The unbearable tightness of being in a monetary union...

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European Economic Review 51 (2007) 1492–1513

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The unbearable tightness of being in a monetaryunion: Fiscal restrictions and regional stability

Evi Pappaa,�, Vanghelis Vassilatosb

aCEPR, Departament de Economia y d’ Historia Economica, Universitat Autonoma de Barcelona,

Edifici B - Campus de UAB, 08193 Bellaterra, Barcelona, SpainbDepartment of Economics, Athens University of Economics and Business, Patission Street 76, Greece

Received 22 December 2004; accepted 9 October 2006

Available online 17 January 2007

Abstract

We study how constrained fiscal policy can affect macroeconomic stability and welfare in a two-

region model of a monetary union with sticky prices and distortionary taxation. Both government

spending and taxes can be used to stabilize regional variables; however, the best welfare outcome is

obtained under some tax variability and constant regional inflations. We use a variety of rules to

characterize constrained fiscal policy and find that strict fiscal rules coupled with a monetary policy

that targets union-wide inflation result in regional inflation stability and the welfare costs of such

rules are not as unbearable as one would expect. Fiscal authorities can enhance welfare by targeting

the regional output gap, while targeting regional inflation is less successful since inflation stability is

guaranteed by the central bank.

r 2007 Elsevier B.V. All rights reserved.

JEL classification: E63; F41; F42

Keywords: Optimal policy; Monetary union; Budgetary restrictions; Fiscal rules

1. Introduction

The creation of a monetary union implies that domestic monetary policy cannot be usedto respond to region-specific economic disturbances. Interest rates, in fact, can no longerserve to meet regional targets for inflation and output and, for a region wishing to exert

see front matter r 2007 Elsevier B.V. All rights reserved.

.euroecorev.2006.10.006

nding author. Tel.: +34 93 5814695; fax: +3493 5812012.

dresses: [email protected] (E. Pappa), [email protected] (V. Vassilatos).

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ARTICLE IN PRESSE. Pappa, V. Vassilatos / European Economic Review 51 (2007) 1492–1513 1493

influence over its domestic economic conditions, fiscal policy is the only instrument left formaneuver.

The use of fiscal policy as a stabilization tool in a monetary union poses severalquestions: Can regional fiscal policy affect domestic macroeconomic conditions and how?Are country-members bound by fiscal constraints (as the ones imposed by the Stability andGrowth Pact (SGP) in the European Monetary Union, EMU) able to offset the effects ofshocks to regional variables? Can fiscal constraints be sustainable? What are their welfareconsequences? Are there alternative arrangements to fiscal constraints that are welfareimproving?

All these questions arise naturally in the EMU. The fiscal framework exemplified in theSGP attempts to combine flexibility, for coping with cyclical downturns, with discipline,for deterring negative externalities produced by individual members’ irresponsible policies.This paper addresses these questions: It investigates how regional fiscal policy can affectregional inflation and output in a two-region model of a monetary union where agentsderive utility from private and public spending, prices are sticky and taxes aredistortionary, and analyzes the macroeconomic and welfare properties of different typesof fiscal constraints.

In particular, we construct a DSGE model of a monetary union where regionalgovernment spending is financed with distortionary (income) taxation and study thedynamics of the economy under alternative fiscal rules when regions are subject toasymmetric productivity shocks.

We first obtain an analytical expression for the welfare criterion that can be used tocompare outcomes of different policies and characterize the optimal monetary and fiscalpolicy problem under commitment. In the optimal solution regional inflations arestabilized, while taxes and government spending vary relatively smoothly. We, then,consider general rules for fiscal policy in the two regions that try to imitate the SGPrequirements for fiscal policy performance and study the welfare and stability propertiesfor different specifications of these rules. We formulate the fiscal policy rules using taxesand/or government spending as instruments. We assume that the fiscal instrument in eachregion responds simultaneously to changes in the real debt, or deficit, from some targetlevel and/or can be used for regional stabilization purposes.

The tightness of fiscal constraints is not that unbearable in terms of welfare losses. Yet,when we contrast more flexible with rigid fiscal rules, we find that the fiscal authorities canimprove domestic welfare by targeting the regional output gap, while targeting regionalinflation is less effective when the central bank targets union-wide inflation. Our results arerobust to the fiscal instrument used and to the fiscal target adopted. We also find that usinggovernment spending to consolidate debt might result in instability and the welfare lossesassociated with a government spending rule that targets regional debt are positively relatedwith the usefulness of public expenditure. Finally, our theoretical predictions are consistentwith the empirical results for US states in Canova and Pappa (2006) who find that thesecond moments of macroeconomic variables in states with different budgetary restrictionsare economically and statistically similar.

The literature so far has mostly concentrated in analyzing monetary–fiscal interactionsin a monetary union. Most studies highlight that countercyclical fiscal policy may createcoordination failures between the central bank and regional fiscal authorities. Dixit andLambertini (2001, 2003) provide an excellent review of this literature. Others have studiedthe desirability of fiscal constraints in a monetary union and reached conflicting

ARTICLE IN PRESSE. Pappa, V. Vassilatos / European Economic Review 51 (2007) 1492–15131494

conclusions. For example, Dixit (2001) shows that fiscal freedom at the regional levelmight undermine the central bank’s objectives and provides arguments in favor of fiscalconstraints; Beetsma and Bovenberg (1998) and Beetsma and Uhlig (1999) argue that fiscalconstraints improve welfare because they correct the debt bias originating fromgovernment myopia; Uhlig (2002) shows that budgetary rules help avoid the free-ridingproblems arising from the interaction between many fiscal and one monetary authority inthe monetary union, while Chari and Kehoe (1998) and recently Adams and Billi (2004)claim that fiscal constraints are not necessary when the monetary authorities can commit.The importance of monetary policy commitment in a monetary union is also stressed inCooper and Kempf (2004).In the New Open Economy Macroeconomic Literature (NOEM) Beetsma and Jensen

(2004, 2005), Canzoneri et al. (2005), Ferrero (2005) and Gali and Monacelli (2005) alsostudy optimal monetary and fiscal policy in a currency area. Beetsma and Jensen (2004,2005) employ different assumptions and techniques to derive an analytical expression forthe welfare criterion. Gali and Monacelli (2005) study the problem of optimal monetaryand fiscal policy in a currency union composed of small open economies and do not allowfor variable distortionary taxation in equilibrium, while Canzoneri et al. (2005) focus onthe asymmetric effects of monetary policy for different regions within a monetary unionusing a different modeling scheme and metric for welfare evaluations. Our study is mostrelated to the work of Ferrero (2005). Relative to the latter, we endogenize governmentspending and allow agents to derive utility from public consumption (as in Gali andMonacelli, 2005) and employ taxes on labor instead of VAT taxes as a tax instrument.Also, we mostly focus on the macroeconomic stability and welfare evaluation of differentfiscal rules for a given monetary policy and employ government spending and/or taxes asfiscal instruments instead of debt for regional stabilization.The rest of the paper is organized as follows: The next section describes the model.

