}^{r}B_{H,t-1}^{r}-s_{H,t}^{r},$
$\displaystyle s_{H,t}^{r}$	$\displaystyle =\tau_{t}^{L}w_{H,t}L_{t}+\tau_{t}^{C}C_{t}-\frac{P_{H,t}% }{P_{t}}G_{H,t},$

with analogous equations holding for the foreign country. Notice that the primary surplus depends on three separate fiscal instruments ( $\tau_{t}% ^{L},\tau_{t}^{C},G_{H,t}$ ), allowing, in principle, for a large range of fiscal 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 consumption tax on home and foreign variables in a number of distinct general equilibrium scenarios. Our benchmark scenario exhibits two particular assumptions, in line with the fiscal devaluation hypothesis. First, in response to the change in the home consumption tax by $\Delta\tau^{C}$ 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. $B_{H,t}^{r}=B_{H}^{r}$ and $B_{F,t}^{r}=B_{F}^{r}$ $\forall$ For given target levels of real debt this implies that real primary surpluses are given by:

$\displaystyle s_{H,t}^{r,\text{ }BB}=(R_{H,t-1}^{r}-1)B_{H}^{r}\text{\ \ \ \ and\ \ \ \ }% s_{F,t}^{r,\text{ }BB}=(R_{F,t-1}^{r}-1)B_{F}^{r}.%$

(10)

Second, our benchmark assumes that budget balance is achieved by adjustments in labour taxes. In other words, in response to the permanent change in $\tau^{C}$ by $\Delta\tau^{C},$ we treat $\tau_{t}^{L}$ and $\tau_{t}^{L\ast}$ as the residual instruments which ensure that (10) is satisfied, taking as given $G_{H}$ and $G_{F}$ (which are held constant at their steady-state values). These two assumptions imply for $\tau_{t}^{L}$ and $\tau_{t}^{L\ast}$ the following law of motions:

$\displaystyle \tau_{t}^{L_{BB}}=\frac{(R_{H,t-1}^{r}-1)B_{H}^{r}-(\tau^{C}+\Delta\tau ^{C})C_{t}+\frac{P_{H,t}}{P_{t}}G_{H}}{w_{H,t}L_{t}}$ and $\displaystyle \tau _{t}^{L\ast_{BB}}=\frac{(R_{F,t-1}^{r}-1)B_{F}^{r}-\tau^{C\ast}C_{t}^{\ast }+\frac{P_{F,t}}{P_{t}^{\ast}}G_{F}}{w_{F,t}L_{t}^{\ast}}.%$

(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 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:

$\displaystyle \frac{U_{C}(C_{t+1}^{\ast})}{U_{C}(C_{t}^{\ast})}\frac{P_{t+1}}{P_{t}}% \frac{1+\tau_{t+1}^{C}}{1+\tau_{t}^{C}}=\frac{U_{C}(C_{t+1})}{U_{C}(C_{t}% )}\frac{P_{t+1}^{\ast}}{P_{t}^{\ast}}\frac{1+\tau_{t+1}^{C\ast}}{1+\tau _{t}^{C\ast}}.$

After choosing appropriately the distribution of initial wealth, one obtains:

$\displaystyle \frac{U_{C}(C_{t})}{U_{C}(C_{t}^{\ast})}=\upsilon\frac{P_{t}}{P_{t}^{\ast}% }\frac{1+\tau_{t}^{C}}{1+\tau_{t}^{C\ast}},%$

(12)

where the parameter $\upsilon>0$ depends on the initial wealth distribution, measured in terms of after-tax 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 assumption implies that marginal rates of substitution in consumption are equalised between countries only on average. Intertemporal optimality of bond holdings leads to the following Euler equation for home and foreign consumers:

$\displaystyle E_{t}\left( \frac{U_{C}(C_{t+1})P_{t}(1+\tau_{t}^{C})}{U_{C}(C_{t}% )P_{t+1}(1+\tau_{t+1}^{C})}\right) \frac{\beta R_{t}}{1+\chi(\frac{D_{H,t}% }{P_{t}}-{\overline{d}_{H}})}=1.$

(13)

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:

$\displaystyle C_{t}=p_{H,t}(Y_{H,t}-G_{H,t}).%$

(14)

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 variables. To this end, the central bank follows a New Keynesian interest rate feedback rule:

$\displaystyle 1+\widetilde{i}_{t}=\left( \frac{Y_{U,t}}{Y_{U,t}^{n}}\right) ^{\mu _{y_{_{u}}}}\left( \frac{\pi_{U,t}}{\pi_{U}}\right) ^{\mu_{\pi_{_{u}}}% }(1+i),%$

(15)

where

denotes the steady-state nominal interest rate, while $\mu_{y_{u}}$ and $\mu_{\pi_{u}}$ denote the feedback coefficients associated with the union-wide output gap (with $Y_{U,t}$ and $Y_{U,t}^{n}$ denoting the current union-wide output level and the natural union-wide output level under flexible prices, respectively) and pre-tax union-wide consumer price inflation ( $\pi_{U,t}$ ) in deviation from the target rate $\pi_{U},$ normalised to $\pi_{U}=1.$ Moreover, to allow for interest rate smoothing we assume:

$\displaystyle (1+i_{t})=(1+\widetilde{i}_{t})^{1-\kappa}(1+i_{t-1})^{\kappa},$

where $\kappa\in(0,1)$ captures the degree of interest rate smoothing. Union-wide real output $Y_{U,t}$ is obtained from the corresponding values of union-wide nominal output:

$\displaystyle nP_{H,t}Y_{H,t}+(1-n)P_{F,t}Y_{F,t}=P_{U,t}Y_{U,t},,$

and the deflator $P_{U,t}$ corresponds to the pre-tax union-wide consumer price level (i.e. net of consumption taxes), with $P_{U,t}=s_{C}P_{t}% +(1-s_{C})P_{t}^{\ast},$ where $s_{C}=\frac{nPC}{nPC+(1-n)P^{\ast}C^{\ast}}$ denotes the steady-state share of the home country in union-wide nominal consumption. Because of $\pi_{U,t}=P_{U,t}/P_{U,t-1}$ the central bank's inflation objective in our benchmark specification is based on the index $P_{U,t}$ which measures 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) $P_{H,t}:$ producer price level of the (composite) home produced good, for short: home producer price level.

(ii) $P_{t}:$ consumer price level prevailing in the home country net of the home consumption tax, for short: pre-tax home consumer price level.

(iii) $P_{U,t}:$ union-wide consumer price level net of consumption taxes, for short: pre-tax union-wide consumer price level, with $P_{U,t}=s_{C}P_{t}+(1-s_{C})P_{t}^{\ast},$ $s_{C}=\frac{nPC}{nPC+(1-n)P^{\ast}C^{\ast}}$ and the corresponding inflation measure $\pi_{U,t}=P_{U,t}% /P_{U,t-1}.$

(iv) $(1+\tau_{t}^{C})P_{t}:$ consumer price level prevailing in the home country including home consumption taxes, for short: after-tax home consumer price level.

(v) $P_{U,t}^{\tau^{C}}:$ union-wide consumer price level including consumption taxes of both countries, for short: after-tax union-wide consumer price level, with $P_{U,t}^{\tau^{C}}=s_{C}^{\tau^{C}% }(1+\tau_{t}^{C})P_{t}+(1-s_{C}^{\tau^{C}})(1+\tau_{t}^{C\ast})P_{t}^{\ast},$ $s_{C}^{\tau^{C}}=\frac{n(1+\tau^{C})PC}{n(1+\tau^{C})PC+(1-n)(1+\tau^{C\ast })P^{\ast}C^{\ast}}$ and the corresponding inflation measure $\pi_{U,t}% ^{\tau^{C}}=P_{U,t}^{\tau^{C}}/P_{U,t-1}^{\tau^{C}}.$

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:

$\displaystyle w_{H,t}^{p}=\frac{W_{H,t}}{P_{H,t}}$ and $\displaystyle w_{H,t}^{c}% =\frac{1-\tau_{t}^{L}}{1+\tau_{t}^{C}}\frac{W_{H,t}}{P_{t}},$

where $w_{H,t}^{p}$ and $w_{H,t}^{c}$ denote the real producer and real consumer wage in the home country, respectively. Since the producer real wage is deflated by $P_{H,t}$ it is directly linked to real marginal costs, i.e.:

$\displaystyle MC_{H,t}^{r}=\frac{w_{H,t}^{p}}{A_{H,t}},$

implying that $w_{H,t}^{p},$ $w_{H,t}^{c},$ and $MC_{H,t}^{r}$ are related to each other according to:

$\displaystyle w_{H,t}^{c}=\frac{1-\tau_{t}^{L}}{1+\tau_{t}^{C}}\frac{P_{t}^{H}}{P_{t}% }w_{H,t}^{p}=\frac{1-\tau_{t}^{L}}{1+\tau_{t}^{C}}\frac{P_{t}^{H}}{P_{t}% }A_{H,t}MC_{H,t}^{r}.%$

(16)

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, $A_{H,t}=A_{F,t}=1,\forall t\geqslant0)$ and refrain from the specification of any other shock processes.

