INTRODUCTION
The macroeconomics of international fiscal spillovers, traditionally based on the Mundell–Fleming model, are being reinvestigated within the emerging “new open economy macroeconomics” framework [see Lane and Ganelli (2003, Sect. 4). The starting point of this literature is the redux model presented by Obstfeld and Rogoff (1995, 1996). In the redux model, an increase in government spending in one country decreases domestic consumption and increases consumption abroad.1
This in turn causes a fall in relative money demand, which depreciates the domestic currency and, through the expenditure switching effect, raises relative output.
This result follows from the wealth effect due to the fact that residents of the country that expands have to face all the costs of this policy (the increase in taxes) whereas, with no home bias in government spending, the benefits (the increase in demand) are shared with the other country.
We show how introducing home bias in public consumption in the redux model generates a quasi-neutrality result: Temporary fiscal expansions increase domestic output on a one-to-one basis, without any effect on the other (domestic and foreign) macroeconomic variables.2
This property was first discussed by Rankin (1990). Other examples of models in which the property holds are Svensson (1987) and Corsetti and Pesenti (2001). Although in these models government spending falls only on domestically produced goods, the link between this assumption and the quasi-neutrality property has not yet been fully investigated.
Our exercise has two main implications. First, it provides a warning on the realism of some predictions of the redux model. Caselli (
2001), for instance, empirically estimates the response of relative consumption for a panel of EU countries to a fiscal shock in Germany (considered as the “foreign” country), finding that the coefficient is closer to zero than to one.
3 The magnitude of the coefficient is about 0.2.
Although further empirical research on the international spillover effects of fiscal policy is warranted, Caselli's results suggest that the original redux model might overemphasize the importance of consumption spillovers following a fiscal shock.
4 Although Obstfeld and Rogoff (1995, 1996) do not provide a quantitative calibration of the redux model, they highlight the decrease in relative consumption following a domestic fiscal expansion as a crucial result, from both the positive and the welfare points of view.
Second, our exercise has some important policy implications. In particular, it points out that policymakers, when assessing the international effects of fiscal policies, should take into account not only the level of public expenditure but also its composition. The latter aspect tends to be neglected in the policy arena, where the emphasis falls more on numerical targets for the government budget or for the level of spending, regardless of the composition of the latter. In this note, we assume complete home bias for analytical convenience. The actual degree of home bias from an empirical point of view is likely to be considerable but less than what our assumption implies.5
Although empirical estimates of the degree of home bias in government spending are not readily available, some indirect evidence shows that this might be very high. In the United States, for example, current expenditure (which largely falls on government employment and therefore exhibits full home bias almost by definition) as a share of total government expenditure amounted to 96% in 2003 (Bureau of Economic Analysis), http://www.bea.org.
We believe, however, that comparing the two extreme assumptions used respectively in the redux and in this note can give some insights on the direction in which the effects of fiscal policy change as the weight of domestic spending in public consumption changes.
6 Of course, a more thorough analysis would imply introducing intermediate degrees of home bias in the model; this is left for future research.
The zero effect on consumption that we derive shows how, in a one-period fixed-price model, government spending cannot crowd out consumption through higher prices. Since in the presence of price rigidities the labor market efficiency condition does not hold and output is demand determined, domestic output increases one-to-one with aggregate demand.
The basic intuition for our results is that, when government spending is used to purchase only domestically produced goods, the wealth costs of this policy for home agents are perfectly offset by the gains deriving from the stimulation of domestic demand. This implies that there is no effect on domestic consumption. Since in the redux model real balances are a function of consumption, the unchanged pressure on money demand implies no effect on the exchange rate and therefore no expenditure switching effect. This in turn implies a zero output spillover.
MODEL
The model presented here is an extension of the redux model that allows for home bias in public spending.7
Warnock (2003) investigates the implications of home bias in private consumption in this framework.
The world is populated by a continuum of infinitely lived agents who are both consumers and monopolistic producers of a continuum of differentiated goods. Home agents are on the interval [0,
n], while foreign agents are on the interval (
n,1].
8 Since the model is symmetric, we will introduce the equations only for the domestic agents.
A representative agent
j maximizes the following intertemporal utility function:
subject to the budget constraint
where 0 < β < 1 is the discount factor, and all the parameters are positive. The arguments of the utility function are a real private consumption index, real money balances, and an output term, which captures the disutility of having to give up leisure in order to produce more. The private consumption index C, defined as
aggregates over the consumption of the continuum of goods, and θ > 1 is the price elasticity of demand faced by each monopolist. B is a riskless real bond denominated in the composite consumption good, which gives account of international shifts in wealth; rt is the real interest rate on bonds between t - 1 and t; Yt (j) is output of good j; and pt (j) is its domestic currency price. Mt - 1 denotes nominal money balances held at the beginning period t, and τt lump-sum taxes, which are assumed to be payable in the consumption good Ct.
Whereas in the redux model, government spending is defined exactly as private consumption, that is, as an aggregate over the continuum of goods regardless of their place of production, we assume in this model complete home bias in public consumption. With home bias, the domestic government consumption index takes the form
The index for the foreign country is, similarly, an integral between n and 1. In this framework, public demand for the domestic representative agent's good comes only from domestic government and it is given by
where government expenditure is now deflated by a price index that is different from the private consumption one.