Section 3 examines equilibrium dynamics. Section 4 discusses optimal monetary and fiscalpolicy in our currency area and Section 5 studies the performance of different types of rulesfor regional deficits and debts. Section 6 concludes.

2. The model

The economy is a monetary union which consists of two regions, home and foreign, eachpopulated by a continuum of identical, infinitely lived agents. The representativehousehold in each region is endowed with one unit of time, and derives utility fromconsuming a basket of goods produced in both regions. Agents also derive utility frompublic expenditures that are made solely on home goods. There is no migration, sohouseholds supply labor to domestic firms only.Time is discrete. At each t ¼ 0; 1; . . . ; supply (productivity) shocks occur. Firms and

households make their decisions after observing the shocks. International financialmarkets are complete. That is, all agents have access to an international financial market,where they can trade a state-contingent nominal bond. The government in each regiondecides the amount of government expenditure in domestic goods, lump-sum taxes andtaxes on labor, and the level of debt. Monetary policy is conducted at the union level by acentral bank who sets the union-wide interest rate.


2.1. Representative households

The preferences of households are symmetric across regions, so we present the problemof the representative household in the home region. Utility is characterized by thefollowing function:

EX1t¼0

bt½o lnCt þ ð1� oÞ lnGt � Lt�, (2.1)

where 0obo1 is the subjective discount factor, Ct40 denotes private consumption, Gt

denotes government consumption that is valued positively by the private households whenoo1, Lt 2 ð0; 1Þ denotes hours worked, and E is an expectation operator.

The purchase of consumption goods is financed by after-tax labor income, profitincome, and lump-sum transfers from the government. The household can purchasenominal risk-free bonds from the domestic and the foreign government and has also accessto an international financial market, where state-contingent nominal bonds can be traded.The period–budget constraint facing the household is given by

PtCt þ EtQt;tþ1Dtþ1 þ Btþ1pð1� tltÞW tLt þDt þ ð1þ Rt�1ÞBt þPt þ tt,

t ¼ 0; 1; . . . , ð2:2Þ

where Pt is the price level, Dtþ1 is the holdings of the state-contingent nominal bond thatpays one unit of currency in period tþ 1 if a specified state is realized, Qt;tþ1 is the period-tprice of such bonds, Btþ1 is the holdings of the risk-free nominal government bonds in thetwo regions which yield ð1þ RtÞ in the coming period,1 W t is the nominal wage rate, tl

t, is atax on labor income, Pt is profit income, and tt is a lump-sum transfer from thegovernment.

The household maximizes (2.1) subject to (2.2). The supply of labor is, then, determinedby

Ct ¼ oð1� tltÞ

W t

Pt

, (2.3)

which states that the marginal rate of substitution between leisure and consumption equalsthe real after-tax consumption wage. The optimal consumption-saving decision isdescribed by

EtQt;tþ1 ¼ bEt

Ct

Ctþ1

Pt

Ptþ1, (2.4)

so that the intertemporal marginal rate of substitution equals the price of the state-contingent bond. The decision regarding the government bonds defines the Euler equation:

1

Ct

¼ bEt

1

Ctþ1

Pt

Ptþ1ð1þ RtÞ

� �. (2.5)

The private consumption basket consists of domestically produced and imported goods.Denote CHt the composite of domestically produced goods, and CFt the composite of

1Although households can hold foreign debt, we do not allow regional governments to do so. Still, regional

governments can implicitly finance each other’s deficit by lending to the other region’s households who have

purchased debt issued by them.


goods that are imported. Then, we define

Ct ¼ aCaHtC

1�aFt ; a ¼ a�að1� aÞa�1. (2.6)

Solving the household’s expenditure-minimizing problem yields the following demandfunctions for domestically produced and imported goods:

CHt ¼ aPtCt=PHt; CFt ¼ ð1� aÞPtCt=P�

Ft, (2.7)

where PHt is the price index of domestically produced goods, and P�

Ft is the price index ofimported goods, which are related to the home price level Pt by

Pt ¼ PaHtP�1�aFt . (2.8)

Throughout the analysis, we assume that firms set prices in the sellers’ local currency andthe law-of-one-price holds, so that the cost of imported goods in the home consumptionbasket is simply the price charged by foreign exporting firms since the exchange rate isfixed in a monetary union.

2.2. Firms

There is a continuum of firms producing differentiated goods indexed in the interval½0; 1�. The production of goods requires labor input, with constant-returns-to-scale (CRS)technologies

Y HtðjÞ þ Y �HtðjÞ þ Y GHtðjÞ ¼ AtLtðjÞ; j 2 ½0; 1�, (2.9)

where Y HtðjÞ is the output of type-j goods sold in the domestic market; Y �HtðjÞ is the outputof type-j goods exported to the foreign market; Y G

HtðjÞ is the output of type-j goods sold tothe domestic government, At is a productivity shock; and Lt is the labor input. Thelogarithm of the productivity shock follows an AR(1) process, that is,

lnðAtþ1Þ ¼ rA lnðAtÞ þ �Atþ1, (2.10)

where �At is a zero mean, iid normal process with finite variance s2A. Productivity shocks

across regions can be correlated with a correlation coefficient, rAHF .

We assume that the goods produced by firms are transformed into final consumptionaccording to

CHt ¼

Z 1

0

Y HtðjÞðy�1Þ=y dj

� �y=ðy�1Þ; C�Ht ¼

Z 1

0

Y �HtðjÞðy�1Þ=y dj

� �y=ðy�1Þ,

Gt ¼

Z 1

0

Y GHtðjÞ

ðy�1Þ=y dj

� �y=ðy�1Þ, ð2:11Þ

where y41, denotes the elasticity of substitution between differentiated products and Gt

the composite of domestically produced goods purchased by the government.The cost-minimizing problem of the final good sector implies demand functions for each

type of goods:

Y dHtðjÞ ¼

PHtðjÞ

PHt

� ��yCHt; Y d�

HtðjÞ ¼PHtðjÞ

PHt

� ��yC�Ht; Y Gd

Ht ðjÞ ¼PHtðjÞ

PHt

� ��yGt,

(2.12)


where PHtðjÞ is the price of type-j good, and PHt ¼ ½R 10 PHtðjÞ

1�y dj�1=ð1�yÞ is thecorresponding price index.

Firms are price takers in the input market and monopolistic competitors in theproduct markets. Following Calvo (1983), at each t each domestic producer is allowedto reset her price with a constant probability, ð1� gÞ, independently of the timeelapsed since the last adjustment. Producers face domestic (private and public) and foreigndemand for their product. Since they do not engage in international price discrimi-nation and the exchange rate is fixed, the real exchange rate is equal to the ratio of foreignto domestic prices: qt ¼ P�t =Pt. When a type-j producer receives a signal to change herprice, she chooses her new price PHtðjÞ so as to maximize her expected present value ofprofits

Et

X1t¼t

gt�tQt;t½PHtðjÞ �MCt�Ydt ðjÞ, (2.13)

where MCt is the nominal marginal cost, which is identical across firms since all firms face

the same input market, and Y dt ðjÞ is the demand schedule for type-j good described by the

sum of demands in (2.12), that is Y dt ðjÞ ¼ Y d

HtðjÞ þ Y �dHtðjÞ þ Y GdHtðjÞ. The cost-minimizing

problem of the firm yields the marginal cost function

MCt ¼W t=At, (2.14)

and a conditional labor demand function

Lt ¼1

At

Z 1

0

Y dt ðjÞdj. (2.15)

The solution to the profit-maximizing problem gives the optimal pricing rule

PHtðjÞ ¼ mEt

P1t¼t g

t�tQt;tMCtYdt

Et

P1t¼t gt�tQt;tY

dt

, (2.16)

where m ¼ y=ðy� 1Þ measures the steady-state markup.