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 $\tau^{C}$ by $\Delta\tau^{C}$ 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 $U\left( C\right) =\frac{1}{1-\rho}C^{1-\rho}$ and $V\left( L\right) =\frac{1}{1+\eta}L^{1+\eta}$ , with $\rho>0$ and $\eta>0$ denoting the inverse of the intertemporal elasticity of substitution in consumption and of the Frisch elasticity of labour supply, respectively. Notice that (9) implies $MC_{H}^{r}=\frac{\sigma-1}{\sigma}.$ Moreover, $\beta =1/(1+i)=1/(1+r)$ because of $\pi_{U}=1.$ By symmetry, $\frac{p(h)}{P_{H}% }=\frac{p(f)}{P_{F}}=1$ . Finally, we define $\frac{P^{H}}{P}\equiv p_{H}$ and $\frac{P^{F}}{P^{\ast}}\equiv p_{F}.$

Then, using (8) and (16), the steady-state counterparts of (2), (3), (12) or (14)¹¹, (5), (6) and (7) for both countries can be compactly summarised as the following system of nine equations in the nine unknowns $Y_{H},$ $Y_{F},$ $C^{\ast},$ $p_{H},$ $p_{F}$ , $\tau^{L},$ $\tau^{L\ast },RS,$ taking as given constant values of the fiscal variables $B_{H}^{r},$ $B_{F}^{r},$ $\tau^{C}$ , $\tau^{C\ast},$ $G_{H},$ $G_{F}$ :

$\displaystyle Y_{H} =p_{H}^{-\phi}\nu C+G_{H}+p_{H}^{-\phi^{\ast}}RS^{\phi^{\ast}}\frac {\nu^{\ast}(1-n)}{n}C^{\ast}$	(17)
$\displaystyle Y_{F} =(p_{F}RS)^{-\phi}\frac{(1-\nu)n}{1-n}C+G_{F}+(p_{F})^{-\phi^{\ast}% }(1-\nu^{\ast})C^{\ast}$	(18)
$\displaystyle (Y_{H})^{\eta} =C^{-\rho}\frac{1-\tau^{L}}{1+\tau^{C}}\frac{\sigma-1}{\sigma }p_{H}$	(19)
$\displaystyle (Y_{F})^{\eta^{\ast}} =(C^{\ast})^{-\rho^{\ast}}\frac{1-\tau^{L\ast}}% {1+\tau^{C\ast}}\frac{\sigma^{\ast}-1}{\sigma^{\ast}}p_{F}$	(20)
$\displaystyle 1 =\nu p_{H}^{1-\phi}+(1-\nu)(p_{F}RS)^{1-\phi}$	(21)
$\displaystyle 1 =\nu^{\ast}(p_{H}RS^{-1})^{1-\phi^{\ast}}+(1-\nu^{\ast})p_{F}^{1-\phi^{\ast }}$	(22)
$\displaystyle B_{H}^{r} =\frac{\beta}{1-\beta}s_{H}^{r}=\frac{\beta}{1-\beta}\left[ \tau^{L}\frac{\sigma-1}{\sigma}p_{H}Y_{H}+\tau^{C}C-p_{H}G_{H}\right]$	(23)
$\displaystyle B_{F}^{r} =\frac{\beta}{1-\beta}s_{F}^{r}=\frac{\beta}{1-\beta}\left[ \tau^{L\ast}\frac{\sigma^{\ast}-1}{\sigma^{\ast}}p_{F}Y_{F}+\tau^{C\ast }C^{\ast}-p_{F}G_{F}\right]$	(24)
$\displaystyle \frac{C^{-\rho}}{(C^{\ast})^{-\rho^{\ast}}}=\upsilon RS^{-1}\frac{1+\tau^{C}% }{1+\tau^{C\ast}} \mathit{ or } C=p_{H}(Y_{H}-G_{H})$	(25)

Below we solve numerically a calibrated version of this system for the nine unknowns, and, using 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 $T=RSp_{F}/p_{H}.$

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 and a symmetric home bias because of $\lambda=0.5$ . 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. $\rho=2),$ as in (Stockman & Tesar, 1995). The labour supply elasticity is chosen to be 0.4 (i.e. $\eta=2.5),$ striking a balance between micro data evidence and macro aspects, in line with the DSGE literature concerned with the euro area (e.g. (Smets & Wouters, 2003), (Altissimo et al., 2011), (Coenen et al., 2010), (Christiano et al., 2005)). The discount factor equals $\beta=0.99,$ implying an annual interest rate of around four percent. As in (Rotemberg & Woodford, 1997) and (Altissimo et al., 2011), the elasticity of substitution between differentiated goods within countries is assumed to be $\sigma=7.88,$ consistent with a steady-state markup of $15\%$ . The elasticity of substitution between home and foreign goods is set as $\phi=1.5$ (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. $\phi>\frac{1}{\rho}$ ), home and foreign goods are substitutes in the preferences of agents. Like (Duarte & Wolman, 2008), the degree of openness in both countries equals $\lambda=0.5,$ 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 $\alpha=0.85,$ 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 & Wouters, 2003) and (Coenen et al., 2010). The portfolio cost adjustment parameter, $\chi$ , is set to 0.001 which corresponds to an average annual interest rate premium of $0.405\%$ , in line with (Schmitt-Grohe & Uribe, 2003). Moreover, we assume that the steady-state value of bond holdings is zero, i.e. ${\overline{d}_{H}}=0$ .

Table 1: Structural parameters
Size of the (home) country		0.5
Inverse of the intertemporal elasticity of substitution	$\rho$	2
Inverse of the labour supply elasticity	$\eta$	2.5
Discount factor	$\beta$	0.99
Elasticity of substitution between goods within countries	$\sigma$	7.88
Elasticity of substitution between home and foreign goods	$\phi$	1.5
Degree of openness	$\lambda$	0.5
Degree of nominal price stickiness	$\alpha$	0.85
Portfolio cost adjustment	$\chi$	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 7 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.¹²

Table 2: Fiscal characteristics of the initial steady state
Consumption tax rate	$\tau^{C}=\tau^{C\ast}$	0.15
Labour tax rate	$\tau^{L}=\tau^{L\ast}$	0.30
Share of government expenditures in output	$d_{GH}=\frac{G_{H}}{Y_{H}% }=d_{GF}=\frac{G_{F}}{Y_{F}}$	0.33
Debt-output ratio	$b_{H}=\frac{B_{H}}{P_{H}Y_{H}}=b_{F}=\frac{B_{F}}% {P_{F}Y_{F}}$	2.64

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 $\kappa=0.95$ . Moreover, the benchmark response coefficient to inflation is set equal to $\mu_{\pi_{u}}=2,$ while we assume that monetary policy does not respond to output fluctuations ( $\mu_{y_{u}}=0$ ).¹³ Notice that the benchmark balanced-budget rule (11) does not require any additional fiscal parameter.