Aggregating demand from home government with demand from domestic and foreign private agents gives the new world demand for the domestic agent's output as
where the superscript w denotes world variables. Equation (5) states that demand for domestic output comes from world private consumption and from domestic public consumption.9
In the basic redux model with no home bias, world public consumption would enter equation (5).
The model assumes no impediments to trade, so that the law of one price and the purchasing power parity hold. In each period, the government is subject to the budget constraint10
Since we are focusing on fiscal policy, we ignore seignorage and we set monetary shocks to zero. We also focus on balanced-budget fiscal expansions. Since Ricardian equivalence holds in the model, government deficits would not have real effects. The existence of two different price indexes for private and public consumption implies that a more precise expression for the government budget constraint would be
.
However, since in what follows we loglinearize the model around a symmetric steady state where
, we can ignore this minor complication.
Finally, the model displays nominal rigidities in the form of one-period preset prices.11
We follow the original redux framework, assuming that the rigidity is in prices denominated in the producers' currencies.
Quasi Neutrality of Fiscal Shocks
As standard in this literature, we loglinearize the model around a symmetric steady state in which all producers set the same price and in which both government spending and foreign assets are equal to zero. In what follows, lowercase letters with a tilde denote log deviations in the short run (the period in which the shock hits and prices cannot adjust); lowercase letters with a hat denote log deviations in the long run, when prices are free to adjust to their long-run values.
Loglinearization of (5), taking into account that, in the initial symmetric steady state, P0=PG0 = p0 (z), yields
Proceeding in a symmetric way for the foreign country, we find a corresponding expression, which enables us to express relative output as
Because the only changes in the algebra, compared to the redux model, concern the demand equations (equation 5 and its foreign equivalent), the equations of the redux that can be derived without using the demand equations are still valid. This is the case for the following expression for net foreign assets12
Equation (8) corresponds to equation (62) in Obstfeld and Rogoff (1996), for the version of the model that encompasses public spending.
:
where
denotes the log deviation of the exchange rate. Substituting (7) into (8) yields an expression for net foreign assets as a function of the exchange rate and of the consumption differential, in which the effects of the temporary components of fiscal policy cancel out:
In the redux model, it would be possible to derive an equation corresponding to (9). The corresponding redux equation, however, would be a function of
as well. The fact that, in our model, differential fiscal expansions affect differential demand (because there is home bias) implies the disappearance of differential effects of fiscal expansions on net foreign assets, which were present in the redux model. Intuitively, the gains that home agents derive, in terms of increased demand for their goods, from domestic expansions, perfectly offset the costs deriving from the taxes that they have to pay to finance this policy. Equation (9) is a first step in proving that quasi neutrality holds under the new assumptions: It shows that the net foreign assets position is not directly affected by temporary fiscal policy expansions. As pointed out by an anonymous referee, this result could also have been shown by decomposing total nominal demand in nominal consumer demand and nominal government demand and imposing the government balanced budget condition in the household budget constraint [equation (2)]. The key implication is that, under our assumptions, a balanced budget increase in government spending does not affect households' savings.
Obstfeld and Rogoff (1995, 1996) and Ganelli (2003) show how the redux model can be reduced to two relationships between relative consumption and the exchange rate.13
See Obstfeld and Rogoff [1996, Eqs. (60) and (127)].
In the redux model, one of the two schedules that can summarize the model in the (
) space is a function of
In the model presented here, however, the fact that
does not enter equation (9) implies that the two schedules are not a function of short-run fiscal expansions. This also means that it is not necessary to carry out explicitly the rest of the calculations in order to prove our claim.
The changes to the algebra, compared to the redux case, are concerned only with the long-run effects of fiscal policy. Since we are only interested in the temporary ones, we can write the variables as implicit functions of the long-run “anticipated” components
. This leads to the following reduced forms for the nominal exchange rate and for the consumption differential14
Notice that we have replaced
exploiting a well-known property of the redux model. The result that the exchange rate and relative consumption are not functions of temporary shocks stems from the fact that
does not affect
.
.
Equation (10) shows that the nominal exchange rate is a function only of the anticipated components, and is therefore not affected by temporary policies. Following Aoki (1981), we can solve (11) for levels as follows:
Obstfeld and Rogoff [1996, Eq. (124)] show that world consumption
is not affected by temporary fiscal expansions. Therefore (12) proves that temporary expansions do not affect consumption. What about output? Again, using Aoki's method to solve equation (7) for levels, and substituting (10) for the nominal exchange rate, gives
Neglecting the effects of the anticipated component and using the fact that, since
equilibrium in the world goods market implies
equation (13) gives
From (14), we can derive the following effects on domestic output, following, respectively, a domestic and a foreign temporary fiscal expansion:
and
This completes our proof. After the introduction of home bias in government spending, the model displays the quasi-neutrality property: A temporary fiscal expansion in one country implies a unit multiplier on that country's output, while none of the other macroeconomic variables (output in the other country, consumption in both countries, the current account, and the nominal exchange rate) are affected.
