Fiscal Policy in a Monetary Union Model with Home Bias in

Consumption

Ingo Pitterle∗ Dirk Steffen†‡

13th February 2004

ABSTRACT

The European Growth and Stability Pact postulates that the member countries of the EMUestablish fiscal policies according to the deficit rules of the Maastricht Treaty. Theoreticalmodels may provide a rationale for imposing fiscal discipline on the member countries once fiscalpolicy is beggar-thy-neighbor. This paper focuses on the international transmission of fiscalpolicy shocks when the exchange rate channel is absent and prices are rigid. Using a monetaryunion model in the spirit of new open economy macroeconomics (NOEM) we show that a homebias in consumption gives way to output stimulation via expansive fiscal policy. The negativewelfare effect that is associated with a rise in tax-financed public expenditure is then mitigatedat the expense of the foreign country. Biased preferences enhance the international spillovereffects of fiscal policy as the composition of world demand becomes more important for theproduction structure.

Keywords: Fiscal Shocks, Monetary Union, Home Bias, Cash-in-AdvanceJEL Classification: F31, F32, F41 and F42

∗University of Frankfurt, pitterle@wiwi.uni-frankfurt.de†University of Frankfurt, steffen@wiwi.uni-frankfurt.de‡The authors wish to express their appreciation to Uwe Walz for helpful comments.

1 INTRODUCTION

The recent experience of the European Monetary Union (EMU) member countries revives

the question, how open economies cope with asymmetric shocks. Once a country abandons

its sovereign monetary policy in favor of a common central bank that decides upon money

supply for all member countries, it faces different international transmission mechanisms of

macroeconomic shocks than before. This is due to a regime switch towards a common currency

implying that the exchange rate can no longer work as a shock absorbing instrument.

The European Growth and Stability Pact postulates that the member countries of the EMU

establish fiscal policies according to the deficit rules of the Maastricht Treaty. Theoretical

models may provide a rationale for imposing fiscal discipline on the member countries once

fiscal policy is beggar-thy-neighbor. We focus on the international transmission of fiscal policy

shocks when the exchange rate channel is absent and prices are rigid. Using a monetary union

model in the spirit of new open economy macroeconomics (NOEM) we show that a home bias in

consumption gives way to output stimulation via expansive fiscal policy. The negative welfare

effect that is associated with a rise in tax-financed public expenditure is then mitigated at the

expense of the foreign country. Biased preferences enhance the international spillover effects of

fiscal policy as the composition of world demand becomes more important for the production

structure.

While a home bias in consumption plays a prominent role in the theoretical analysis of

asymmetric shocks, we also find strong empirical support for biased preferences. Starting

with the reasoning of Meade (1951) there is an agreement among economists that a home

bias in preferences exists, even if it is difficult to find sound theoretical foundations for this

phenomenon. Recent empirical studies by McCallum (1995), Helliwell (1996), and Wei (1996),

that investigate so called border effects in international trade, confirm that there is a persisting

home bias in consumption despite the opening up of the industrial countries. In a well known

study, McCallum (1995) showed that in 1988 trade between two Canadian provinces was more

than twenty times larger than trade between a Canadian province and a U.S. state, after one

has controlled for distance and size. Covering the period 1988-94 and performing robustness

checks, Helliwell (1996) endorses McCallum’s basic result of a highly biased trade structure.

Wei (1996) extends the sample to analyze the trade structure in the OECD countries for the

period 1982-94. He also finds a considerable home bias in the goods market, though of a smaller

1

magnitude than the one obtained by McCallum.

There is a long tradition of investigating the effects of the exchange rate regime on the

international transmission of asymmetric shocks dating back to Mundell (1963) and Fleming

(1962). However, the NOEM literature mainly concentrates on flexible exchange rate regimes.

There are a few notable exceptions, though. In a recent study, Carre and Collard (2003)

compare the flexible exchange rate case with a monetary union. Though their model lacks a

closed form solution, it gives some important insights into the intrinsic positive and normative

implications of the NOEM approach: In the event of a domestic expansive fiscal policy the

implementation of a monetary union is welfare enhancing for the domestic country. At the

same time, foreign households suffer a welfare loss, when a flexible exchange rate regime is

replaced by a monetary union. The model allows for biased preferences for the sake of a

better empirical fit, but the implications of this feature are not analyzed in any detail. Caselli

(2001) investigates the welfare effects of fiscal consolidations in a fixed exchange rate regime

under both symmetric and asymmetric intervention schemes, the former of which resembles

the monetary union case.1 Her model is inspired by the dominant role of Germany in the

European Exchange Rate Mechanism and yields the unexpected result, that an asymmetric

exchange rate fix is preferable to a symmetric one. While the model represents a straightforward

fixed exchange rate version of Obstfeld and Rogoff’s (1995a) Redux model, the possibility of

biased preferences is not considered. Only a few NOEM papers address the role of a home bias

in consumption for the international transmission mechanisms of asymmetric shocks. Warnock

(2000) and Michaelis (2000) restrict the analysis to monetary policy under flexible exchange

rates. Warnock (1999) allows for biased preferences when analyzing fiscal policy. However, he

only considers flexible exchange rates and does not provide a welfare evaluation.