Table 3: Parameters of monetary policy rule
Response parameter of monetary policy to union output gap	$\mu_{y_{u}}$	0
Response parameter of monetary policy to union inflation	$\mu_{\pi_{u}}$	2
Smoothing parameter	$\kappa$	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 from 15% to 16% (i.e. $\Delta\tau^{C}=0.01)$ and uses the additional revenues to finance a permanent cut in the 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 the benchmark `monetary union with countries of equal size and symmetric home bias' (as summarised 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 and ii) the strength of the home bias (captured by $\lambda)$ , 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, 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 $n\rightarrow1$ 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 well-known channels as summarised, for example, in (Layard et al., 1996), (Bovenberg, 2006), and (European Commission, 2008). Specifically, in order for a revenue-neutral shift from labour taxes to indirect taxes to be able to increase output and employment it is crucial that this shift reduces the effective tax burden on labour. Given our simplifying assumption of linear tax schedules, this in turn requires that the share of non-labour income (related, in particular, to non-indexed unemployment benefits and pensions as well as capital income) is sufficiently large.¹⁴ 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.

Table 4: Permanent shift in the home tax structure - complete markets, % changes
Country size/Home Bias	Closed economy:	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: home bias ( $\lambda=0.5$ )
Change in $\tau^{C}$ in pp	1	1	1	1	1
Change in $\tau^{L}$ 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 & Crucini, 1995), who find that the extent of financial integration is central to the international transmission mechanism 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 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.¹⁵ 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, home consumption increases as a result of the positive wealth effect. It is worth noting that the strength of this wealth effect depends on the permanent character of the tax shift.¹⁶ Moreover, the increase in home output is significantly dampened (reflecting that home labour supply is subject to opposite effects from the wealth channel and the significant rise in the home wage rate). These changes in home variables are accompanied by a small terms of trade increase, supporting an increase in foreign consumption and a decrease in foreign output. Quantitatively, however, the effects on foreign variables 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.¹⁷

Table 5: Permanent shift in the home tax structure - complete markets vs incomplete markets: Comparison for the symmetric no home bias case.
	Complete markets	Financial autarky
Change in $\tau^{C}$ in pp	1	1
Change in $\tau^{L}$ 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

4.3 Monetary unions with countries of different size (no home bias)

The results established so far can be generalised if one looks at monetary unions consisting of countries 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 8 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 () and a `small' home country (). 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 & Krugman, 1990). Similarly, as concerns the foreign country, the magnitude of the terms of trade related effects on production, consumption and the real consumer wage decreases in the size of the foreign country, i.e. the leverage of a change in the home tax structure 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 is instructive to analyse key equations which come from a first-order approximation of the equilibrium conditions of the model. As derived in Appendix C.3, one can show that in the case of complete markets 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:¹⁸

$\displaystyle \widehat{T}_{t}=\frac{1}{1+\eta\phi\left( d_{C}+d_{C^{\ast}}\right) }(w^{L^{\ast}}\widehat{\tau}_{t}^{L\ast}-w^{L}\widehat{\tau}_{t}^{L}). %$

(26)

Because of the assumption of constant productivity levels, the home real producer wage stays constant 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:

$\displaystyle \widehat{\omega}_{H,t}^{p}$	$\displaystyle =0,$
$\displaystyle \widehat{\omega}_{H,t}^{c}$	$\displaystyle =-(1-n)\widehat{T}_{t}-w^{C}\widehat{\tau}% _{t}^{C}-w^{L}\widehat{\tau}_{t}^{L}.$

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.

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.:

$\displaystyle \widehat{C}_{t}=-(1-n)\frac{1+\eta\phi(d_{C}+d_{C^{\ast}})}{\eta (d_{C}+d_{C^{\ast}})+\rho}\widehat{T}_{t}-\frac{1+\frac{\eta}{\rho}d_{C^{\ast }}}{\eta(d_{C}+d_{C^{\ast}})+\rho}w^{C}\widehat{\tau}_{t}^{C}-\frac{1}% {\eta(d_{C}+d_{C^{\ast}})+\rho}w^{L}\widehat{\tau}_{t}^{L}%$

(27)

$\displaystyle \widehat{Y}_{H,t}$	$\displaystyle =(1-n)\left( \rho\phi-1\right) \frac{\phi (d_{C}+d_{C^{\ast}})}{\eta\phi(d_{C}+d_{C^{\ast}})+\rho\phi}\widehat{T}% _{t}$	(28)
	$\displaystyle -\frac{d_{C}}{\eta(d_{C}+d_{C^{\ast}})+\rho}w^{C}\widehat{\tau}_{t}% ^{C}-\frac{d_{C}+d_{C^{\ast}}}{\eta(d_{C}+d_{C^{\ast}})+\rho}w^{L}% \widehat{\tau}_{t}^{L}.$

Equations (27) and (28) reveal that the terms of trade effects on $\widehat{C}_{t}$ and $\widehat{Y}_{H,t}$ are largest in the case of a small home economy. Moreover, the partial effects of $\widehat{T},$ $\widehat{\tau}_{t}^{C},$ and $\widehat{\tau}_{t}^{L}$ on home consumption have the same sign structure as established for the home real consumer wage. By contrast, the effect of $\widehat{T}$ on home output is of opposite sign (i.e. positive) whenever $\rho\phi>1,$ 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 & Pesenti, 2001) and (Tille, 2001).¹⁹

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:

$\displaystyle \widehat{T}_{t}=\gamma_{fa}(w^{L^{\ast}}\widehat{\tau}_{t}^{L\ast}% -w^{L}\widehat{\tau}_{t}^{L}-w^{C}\widehat{\tau}_{t}^{C}),%$

(29)

where $\gamma_{fa}$ is defined in the Appendix C.3. As a result, under incomplete markets the implied change 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

Building on these insights it is straightforward to see how the results change if one considers a monetary 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 8 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 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 in Section 4. To characterise core features of the short-run dynamics in a tractable manner, this Section 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 ahead and therefore anticipated by the private sector. Finally, Section 5.4 assumes that nominal wages 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 output and the terms of trade, the impulse responses are qualitatively of similar shape, notwithstanding their quantitative differences. In all cases, short-run adjustments leave core union-wide CPI inflation dynamics unaffected. This implies that the home country can implement its reform of the tax structure 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.²⁰ Irrespective of the degree of financial integration, nominal price stickiness ensures that the terms of trade increase relatively slowly over time 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:

$\displaystyle \widehat{\pi}_{H,t}=k_{H}\widehat{MC}_{H,t}^{r}+\beta E_{t}\widehat{\pi }_{H,t+1}\text{\ \ \ with:\ \ \ \ }\widehat{MC}_{H,t}^{r}=\widehat{w}% _{H,t}^{p},$

this implies that the change in the tax structure exerts on impact a deflationary effect on home producer prices. This deflationary effect is very small, i.e. $\widehat{\pi}_{H,t}$ drops on impact by about 5 basis points in 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.²¹ 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:

$\displaystyle \widehat{\pi}_{U,t}=s_{C}\widehat{\pi}_{t}+(1-s_{C})\widehat{\pi}_{t}^{\ast},$

with the country-specific elements being given by:

$\displaystyle \widehat{\pi}_{t}$	$\displaystyle =\nu\widehat{\pi}_{H,t}+(1-\nu)\widehat{\pi}_{F,t},$
$\displaystyle \widehat{\pi}_{t}^{\ast}$	$\displaystyle =\nu^{\ast}\widehat{\pi}_{H,t}+(1-\nu^{\ast })\widehat{\pi}_{F,t}.$

Our benchmark calibration of $n=\lambda=0.5$ implies $\nu=0.75$ and $\nu ^{\ast}=0.25,$ while $s_{C}=0.5.$ Hence, $\widehat{\pi}_{U,t}=0.5\widehat{\pi }_{H,t}+0.5\widehat{\pi}_{F,t},$ implying that deflationary and inflationary producer price effects of equal size 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 $\widehat{\pi}_{t}^{U}%$ carried by the home country.²²

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 this reasoning needs to modified. For example, if the home country is characterised by a stronger home 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 union the union-wide output gap (i.e. the difference between union-wide output levels under sticky and flexible prices) is zero. Because of this feature, the assumption of $\mu_{y_{u}}=0$ in (15) is inconsequential, 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 alternative specification (dashed lines) in which, everything else being equal, the after-tax union-wide CPI inflation rate $\pi_{U,t}^{\tau^{C}}$ replaces $\pi_{U,t}$ in the monetary feedback rule (15). This change in the target 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 depends on the index which underlies the inflation objective. By this we mean that, if monetary policy reacts to $\pi_{U,t}% ^{\tau^{C}},$ both the pre-tax and the after-tax inflation rates will be lower during the transition than in the benchmark specification.²³ Quantitatively, however, with the tax change being modelled as a genuine surprise and with producer prices being largely predetermined, this relative decline in both inflation measures is insignificant. Second, the change in $\tau^{C}$ pushes after-tax union wide inflation 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 the reaction of monetary policy to union-wide variables. Moreover, under the two assumptions of i) 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 trade-off 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 `second-round' 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 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).²⁴

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 & 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 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 à la Calvo (for details, see the specific equations in the Appendix C.4).²⁵ 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.