2.3. Regional fiscal variables

In accordance with (2.11), government expenditures are solely allocated to domesticgoods. As we discuss later on, this assumption is not innocuous but is made here forsimplicity.

Apart from consuming domestic goods, the fiscal authority in the home region issuesnominal debt, Bt, taxes nominal wage income at the rate tl

t and has access to lump-sumtaxes, tt. These revenues finance domestic government spending, Gt, and interest paymentson debt. The government budget constraint in the home region is given by

Btþ1pð1þ RtÞBt þ PHtGt � Tt, (2.17)

where

Tt ¼ tltW tLt þ tt. (2.18)


2.4. Risk sharing, market clearing and aggregation

Since the state-contingent nominal bond is traded in the international financial market,the foreign household’s optimal consumption-saving decision leads to

EtQt;tþ1 ¼ bEt

C�tC�tþ1

P�tP�tþ1

. (2.19)

By combining this equation with its home region counterpart (2.4) and iterating withrespect to t, we obtain a risk-sharing condition

P�tPt

¼ c0

Ct

C�t, (2.20)

where c0 ¼ P�0C�0=P0C0. The risk-sharing condition links the ratio of foreign to domesticprices (i.e., the real exchange rate) to the marginal rate of substitution betweenconsumption in the two regions, so that all households face identical relative prices ofconsumption goods in the world market.In equilibrium, state-contingent bonds are in zero net supply in the world market, so

that Dt þD�t ¼ 0. Aggregate domestic demand in the home economy is given by

PHtY t ¼ PtCt þ PHtGt, (2.21)

where we have used the demand functions for domestic goods in (2.7) and (2.12) and theirforeign counterparts, and the risk-sharing condition (2.20). Similarly, we can show thataggregate demand in the foreign economy is

P�

FtY�t ¼ P�t C�t þ P

�

FtG�t . (2.22)

Let St ¼ P�

Ft=PHt denote the terms of trade. Then, it follows from (2.21) and (2.22),along with (2.20), that the terms of trade is given by

St ¼Y t � Gt

Y �t � G�t

� �. (2.23)

Eq. (2.21) and the price index relation Pt ¼ PaHtP�1�aFt imply that real domestic demand is

given by

Y t ¼ CtS1�at þ Gt, (2.24)

If we do the same for the foreign real domestic demand and use the risk-sharing conditionwe find that aggregate consumption in the home region is given by

Ct ¼ ½Y t � Gt�a½Y �t � G�t �

1�a. (2.25)

Similar conditions hold for demand and consumption in the foreign region.From (2.12) and (2.15), the aggregate demand for labor is given by

Lt ¼

Z 1

0

LtðjÞdj ¼1

At

Z 1

0

Y dt ðjÞdj ¼

DHt

At

Y t, (2.26)

where DH ¼R 10 ðPH ðjÞ=PH Þ

�yT dj is the domestic price dispersion index.To fully characterize the equilibrium we need to describe how monetary and fiscal policy

is conducted in each region. Our goal is to analyze the welfare and macroeconomicstability properties of different fiscal policy arrangements for a given monetary policy. As a


benchmark, we first analyze the optimal regime in which both fiscal authorities and thecentral bank cooperate. We model such a regime by assuming that a world planner choosesthe fiscal instruments in the two regions and the monetary instrument so as to maximizeworld welfare. Then, we study the welfare and stability properties of alternative fiscal rulesfor a given monetary policy. We assume that regional governments commit to followingthe fiscal rules.

3. Equilibrium dynamics

Before analyzing the behavior of our economy under sticky prices, we examine thedetermination of the key variables of interest under flexible prices. Output under flexibleprices is determined by

Y nt ¼ At, (3.1)

while government and private consumptions are

Gnt ¼ ð1� oÞAt; Cn

t ¼ oAat A�1�at . (3.2)

The behavior of public and private consumption in the flexible-price equilibrium mainlyreflects the composition of the corresponding consumption baskets. Since governmentconsumption is a composite of domestic goods only, it responds positively solely tochanges in domestic productivity. On the other hand, domestic private consumption, dueto risk sharing, reacts positively to productivity shocks, independently from their origin.

Also, the flexible-price level of the terms of trade is given by

Snt ¼

At

A�t. (3.3)

That is, an increase in the relative productivity in the home economy tends to lower therelative price of home goods.

In turn, the equilibrium of the sticky price economy is characterized by the optimizingconditions of households and firms. We denote ~xt ¼ xt � xn

t the deviation of equilibriumvariable xt from its flexible-price level xn

t , and we refer to this variable as the gap. Theprivate sector’s optimizing conditions in log-linear form for the home region can besummarized as follows:

pHt ¼ bEtpH;tþ1 þ kfmct, ð3:4Þ

fmct ¼1

o~yt �

1� oo

egt þtl

1� tlbtl

t, ð3:5Þ

~yt ¼ Et ~ytþ1 � o½brt � EtpH;tþ1� � ð1� oÞEtDegtþ1 þ oDbat, ð3:6Þ

Dest ¼ pHt � p�Ft � ½Dbat � Dba�t �, ð3:7Þ

where pHt denotes the domestic growth rate of prices, ~yt denotes the domestic output gap,egt the government consumption gap, est the terms-of-trade gap and btlt, brt and bat; ba�t the log

deviations of the tax rate, the nominal interest rate, and the home and foreign productivityshocks from their steady-state values, respectively. The constant k ¼ ð1� bgÞð1� gÞ=gmeasures the responsiveness of the pricing decisions to variations in the real marginal costgap, fmct. The foreign region’s optimizing conditions are similar.