In contrast to these contributions, we focus on the specific role of a home bias in consump-

tion for the international transmission of fiscal policy in a monetary union. To address this issue

we deploy a two-country NOEM model that is by and large standard except for a money de-

mand specification, where government expenditures trigger additional money demand. Tracing

back to Mankiw and Summers (1986), empirical research suggests that government purchases

are relevant for money demand. Our model captures this effect as households need cash in1In the realm of stabilization policy, Lane (2000) stresses the differences between symmetric fixed exchange

rate arrangements and currency unions. He concludes that monetary policy does react to aggregate productivityshocks in a currency union while it remains passive under a symmetric fixed exchange rate regime.

2

order to purchase consumption goods and to pay taxes. In this cash-in-advance setting money

demand is absorption based while money-in-the-utility models yield money demand functions

that are consumption based.

Abstracting from capital accumulation and relying on exogenous price rigidities, we obtain

a closed form solution of the model. It turns out that an expansive domestic fiscal policy only

stimulates short run output as long as there is a home bias in consumption. The intuition for

this result is the following: Once the domestic government decides to raise public expenditure,

domestic households face a direct negative wealth effect as public purchases are financed by

taxes. Therefore, private consumption will be subdued. However, because households smooth

consumption over time, the crowding out of private consumption will be limited and domestic

overall expenditures are above the steady state level. At the same time, the evolution of foreign

consumption is mirroring the events in the domestic economy due to the combination of cash-in-

advance constraints and a passive common monetary policy that does not accommodate fiscal

expansions. That is, foreign consumption decreases by exactly the same amount as domestic

expenditure increases, leaving the overall world demand unchanged. As both private and public

spending are exposed to a home bias, the domestically biased structure of world demand

translates into different production levels at home and abroad. While domestic production

is stimulated, foreign production is below steady state. As for the welfare analysis of these

positive results, the domestic welfare loss associated with the negative wealth effect is mitigated

at the expense of the foreign country. This is due to the fact that output stimulation is welfare

enhancing in model economies that suffer from monopolistic distortions in the goods markets,

and hence from suboptimally low production levels. Comparative statics reveal that a strong

home bias implies a weak current account response because the additional domestic short term

expenditure is then mainly financed via a higher level of short term production. The degree of

a home bias in consumption thereby determines the intertemporal structure of utility in both

countries.

The paper is organized as follows. Section 2 gives a description of the model. Section 3

provides long run and short run solutions of the model, while section 4 explores the welfare

implications of fiscal shocks in a monetary union with a specific focus on home bias issues.

Section 5 concludes.

3

2 MODEL SETUP

The considered model consists of two countries, home and foreign, of equal size. This feature

is mandatory because households display a home bias in consumption. We normalize the

population size in each country to one. The description of the model will be carried out in

detail for the home country. As for the foreign country, most of the equations are defined

analogously, while all foreign variables will be denoted with an asterisk.

2.1 Households

Agents in both countries derive utility from two sources: consumption and leisure. As we are

interested in obtaining a manageable closed form solution of the model we use a special case

of the general isoelastic utility function: The elasticity of intertemporal substitution is set to

one and consumption and leisure enter with equal weight.2 Thus, households maximize their

discounted utility given by

U =∞∑

t=0

βt(log ct + log(1− ht)

), (1)

where β ∈ [0, 1] denotes the discount factor, ht represents hours worked by the household, and

ct is a constant elasticity of substitution (CES) real consumption index. The latter consists of

a basket of goods produced in the domestic economy, cht , and a basket of goods produced in

the foreign country, cft :

ct =[ω

1θ ch

θ−1θ

t + (1− ω)1θ cf

θ−1θ

t

] θθ−1

(2)

By determining the weight of the domestically produced goods in the consumption index,

ω ∈ [0.5, 1) serves as a measure of the home bias in consumption.3 If ω > 0.5, home and

foreign households have a biased demand for goods that are produced in their own country,

whereas the fraction of imported goods in the consumption bundle is smaller than 0.5.4 The

parameter θ > 1 denotes the elasticity of substitution between the two consumption baskets,2Attaching different weights to consumption and leisure would complicate the analysis substantially without

changing the qualitative results of the model.3Warnock (2003) uses a similar specification of consumption preferences.4We rule out a complete home bias, i.e. ω = 1, as bond markets would be disconnected in that case, and

therefore there would be no international transmission of fiscal policy shocks.

4

which are given by

cht =

(∫ 1

0ct(h)

θ−1θ dh

) θθ−1

(3)

cft =

(∫ 1

0ct(f)

θ−1θ df

) θθ−1

(4)

To keep the preference structure simple, we follow Obstfeld and Rogoff (1995a) and Betts

and Devereux (2000) assuming the same cross-country and within-country substitutability of

goods.5 The price indices that correspond to the consumption bundles (2)-(4) are obtained by

expenditure minimization:

pt =(ωph1−θ

t + (1− ω)pf1−θ

t

) 11−θ (5)

with

pht =

(∫ 1

0pt(h)1−θdh

) 11−θ

(6)

and

pft =

(∫ 1

0pt(f)1−θdf

) 11−θ

(7)

The aggregate price level pt is a home biased function of import prices pft , and prices of domestic

goods pht . The price index for domestic goods ph

t and the import price index pft aggregate over

the prices of the individual goods, pt(h) and pt(f). Note that home and foreign prices are

denominated in the common currency.