To obtain clear analytical findings the paper makes a number of simplifying assumptions. In particular, 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.

A. Calibration

Table 7: 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: All the data are taken from Eurostat (source folders: Economy and Finance, Annual Government 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.

B. Financial autarky - long-run effects

Table 8: Permanent shift in the home tax structure - incomplete markets, % changes
Country size/Home Bias	Closed economy:	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: no home bias ( $\lambda=1$ )	Monetary union: home bias ( $\lambda=0.5$ )
Change in $\tau^{C}$ in pp	1	1	1	1	1
Change in $\tau^{L}$ 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.

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:

$\displaystyle d_{GH}$	$\displaystyle =\frac{G_{H}}{Y_{H}},$ $\displaystyle d_{GF}=\frac{G_{F}}{Y_{F}}$
$\displaystyle d_{CH}$	$\displaystyle =\nu\frac{C}{Y_{H}},$ $\displaystyle d_{C^{\ast}H}=\nu^{\ast}\frac {1-n}{n}\frac{C^{\ast}}{Y_{H}}$
$\displaystyle d_{CF}$	$\displaystyle =\left( 1-\nu\right) \frac{n}{1-n}\frac{C}{Y_{F}},$ $\displaystyle % d_{C^{\ast}F}=\left( 1-\nu^{\ast}\right) \frac{C^{\ast}}{Y_{F}}%$

$\displaystyle w^{C}$	$\displaystyle =\frac{\tau^{C}}{1+\tau^{C}},w^{L}=\frac{\tau^{L}}{1-\tau^{L}}$
$\displaystyle w^{C^{\ast}}$	$\displaystyle =\frac{\tau^{C^{\ast}}}{1+\tau^{C^{\ast}}},w^{L^{\ast}}% =\frac{\tau^{L^{\ast}}}{1-\tau^{L^{\ast}}}%$

C.1 The flexible price economy

Real consumer wage:

$\displaystyle \widehat{\omega}_{H,t}^{c}$	$\displaystyle =\widehat{p}_{H,t}-w^{C}\widehat{\tau}_{t}% ^{C}-w^{L}\widehat{\tau}_{t}^{L}$
$\displaystyle \widehat{\omega}_{F,t}^{c}$	$\displaystyle =\widehat{p}_{F,t}-w^{C\ast}\widehat{\tau}% _{t}^{C\ast}-w^{L\ast}\widehat{\tau}_{t}^{L\ast},$

with:

$\displaystyle \widehat{p}_{H,t}=-(1-\nu)\widehat{T}_{t}$ and $\displaystyle % \widehat{p}_{F,t}=\nu^{\ast}\widehat{T}_{t}.$

Labour supply:

$\displaystyle \widehat{\omega}_{H,t}^{c}$	$\displaystyle =\eta\widehat{Y}_{H,t}+\rho\widehat{C}_{t}$
$\displaystyle \widehat{\omega}_{F,t}^{c}$	$\displaystyle =\eta\widehat{Y}_{F,t}+\rho\widehat{C}% _{t}^{\ast}%$

Market clearing:

$\displaystyle \widehat{Y}_{H,t}$	$\displaystyle =d_{CH}(\widehat{C_{t}}+\phi(1-\nu)\widehat{T}% _{t})+d_{C^{\ast}H}(\widehat{C}_{t}^{\ast}+\phi(1-\nu^{\ast})\widehat{T}% _{t})+d_{GH}\widehat{G}_{H,t}$
$\displaystyle \widehat{Y}_{F,t}$	$\displaystyle =d_{CF}(\widehat{C_{t}}-\phi\nu\widehat{T}% _{t})+d_{C^{\ast}F}(\widehat{C}_{t}^{\ast}-\phi\nu^{\ast}\widehat{T}% _{t})+d_{GF}\widehat{G}_{F,t}%$

Euler conditions:

$\displaystyle \widehat{R}_{H,t}^{r}+w^{C}\left( \widehat{\tau}_{t}^{C}-\widehat{\tau}% _{t+1}^{C}\right)$	$\displaystyle =\rho(E_{t}\widehat{C}_{t+1}-\widehat{C}_{t})$
$\displaystyle \widehat{R}_{F,t}^{r}+w^{C\ast}\left( \widehat{\tau}_{t}^{C\ast }-\widehat{\tau}_{t+1}^{C\ast}\right)$	$\displaystyle =\rho(E_{t}\widehat{C}_{t+1}^{\ast }-\widehat{C}_{t}^{\ast}),$

with:

$\displaystyle \widehat{R}_{H,t}^{r}=\widehat{R}_{t}-\widehat{\pi}_{t+1}$ and $\displaystyle \widehat{R}_{F,t}^{r}=\widehat{R}_{t}-\widehat{\pi}% _{t+1}^{\ast}%$

In case of bond economy:

$\displaystyle \widehat{R}_{H,t}^{r}-\chi\widehat{B}_{H,t}^{u,r}+w^{C}\left( \widehat{\tau }_{t}^{C}-\widehat{\tau}_{t+1}^{C}\right)$	$\displaystyle =\rho(E_{t}\widehat{C}% _{t+1}-\widehat{C}_{t})$
$\displaystyle \widehat{R}_{F,t}^{r}-\chi^{\ast}\widehat{B}_{F,t}^{u,r}+w^{C\ast}\left( \widehat{\tau}_{t}^{C\ast}-\widehat{\tau}_{t+1}^{C\ast}\right)$	$\displaystyle =\rho(E_{t}\widehat{C}_{t+1}^{\ast}-\widehat{C}_{t}^{\ast}).$

Market clearing condition for the international bond:

$\displaystyle n\widehat{B}_{H,t}^{u,r}+(1-n)\overline{RS}\widehat{B}_{F,t}^{u,r}=0.$

Relationship between real exchange rate and terms of trade:

$\displaystyle \widehat{RS}_{t}=\left( \nu-\nu^{\ast}\right) \widehat{T}_{t}%$

Fiscal policy (flow budget constraint):

$\displaystyle \widehat{B}_{H,t}^{r}$	$\displaystyle =\frac{1}{\beta}\left( \widehat{B}_{H,t-1}% ^{r}+\widehat{R}_{H,t-1}^{r}\right)$
	$\displaystyle -\frac{s_{H}^{r}}{B_{H}^{r}}\left( \frac{\tau^{L}p_{H}Y_{H}(\sigma -1)}{\sigma s_{H}^{r}}(\widehat{\tau}_{t}^{L}+\widehat{\omega}_{H,t}% ^{p}+\widehat{p}_{H,t}+\widehat{Y}_{H,t})+\frac{\tau^{C}C}{s_{H}^{r}% }(\widehat{\tau}_{t}^{C}+\widehat{C}_{t})-\frac{p_{H}G_{H}}{s_{H}^{r}% }(\widehat{p}_{H,t}+\widehat{G}_{H,t})\right)$

$\displaystyle \widehat{B}_{F,t}^{r}$	$\displaystyle =\frac{1}{\beta}\left( \widehat{B}_{F,t-1}% ^{r}+\widehat{R}_{F,t-1}^{r}\right)$
	$\displaystyle -\frac{s_{F}^{r}}{B_{F}^{r}}\left( \frac{\tau^{L\ast}p_{F}Y_{F}(\sigma -1)}{\sigma s_{F}^{r}}(\widehat{\tau}_{t}^{L\ast}+\widehat{\omega}_{F,t}% ^{p}+\widehat{p}_{F,t}+\widehat{Y}_{F,t})+\frac{\tau^{C\ast}C^{\ast}}% {s_{F}^{r}}(\widehat{\tau}_{t}^{C\ast}+\widehat{C}_{t}^{\ast})-\frac {p_{F}G_{F}}{s_{F}^{r}}(\widehat{p}_{F,t}+\widehat{G}_{F,t})\right)$

