fiscal policy in a monetary union model with home bias in consumption · fiscal policy in a...
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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, [email protected]†University of Frankfurt, [email protected]‡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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