Maximizing the consumption index for any fixed total nominal expenditure on goods yields

the respective domestic demand functions:

ct(h) =(

pt(h)pt

)−θ

ωct (8)

ct(f) =(

pt(f)pt

)−θ)

(1− ω)ct (9)

5Tille (2001) investigates the role of consumption substitutability in the international transmission of shocks.

5

The household’s optimization problem is constrained by

mdt + Rtft+1 ≤ ft + ptwtht + Πt (10)

mdt ≥ pt(ct + Tt) (11)

The budget constraint (10) is a short cut to Helpman (1981) as money holdings are not carried

over from the previous period, though it is theoretically possible to do so. As Helpman points

out, households will not find it reasonable to hold money over periods in the presence of interest

yielding bonds. Money thereby reduces to “money to spend”. Another important aspect of

the budget constraint is the timing of payments. Households receive nominal labor income,

ptwtht, and profits, Πt, instantaneously. 6 As a result, neither firms nor households hold money

longer than an instant. We thereby avoid an additional source of distortion that might blur

our analysis of nominal rigidities.7 In order to smooth consumption, households may purchase

nominal one-period bonds ft+1. The bond price Rt is inversely related to the nominal interest

rate.8 Our timing convention is the following: Bonds denoted with t + 1 are acquired at the

beginning of period t and mature at the beginning of period t+1. The absence of real, indexed

bonds implies that real interest rates may differ internationally. As opposed to Obstfeld and

Rogoff (1995a), real bond payoffs depend on the rate of inflation, which may not be the same

in the two countries.

Additionally, households face a cash-in-advance constraint (11) a la Helpman (1981) and

Lucas (1982). Households need money in order to carry out their consumption goods purchases

and tax payments. Our specification avoids possible distortions of the consumption decision by

unexpected inflation as households decide on money holdings after the occurrence of shocks.

In the light of positive nominal interest rates the constraint is binding. We are quite aware

of the fact that the specification of money demand influences the outcome of our analysis

substantially.9 In contrast to money-in-the-utility approaches, the cash-in-advance constraint

implies that money demand depends not only on the consumption level, but also on the amount

of taxes paid. Therefore, tax-financed government expenditures increase ceteris paribus the6We assume that domestic households are the sole owners of domestic firms. This is motivated by the strong

portfolio home bias in the real world.7Thanks to Fabrice Collard who gave us some clarifying remarks on that subject.8Accordingly, we have Rt = 1

1+it+1= pt

pt+1(1 + rt+1), where it+1 and rt+1 denote the nominal and real

interest rate, respectively.9See Chang and Lai (1997) for a detailed discussion of this issue in the context of flexible exchange rates.

6

demand for money in equilibrium.

The households maximize their intertemporal utility (1) subject to (10) and (11). The

decision variables at time t are ft+1, ht, and ct. Optimal bond holdings yield a standard Euler

equation

β pt ct = Rt pt+1 ct+1 (12)

The optimal labor supply decision is characterized by the labor leisure trade off

11− ht

=wt

ct, (13)

whereas the cash-in-advance constraint (11) may be interpreted as the money demand function

mdt = pt(ct + Tt) (14)

Note that this implies a consumption elasticity of money demand equal to one.

2.2 Government and Central Bank

The government decides in every period on the amount of lump sum taxes Tt in order to finance

purchases of public goods gt. Let the public consumption index be defined analogously to the

real consumption indices of the households.10Thus, governments in both countries have the

same biased demand for goods that are produced in their own country as private households

do. Since the public good does not enter the household’s utility function at all, government

spending is purely dissipative.11 We may abstract from public debt issues since Ricardian

equivalence holds in our setup. The government budget constraint therefore reduces to

gt = Tt (15)10Assuming a stronger home bias in public expenditure than in private consumption would reinforce the

international transmission of fiscal policy. This is opposed to Ganelli (2002) who analyzes a complete home biasin government spending in the standard Redux model.

11Ganelli (2003) investigates the implications of welfare enhancing government spending under the assumptionof non-separability. Take Beetsma and Jensen (2002) for the general preference case. In their model, the utilityof public spending is additively separable from private consumption.

7

In a monetary union, a common central bank is responsible for the money supply. As central

banks across industrial countries tend to pursue price stability, we assume here that the overall

money supply is unchanged.

mst+1 = ms

t (16)

The money market equilibrium is given by

mst = md

t + md∗t (17)

As households need cash for consumption and tax payments, equation (17) implies that

higher expenditures in one country will automatically be accompanied by lower expenditures

in the other country.