Balanced-budget rule ( $\widehat{G}_{H,t}=\widehat{G}_{F,t}=0$ )

	$\displaystyle \frac{1}{\beta}\left( \widehat{B}_{H,t-1}^{r}+\widehat{R}_{H,t-1}% ^{r}\right)$
	$\displaystyle =\frac{s_{H}^{r}}{B_{H}^{r}}\left( \frac{\tau^{L}p_{H}Y_{H}(\sigma -1)}{\sigma s_{H}^{r}}(\widehat{\tau}_{t}^{L}+\widehat{\omega}_{H,t}% ^{p}+\widehat{p}_{H,t}+\widehat{Y}_{H,t})+\frac{\tau^{C}C}{s_{H}^{r}% }(\widehat{\tau}_{t}^{C}+\widehat{C}_{t})-\frac{p_{H}G_{H}}{s_{H}^{r}% }(\widehat{p}_{H,t}+\widehat{G}_{H,t})\right)$

	$\displaystyle \frac{1}{\beta}\left( \widehat{B}_{F,t-1}^{r}+\widehat{R}_{F,t-1}% ^{r}\right)$
	$\displaystyle =\frac{s_{F}^{r}}{B_{F}^{r}}\left( \frac{\tau^{L\ast}p_{F}Y_{F}(\sigma -1)}{\sigma s_{F}^{r}}(\widehat{\tau}_{t}^{L\ast}+\widehat{\omega}_{F,t}% ^{p}+\widehat{p}_{F,t}+\widehat{Y}_{F,t})+\frac{\tau^{C\ast}C^{\ast}}% {s_{F}^{r}}(\widehat{\tau}_{t}^{C\ast}+\widehat{C}_{t}^{\ast})-\frac {p_{F}G_{F}}{s_{F}^{r}}(\widehat{p}_{F,t}+\widehat{G}_{F,t})\right)$

Asset markets:

1) Complete markets:

$\displaystyle \widehat{C}_{t}^{\ast}=\widehat{C}_{t}-\frac{1}{\rho}\widehat{RS}_{t}+\frac {1}{\rho}\left( w^{C}\widehat{\tau}_{t}^{C}-w^{C\ast}\widehat{\tau}% _{t}^{C\ast}\right)$

2) Financial autarky:

$\displaystyle \widehat{C}_{t}=(n-1)\widehat{T}_{t}+d_{Y_{h}}\widehat{Y_{H}}_{t}.$

3) Bond economy:

$\displaystyle \widehat{C_{t}}+\frac{1}{\overline{C}}\widehat{B}_{H,t}^{u,r}-\frac{1}% {\beta\overline{C}}\widehat{B}_{H,t-1}^{u,r}=\frac{\overline{p_{H}}% \overline{Y_{H}}}{\overline{C}}(\widehat{p}_{H,t}+\widehat{Y}_{H,t}% )-\frac{\overline{p_{H}}\overline{G_{H}}}{\overline{C}}(\widehat{p}% _{H,t}+\widehat{G}_{H,t}).$

C.2 The sticky price economy

The equations for the labour supply, market clearing, complete asset markets, the Euler conditions, 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:

$\displaystyle \widehat{\pi}_{H,t}$	$\displaystyle =k_{H}(\widehat{\omega}_{H,t}^{c}+w^{C}\widehat{\tau }_{t}^{C}+w^{L}\widehat{\tau}_{t}^{L}+(1-\nu)\widehat{T}_{t})+\beta E_{t}\widehat{\pi}_{H,t+1}$
$\displaystyle \widehat{\pi}_{F,t}$	$\displaystyle =k_{F}(\widehat{\omega}_{F,t}^{c}+w^{C\ast }\widehat{\tau}_{t}^{C\ast}+w^{L\ast}\widehat{\tau}_{t}^{L\ast}-\nu^{\ast }\widehat{T}_{t})+\beta E_{t}\widehat{\pi}_{F,t+1}%$

Monetary policy rule:

$\displaystyle \widehat{R}_{t}=\mu_{y_{u}}(1-\kappa)\widehat{Y}_{t-1}^{U}+\mu_{\pi_{u}% }(1-\kappa)\widehat{\pi}_{t-1}^{U}+\kappa\widehat{R}_{t-1}%$

$\displaystyle \widehat{\pi}_{t}^{U}=s_{C}\widehat{\pi}_{t}+(1-s_{C})\widehat{\pi}_{t}^{\ast}%$

$\displaystyle \widehat{Y}_{t}^{U}=\left( (1-s_{C})\nu^{\ast}-s_{Y}+s_{C}\nu\right) \widehat{T}_{t}+s_{Y}\widehat{Y}_{H,t}+\left( 1-s_{Y}\right) \widehat{Y}% _{F,t}%$

where $s_{Y}=\frac{nP_{H}Y_{H}}{P_{U}Y_{U}}.$

After-tax union-wide CPI inflation rate (used in Section 5.3):

$\displaystyle \widehat{\pi}_{U,t}^{\tau^{C}}=s_{C}^{\tau^{C}}(1+\tau^{C})\pi_{t}% +(1-s_{C}^{\tau^{C}})(1+\tau^{C\ast})\widehat{\pi}_{t}^{\ast}+s_{C}^{\tau^{C}% }(1+\tau^{C})w_{C}\left( \widehat{\tau}_{t}^{C}-\widehat{\tau}_{t-1}% ^{C}\right) +(1-s_{C}^{\tau^{C}})(1+\tau^{C\ast})w_{C}^{\ast}\left( \widehat{\tau}_{t}^{C\ast}-\widehat{\tau}_{t-1}^{C\ast}\right)$

Relationships between inflation rates and terms of trade:

$\displaystyle \widehat{\pi}_{t}$	$\displaystyle =\nu\widehat{\pi}_{H,t}+(1-\nu)\widehat{\pi}_{F,t}$
$\displaystyle \widehat{\pi}_{t}^{\ast}$	$\displaystyle =\nu^{\ast}\widehat{\pi}_{H,t}+(1-\nu^{\ast })\widehat{\pi}_{F,t}$
$\displaystyle \widehat{T}_{t}$	$\displaystyle =\widehat{\pi}_{F,t}-\widehat{\pi}_{H,t}+\widehat{T}_{t-1}%$

C.3 Equations used in Section 4

To derive equation (26), let $\widehat{\tau}_{t}^{C\ast}=0,$ $\widehat{G}_{H,t}=\widehat{G}_{F,t}=0.$ Moreover, assuming there exists no home bias ( $\lambda=\lambda^{\ast}=1$ ), this implies $\nu=\nu^{\ast}=n$ and $\widehat{RS}_{t}=0.$ Combining the equations for real consumer wages, labour supplies and complete asset markets yields

$\displaystyle \widehat{Y}_{H,t}$	$\displaystyle =\frac{1}{\eta}\left[ -(1-n)\widehat{T}_{t}% -w^{C}\widehat{\tau}_{t}^{C}-w^{L}\widehat{\tau}_{t}^{L}-\rho\widehat{C}% _{t}\right]$
$\displaystyle \widehat{Y}_{F,t}$	$\displaystyle =\frac{1}{\eta}\left[ n\widehat{T}_{t}-w^{L\ast }\widehat{\tau}_{t}^{L\ast}-\rho\widehat{C}_{t}-w^{C}\widehat{\tau}_{t}% ^{C}\right]$

Combining the equations for market clearing and complete asset markets yields

$\displaystyle \widehat{Y}_{H,t}$	$\displaystyle =d_{CH}(\widehat{C_{t}}+\phi(1-n)\widehat{T}% _{t})+d_{C^{\ast}H}\left( \widehat{C}_{t}+\frac{1}{\rho}w^{C}\widehat{\tau }_{t}^{C}+\phi(1-n)\widehat{T}_{t}\right)$
$\displaystyle \widehat{Y}_{F,t}$	$\displaystyle =d_{CF}(\widehat{C_{t}}-\phi n\widehat{T}_{t}% )+d_{C^{\ast}F}\left( \widehat{C}_{t}+\frac{1}{\rho}w^{C}\widehat{\tau}% _{t}^{C}-\phi n\widehat{T}_{t}\right)$