Eqs. (3.4)–(3.7) are crucial for understanding the results we obtain. Eq. (3.4) describesthe Phillips-curve, relating domestic growth rate of prices to current and future marginalcosts. Eq. (3.5) has important implications for our results: Real marginal costs in the homeregion can be affected by regional fiscal policy because the latter affects the labor marketvariables. Taxes on labor income affect real wages and, thus, marginal costs, whileincreases in government spending affect marginal costs through their impact on demandand, thus, on employment. Eq. (3.6) is derived from log-linearizing the intertemporal Eulerequation (2.5) for the home household, with the consumption gap replaced by the outputgaps using Eq. (2.24). Finally, Eq. (3.7) gives the definition of the terms of trade.Eqs. (3.7), (3.4) and (3.5) imply that regional inflation stabilization is not compatible

with the terms-of-trade stabilization. Thus, the flexible-price equilibrium cannot beimplemented by stabilizing real marginal costs, as in closed economies, or open economieswith flexible exchange rates. This happens since by (3.7) the terms of trade under regionalinflation stability will deviate from their flexible-price value and the reallocation ofresources under flexible-prices cannot be achieved. In other words, the constancy of theexchange rate in a currency area makes the implementation of the flexible-priceequilibrium unfeasible. Thus, the creation of the monetary union is costly (see Pappa,2004) despite the presence of additional instruments (government spending and taxes) tosubstitute for the lack of the exchange rate instrument.To complete the analysis, we present the equation characterizing the dynamics of real

debt in the home region in log-linear form:

bssbbtþ1 þ bsspHtþ1 þ bssð1� aÞDestþ1 ¼

bss

bbbt þ

1� bb

brt �tl

1� tl

1þ oo

eyt

þ ð1� oÞ 1þtl

ð1� tlÞo

� �egt �tl

ð1� tlÞ2btl

t

� ð1� aÞ ð1� oÞ �tl

1� tl

� �est þ ft, ð3:8Þ

where bss is the steady-state value of debt and ft is a function of domestic and foreignproductivity shocks, ft ¼ ½afð1� oÞ � tl=ð1� tlÞg þ ð1� aÞð1� rAÞbss

�bat þ ð1� aÞ½1� o� ð1� rAÞbss

� tl=ð1� tlÞ�ba�t . The evolution of debt in the foreign economy isdefined by a similar equation.In order to characterize fully the equilibrium we need to define how monetary and

regional fiscal policies are determined.

4. Optimal monetary and fiscal policy

The optimal monetary and fiscal policy problem can be described as the problem of asocial planner that maximizes a weighted average of the two-regions households utilityfunctions, subject to the aggregate constraints in the two regions, the regional debtsevolution and the definition of the terms of trade. The policy problem we analyze is undercommitment on the part of the policymaker since, in this setting, the planner has incentivesto default from her initial decision when she is given the possibility to reoptimize. Inparticular, the planner would choose to create high/low inflation in the period shereoptimizes depending on the sign of the preceding shocks and keep inflation low/highthereafter.


We solve for the approximate policy problem. In order to characterize this and comparealternative fiscal policy arrangements we need a welfare metric. A natural welfare criterionin our model is the representative household’s expected life-time utility. Following theapproach described in Liu and Pappa (2005),2 we derive an analytical, quadraticexpression for the welfare criterion based on second-order approximations to the periodutility functions for the households in the home and the foreign region. We, then, find theallocations under optimal policy by maximizing the quadratic objective subject to the set oflog-linear equilibrium conditions.

In order to derive the welfare objective, we first describe the steady-state problem of thesocial planner. We, then, derive the objective through quadratic approximations to thetwo-regions representative households’ utility around that steady state. Finally, we solvethe optimal policy problem for small perturbations around the optimal steady state.3

We solve the steady-state problem of the planner in two stages. In the first stage shechooses the steady-state levels of public and private consumption and labor in the tworegions to maximize the union’s welfare. In the second stage she chooses the level of lump-sum taxes that determine the level of debt in the steady state.4 Since the population size isequal across countries, we assume that the planner assigns equal weights to each membercountry’s national welfare. The problem of the planner is to maximize 1

2½o lnC þ ð1�

oÞ lnG � L� þ 12½o lnC� þ ð1� oÞ lnG� � L�� subject to the national resource constraints

(2.25) and imposing A ¼ A� ¼ 1, Y j ¼ Lj and Y �j ¼ L�j and NX ¼ 0.5 The first-orderconditions for the planner’s steady-state problem lead to

Y ¼ L ¼ Y � ¼ L� ¼ 1, (4.1)

C ¼ C� ¼ o; G ¼ G� ¼ ð1� oÞ. (4.2)

The optimal tax rates for the social planner are, then, given by

1� tl ¼ 1� tl� ¼ m. (4.3)

The optimal tax rate is negative. That is, the planner’s optimal steady-state solutioninvolves a labor subsidy that exactly offsets the steady-state markup distortions. As aresult, the steady-state equilibrium allocations for the planner coincide with those underperfect competition and are, hence, Pareto optimal. Finally, given a steady-state level ofdebt-to-GDP ratio, lump-sum taxes are set to satisfy the government budget constraint inthe steady state.

2The approach of Liu–Pappa (2005) is similar with the approach of Benigno and Woodford (2005) for a closed

economy and Ferrero (2005) for an open economy.3The linearization of a model of fiscal policy is always troubling (see Giavazzi et al., 2000). Fiscal policies have

strong non-linear effects and might involve explosive paths for debt without violating the transversality condition.

Our approximate equilibrium avoids these problems by requiring solutions for the endogenous variables that

deviate little from the optimal steady state. Thus, in the approximate problem strong non-linear effects of fiscal

policy are ruled out.4The second stage problem is introduced to guarantee steady-state debt-to-GDP ratios that match their data

analogues for Germany and France.5Net exports are given by NX t ¼ PHtC

�Ht � P�FtCFt ¼ ð1� aÞP�t C�t ½1� ðPt=P�t ÞCt=C�t �. For net exports to be

zero in the steady state, the parameter c0 in the risk-sharing condition (2.20) should be set equal to one.


In the Appendix, we derive the planner’s welfare objective, which is given by

WPlanner ¼ �1

4E0

X1t¼0

btLPlannert þ t:i:p:þOðkxk3Þ, (4.4)

where t:i:p. refers to terms independent of policy (such as constants and exogenousprocesses) and Oðkxk3Þ denotes terms of order higher than second.The period loss function is

LPlannert ¼ yk�1p2Ht þ yk��1p�2Ft þ ~y2

t þ ~y�2t þ1� ooðeyt � egtÞ

2þ

1� ooðey�t � eg�t Þ2.

(4.5)

To gain some intuition for the planner’s loss function, we show in the Appendix that wecan express (4.5) in terms of consumption gaps using (2.24) as