2.3 Firms

Suppose that production is linear in the only production factor labor. We abstract from

technology shocks and thus define the production functions for the producers in its simplest

form:

yt(h) = ht(h) (18)

Producers maximize profits that are given by

maxpt(h)

Πt(h) = pt(h)yt(h)− ptwtht(h) (19)

subject to the overall demand for their good

yt(h) =(

pt(h)pt

)−θ

ω(ct + gt) +(

pt(h)p∗t

)−θ

(1− ω)(c∗t + g∗t ) (20)

The optimal price is always given as a markup on nominal marginal production costs:

pht =

θ

θ − 1wtpt (21)

As a result of the assumed constant elasticity of substitution (CES) consumption baskets

8

the level of overall demand has no impact on the pricing rule. Producers will adjust their

prices when either the real wage wt or the overall price level pt changes. This is the key for

understanding international price differentials: if whatever macroeconomic shock leads to an

international real wage differential, individual prices and hence overall price levels may differ

across countries.

3 FISCAL SHOCKS AND MONETARY UNION

3.1 Steady state

To get a first feel for the characteristics of the model it is useful to start with the calculation of a

steady state. It is convenient to choose the most simple form of it, the one where all exogenous

variables are constant. Furthermore, we assume that there are no initial bond holdings and

that steady state government expenditure equals zero. The steady state exercise yields at the

same time the flexible price version of the model which serves as a benchmark for the following

shock analysis in the presence of price rigidities. From a technical perspective, we need the

steady state of the model as we evaluate the dynamic system around a stationary equilibrium.

In fact, the propagation of shocks will be analyzed only locally. In the sequel, steady state

values of the variables will be barred.

One of the most important features of Redux style models is the incorporation of monop-

olistic competition. This facilitates demand driven welfare improvements in the short run,

because production is inefficiently low in equilibrium. You may derive this from the steady

state labor markets:

h = h∗ =θ−1

θ

1 + θ−1θ

(22)

whereas the socially optimal employment (production) level would be 12 . The inverse markup

θ−1θ , that defines the market power of firms, enters the labor market equilibrium through the

(distorted) real wage that workers receive for an hour worked, see pricing equation (21). Steady

state consumption may be derived from barred versions of the current account (28)

c =ph

py =

ph

ph = h (23)

9

Obviously, an inefficiently low level of hours worked translates into inefficiently low production

and thereby lower consumption. Barred versions of the Euler equation (12) link the steady

state real interest rate to the time-preference factor β

r =1− β

β(24)

Finally, we may look at the steady state money market of the monetary union:

ms = md + md∗ = pc + p∗c∗ (25)

As government expenditures are assumed to be zero in the steady state, home and foreign

money demand only depend on the level of consumption expenditure. In equilibrium, as

both countries meet on the common money market, money supply equals total consumption

expenditure in the monetary union.

3.2 Long run equilibrium

We now turn to the policy experiment of an unanticipated temporary fiscal shock in the

domestic economy. What will happen to the key variables if the government raises its tax-

financed expenditures? And how will the existence of a home bias in private consumption and

government expenditure affect the adjustment process and the new equilibrium?

Though our set of equations is complex, it is possible to solve for the individual variables

because the dynamic system reaches its new steady state right after the shock period. This

feature is due to the special form of exogenous price rigidities12 - prices have to be set be-

fore the occurrence of shocks but may be changed in the following period. Given this special

structure, we may split the mathematical problem into two parts that can be treated (almost)

independently. First, we solve for the long run (post shock, flexible price) values of the con-

sumption differential. It will turn out that these depend on endogenous bond holdings that

are determined in the short run (post shock, rigid prices). Second, we solve for the short run

equilibrium given the long run values of the variables. The combination of the short and long12Models that endogenize price rigidities via explicit price adjustment costs like Hairault and Portier (1993)

or use Calvo (1983) style price determination as in Kollmann (2001a, 2001b) yield more dynamic optimizationproblems of the firm. Though these approaches capture the empirical finding of gradual price adjustments theyhamper the finding of analytical solutions.

10

run solution finally yields the solution for consumption levels, hours worked, interest rates,

and price levels. The essential link between the short and long run system will be the bond

holdings acquired in the shock period.13 The following system of equations includes the market

clearing and optimality conditions that define the long run equilibrium.

Money markets

mdt+1 = pt+1ct+1 (26)

md∗t+1 = p∗t+1c

∗t+1 (27)

Current accounts

pt+1ct+1 + Rt+1ft+2 = pht+1yt+1 + ft+1 (28)

p∗t+1c∗t+1 + Rt+1f

∗t+2 = pf

t+1y∗t+1 + f∗t+1 (29)

Goods markets

yt+1 =

(ph

t+1

pt+1

)−θ

ω ct+1 +

(ph

t+1

p∗t+1

)−θ

(1− ω) c∗t+1 (30)

y∗t+1 =

(pf

t+1

p∗t+1

)−θ

ω c∗t+1 +

(pf

t+1

pt+1

)−θ

(1− ω) ct+1 (31)

Euler equations

β pt+1 ct+1 = Rt+1 pt+2 ct+2 (32)

β p∗t+1 c∗t+1 = Rt+1 p∗t+2 c∗t+2 (33)

Labor markets

11− ht+1

=θ − 1

θ

pht+1

pt+1ct+1(34)

13The importance of the current account as a main channel of international transmission of shocks is stressedby the intertemporal approach to the current account, see Obstfeld and Rogoff (1995b).