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 $d_{CH}=d_{CF}\equiv d_{C}$ and $d_{C^{\ast}% H}=d_{C^{\ast}F}\equiv d_{C^{\ast}}.$ Then, by combining the two pairs of equations and substituting out for i) $\widehat{Y}_{H,t}$ and $\widehat{Y}% _{F,t}$ and ii) $\widehat{C}_{t}$ one can solve for $\widehat{T}_{t},$ leading to

$\displaystyle \widehat{T}_{t}=\frac{1}{1+\eta\phi\left( d_{C}+d_{C^{\ast}}\right) }(w^{L\ast}\widehat{\tau}_{t}^{L\ast}-w^{L}\widehat{\tau}_{t}^{L})$

which is equation (26) in the main text. Using this expression in the above derived expressions for $\widehat{C_{t}}$ and $\widehat{Y}_{H,t}$ , one readily verifies

$\displaystyle \widehat{C_{t}}=-\frac{1+d_{C^{\ast}}\frac{\eta}{\rho}}{\eta\left( d_{C}+d_{C^{\ast}}\right) +\rho}w^{C}\widehat{\tau}_{t}^{C}-n\frac{1}% {\eta\left( d_{C}+d_{C^{\ast}}\right) +\rho}w^{L}\widehat{\tau}_{t}% ^{L}-(1-n)\frac{1}{\eta\left( d_{C}+d_{C^{\ast}}\right) +\rho}w^{L\ast }\widehat{\tau}_{t}^{L\ast}%$

$\displaystyle \widehat{Y}_{H,t}=\frac{1}{\eta}\left[ -\frac{\eta d_{C}}{\eta\left( d_{C}+d_{C^{\ast}}\right) +\rho}w^{C}\widehat{\tau}_{t}^{C}+\left[ n\theta-\frac{\eta\phi\left( d_{C}+d_{C^{\ast}}\right) }{1+\eta\phi\left( d_{C}+d_{C^{\ast}}\right) }\right] w^{L}\widehat{\tau}_{t}^{L}+(1-n)\theta w^{L\ast}\widehat{\tau}_{t}^{L\ast}\right]$

with

$\displaystyle \theta=\frac{1}{1+\frac{\eta}{\rho}\left( d_{C}+d_{C^{\ast}}\right) }% -\frac{1}{1+\eta\phi\left( d_{C}+d_{C^{\ast}}\right) }%$

and $\theta>0$ if $\phi\rho>1.$ Moreover, one can also verify that the equations (27) and (28), in which $\widehat{T}_{t}$ has not yet been substituted out, are equivalent to these expressions for $\widehat{C_{t}}$ and $\widehat{Y}_{H,t}.$

Similarly, one can derive equivalent equations for the case of financial autarky. In particular, the coefficient $\gamma_{fa}$ in equation (29) is equal to $\gamma_{fa}=\frac{1}{(\rho\phi-\rho+1)+(\phi -1)\eta d_{C}+\eta d_{C^{\ast}}(\phi+n(1-\phi))}$ .

C.4 Sticky wages in Section 5.4

We assume that in the short run nominal wages are sticky à 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 can be derived from the minimization problem of firms and is given by:

$\displaystyle L_{t}(j)=\left( \frac{w_{t}(j)}{w_{t}}\right) ^{-\sigma_{w}}L_{t},$

(30)

where $\sigma_{w}$ is the elasticity of demand for differentiated labour,

is the economy-wide real wage and $L_{t}$ is the economy-wide labour. Note that the total labour supply by worker

is given by $L_{t}(j)=\int_{0}% ^{n}L_{t,j}(i)di$ , where $L_{t,j}(i)$ is the amount of labour supplied by worker

to firm

We follow (Erceg et al., 2000) and assume that in each period only a fraction ( $1-\alpha_{w}$ ) of households can change their wages optimally. We assume that $\alpha_{w}=\alpha$ (i.e. the degree of wage stickiness is equal to the degree of price stickiness). The problem for a worker who is able to reset his or her wage is to choose a wage so as to maximize:

$\displaystyle \max E_{t_{0}}\sum\limits_{t=t_{0}}^{\infty}\beta^{t}{\alpha}_{w}% ^{t}(U_{C,t_{0}+t}w_{t}(j)-V_{L(j),t_{0}+t})L_{t_{0}+t}(j).$

(31)

The associated aggregate wage index is given by:

$\displaystyle W_{t}^{1-\sigma_{w}}=\alpha_{w} W_{t-1}^{1-\sigma_{w}}+(1-\alpha _{w})\widetilde{W}_{t}^{1-\sigma_{w}},$

(32)

where $\widetilde{W}$ is the nominal wage that will be set by all workers who are able to reset their wages and

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:

$\displaystyle \widehat{\pi}_{w,t}=\frac{(1-\alpha_{w})(1-\beta\alpha_{w})}{(1+\sigma_{w}% \eta)\alpha_{w}}(\eta\widehat{Y}_{H,t}+\rho\widehat{C}_{t}-\widehat{w}% _{H,t}^{c})+\beta\widehat{\pi}_{w,t+1}.$

(33)

D. Short-run analysis

Figure 1: Short-run effects of the tax shift - complete markets $Figure 1: Short-run effects of the tax shift - complete markets. Six Panels. The figure plots impulse responses to the tax shift shock for the case of complete markets. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Terms of trade. Terms of trade increases on impact and continues to rise following a hump-shape pattern to reach a new higher steady state level. Top-middle panel: Output. Home output rises in response to the shock following a hump-shape pattern, while foreign output decreases. Top-right: Consumption. Home consumption declines on impact and then it rises somewhat but its new steady state level is smaller than the original steady state level. Foreign consumption increases on impact and then it declines somewhat but reaches the new steady state level that is higher than the original one. Bottom-left panel: Real consumer wage. Home real consumer wage declines on impact and then it increases following a hump-shape pattern to reach a new higher steady state level. Foreign real consumer wage increases on impact and then declines somewhat but reaches a new higher steady state level. Bottom-middle panel: Producer inflation. Home producer inflation declines on impact and then increases to reach zero after approximately 20 quarters. Foreign producer inflation increases on impact and then declines to reach zero after approximately 20 quarters. Bottom-right panel: Union-wide inflation. Core inflation does not respond to the shock. Headline inflation increases on impact but in the second quarter reaches zero.$

Figure 2: Short-run effects of the tax shift - comparison of different asset markets $Figure 2: Short-run effects of the tax shift - comparison of different asset markets. Six panels. The figure plots impulse responses to the tax shift shock for different asset market structures: complete markets, incomplete markets, financial autarky. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under three different assumptions about asset market structure in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Terms of trade. In all cases terms of trade increase. However under complete markets terms of trade increase is much stronger (the new long run level is 10 times higher) than in the case of financial autarky and incomplete markets (here response of terms of trade is almost identical). Top-middle panel: Home output. Home output increases in all cases. Under complete markets it increases steadily to reach its new steady state level. In the case of financial autarky and incomplete markets home output rises on impact and stays at this new level. Top-right panel: Home consumption. Under complete markets home consumption declines permanently, while under financial autarky and incomplete markets home consumption increases permanently. Bottom-left panel: Home real consumer wage. Under complete markets home real consumer wage declines on impact and then it increases to reach a new higher steady state level. Under financial autarky and incomplete markets home real consumer wage increases on impact and stays at this new level (higher than under complete markets). Bottom-middle panel: Foreign output. Under complete markets foreign output declines steadily to reach a new lower level. Under financial autarky and incomplete markets foreign output declines slightly on impact and stays at this new lower level (which is however higher than under complete markets). Bottom-right panel: Foreign consumption. In all cases foreign consumption increases and then reaches a higher steady state level. However, under complete markets the long run rise in consumption is around 10 times higher than under incomplete markets and financial autarky.$