LPlannert ¼ yk�1p2Ht þ yk��1p�2Ft þ ½oect þ ð1� oÞegt�

2 þ ½oec�t þ ð1� oÞeg�t �2þ ð1� oÞoðect � egtÞ

2þ ð1� oÞoðect � egtÞ

2þ 2oað1� aÞes2t . ð4:6Þ

Since the planner chooses subsidy rates to fully offset all markup distortions, the flexible-price equilibrium allocations are Pareto optimal and the planner’s objective reflects herwillingness to close all the relative gaps when conducting optimal policy. In order,however, to minimize the output gaps, the planner has to stabilize fluctuations in theterms-of-trade gap and to induce comovements in regional private and publicconsumptions that guarantee movements in regional output under sticky prices thatresemble the dynamics of output under flexible prices.Notice that when the economy is closed, a ¼ 1, and agents derive no utility from

government consumption, o ¼ 1, the welfare objective in (4.5) reduces to a similarexpression as the one in Benigno and Woodford (2005). On the other hand, for ao1 ando ¼ 1, the period loss utility in (4.5) becomes similar to the one presented in Ferrero(2005). Also, our welfare criterion is directly comparable with the one presented in Galiand Monacelli (2005) except that, in our case, the members of the monetary union are twoequally large regions and for that reason they can affect the terms of trade in general.The optimal monetary and fiscal policy problem is to choose home and foreign inflation,

home and foreign output and government consumption gaps, tax rates,6 next period homeand foreign debt and the union-wide interest rate, to maximize the welfare objective (4.4)subject to the log-linearized private sector’s optimizing conditions summarized in(3.4)–(3.7), the debt evolution equation (3.8) and their foreign counterparts, as well asconstraints on period-zero terms (so as to respect the initial conditions).As it was first documented in Ferrero (2005), the main feature of the optimal policy plan

is the unit root behavior of the Lagrange multipliers on debt.7 This is also inherited by theoutput, the government consumption and the terms-of-trade gap, as well as the real valueof debt. In the optimal solution some tax smoothing occurs. This is because debt changes

6When lump-sum taxes are available, home and foreign deficits and debts can be zero in equilibrium with no

effects for the macroeconomy. Hence, conclusions on the welfare effects of fiscal policy rules will differ depending

on the type of taxation assumed. Since the assumption of variable distortionary taxation offers more interesting

trade-offs and dynamics, we will focus our analysis on the case of distortionary taxation and assume that lump-

sum taxes are kept constant to their steady-state values.7The first-order conditions of the planner’s solution are available upon request.


permanently to guarantee the sustainability of the intertemporal government budgetconstraint. Moreover, in the optimal solution inflation is stationary (see also Ferrero,2005).

Optimal policy is characterized by the solution of the system of equations (3.4)–(3.6),(3.8) and their foreign counterparts, Eq. (3.7) and the first-order conditions of the optimalpolicy problem. Here we present only the qualitative features of the optimal plan. Thesewill be used as a guide for the intuition of our results in the next section. We abstract fromthe complete characterization of the optimal solution, given the unit root behavior of mostof the variables and its considerable complexity.

We can summarize the qualitative properties of the optimal solution as follows:Regional inflation rates are completely stabilized, while taxes and debt vary and, as aresult, the regional output gaps are non-zero. Given the stabilization of regional inflation,the terms-of-trade gap is also non-zero and, in turn, private and public consumptionsdeviate from their flexible-price values as well. Thus, the planner opts for a policy ofinflation stabilization using the tax rate as an instrument for smoothing variations in realmarginal costs and allows for variations in the private and public consumption and outputgaps.8 Such a policy can be easily rationalized by inspecting the coefficients on inflationand output gaps in (4.5): The coefficient for regional inflation is much higher than thecoefficients in front of the output gaps. This property of the optimal plan is essential tounderstand the results presented in the next section.

5. Constraints on regional debts and deficits

The previous section has underlined an important feature of our economy: In amonetary union the most advantageous reallocation of resources can be achieved whenregional inflation is stabilized. In this section we study what are the effects that alternativeconstraints on debt and deficit have on regional stability and welfare. We assume that thecentral bank follows a monetary policy that targets union-wide inflation, while regionalfiscal authorities commit to following specific fiscal policy rules.

We define union-wide inflation as

put ¼

12pt þ

12p�t ¼

12ðpHt þ p�FtÞ. (5.1)

We model the behavior of the central bank by assuming a Taylor-type of rule for thesetting of the union-wide interest rate:

brt ¼ rþ V Up p

ut , (5.2)

where r is a constant and V Up 40, determines the reaction of the interest rate to changes in

union-wide inflation.We consider general rules for fiscal policy in the two regions that try to imitate the SGP

requirements for fiscal policy performance and study the welfare and stability propertiesfor different specializations of these rules. The government deficit is defined according to

8Collard and Dellas (2004) also show find that in a closed economy with distortionary taxation the case of

perfect price stability, although not optimal, implies insignificant welfare losses. In different frameworks,

Andersen (2002) and Mundschenk and von Hagen (2003) also show that the presence of inflation differentials

creates incentives for policy competition among regional fiscal authorities and regional inflation stability is an

optimal outcome.


the accounting definition of the SGP, as the sum of government spending and interestpayments on debt minus tax revenues. That is, DFt ¼ RtBt þ PHtGt � Tt.We formulate the fiscal policy rules using both real government spending and income

taxes as tools, since both can be used to determine the fiscal stance and can affect marginalcosts and output in equilibrium:

btlt ¼ lrtbtl

t�1 þ ð1� lrtÞlbðbbt � bss

Þ þ ð1� lrtÞldf ðcdf t � df ss

Þ

þ ð1� lrtÞlppHt þ ð1� lrtÞlyeyt, ð5:3Þ

bgt ¼ lrgbgt�1 � ð1� lrgÞlbðbbt � bss

Þ � ð1� lrgÞldf ðcdf t � df ss

Þ � ð1� lrgÞlppHt

� ð1� lrgÞlyeyt, ð5:4Þ

where cdf t denotes log deviations of the real deficit from its steady-state value, df ss.Although in practice the budgetary planning process is in nominal terms, we express the

fiscal policy rules in real terms since the social planner’s decisions are on real variables toestablish a correspondence between the optimal solution and the solution under thedifferent fiscal rules considered.The two instruments are not allowed to be simultaneously active. When taxes vary

according to (5.3), government spending is assumed to be constant and, by the same token,when government spending is used as the fiscal instrument, taxes are assumed to beconstant.9

We allow for the possibility of tax and government spending smoothing ð0plrg; lrtp1Þ.We also allow tax rates and government spending to respond simultaneously to changes inreal debt and deficit from some target level, as well as to the growth rate of domestic pricesand the regional output gap.The parameters ldf , lb determine the speed of adjustment for the tax and government

spending rules in (5.3) and (5.4). When ldf , lb assume high values, fiscal policy is passive inthe sense defined in Leeper (1991) and its role is constrained in generating sufficient taxrevenues, or managing government spending to meet the debt/deficit requirements.Instead, when ldf , lb assume values close to zero, fiscal policy is active in the sense that it isnot constrained by restrictions on the level of debt and deficit and is allowed to engage inregional stabilization policies (when ly; lp40). Notice that the government debt evolutionand the definition of deficit imply that when regional fiscal policies target deficits theyactually control the evolution of debt and vice versa. Thus, when, for example, the fiscalinstrument focuses on the stabilization of debt, deficit is also under control. In whatfollows, we consider rules in which the tax rate and government spending target eitherdebt, or deficit.10

Thus, the rules defined in (5.3) and (5.4) can incorporate different types of fiscal policyregimes. Von Hagen et al. (2001) have suggested that successful consolidations inindustrialized countries involve movements of public expenditures as in (5.4). On the otherhand, Leeper (1991) introduces fiscal rules in which taxes respond to debt variability as in(5.3). Our analysis allows to study the effectiveness of the two fiscal policy instruments.