11

11− h∗t+1

=θ − 1

θ

pft+1

p∗t+1c∗t+1

(35)

Note that government expenditures do not enter the long run system of equations as we

concentrate on the analysis of a temporary fiscal shock. Equations (26) and (27) assure that

the money markets in both countries clear. The national budget constraints are described by

(28) and (29): Nominal expenditures on private consumption and on bonds must equal nominal

income from goods sales and the repayment of bonds acquired in the previous period. (30)

and (31) represent the goods market clearing equations. Equations (32) and (33) are the Euler

equations, that describe the optimal path of consumption growth in both countries. Finally,

(34) and (35) represent the labor markets, which combine the households’ optimal labor supply

decision and the firms’ pricing rule, i.e. the optimal price as a markup on wages.

Since the model we consider is non-linear we have to recur to a method of linearization

before proceeding. Therefore, we will log-linearize the model around the initial flexible-price

steady state.14 From now on, let the percentage deviation15 of a variable x from its steady state

value x be defined as x = dxx . As we assume zero bond holdings and no government expenditure

in the initial steady state, the respective deviation of these variables will be related to steady

state domestic consumption c.16

An important feature of our model are the long run implications of fiscal shocks for the

price levels. Due to the home bias in private and public consumption, changes in the marginal

production cost differential are reflected in a deviation from purchasing power parity. We shall

demonstrate this by considering linearized versions of the domestic price indices (5), (6), (7),

and its foreign counterparts.

pt+1 = ωpht+1 + (1− ω)pf

t+1 (36)

14This implies that we may not consider shocks to the system that are ”too big” as the approximation errorwould grow too much once you leave the steady state. See Corsetti and Pesenti (2001) who shut down thecurrent account transmission channel because of stationarity concerns. By modelling preferences Cobb-Douglasstyle their model may be solved without reverting to linearization techniques. Ghironi (2000) instead, proposesan overlapping generations (OLG) framework that allows for current account imbalances while avoiding non-stationarities.

15For the sake of lean exposition, we will always refer to the deviation of a variable, if not otherwise stated.16Due to our assumption of a population size of one in both countries it is convenient to relate bond holdings

and government expenditure to steady state domestic consumption rather than to steady state world consump-tion.

12

p∗t+1 = ωpft+1 + (1− ω)ph

t+1 (37)

pht+1 = pt+1(h) (38)

pft+1 = pt+1(f) (39)

In the long run, producers are free to set their prices. The law of one price will hold for all

types of goods, because the optimal price across producers is derived as a markup on marginal

production costs and is independent of the demand levels in the respective markets. However,

the law of one price, does not imply purchasing power parity, as marginal production costs

across countries may differ and a home bias in private and government consumption exists.

For example, if the real wage at home is higher than abroad, domestic producers will set a

higher price than their foreign competitors. Then, it is the mix of (expensive) domestic and

(cheap) foreign goods in the consumption bundles that governs the international price level

differential:

pt+1 − p∗t+1 = (2ω − 1)(pht+1 − pf

t+1) (40)

Using linearized versions of equations (28)-(35) we may derive the long run consumption

differential following some deviations from the steady state in the short run:17

ct+1 − c∗t+1 =2θ(1− β)

2θ − 1dft+1

pc(41)

Equation (41) reflects the fact that a long run consumption differential only arises if bonds

are carried over from the short run. For instance, negative domestic bond holdings f induce

a negative consumption differential ct+1 − c∗t+1: domestic households consume less than for-

eigners. The permanent interest payments of home residents that ran into debts facilitate

greater relative consumption of foreign residents. The sign of domestic bond holdings will be

determined by the short run solution of the model. Note that the home bias parameter ω does

not enter the above equation. However, a home bias in consumption influences the long run

consumption levels via its effect on bond holdings.17The linearized long run system of equations is stated in appendix A

13

3.3 Short Run Effects of a Temporary Fiscal Shock

We can now proceed to the analysis of the short run (period t) equilibrium, which is charac-

terized by sticky prices. Producers fix their prices before the occurrence of the fiscal shock and

cannot change them within the period. As usual in this type of model, production becomes

entirely demand determined. This, in turn, implies that the labor market clearing condition

is not binding. Firms adjust production to the demand faced at the previously fixed prices as

long as marginal costs do not exceed the price. The short run equilibrium system is stated at

full length in Appendix B.

We now turn to the derivation of the short run variables of interest. We prioritize the

economic mechanisms at work when it comes to the interpretation of how an economy copes

with macroeconomic shocks. First of all, it is the consumption smoothing motive of domestic

households that drives the model results. In a second step, we investigate the possible financing

channels of the optimal consumption path when short run prices are fixed. Having the domestic

picture at hand, we may analyze the international transmission mechanisms of the domestic

shock, i.e. how the domestic fiscal expansion affects the foreign country.

