Vito Tanzi in his recent article on the effects of fiscal deficits on interest rates in the United States (Tanzi (1985)) concluded that the cyclically adjusted U.S. federal deficit had a significant effect in raising interest rates. Unfortunately, he appears to have misinterpreted the sign on the deficit variable. The government balance, when it is a deficit, has a negative value, and therefore it should have had a negative coefficient. Instead, Tanzi’s empirical results, which have positive coefficients on the deficit variable, indicate that a higher government deficit causes lower interest rates.

This result is, of course, contrary to the predictions of economic theory. The extreme difficulty noted elsewhere in the empirical literature in finding support for the theoretical prediction of the effects of government deficits on interest rates, however, ought to make one immediately suspicious of the ease with which Tanzi found support for it. In his survey article on the subject, Dwyer (1985, p, 656) found that “unrestricted reduced-form estimates provide no support for such a relationship, and restricted estimates are sensitive to the specification.” In his article Dwyer concentrated on potential explanations of why the data do not support the theory.

To say merely that there is no support for the standard theoretical view is a euphemism. In fact, as my own investigations have shown, it is easy to find support for the opposite of the theoretical prediction. Tanzi, in publishing his misinterpreted regression results, has inadvertently shown that the emperor has no clothes. I should say that I have not previously belonged to the doctrinal school that claims that deficits should have no effect on interest rates. In a recent article (Spiro (1987)) I approvingly cited Hoelscher (1986) to the effect that deficits raise bond yields.

To verify my contention about Tanzi’s results, I tried to replicate some of his regressions with my own data (Table 1). The results are not identical, probably because of data revisions, but they are quite close, and bear out that Tanzi’s regressions are showing that government deficits reduce interest rates. The dependent variable is R, the yield on one-year U.S. Treasury bills. The explanatory variables are P, the 12-month Livingston index of expected inflation; G, the gap between actual and potential real GNP; and DL, the cyclically adjusted federal government deficit as a percentage of GNP. The data source for G and DL is the March 1986 issue of the Survey of Current Business, published by the U.S. Department of Commerce.

Table 1.

Regressions Explaining One-Year Yield on U.S. Treasury Bills

Note: Annual data were used, with Cochrane-Orcutt autocorrelation correction in equations (2)–(5); t-statistics appear In parentheses. P is the Livingston survey inflation expectation; G is the gap between actual and potential real GNP; DL is the cyclically adjusted federal government deficit as a percent of GNP; DL(-2) denotes the value_of DL two years ago; and MR is the monetary base as a percent of GNP; DW is the Durbin-Watson test statistic; and ${\overline{R}}^2$ is the adjusted coefficient of determination.

Table 1.

Regressions Explaining One-Year Yield on U.S. Treasury Bills

Equation	Period	Constant	P	C	DL	DL(-2)	MR	ρ	DW	${\overline{R}}^2$
(1)	1960–80	2.5	1.06	0.36	0.6.8	—	—	—	1.97	0.94
		(9.9)	(16.8)	(6.6)	(4.2)
(2)	1960–80	1.5	0.95	0.28	—	-0.36	—	0.54	1.53	0.92
		(1.7)	(6.4)	(2.6)		(-1.75)		(2.1)
(3)	1960–85	1.9	1.02	0.16	—	-0.35	—	0.69	1.44	0.88
		(1.4)	(4.7)	(1.4)		(-1.35)		(4.0)
(4)	1960–85	44.0	0.68	-0.03	—	-0.22	-7.5	0.92	1.41	0.91
		(3.4)	(3.3)	(-0.2)		(-1.0)	(-3.1)	(32.1)
(5)	1960–85	23.6	0.70	0.11	0.45	—	-2.9	0.79	1.54	0.91
		(2.2)	(3.2)	(1.2)	(2.0)		(-1.68)	(4.9)

Note: Annual data were used, with Cochrane-Orcutt autocorrelation correction in equations (2)–(5); t-statistics appear In parentheses. P is the Livingston survey inflation expectation; G is the gap between actual and potential real GNP; DL is the cyclically adjusted federal government deficit as a percent of GNP; DL(-2) denotes the value_of DL two years ago; and MR is the monetary base as a percent of GNP; DW is the Durbin-Watson test statistic; and ${\overline{R}}^2$ is the adjusted coefficient of determination.

