< HO) + HO) +

(2.44)

The integral on the right-hand side of (2.44) equals the present value of labor income minus the present value of taxes. The go\ernment budget constraint, (2.42), implies that the present value of taxes equals initial debt, fo(0), plus the present value of government spending, J/Iq eG(t)e*"Mt. Thus we can rewrite (2.44) as

(2.45)

< kiO) +

e R(f)w(f)e<+3)t e-<G(t)e<+e dt.

Equation (2.45) shows that we can express households budget constraint in terms of the present value of government purchases without reference to the division of the financing of those purchases at any point in time between taxes and bonds. In addition, neither government purchases nor taxes enter households preferences (see equation [2.14]), and it is only purchases that affect the dynamics of the capital stock (see equation [2.38]).

Thus we have a key result: only the path of government purchases, and not the path of the taxes that finance those purchases, affects the economy. For example, the impact of the temporary increase in government purchases considered in the previous section is the same if those purchases are financed by bond issues paid off by taxes levied at some point in the future rather than by current taxes.

2.9 The Ricardian Equivalence Debate

Overview

The result of the irrelevance of the governments financing decisions is the famous Ricardian equivalence between debt and taxes." The logic of the result is simple. To see it clearly, think of the government giving some amount of bonds to each household at some date ti and planning to re-

-"The name comes from the fact that this idea appears to have first been proposed (though ultimately rejected) by David Ricardo; see Buchanan (1976).

this condition is

e «<"c(f)e*+9f dt

The Entry of New Households into the Economy

One obvious reason that Ricardian equivalence is likely not to be exactly correct is that there is turnover in the population. When new individuals are entering the economy, some of the future tax burden associated with a bond issue is borne by individuals who are not alive when the bond is issued. Because of this, the bond represents net wealth to the individuals who are living at the time of the bond issue, and it thus affects their behavior. This possibility is illustrated by the Diamond overlapping-generations model developed in the second half of this chapter.

There are two difficulties with this objection to Ricardian equivalence. First, a series of individuals with finite lifetimes may behave as if they are a single household. In particular, if individuals care about the welfare of their descendants and if that concern is sufficiently strong that they make positive bequests, the governments financing decisions may again be irrelevant.

tire this debt at a later date tz; this requires that each household be taxed amount e(f2)(fi)B at tz. Such a policy has two effects on the representative household. First, the household has acquired an asset-the bond-that has present value as of fi of . Second, it has acquired a liability-the future tax obligation-that also has present value as of fi of B. Thus the bond does not represent "net wealth" to the household, and it therefore does not affect the households consumption behavior. In effect, the household simply saves the bond and the interest that the bond is accumulating until tz, at which point it uses the bond and the interest to pay the taxes the government is levying to rethe the bond. This conclusion follows solely from the households and the governments budget constraints, and not from any other featiires of the model.

Traditional economic models, and many informal discussions, assume that a shift from tax to bond finance increases consumption. Traditional analyses of consumption, for example, often model consumption as depending only on current disposable income, Y-T. The Ricardian and traditional views of consumption have very different implications for important policy issues. For example, the United States has run large budget deficits since the early 1980s. The traditional view implies that these deficits are increasing consumption, and thus reducing capital accumulation and growth. But the Ricardian view implies that they are having no effect on consumption or capital accumulation. To give another example, governments often cut taxes during recessions to increase consumption spending. But if Ricardian equivalence holds, these efforts are futile. Thus it is important to determine which view is closer to the truth.

There are of course many reasons that Ricardian equivalence may not hold exactly. The relevant question, however, is not whether it is exactly correct, but whether there are large departures from it.

For a few examples, see Bernheim, Shleifer, and Summers (1985); Bernheim and Bagwell (1988); Bernheim (1991); and Altonji, Hayashi, and Kotlikoff (1992). See Bernheim (1987a) for a survey.

Again this result follows from the logic of budget constraints. Consider the example of a bond issue today repaid by a tax levied several generations in the future. It is possible for the consumption of all of the generations involved to remain unchanged. All that is needed is for each generation, beginning with the one alive at the time of the bond issue, to increase its bequest by the size of the bond issue plus the accumulated interest; the generation living at the time of the tax increase can then use those funds to pay the tax levied to retire the bond.

Thus individuals can keep their consumption paths unchanged in response to the bond issue. But this leaves the question of whether they do. The bond issue does provide each generation involved (other than the last) with some possibilities it did not have before. Because government spending is assumed unchanged, the bond issue is associated with a cut m current taxes. The bond issue therefore increases the lifetime resources available to the individuals then alive. But the fact that the individuals are already planning to leave positive bequests means that they are at an interior optimum in choosing between their own consumption and that of their descendants; thus they do not change their behavior. Only if the requirement that bequests cannot be negative is a binding constraint-that is, only if bequests are zero-does the bond issue affect consumption. Since we have assumed that this is not the case, the individuals do not change their consumption; instead they pass the bond and the accumulated interest on to the next generation. Those individuals, for the same reason, do the same, and the process continues until the generation that has to retire the debt uses its additional inheritance to do so.

The resuh that intergenerational links might cause a series of individuals with finite hfetimes to behave as if they are a household with an infinite horizon is due to Barro (1974). It was this insight that started the debate on Ricardian equivalence, and it has led to a large hterature on the reasons for bequests and transfers among generations, their extent, and their implications tor Ricardian equivalence and many other issues.

The second difficulty with the argument that finite lifetimes cause Ricardian equivalence to fail is more prosaic: as a practical matter, lifetimes are long enough that if the only reason that governments financing decisions matter is because lifetimes are finite, Ricardian equivalence remams a good approximation (Poterba and Summers, 1987). There are two reasons for this. First, for realistic cases, large parts of the present value of the taxes associated with bond issues are levied during the lifetimes of the individuals alive at the time of the issue. For example, Poterba and Summers calculate that most of the burden of retiring the United Statess World War II debt was borne by people who were already of working age at the time of the war;