In the first place, an unanticipated temporary increase in tax-financed public expenditure

distorts the projected consumption path of the households. To solve for the domestic con-

sumption response in the short run, we use the fact that the level of any individual variable

may be stated as a combination of its world aggregate and its differential:

ct = cwt +

12(ct − c∗t ) (42)

In a next step, we derive the short term consumption differential between both countries:

ct − c∗t = − (1− β)(2ω − 1 + 2θ(1− ω))2ω − 1 + 2θ(1− ω) + 2βω(θ − 1)

(dgt − dg∗tc

)(43)

Though simply stated, there is a lot of calculus behind equation (43). One takes into account

both long and short run market clearing and optimality conditions, noting that the essential

link between both systems of equations is the amount of bond holdings acquired in the short

run. World consumption is derived from the common money market. Adding up linearized

14

versions of the short run money demand equations (A-11) and (A-12) we arrive at

mst =

12

(md

t + md∗t

)=

12

(pt + ct +

dgt

c+ p∗t + c∗t +

dg∗tc

)=

12

(ct + c∗t +

dgt

c

)= 0 (44)

Remember that the overall money demand in a monetary union has to remain unchanged as

long as the monetary authority does not accommodate the fiscal shock. Furthermore, the

price deviation terms disappear as of the nominal rigidities, while we drop foreign government

expenditure from the equation due to the asymmetric nature of the fiscal shock. Then, the

response of world consumption may be stated as:

cwt = 0.5 ct + 0.5 c∗t = −1

2dgt

c= −dgt

cw(45)

Thus, a fiscal expansion implies a complete crowding out of world consumption. Combining

equations (42), (43), and (45) yields

ct = −(2− β)(2θ − 1)− 4ω(β − 1 + θ − βθ)4θ − 2− 4ω(1− β)(θ − 1)

(dgt

c

)(46)

For the assumed parameter space, i.e. β ∈ [0, 1], ω ∈ [0.5, 1), and θ > 1, the sign of the

government expenditure term is unambiguously negative.18 Therefore, a domestic fiscal ex-

pansion always reduces domestic consumption. Restating equation (46) we may deduce that

the crowding out of domestic consumption by public expenditure is limited:

ct = −dgt

c+

β(2θ − 1)4θ − 2− 4ω(1− β)(θ − 1)

(dgt

c

)(47)

Basically, there are two effects of expansionary fiscal policy that govern the short term con-

sumption response. First, domestic consumption is reduced by dgt

c , loosely speaking the amount

of taxes levied on consumers by the government. The second government expenditure term en-

ters positively into equation (47) and points to feasible consumption smoothing. The domestic

households know about the temporary nature of the fiscal expansion. Therefore, they antici-

pate that the tax burden in the short run will not last for future periods. A higher consumption

level in the long run induces a reincrease of consumption today. This effect is reinforced by a

biased preference structure: A rising ω implies a stronger reincrease of consumption because

18Expanding equation (46) as ctT = − 12

�dgtc

�− 1

2

h(1−β)(2θ(1−ω)+2ω−1)

2ωβ(θ−1)+2θ(1−ω)+2ω−1

i�dgtc

�shows the conjectured un-

ambiguity.

15

of the associated demand deviation effects.19 For any level of ω, the overall effect on domestic

expenditure, i.e. private consumption plus public expenditures, will be positive.

Having established the expansive effect on domestic demand, we now turn to the financ-

ing scheme of the optimal consumption path. There are two possible sources: income from

production and the issuance of bonds. The response of domestic production stems from the

definition of the goods markets. We substitute for consumption using equation (47) and its

foreign counterpart:

yt =β(2θ − 1)(2ω − 1)

4θ − 2− 4ω(1− β)(θ − 1)

(dgt

c

)(48)

The trade balance effect of a temporary domestic fiscal expansion is

dft+1

pc= − (1− ω)(2θ − 1)

2θ − 1− 2ω(1− β)(θ − 1)

(dgt

c

)(49)

As long as there is a home bias in consumption, i.e. ω > 0.5, domestic households work

more than in the steady state. Without home bias, domestic production remains unchanged.

This effect may be explained by the symmetric nature of demand in both economies and the

fact that world demand has to remain unchanged.20 Then, the extension of overall domestic

expenditure is solely financed via debt. On the other hand, with almost disconnected goods

markets, i.e. ω → 1, the only feasible financing channel is production. We will come back to

the specific home bias issues in section 4.

The common money market clearing condition (44) represents the most evident interna-

tional transmission mechanism of a domestic fiscal disturbance. Rewriting the last part of

equation (44) reveals that the deviation of foreign consumption mirrors the action taken in the

home country:

c∗t = −(

ct +dgt

c

)(50)

As stated above, money market clearing requires that world demand remain unchanged in the

short run. Therefore, an increase in overall domestic expenditure goes hand in hand with a

reduction of foreign consumption of the same magnitude. Substituting for ct we state foreign19The economic intuition behind this result will become clear in the next section when we explore the welfare

effects of fiscal policy.20Remember that short run prices and the world money supply are fixed.

16

consumption as a function of the domestic fiscal shock:

c∗t = − β(2θ − 1)4θ − 2− 4ω(1− β)(θ − 1)

(dgt

c

)(51)

To sum up the effects on the composition of world demand: domestic overall demand expands

while the foreign one declines. As a consequence, foreigners will work less as long as ω > 0.5:

y∗t = − β(2θ − 1)(2ω − 1)4θ − 2− 4ω(1− β)(θ − 1)

(dgt

c

)(52)

In other words, a greater part of world demand falls on domestic producers if the home country

favors domestic products.