9Assuming some variability in taxes, when government spending is the fiscal instrument, or some variability in

government spending when taxes are used as the fiscal instrument, would not change our qualitative results.10We have also considered specifications in which the policy is mixed and both ldf and lb are positive. The

results on the welfare costs of fiscal restrictions are robust.

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Table 1

Baseline parameter calibration

Discounting b ¼ 0:99Imports share 1� a ¼ 0:2Markup y ¼ 10

Price stickiness g ¼ 0:75Government consumption as % of GDP o ¼ 0:8Steady-state debt-to-GDP ratio 60%

Standard deviations sA ¼ 0:01Persistence rA ¼ 0:9Correlations rA

HF ¼ 0

E. Pappa, V. Vassilatos / European Economic Review 51 (2007) 1492–1513 1505

We will analyze the welfare and macroeconomic stability properties of different variantsof (5.3) and (5.4). Since our model does not have closed-form solution under the rulesspecified in (5.2)–(5.4), we resort to numerical simulations in order to calculate the welfareoutcomes of different fiscal policy regimes. For this purpose, we calibrate the parameters inthe model using France and Germany to approximate the economies of the two regions.11

Our baseline calibration is summarized in Table 1. We take periods to be quarters andset b ¼ 0:99, so that the steady-state annualized real interest rate is 4%. The para-meter characterizing the share of imports in consumption 1� a is set equal to 0.2. Weset also 1� o ¼ 0:2 to capture the average share of government spending in total outputin Germany and France. Steady-state inflation in both regions and union-wide is zero.The steady-state debt-to-GDP ratio is set to 60%, which corresponds roughly to theaverage value of debt-to-GDP ratios for France and Germany between 2000 and 2005.12

We set y ¼ 10, so that the steady-state markup is 11%; and g ¼ 0:75, so that pricestickiness lasts one year on average. The standard deviation of both productivity shocks isequal to 0:01 and their persistence is set to 0.9. In all the analysis that follows monetarypolicy will be given and in all the experiments VU

p is set equal to 3.0. We start our analysisby assuming very strict rules in which deficit and debt should remain constant at theirsteady-state level.

5.1. Strict fiscal rules

The case of constant deficits and debt is obtained from the fiscal rules in (5.3) and (5.4)when lb, and/or ldf are very high and lrt, lrg are relatively small, while fiscal policy doesnot use its instruments for stabilization purposes ðly ¼ lp ¼ 0Þ. We consider four differentspecializations to represent strict fiscal regimes: (a) Deficit stabilization through variabletaxation, (b) debt stabilization through variable taxation, (c) deficit stabilization throughvariable government spending and (d) debt stabilization through variable governmentspending. We present the values for the coefficients in the fiscal policy rules in (5.3) and(5.4) for the four scenarios in the first row of Table 2. The rest of the rows report thewelfare losses and the macroeconomic stability properties of the different regimes.

11We believe that assuming symmetry for France and Germany is not an unreasonable assumption, although

the two countries are not equally sized.12Source: Euro Area Statistics (EAS) database of the ECB.

ARTICLE IN PRESS

Table 2

Welfare losses for different fiscal rules

Fiscal rules (a) df tðtl Þ (b) btðtl Þ (c) df tðgÞ (d) btðgÞ

Coefficients lrt ¼ 0:1; ldf ¼ 7 lrt ¼ 0:1; lb ¼ 7 lrg ¼ 0:1; ldf ¼ 7 lrg ¼ 0:1; lb ¼ 40

lb ¼ ly ¼ lp ¼ 0 ldf ¼ ly ¼ lp ¼ 0 lb ¼ ly ¼ lp ¼ 0 ldf ¼ ly ¼ lp ¼ 0

Welfare loss (%) 3.6 2.8 3.4 4.5

VarðpH Þ 0.0005 0.0003 0.0004 0.0004

VarðeyÞ 0.0087 0.0121 0.0116 0.0246

VarðesÞ 0.3454 0.2724 0.2819 0.2780

VarðegÞ 0.0526 0.0526 0.0782 0.1903

VarðecÞ 0.0174 0.0060 0.0061 0.0063

VarðtlÞ 0.2574 0.0572 0.0 0.0

E. Pappa, V. Vassilatos / European Economic Review 51 (2007) 1492–15131506

The welfare loss here is measured as the percentage of steady-state consumptionequivalence, that is, the percentage increase in steady-state consumption required to keepthe households indifferent between living in a world with optimal policy and in one withfiscal constraints.The presence of strict debt and deficit constraints is costly. However, the losses, although

considerable, are not as severe as one would expect. They range between 2.8% and 4.5% ofconsumption equivalence. This is of a substantial magnitude but not extremely high,compared to the welfare losses stemming from other distortions in a two-country model,as, for example, the inefficient fluctuations in the relative price of non-traded goods due toprice stickiness in Liu and Pappa (2005).13

In order to understand the intuition of this result, note that the constancy of debt anddeficits does not impede the achievement of an equilibrium where inflation is stable in bothregions and, thus, the entire union. In other words, strict regional debt and deficitconstraints together with a union-wide inflation target from the part of the central bank,can implement an equilibrium with regional inflation stability, which is highly importantfor welfare. This is because when government spending and taxes move to balance thebudget they do not affect adversely the behavior of real marginal costs.For example, suppose that taxes are the fiscal instrument that targets real debt (i.e.,

scenario (b)) and a positive productivity shock occurs. From (3.8), a positive productivityshock, other things equal, increases debt. Since in equilibrium taxes are negative, i.e., theysubsidize employment, subsidies have to be reduced according to (5.3) so as to keep thedebt and deficit constant. These movements in taxation do not affect marginal costs inequilibrium. This is because productivity shocks decrease marginal costs, but on the otherhand, the reductions in subsidies tend to increase them. Overall, marginal costs remainalmost constant in equilibrium and, thus, inflation is stabilized.However, the movements in taxation and government spending do alter the behavior of

the output and consumption gaps. Movements in taxes make output deviate frompotential and movements in government spending under constant taxes imply a trade-offbetween output, government consumption and inflation stabilization in (3.5). Moreover,since the inflation rates in the two regions remain almost constant, the terms- of trade

13Liu and Pappa (2005) find that the losses stemming from inefficient movements in relative prices of non-

traded goods can reach 5% of steady-state consumption.


cannot adjust to implement the reallocation of consumption under flexible prices. Thisterms-of-trade behavior generates non-zero private consumption gaps in the two regions.

The variabilities of these gaps for the four different strict regimes are presented in Table2. Variances and, thus, welfare are of comparable magnitude across regimes except forregime (d). In regime (d), where government spending reacts to changes in debt, the trade-offs between output, government consumption gap and inflation stabilization are moresevere generating higher output gap and government spending gap variabilities. This, inturn, leads to higher welfare losses.