Figure 3: Short-run effects of the tax shift - incomplete markets $Figure 3: Short-run effects of the tax shift - incomplete markets. Six Panels. The figure plots impulse responses to the tax shift shock for the case of incomplete markets. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables in $\%$ deviations from the steady state to the tax shift shock. Note that responses of some variables are similar in qualitative sense to complete markets, however quantitatively responses are much smaller. Top-left panel: Terms of trade. Terms of trade increases on impact and continues to rise following a hump-shape pattern to reach a new higher steady state level. Top-middle panel: Output. Home output rises in response to the shock following a hump-shape pattern, while foreign output first increases on impact (but by much less than home output) and then it decreases. Top-right: Consumption. Home consumption increases on impact and then it rises somewhat to reach its new higher steady state level. Foreign consumption increases on impact and then it declines somewhat but reaches a new higher steady state level, but smaller (around 6 times) than that of home consumption. Bottom-left panel: Real consumer wage. Home real consumer wage increases on impact and then it increases following a hump-shape pattern to reach a new higher steady state level. Foreign real consumer wage increases on impact and then declines almost to its original steady state level. Bottom-middle panel: Producer inflation. Home producer inflation declines on impact and then increases to reach zero after approximately 20 quarters. Foreign producer inflation increases on impact and then declines to reach zero after approximately 20 quarters. Bottom-right panel: Union-wide inflation. Core inflation does not respond to the shock. Headline inflation increases on impact but in the second quarter reaches zero.$

Figure 4: Short-run effects of the tax shift - target of monetary policy (complete markets) $Figure 4: Short-run effects of the tax shift - target of monetary policy (complete markets). Six panels. The figure plots impulse responses to the tax shift shock for different targets of monetary policy: core CPI targeting and headline CPI targeting. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about target of monetary policy in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. Under core CPI targeting core union-wide inflation does not respond to the shock. Under headline CPI targeting core union-wide inflation decreases on impact to return to its steady state after around 20 quarters. Top-middle panel: Home output. In both cases home output decreases on impact and then rises to reach a new higher steady state level. The initial decline of home output is much stronger for headline CPI targeting. Top-right panel: Home consumption. In both cases home consumption decreases on impact and then rises to reach a new lower steady state level. The initial decline of home consumption is much stronger for headline CPI targeting. Bottom-left panel: Headline union-wide inflation. In both cases headline union-wide inflation increases on impact. Under core CPI targeting headline union-wide inflation reaches zero in the next period. Under headline CPI targeting the initial rise in headline union-wide inflation is smaller and then in the subsequent quarters it falls below zero to reach the initial steady state only after 10 quarters. Bottom-middle panel: Foreign output. Under core CPI targeting foreign output increases on impact and then declines to reach a new lower steady state level. Under headline CPI targeting foreign output declines on impact to the new lower steady state level and stays there. Bottom-right panel: Foreign consumption. Under core CPI targeting foreign consumption increases on impact and then declines somewhat to reach a new higher steady state level. Under headline CPI targeting foreign consumption declines on impact and then starts rising to reach a new higher steady state level.$

Figure 5: Short-run effects of the tax shift - anticipation of fiscal policy (complete markets) $Figure 5: Short-run effects of the tax shift - anticipation of fiscal policy (complete markets). Eight panels. The figure plots impulse responses to the tax shift shock under two different assumptions about the shock : anticipated and unanticipated. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about the tax shock in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. If the shock is unanticipated core union-wide inflation does not respond to the shock. If the shock is anticipated core union-wide inflation increases on impact and then declines below zero to reach the steady state after 20 quarters. Top-middle panel: Home output. If the shock is unanticipated home output declines modestly on impact and then start rising to reach a new higher steady state level. If the shock is anticipated home output first rises and then declines when the tax shift is realised and eventually rises to reach a new higher steady state level. Top-middle panel: Home consumption. If the shock is unanticipated home consumption declines on impact and then rises to a new lower steady state level. If the shock is anticipated home consumption increases on impact and then it declines to rise a bit later to a new lower steady state level. Top-right panel: Home producer inflation. If the shock is unanticipated home producer inflation declines on impact and then starts rising to reach the steady state after 20 quarters. If the shock is anticipated home producer inflation increases on impact and then declines to start rising to reach the original steady state level after 20 quarters. Bottom-left panel: Foreign output. In both cases foreign output increases on impact and then it declines to reach a new lower steady state level. If the shock is anticipated an initial increase in foreign output is higher. Bottom-middle panel: Foreign consumption. If the shock is unanticipated foreign consumption increases on impact and then declines to reach a new higher steady state level.If the shock is anticipated an initial increase in foreign consumption is smaller. Subsequently, foreign consumption declines and later rises to reach a new higher steady state level. Bottom-middle panel: Foreign producer inflation. In both cases foreign producer inflation increases on impact and then starts decreasing to reach the steady state after 20 quarters. An initial increase is stronger for the case of the anticipated shocks. Bottom-right panel: Terms of trade. In both cases terms of trade increase on impact and keep on rising to reach a new higher steady state level. In case of the anticipated shock the initial increase of terms of trade is smaller.$

Figure 6: Short-run effects of the tax shift - target of monetary policy (incomplete markets) $Figure 6: Short-run effects of the tax shift - target of monetary policy (incomplete markets). Six panels. The figure plots impulse responses to the tax shift shock for different targets of monetary policy: core CPI targeting and headline CPI targeting. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about target of monetary policy in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. Under core CPI targeting core union-wide inflation does not respond to the shock. Under headline CPI targeting core union-wide inflation decreases on impact to return to its steady state after around 20 quarters. Top-middle panel: Home output. Under core CPI targeting home output increases on impact and continues to rise to a reach a new higher steady state level. Under headline CPI targeting home output initially decreases and then starts rising to reach a new higher steady state level. Top-right panel: Home consumption. Under core CPI targeting home consumption increases on impact and reaches its new higher steady state level. Under headline CPI targeting home consumption declines on impact and then starts rising to reach its new higher steady state level. Bottom-left panel: Headline union-wide inflation. In both cases headline union-wide inflation increases on impact. Under core CPI targeting headline union-wide inflation reaches zero in the next period. Under headline CPI targeting the initial rise in headline union-wide inflation is smaller and then in the subsequent quarters it falls below zero to reach the initial steady state only after 10 quarters. Bottom-middle panel: Foreign output. Under core CPI targeting foreign output increases little on impact and then declines to reach a new lower steady state level. Under headline CPI targeting foreign output declines on impact and then rises to reach a new lower steady state level. Bottom-right panel: Foreign consumption. Under core CPI targeting foreign consumption increases slightly on impact and stays at this level. Under headline CPI targeting foreign consumption declines on impact and then starts rising to reach a new slightly higher steady state level.$

Figure 7: Short-run effects of the tax shift - anticipation of fiscal policy (incomplete markets) $Figure 7: Short-run effects of the tax shift - anticipation of fiscal policy (incomplete markets). Eight panels. The figure plots impulse responses to the tax shift shock under two different assumptions about the shock : anticipated and unanticipated. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about the tax shock in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. If the shock is unanticipated core union-wide inflation does not respond to the shock. If the shock is anticipated core union-wide inflation increases on impact and then declines below zero to reach the steady state after 20 quarters. Top-middle panel: Home output. If the shock is unanticipated home output increases on impact and then keeps rising to reach a new higher steady state level. If the shock is anticipated home output first rises and then declines when the tax shift is realised and eventually rises to reach a new higher steady state level. Top-middle panel: Home consumption. If the shock is unanticipated home consumption increases on impact and stays at this level. If the shock is anticipated home consumption increases on impact and then it declines to rise a bit later to a new higher steady state level. Top-right panel: Home producer inflation. If the shock is unanticipated home producer inflation declines on impact and then starts rising to reach the steady state after 20 quarters. If the shock is anticipated home producer inflation increases on impact and then declines to start rising to reach the original steady state level after 20 quarters. Bottom-left panel: Foreign output. In both cases foreign output increases on impact and then it declines to reach a new lower steady state level. If the shock is anticipated an initial increase in foreign output is higher. Bottom-middle panel: Foreign consumption. If the shock is unanticipated foreign consumption increases on impact and then declines to reach a new higher steady state level.If the shock is anticipated foreign consumption initially declines and then starts rising to reach a new higher steady state level. Bottom-middle panel: Foreign producer inflation. In both cases foreign producer inflation increases on impact and then starts decreasing to reach the steady state after 20 quarters. An initial increase is stronger for the case of the anticipated shocks. Bottom-right panel: Terms of trade. If the shock is unanticipated terms of trade increase on impact and keep on increasing to reach a new higher steady state level. If the shock is anticipated terms of trade decrease on impact and then increase to reach a new higher steady state level.$