It remains to be clarified why it is optimal for foreign households to deviate from the steady

state consumption path. The key to this puzzling effect lies in the bond market: the foreign

real interest rate rises in equilibrium:21

r∗t+1 =2θ(1− ω) + β(2θω − 1)

2(1− β)(2ω − 1 + 2θ(1− ω) + 2βω(θ − 1))

(dgt

c

)> 0 (53)

A look at the Euler equations (A-17) and (A-18), that follow from the optimal bond holding

decisions at home and abroad, yields the economic intuition for this result. The domestic

picture is the following: the short run consumption decision is distorted by the unanticipated

payment of taxes. Without any change in interest rates, home residents will try to increase short

run consumption and reduce future consumption so as to equilibrate the respective marginal

utilities. To put it simply: they will try to smooth consumption over time by selling bonds.

In the foreign country, buying bonds results in a decrease of short run consumption and a

boost in future consumption. According to the foreign Euler equation, this has to be accom-

panied by a rise in foreign real interest rates in order to be optimal. Higher real interest rates

render the decision to delay consumption more attractive. In equilibrium, the excess supply of

bonds on behalf of domestic households and the reluctance of foreign households to buy bonds

result in a rise of both domestic and foreign real interest rates.22

21Note, that we do not rely on real consumption indexed bonds, and purchasing power parity does not holdin the long run. Therefore, the model allows for a real interest rate differential, i.e. rt+1 − r∗t+1 6= 0.

22Taking into account long run price deviations, one can show that the nominal interest rate rises even morethan the foreign real interest rate.

17

4 Home Bias: Beggar- or Prosper-thy-Neighbor?

We now derive the welfare implications of a domestic fiscal expansion with a specific focus

on home bias issues. According to equation (1) utility depends on current and future levels

of consumption and leisure. Home residents enter the long run as debtors while foreigners

are creditors, see the short run current account (49). Therefore, we get long run effects on

consumption and production.23

Note, that the long run response of world consumption and world production is zero. Hence,

home and foreign consumption and production react in a symmetric way, see equation (42).

Using the temporary shock version of the long run consumption differential (41) we arrive at:

ct+1 = − c∗t+1 = − θ(1− β)(1− ω)2θ − 1− 2ω(1− β)(θ − 1)

(dgt

c

)(54)

In the same way, we calculate the long run production differential:

yt+1 = − y∗t+1 =θ(1− β)(1− ω)

2θ − 1− 2ω(1− β)(θ − 1)

(dgt

c

)(55)

In the long run, domestic (foreign) consumption falls (rises), while domestic (foreign) produc-

tion rises (falls). The underlying mechanisms for this result are a direct wealth effect and a

change in the real wage rates. Stepping back to the financing scheme of a domestic consump-

tion reincrease stated in equations (48) and (49), we see that a lower home bias raises the

financing via debt. This acts like a strong negative wealth effect on the domestic economy.

Then, since consumption and leisure are normal goods, the demand for both will be reduced.

So we get all else equal less consumption and more work. In the foreign country, it is the other

way around: households consume more and work less. Therefore, a lower home bias enables

foreigners to run higher current account deficits in the long run.

On the demand side, less domestic and more foreign consumption point to less domestic

and more foreign production as long as there is a home bias in consumption. Hence, at the

prevailing wage rates and unchanged individual and aggregate prices, domestic labor demand

tends to fall, while foreign labor demand will increase. In order to restore the labor market

equilibrium, the domestic real wage has to has to decrease while the foreign counterpart has23Remember that production always equals hours worked.

18

to rise:

wt+1 = −w∗t+1 = − (1− β)(1− ω)2θ − 1− 2ω(1− β)(θ − 1)

(dgt

c

)(56)

A lower real wage induces a lower optimal relative good price and ensures an increase in demand

for domestic products that raises domestic labor demand. We observe that a weak home bias

implies a strong real wage response, as the initial supply side driven effects on consumption

and production will be more pronounced.

At the same time, the fall of the domestic real wage has standard substitution and wealth

effects. As the relative price of domestic leisure falls, the household’s demand for leisure rises

while domestic consumption falls even further. Besides, we get a negative wealth effect lowering

both the demand for consumption and leisure. Hence, the effect on leisure arising from the

domestic real wage deviation is ambiguous. In our setting, the two negative wealth effects on

the domestic labor decision dominate the substitution effect, while the effects on consumption

are all negative.

With the short and long run responses of consumption and hours worked at hand, we can

now calculate and discuss the welfare effects of a fiscal expansion in the home country. It

turns out that households in the foreign country suffer a welfare loss as long as there is a home

bias in consumption. As for the welfare of domestic households, we observe a direct negative

effect stemming from the higher tax burden and an indirect positive effect brought about by

the subsequent adjustment process. The latter of these effects is positively correlated with the

home bias in consumption.