5.2. Regional stabilization objectives

In what follows we study how relaxing the stringency of the fiscal rules affects regionalstability and welfare in our two-region currency area. To this end we analyze themacroeconomic stability and welfare properties of the four regimes described in Table 2,when we allow the regional governments to also pursue regional stabilization objectives byvarying the coefficients on inflation and the output gap in (5.3) and (5.4). In other words,in the experiments that follow lrg, lrt, ldf , and lb are set as in Table 2 and ly and lp areallowed to be non-zero.

As has already been highlighted in Leeper (1991) for a closed economy, the interactionbetween active monetary and fiscal policy might result in instability, i.e., indeterminacy ofequilibria. For that reason, in what follows we concentrate on specifications (i.e.,parameter value choices) for the policy rules that result in well behaved solutions.

5.2.1. Inflation stabilization

We first consider fiscal rules that also target the domestic growth rate of prices in eachregion. To this end we let lp vary in the interval ð0; 15Þ for tax rules and ð0; 2:5Þ forgovernment spending rules. The results are presented in Fig. 1. The left panel of the figurepresents welfare losses as a function of lp when the income tax is used as the fiscalinstrument and the right panel plots similarly welfare losses when government spending isthe fiscal tool. Circled lines represent deficit targeting and continuous lines debttargeting.14

When the fiscal authorities in the two regions target the domestic growth rate of pricesmore aggressively welfare is improved in almost all cases.15 This is because strongerregional inflation targeting implies greater regional inflation stability, which is veryimportant for welfare, given the size of the weight of regional inflation in the objective ofthe planner. However, since most of inflation stabilization is achieved by the central bank,the additional gains from inflation stabilization at the regional level are relatively small.Hence, the welfare losses decrease with the size of lp but not substantially.

In general, there is more room for welfare improvements when fiscal policy targets realdeficit rather than debt. Observe that the circled lines in Fig. 1 are steeper than thecontinuous lines. Under a tax rule welfare losses are reduced by approximately 35% andunder a government spending rule by approximately 10% when the fiscal authorities relax

14The cases of strict deficit and debt targeting are obtained for lp ¼ 0.15The case of debt stabilization through changes in government spending is always problematic since it often

leads to indeterminacy of equilibria. We present it here for completeness, although it cannot serve as a sound fiscal

policy rule.

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0

1

2

3

4

5

0 9

% w

elf

are

lo

sses

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5

% w

elf

are

lo

sses

4.5 13.5

Government spending instrument

Tax instrument

targeting deficit

targeting debt

targeting deficit

targeting debt

λπλπ λπλπ

Fig. 1. Welfare losses as a function of lp.


deficit targeting constraints, while the corresponding changes when the fiscal authoritiesrelax debt constraints are minimal. In the case of a tax rule it is easy to understand thereasoning behind this result. Note that when lp ¼ 0, a rigid tax rule that consolidates debtis associated with smaller welfare losses than a rigid tax rule that targets deficits. Therefore,there is more scope for fiscal activism in the latter case.Moreover, the tax instrument is more effective to control for regional inflation, and,

thus, to increase welfare than government spending. Notice that the circled line in the leftpanel of Fig. 1 is steeper than the slope of the circled line in the right panel. This is becausevarying taxes is less costly in terms of macroeconomic stability than varying government

spending. To see this, notice that (3.5) can be rewritten as cmct ¼ ð1=oÞbyt � ðð1� oÞ=oÞbgtþ

ðtl=ð1� tlÞÞbtlt � bat. Thus, taxes can vary in response to productivity shocks to stabilize

marginal costs without affecting the evolution of output and government consumption.Instead, under constant taxes, when government consumption moves in response toproductivity shocks, the output has to change to keep marginal costs constant. Thisintroduces a trade-off that makes government spending a less effective instrument.

5.2.2. Output gap stabilization

Can fiscal policy improve welfare when it targets the regional output gap? The answer isyes and is depicted in the two panels of Fig. 2 where we let ly vary in the ð0; 2Þ interval.Again, the left panel shows how variations in ly change the consumption-equivalencelosses when the fiscal instrument is income taxation and the right panel plots the case ofvariable government spending.The general pattern is very similar to the case of inflation stabilization except that

welfare losses decrease more substantially with the size of ly. Starting from a deficittargeting regime, with a tax rule, regional output gap stabilization reduces welfare lossesfrom 3.6% to 2% of steady-state consumption equivalence and with a governmentspending rule from 3.4% to 3%. Strengthening the reaction of regional policy to outputgap variations (i.e., increasing lyÞ delivers higher welfare gains relative to strengthening thereaction of regional policy to inflation variations (i.e., increasing lpÞ. The reasoning behindthis pattern is quite intuitive. Since the central authority targets inflation, regional policycomplements the central authority’s policy by focusing on regional output stability.

ARTICLE IN PRESS

0

1

2

3

4

0 1 2

% w

elf

are

lo

sses

0

1

2

3

4

5

0 1 2

% w

elf

are

lo

sses

targeting deficittargeting debt

0.5 1.5 0.5 1.5

Government spending instrument

targeting debttargeting deficit

Tax instrument

λy λy

Fig. 2. Welfare losses as a function of ly.

E. Pappa, V. Vassilatos / European Economic Review 51 (2007) 1492–1513 1509

5.3. What rule to choose?

The preceding analysis suggests that regional stabilization policies can improve welfare.In particular, the adoption of a regional output-gap target by the fiscal authorities canimprove welfare substantially relative to the case of rigid deficit, or debt targeting. On theother hand, a domestic inflation target is not fruitful as a goal for national fiscal authoritiesin a monetary union when the central bank targets at the same time the union-wideinflation rate.

Further, our analysis indicates that, when rigid rules are considered necessary and whentaxes are used to consolidate debt, it is preferable to adhere to rigid rules for debt ratherthan rigid deficit rules. The opposite is true when government spending is used to controlthe evolution of debt. This mainly reflects the fact that government spending is aninadequate instrument for controlling debt when government spending enters privateagents’ utility functions. When government spending is adjusted to control debt deviationsfrom target it deviates a lot from its natural level. As a result, its gap increases substantiallyaffecting negatively welfare (see Table 2). Thus, whether government spending is anadequate instrument for controlling debt depends on the assumed value of o. In Fig. 3 weplot the welfare losses associated with regime (d) when o varies in the (0.5, 1) interval. Wefind that when government spending is irrelevant for private utility, i.e., as o! 1,adhering to strict government spending rules that consolidate debt is as (if not more)effective as adhering to tax rules. Thus, our results point to the use of governmentexpenditure items that do not enhance private utility as the most effective fiscal instrumentfor fiscal consolidation and stabilization purposes.

Finally, our results on the importance of price stability on the part of the central bankand fiscal activism on the part of regional policymakers confirm the theoretical results ofFerrero (2005) and Canzoneri et al. (2005) on optimal monetary and fiscal policy. The factthat the gains from fiscal activism are relatively small in our framework reflects mainly theabsence of asymmetries across regions and the adoption of different fiscal rules.16

16Also, Ferrero (2005) and Canzoneri et al. (2005) use different metrics from welfare and absolute values for the

losses are not directly comparable.