View Table

Table 1.

Regressions Explaining One-Year Yield on U.S. Treasury Bills

Equation	Period	Constant	P	C	DL	DL(-2)	MR	ρ	DW	${\overline{R}}^2$
(1)	1960–80	2.5	1.06	0.36	0.6.8	—	—	—	1.97	0.94
		(9.9)	(16.8)	(6.6)	(4.2)
(2)	1960–80	1.5	0.95	0.28	—	-0.36	—	0.54	1.53	0.92
		(1.7)	(6.4)	(2.6)		(-1.75)		(2.1)
(3)	1960–85	1.9	1.02	0.16	—	-0.35	—	0.69	1.44	0.88
		(1.4)	(4.7)	(1.4)		(-1.35)		(4.0)
(4)	1960–85	44.0	0.68	-0.03	—	-0.22	-7.5	0.92	1.41	0.91
		(3.4)	(3.3)	(-0.2)		(-1.0)	(-3.1)	(32.1)
(5)	1960–85	23.6	0.70	0.11	0.45	—	-2.9	0.79	1.54	0.91
		(2.2)	(3.2)	(1.2)	(2.0)		(-1.68)	(4.9)

Note: Annual data were used, with Cochrane-Orcutt autocorrelation correction in equations (2)–(5); t-statistics appear In parentheses. P is the Livingston survey inflation expectation; G is the gap between actual and potential real GNP; DL is the cyclically adjusted federal government deficit as a percent of GNP; DL(-2) denotes the value_of DL two years ago; and MR is the monetary base as a percent of GNP; DW is the Durbin-Watson test statistic; and ${\overline{R}}^2$ is the adjusted coefficient of determination.

My regression equation (1) replicates Tanzi’s equation (4) (Tanzi (1985, Table 2, p. 561)). My coefficients are of similar magnitude and of the same sign as his. Tanzi concluded from his equation (4) that a “deficit of 5 percent of GNP would have raised the rate of interest by about 4 percentage points” (Tanzi (1985, p. 563)). The data used in my equation (1) for DL represent a deficit by a negative value, however, so that the equation says that such a deficit would lower the interest rate by 4 percentage points. When I first encountered this result, I thought that it might be due to an insufficient cyclical correction in the deficit data. The result has persisted, however, through many subsequent regressions with the equation, and with a great many alternative explanatory variables added. It is a paradoxical result, but I have rarely encountered a variable that persists in remaining statistically significant under so many different specifications, albeit with the wrong sign.

The data do seem to indicate that the lagged effect of the government deficit has the theoretically predicted sign, and this is shown in my equations (2) and (3), although here the statistical significance is low. This may help to explain why the level of total government debt, used by Tanzi in some other regressions, has the correct sign. One can think of several possible explanations for the delayed effect. In a stock-adjustment model of international capital flows, there might initially be a rush of funds coming into the United States in response to the deficit, to take advantage of expected profits from an appreciating exchange rate. This influx of foreign capital would initially lower interest rates, which would only rise after foreign lenders had achieved their new portfolio equilibrium. In equations (4) and (5) I show the effects of a monetary variable, MR, which is the monetary base expressed as a percentage of GNP. Increases in the money supply are seen to lower the interest rate. A comparison of equations (4) and (5) suggests that part of the reason that the contemporaneous deficit variable does not raise the interest rate is that the deficit is often monetized.

The one remaining study that demonstrates a strong effect of the deficit on interest rates is that of Hoelscher (1986). Hoelscher does not claim to show anything more than that a higher deficit raises bond yields relative to short-term interest rates. But the findings discussed here also place Hoelscher’s results in a new light. Deficits do raise long-term interest rates relative to short-term rates, but at the same time they lower the level of short-term interest rates. Therefore it is difficult to infer from regressions of that type by how much deficits have raised the absolute level of the long-term interest rate.

In conclusion, the empirical evidence for a positive effect of the deficit on the level of interest rates remains as elusive as ever. We know that interest rates are determined by the supply and demand for credit, but we obviously do not know how fiscal deficits affect this supply and demand.