Since the economies reach the new steady state in t + 1, the overall effect on welfare is

given by dVt = dUt + (1/r)dUt+1. The short and long run utility deviations are derived from

the utility function (1):

dUs = cs − θ − 1θ

hs (57)

Plugging in the solutions for consumption and hours worked yields

dVt = −dgt

c+

β(2θ − 1)(2ω − 1)2 θ(2 θ − 1− 2ω(1− β)(θ − 1))

dgt

c(58)

19

In the same manner, we get

dV ∗t = − β(2θ − 1)(2ω − 1)

2 θ(2 θ − 1− 2ω(1− β)(θ − 1))dgt

c(59)

for the foreign country.

Abstracting from the direct negative tax effect,−dgt

c , domestic welfare improves at the ex-

pense of the foreign country. Therefore, a fiscal expansion becomes a beggar-thy-neighbor

policy as long as ω > 0.5. The negative welfare effect on the foreign country is all the more

pronounced the greater the home bias in consumption. The economic intuition for this result

lies in the short run demand composition effects. In the previous section, we established that

domestic households lower consumption by less than the amount of taxes paid. On the other

hand, foreigners are willing to reduce consumption in order to facilitate the domestic demand

expansion. Then, as world demand remains unchanged, a home bias in consumption redi-

rects demand towards domestic producers. The following expansion of domestic production is

welfare enhancing, because initial steady state output is inefficiently low due to monopolistic

competition on the goods markets. The foreign country suffers a welfare loss as the individ-

ual household does not take into account the negative spillover effects on demand and hence

production arising from her consumption decision. Of course, the demand composition effect

is irrelevant for ω = 0.5, and there will be no beggar-thy-neighbor effect from the domestic

reincrease in consumption.

The short and long run welfare effects that are associated with bond holdings are exactly

offsetting. However, the home bias determines the intertemporal structure of utility. As stated

above, a strong home bias reduces the domestic households’ need for debt. Therefore, the

long run negative welfare effects associated with permanent interest payments will be small.

Short run utility, however, is relatively low as domestic households finance consumption mainly

through working.

5 CONCLUDING REMARKS

In this paper we have analyzed the effects of fiscal policy in the context of a monetary union. We

have shown that a home bias in private and government consumption has important implica-

tions for the international transmission of an asymmetric fiscal expansion. In an environment,

20

in which prices are rigid and money demand depends on private consumption and taxes, an

expansive fiscal policy has a positive short run effect on domestic output if there is a home bias

in consumption. As government expenditure only partially crowds out private consumption,

overall home expenditure rises at the expense of foreign expenditure. In the case of biased

preferences this will translate into a different structure of world production: Home production

increases above the steady state level, while foreign production falls below it. As initial output

is suboptimally low due to monopolistic distortions, the shift of production mitigates the neg-

ative effect of higher taxes on domestic welfare at the expense of the foreign country. Thus,

expansive fiscal policy becomes a beggar-thy-neighbor instrument. To draw a cautious policy

implication from the analysis: Asymmetric fiscal policies in a monetary union may be less of

a concern, if product markets are highly integrated.

21

A Log-Linearized Long Run

Money markets

mt+1 = pt+1 + ct+1 (A-1)

m∗t+1 = p∗t+1 + c∗t+1 (A-2)

Current accounts

ct+1 = pht+1 + yt+1 − pt+1 +

(1− β)dft+1

p c(A-3)

c∗t+1 = pf∗t+1 + y∗t+1 − p∗t+1 +

(1− β)df∗t+1

p∗ c(A-4)

Goods markets

yt+1 = −θpht+1 + θωpt+1 + θ(1− ω)p∗t+1 + ωct+1 + (1− ω)c∗t+1 (A-5)

y∗t+1 = −θpf∗t+1 + θωp∗t+1 + θ(1− ω)pt+1 + ωc∗t+1 + (1− ω)ct+1 (A-6)

Euler equations

pt+1 + ct+1 = pt+2 + ct+2 + Rt+1 (A-7)

p∗t+1 + c∗t+1 = p∗t+2 + c∗t+2 + Rt+1 (A-8)

Labor markets

ht+1 =θ

θ − 1(ph

t+1 − ct+1 − pt+1) (A-9)

h∗t+1 =θ

θ − 1(pf∗

t+1 − c∗t+1 − p∗t+1) (A-10)

22

B Non-linear Short Run

Money markets

mt = (ct + gt)pt (A-11)

m∗t = (c∗t + g∗t )p

∗t (A-12)

Current accounts

pt(ct + gt) + Rtft+1 = pht yt (A-13)

p∗t (c∗t + g∗t ) + Rtf

∗t+1 = pf

t y∗t (A-14)

Goods markets

yt =(

pht

pt

)−θ

ω(ct + gt) +(

pht

p∗t

)−θ

(1− ω)(c∗t + g∗t ) (A-15)

y∗t =

(pf

t

p∗t

)−θ

ω(c∗t + g∗t ) +

(pf

t

pt

)−θ

(1− ω)(ct + gt) (A-16)

Euler equations

β pt ct = Rt pt+1 ct+1 (A-17)

β p∗t c∗t = Rt p∗t+1 c∗t+1 (A-18)

23

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