ARTICLE IN PRESS

0

2

4

6

0.5 0.6 0.7 0.8 0.9 1

% w

elf

are

lo

sses

ω

Fig. 3. Welfare losses of regime (d) as a function of o.


6. Concluding remarks and possible extensions

Our analysis reveals that fiscal policies with clear stabilization objectives and a monetarypolicy geared to price stability are fundamental for macroeconomic stability and welfare ina monetary union. When political distortions make the presence of strict constraintsnecessary, rigid constraints on debt are more effective for enhancing welfare thanconstraints on deficits. This is the case especially when regional authorities can movegovernment expenditure items that do not affect significantly the private households’welfare. Our results indicate that strict fiscal rules are compatible with regional inflationstability and are not that unbearable and that regional fiscal authorities have room forimproving regional welfare even under strict fiscal rules by choosing appropriately theirstabilization tools and objectives.We recognize that the current analysis cannot address many of the issues raised in the

fiscal framework of the EMU. First, in the current analysis we consider a union betweentwo countries with similar economic characteristics. The EMU instead is composed ofregions with very different economic structures and we conjecture that examining optimalfiscal policy and fiscal rules in an asymmetric framework will provide further insights forthe design of sound fiscal policies in a currency area. Second, fiscal constraints are usuallymotivated by the presence of a political distortion which is absent in our frameworkmaking our analysis biased against the presence of budgetary restrictions. Theincorporation of political distortions would enrich the framework for evaluating thedesirability of fiscal constraints. Third, the assumption of complete home-bias inthe consumption of government goods implicitly limits the policy instruments available tothe public authorities. Under this assumption, regional policymakers can affect the totalamount of real, or nominal public expenditures, but not the composition of this spending,loosing a degree of freedom in smoothing out terms-of-trade movements. Specificationsthat allow the consumption of foreign goods by the domestic government would enrich thenumber of policy instruments available to the regional policymakers and potentially refine


the transmission channel of shocks. Finally, fiscal policy coordination was also taken asgiven when examining the different fiscal rules and their macroeconomic consequences,while in practice this is not guaranteed and the sustainability of fiscal constraints is still anopen issue in Europe. The derivation of welfare objectives for each regional authority infuture work will help us analyze the sustainability of fiscal constraints in monetary unions.

Acknowledgments

We would like to thank three anonymous referees and the editor, Jurgen Von Hagen, forcomments and suggestions. Financial assistance through project Pythagoras II - EPEAEKco-financed by the European Social Fund and the Ministry of Education in the Greece isacknowledged. Evi Pappa would also like to thank the Spanish Ministry of Education andScience and FEDER through Grant SEC2003-306 from the Generalitat de Catalunyathrough the Barcelona Economics program (CREA) and Grant SGR2005-00447 forfinancial further support.

Appendix A. Deriving the welfare objective

We derive the welfare objective of a central planner by taking second-orderapproximations to the representative household’s period utility function. A second-orderapproximation to the home household’s period utility function is given by

Ut �U ss ¼ oct þ ð1� oÞbgt � Lðlt þ12l2

t Þ þOðkxk3Þ, (A.1)

where for a generic variable xt, bxt characterizes log-deviations from the steady state. Thefirst two components of the approximated utility function are deviations of private andpublic consumption from steady state, which are related to deviations of output throughthe aggregate resource constraint (2.25). The second-order approximation of this relationis given by

oct ¼ a½yt � ð1� oÞbgt� �1

2

ð1� oÞo

a½bgt � byt�2

þ ð1� aÞ½y�t � ð1� oÞbg�t � � 1

2

ð1� oÞoð1� aÞ½bg�t � by�t �2. ðA:2Þ

The second part of the approximated utility involves second-order approximations tolabor. We know that in equilibrium labor is given by Lt ¼ ðDHt=AtÞY t, thus, we can rewritethat in log-linear terms as

lt ¼ bDHt þ yt � bat. (A.3)

A second-order approximation of bDHt yields (see, Woodford, 2003):

X1t¼0

btbDHt ¼1

2

ygð1� bgÞð1� gÞ

X1t¼0

btp2Ht þ t:i:pþOðkxk3Þ, (A.4)

where t:i:p. denotes terms independent of policy, including constant terms and shocks. Theabove result together with Eq. (A.3) implies that l

2

t ¼ y2t þOðkxk3Þ, since bat is exogenous

and bDHt is of second order.


The foreign region’s households utility is given by

U�t �U�ss ¼ oc�t þ ð1� oÞbg�t � L�ðl�

t þ12l�2

t Þ þOðkxk3Þ. (A.5)

Again using the foreign aggregate resource constraint we can express foreign consumptionas

oc�t ¼ a½y�t � ð1� oÞbg�t � � 1

2

ð1� oÞo

a½bg�t � by�t �2þ ð1� aÞ½yt � ð1� oÞbgt� �

1

2

ð1� oÞo

ð1� aÞ½bgt � byt�2. ðA:6Þ

Foreign labor can be written as

l�

t ¼bD�Ft þ y�t � ba�t . (A.7)

The results for the square of foreign output and price dispersion abroad are similar as inthe home economy.The social planner, then, constructs his objective by weighting equally the two-regions

household utilities. That is, the welfare objective of the planner is the sum of (A.1) and(A.5), where its regions’ welfare is weighted by half, given equal population acrosscountries. This implies using (A.2) and (A.6), together with (A.3) and (A.7) that the socialobjective takes the form:

1

2ðUt þU�t Þ

¼ �1

2ey2

t þ ey�2t þð1� oÞ

o½egt � eyt�

2 þð1� oÞ

o½eg�t � ey�t �2

� ��

1

2bDHt �

1

2bD�Ft

¼ �1

2yðk�1p2Ht þ k��1p�2Ft Þ þ ey2

t þ ey�2t þð1� oÞ

o½egt � eyt�

2 þð1� oÞ

o½eg�t � ey�t �2

� �,

ðA:8Þ

where the last equality results from using Eq. (A.4).Finally to rewrite the objective in terms of consumption gap we use the approximation

of (2.24):

eyt � egt ¼ o½ect � egt þ ð1� aÞest�. (A.9)

From this relationship:

ey2t ¼ ½oect þ ð1� oÞegt�

2 þ o2ð1� aÞ2es2t þ 2oð1� aÞ½oect þ ð1� oÞegt�est

and

ey�2t ¼ ½oec�t þ ð1� oÞeg�t �2 þ o2ð1� aÞ2es2t � 2oð1� aÞ½oec�t þ ð1� oÞeg�t �est.

Moreover,

1� ooðeyt � egtÞ

2¼ ð1� oÞo½ðect � egtÞ

2þ ð1� aÞ2es2t þ 2ð1� aÞestðect � egtÞ�

and

1� ooðey�t � eg�t Þ2 ¼ ð1� oÞo½ðec�t � eg�t Þ2 þ ð1� aÞ2es2t � 2ð1� aÞestðec�t � eg�t Þ�.


Adding up the above four relationships and using the fact that ect � ec�t ¼ ð2a� 1Þest

results in (4.6) in the text.

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