Figure 8: Short-run effects of the tax shift - sticky wages (complete markets) $Figure 8: Short-run effects of the tax shift - sticky wages (complete markets). Eight panels. The figure plots impulse responses to the tax shift shock under two different assumptions about wages: flexible or sticky. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about stickiness of wages in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. If wages are flexible core union-wide inflation does not respond to the shock. If wages are sticky core union-wide inflation decreases on impact and then starts rising to reach the steady state after 20 quarters. Top-middle panel: Home output. In both cases home output increases steadily to reach a new higher steady state level. However an increase in home output under flexible wages is stronger. Top-middle panel: Home consumption. Under both cases home consumption declines on impact and then it starts increasing to reach a new lower steady state level. The decline in home consumption under flexible wages is much stronger. Top-right panel: Home real consumer wage. If wages are flexible home real consumer wage declines on impact and starts rising to reach a new higher steady state level. If wages are sticky home real consumer wage increases little on impact and then it continues to rise to reach a new higher steady state level. Bottom-left panel: Foreign output. In both cases foreign output increases on impact and then it declines to reach a new lower steady state level. If wages are sticky an initial increase in foreign output is higher. Bottom-middle panel: Foreign consumption. In both cases foreign consumption increases on impact and then declines to reach a new higher steady state level. If wages are sticky an initial increase in foreign consumption is higher. Bottom-middle panel: Foreign real consumer wage. If wages are flexible foreign real consumer wage increases on impact strongly and then starts declining to reach a new higher steady state level. If wages are sticky foreign real consumer wage increases on impact by much less and then increases to reach a new higher steady state level. Bottom-right panel: Terms of trade. In both cases terms of trade increase on impact and then continue to rise to reach a new higher steady state level. However when wages are flexible the initial increase in terms of trade is higher.$

Figure 9: Short-run effects of the tax shift - sticky wages (incomplete markets) $Figure 9: Short-run effects of the tax shift - sticky wages (incomplete markets). Eight panels. The figure plots impulse responses to the tax shift shock under two different assumptions about wages: flexible or sticky. X axis in all panels displays quarters after the shock. Y axis in all panels displays response of respective variables under two different assumptions about stickiness of wages in $\%$ deviations from the steady state to the tax shift shock. Top-left panel: Core union-wide inflation. If wages are flexible core union-wide inflation does not respond to the shock. If wages are sticky core union-wide inflation decreases on impact and then starts rising to reach the steady state after 20 quarters. Top-middle panel: Home output. In both cases home output increases steadily to reach a new higher steady state level. However an increase in home output under sticky wages is stronger. Top-middle panel: Home consumption. Under both cases home consumption increase on impact and then it starts increasing to reach a new higher steady state level. The initial increase in home consumption under sticky wages is much stronger. Top-right panel: Home real consumer wage. In both cases home real consumer wage increases on impact and then keeps on rising to reach a new higher steady state level. The initial increase of home real consumer wage under is much stronger under flexible prices. Bottom-left panel: Foreign output. In both cases foreign output increases on impact and then it declines to reach a new lower steady state level. If wages are sticky an initial increase in foreign output is higher. Bottom-middle panel: Foreign consumption. In both cases foreign consumption increases on impact and then declines to reach a new higher steady state level. If wages are sticky an initial increase in foreign consumption is higher. Bottom-middle panel: Foreign real consumer wage. If wages are flexible foreign real consumer wage increases on impact strongly and then starts declining to reach a new higher steady state level. If wages are sticky foreign real consumer wage increases on impact by much less and then increases to reach a new higher steady state level. Bottom-right panel: Terms of trade. In both cases terms of trade increase on impact and then continue to rise to reach a new higher steady state level. However when wages are sticky the initial increase in terms of trade is higher.$

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Footnotes

* 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. Return to Text

1. Federal Reserve Board, Monetary Affairs, United States; e-mail: [email protected]. Return to Text

2. European Central Bank, Division Monetary Policy Strategy (currently on leave) and University of Mainz, Germany. e-mail: [email protected]. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Board or the European Central Bank. Return to Text

3. The numbers refer to the year 2006 and are taken from the detailed description of European taxation structures from a cross-country perspective published in (European Commission, 2008). Notwithstanding this variation across countries, indirect taxes have become the main source of tax revenues in the EU (amounting in 2006 to 13.9% of GDP), followed by direct taxes (13.5% of GDP) and social security contributions (12.5% of GDP). Since the onset of the financial crisis the role of indirect taxes as the main revenue source in the EU has further increased (see (European Commission, 2012)). Return to Text

4. In 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 recent policy initiatives and proposals that advocate a shift of tax systems towards indirect taxes, both at the European level and within individual member countries, see (European Commission, 2006), (European Commission, 2008). Return to Text

5. As argued below, our model is too stylised to address closed-economy aspects in detail. Nevertheless, the closed-economy version offers an important benchmark for the discussion of the open economy aspects which are central for the assessment of the fiscal devaluation hypothesis. Return to Text

6. For 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. Return to Text

7. (Canzoneri et al., 2004) develop a monetary union model which allows for countries of different size and asymmetric 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. Return to Text

8. In order to have a well defined maximisation problem we assume that

is twice continuously differentiable, increasing and concave in $C_{t},$ while

is twice continuously differentiable, increasing and convex in $L_{t}$ . For the specific functional forms, see Section 2.7.1. Return to Text

9. One 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 $R_{t-1}$ ), and vice versa, as considered by (Duarte & Wolman, 2008). Given the supply of government bonds introduced below, this would affect none of our results. Return to Text

10. For 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. Return to Text

11. Depending on the degree of financial integration. Return to Text

12. A 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, implying that the residually determined share of government expenditures is too high compared with the data. 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). Return to Text

13. For a discussion of this assumption, see Section 5.1. Return to Text

14. In this spirit, benefits from redirecting the tax structure towards consumption taxes are substantially larger in full-fledged 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 & Stiglitz, 1972), (Cooley & Hansen, 1992), (Mendoza & Tesar, 1998), and (Coleman, 2000). Return to Text

15. This implies that in the case of permanent shocks reactions under incomplete markets are equivalent to those in financial autarky. Return to Text

16. If the tax shift was temporary then foreign consumers could engage in borrowing and thus insure themselves against the tax shift. Return to Text

17. Under 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. Return to Text

18. The following equations use $w^{C}% =\frac{\tau^{C}}{1+\tau^{C}},$ $w^{L}=\frac{\tau^{L}}{1-\tau^{L}},$ $w^{C^{\ast}}=\frac{\tau^{C^{\ast}}}{1+\tau^{C^{\ast}}},$ $w^{L^{\ast}}% =\frac{\tau^{L^{\ast}}}{1-\tau^{L^{\ast}}},$ $d_{C}=\frac{nC}{Y_{H}},$ $d_{C^{\ast}}=\frac{(1-n)C^{\ast}}{Y_{F}}.$ Return to Text

19. Evidently, $\widehat{C}_{t}$ and $\widehat{Y}_{H,t}$ can be entirely expressed as a function of tax-related terms if one uses (26) in (27) and (28), as shown in the Appendix C.3. However, to understand the special role played by the terms of trade, (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:

$\displaystyle \widehat{\omega}_{F,t}^{c}=n\widehat{T}_{t}-w^{C^{\ast}}\widehat{\tau}% _{t}^{C^{\ast}}-w^{L^{\ast}}\widehat{\tau}_{t}^{L^{\ast}},$

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. Return to Text

20. The impulse responses in Figures 1 -3 are based on a first-order approximation of the economy developed in Section 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. Return to Text

21. Foreign real producer wages increase on impact in line with higher foreign consumer real wages. Return to Text

22. This 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). Return to Text

23. Recall 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. Return to Text

24. In the case of incomplete markets foreign consumption actually decreases on impact due to limited risk sharing. Return to Text

25. For simplicity, we assume that in both countries the degree of wage stickiness and of price stickiness are identical to each other. Return to Text

^♣ This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text