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24 (G, 0.067) 1740 1760 1780 1800 1820 1840 1860 1880 1900 FIGURE 2.10 Temporary military spending and the longterm interest rate in the United Kingdom (from Barro, 1987; used with permission) larly, since the analysis implies that permanent increases never change the shortterm rate, it predicts that they do not affect the longterm rate. In addition, the real interest rate equals the nominal rate minus expected inrlation; thus the nominal rate should be corrected for changes in expected mflation. Barro does not find any evidence, however, of systematic changes ji expected inflation in his sample period; thus the data are at least consistent with the view that movements in nominal rates represent changes in real rates. Figure 2.10 plots British military spending as a share of GNP (relative 0 the mean of this series for the full sample) and the longterm interest rate. The spikes in the military spending series correspond to wars; for example, the spike around 1760 reflects the Seven Years War, and the spike around 1780 corresponds to the American Revolution. The figure suggests that the interest rate is indeed higher during periods of temporarily high government purchases. To test this formally, Barro estimates a process for the military purchases series and uses it to construct estimates of the temporary component of military spending. Not surprisingly in light of the figure, the estimated temporary component differs little from the raw series. Barro then regresses the longterm interest rate on this estimate of temporary military "Since there is little permanent variation in military spending, the data cannot be used to investigate the effects of permanent changes in government purchases on interest rates.
The Governments Budget Constraint The governments budget constraint is that the present value of its purchases must be less than or equal to its initial wealth plus the present value of its tax revenues. Let G(f) and T(t) denote government purchases and taxes per unit of effective labor at time t; thus total purchases at f are G{t)e"9)tA(0)W), and total taxes are ( ) "+9 (0)1(0). In addition, let spending. Because the residuals are serially corrected, he includes a firstorder serial correlation correction. The results are Rt = 3.54 + 2.6 Gt, A = 0.91 (0.27) (0.7) (0.03) R = 0.89, s.e.e. = 0.248, D.W. = 2.1. (2.40) Rt is the longterm nominal interest rate, Gr is the estimated value of temporary military spending as a fraction of GNP, A is the firstorder autoregressive parameter of the residual, and the numbers in parentheses are standard errors. Thus there is a statistically significant link between temporary military spending and interest rates. The results are even stronger when World War I is excluded: stopping the sample period in 1914 raises the coefficient on Gt to 6.1 (and the standard error to 1.3). Barro argues that the comparatively small rise in the interest rate given the tremendous rise in military spending in World War I may have occurred because the govemment imposed price controls and used a variety of nonmarket means of allocating resources. If this is right, the results for the shorter sample may provide a better estimate of the impact of government purchases on interest rates in a market economy. Thus the evidence from the United Kingdom supports the predictions of the theory. The success of the theory is not universal, however. In particular, for the United States real interest rates appear to have been, if anything, generally lower during wars than in other periods (Barro, 1993, pp. 321322). The reasons for this anomalous behavior are not well understood. Thus the theory does not provide a full account of how real interest rates respond to changes in government purchases. 2.8 Bond and Tax Finance So far we have assumed that government spending is financed entirely with current taxes. But in fact governments rely not only on taxes but also on bonds as a means of finance. This section therefore examines the choice between tax and bond finance.
= b(0)A(0)L(0) + Note that because b(0) represents debt rather than wealth, it enters negatively into the budget constraint. Dividing both sides of (2.41) by A(0)L(0) \lelds e R(f)G(t)e("+0)trf, = ,(o)+ e <fr(f)e"+e*fdf. (2.42) Just as the households budget constraint, when it is satisfied with equality, implies limjoo e <e*"+«A;(s) = 0 (see equation [2.12J), one can show that (2.42) implies liineR()e(+0)fo(s) = O. (2.43) This condition states that the value of the governments outstanding debt, in units of timezero output, must approach zero. We know that on the balanced growth path, r is equal io p + , which is greater than n+g; thus eventually (*) ("+0) is falling. Equation (2.43) therefore permits the government to follow policies that cause debt per unit of effective labor, b(s), to converge to some positive level. But it rules out pohcies that cause b{s) to grow forever at too rapid a rate. Implications for the Economy When there are taxes, the households budget constraint is that the present value of consumption must be less than or equal to initial wealth plus the present value of lifetime aftertax labor income; the initial wealth now includes both capital and bond holdings. Stated in terms of quantities per unit of effective labor (analogously to equation [2.7] for the case without taxes). Moreover, If the government attempts such a pohcy, an equihbrium may not exist if Its debt is denominated in real terms. See, for example, Aiyagari and Gertler (1985) and Woodford (1994). bit) denote the outstanding stock of government debt per unit of effective labor at t. We assume that the government satisfies its budget constraint with equality. If it did not, its wealth would be growing forever relative to the economy, which does not seem realistic. With this assumption, the governments budget constraint is (2.41) e<f[r(f)e"9>A(0)L(0)]dt.
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