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The Effect of Government Debt on Short-Term Real Interest Rates Comment on Findlay

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1990
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In a recent article in this journal, David W. Findlay reviews further empirical evidence on the effects of government deficits on interest rates. Quoting Spiro (1987) from three years earlier, Findlay concludes that these effects are as “elusive as ever” (1990, p. 438).

I would suggest that the situation is not quite as bleak as that assessment appears to make it. There is a growing realization that fiscal policy can have a variety of effects on different interest rates. A significant amount of empirical evidence indicates that current deficits do affect long-term bond yields, as noted in an exhaustive survey of the literature by Barth and others (1989, p. 55). Spiro (1989, pp. 59–62) concludes that these results are consistent with an interpretation that the government deficit affects bond yields because it is viewed by investors as an indicator of the risk of future inflation.

Even more important is a growing realization that standard economic theory does not predict that higher current budget deficits raise interest rates. This forgotten fact is well described in a little-known paper by Karl Brunner (1984, pp. 18–19): “Prices in markets for durable objects with comparatively low transaction costs are thus controlled, not by flows of new production and a corresponding pro-rata allocation of savings, but the interaction between the accumulated stock and the public’s willingness to hold this stock. Stock demand and stock supply and not a (new) flow demand and (new) flow supply, determine the current price.”

Therefore, econometric tests should be looking for a relation between debt (not deficits) and interest rates.

The hypothesis that debt would act as a determinant of interest rates was raised as a secondary issue by Tanzi (1985, p. 560), and noted as probably being a valid factor by Spiro (1987, p. 401). In this note, I will describe some econometric evidence that provides strong additional support for the proposition that a higher total debt raises interest rates.

Barro (1989, p, 48) suggests that: “Overall, the empirical results on interest rates support the Ricardian view. Given these findings, it is remarkable that most macroeconomists remain confident that budget deficits raise interest rates.” In fact, viewed in the context of Brunner’s stocks model, Ricardian equivalence no longer provides any clear-cut prediction of the effect (or rather, noneffect) of government deficits on interest rates. Even if the public increased its saving exactly in line with the government deficit, it is not obvious that all of this incremental saving would be invested in government debt. If this strong assumption were violated, real interest rates would rise in response to increasing government indebtedness, since the economy’s debt-to-equity ratio would rise relative to investors’ desire to hold debt.

Researchers intent on demonstrating Ricardian equivalence should go directly to the issue of saving, which is what that theory is about. Since saving clearly has not risen in line with Ricardian predictions (as Gram-lich (1989) has graphically demonstrated), it is not surprising that most macroeconomists continue to expect an effect of government dissaving on the cost of capital. The history of economics has shown many times that an effect can be real and important in spite of being econometrically elusive.

I. Empirical Results

We do not have direct data on the stock of liquid wealth available to the portfolio holders who are the potential purchasers of the stock of debt. However, it may be a reasonable approximation to assume that it is roughly proportional to permanent income. Hence, the cyclically adjusted government debt1 expressed as a percentage of trend gross national product (GNP) can serve as a suitable measure of changes in the supply of government debt relative to the demand for it. Expressing it in this form also overcomes some of the problems of measuring the deficit that have been pointed out by Robert Eisner. Indeed, Eisner (1989, p. 89) has proposed that fiscal balance should be measured not by the deficit but by the ratio of debt to income.

Several alternative reduced-form regressions explaining the real interest rate are presented in Table 1. These are not necessarily meant to be the most elegant possible model of the interest rate, but to show that the debt variable is quite robust as a significant explanatory variable in a wide variety of alternative formulations and over different time horizons.

The general form of the model follows Makin (1983), including his important finding that the expected inflation rate reduces the expected real interest rate. Theoretical justification for this phenomenon has been given by Fried and Howitt (1983), among others. 1 have included it in most equations because it significantly increases the explanatory power, even though it remains somewhat controversial. However, omitting it does not affect the significance of the debt variable, as seen in equation (3).

In most equations, the dependent variable is the after-tax expected real interest rate, which is found to work better than the pretax rate. The presence of income tax means that inflation should increase interest rates more than one for one. This is usually known as the Darby hypothesis, but in fact the first statement of it appears to have been by Tanzi (1975). The formulation chosen here, using an after-tax real interest rate as the dependent variable, is justified by the findings of Peek and Wilcox (1984). However, the debt variable is just as effective in equation (5), where the dependent variable is the pretax real rate.

A monetary variable is included to capture the temporary liquidity effect of money supply increases on the real interest rate, and it is found to be significant in all formulations. A variable to proxy the real return on corporate capital is also included, but it is a somewhat imperfect proxy that does not always perform well. In addition, the personal saving rate is included in most of the regressions. On theoretical grounds, it is just as inappropriate an explanatory variable as the deficit itself. Therefore, it is interesting to note an analogous empirical finding—in equation (3), it has a statistically significant coefficient of the wrong sign.

The variable for the ratio of debt to GNP is introduced as a twelve-quarter distributed lag in most equations, representing the gradual and delayed effect of changes in the stock. However, in equations (1), (3), and (5), the ratio of debt to GNP twelve quarters in the past (rather than a distributed lag) is used, with equally good results. Tanzi (1985, p. 560) pointed out that “as the portfolios of individuals come to be laden with government bonds, and as debt is progressively diverted from financing capita] accumulation in the private sector, the rate of return to investment in the private sector would have to go up.” This would tend to imply a delayed and gradual effect, suggesting that one should be looking at distant lagged values of the government debt.

Table 1.Summary of Regression Results Explaining the Real interest Rate
Equations
(1)(2)(3)(4)(5)(6)(7)(8)
Explanatory

Variables
1958:1

to 1988:4
1958:1

to 1988:4
1958:1

to 1988:4
1959:1

to 1988:4
1958:1

to 1988:4
1958:1

to 1978:4
1979:1

to 1988:4
1970:1

to 1988:4
Constant7.910.61.0-0.310.84.821.622.6
(10.4)(7.3)(1.6)(-4.1)(9.6)(2.9)(2.9)(8.7)
Expected inflation-0.53-0.58-0.64-0.20-0.67-0.48-0.76
(-12.2)(-11.9)(-9.5)(-3.2)(-8.6)(-4.3)(-10.8)
Profits (-1)0.170.210.310.200.22-0.040.13
(3.2)(3.6)(4.8)(2.5)(3.0)(-0.2)(1.3)
Money ratio (— 1)-2.56-2.80-2.02-4.39-3.48-2.22-4.20-4.64
(-8.5)(-8.3)(-5.6)(-9.54)(-7.8)(-6.5)(-3.0)(-9.0)
Debt (-12)0.270.310.37
(7.4)(7.1)(6.9)
Debt(-1 to -12)0.250.250.260.190.24
(7.1)(4.9)(5.9)(2.0)(5.1)
Saving0.14-0.03-0.190.120.38-0.040.18
rate (-1)(2.1)(-0.3)(-2.6)(1.1)(4.5)(-0.2)(1.4)
Summary Statistics
MA(1)0.800.800.770.690.830.800.450.78
(8.6)(8.5)(8.3)(7.2)(8.9)(6.8)(2.4)(6.5)
Adjusted R20.820.810.730.680.630.920.730.80
DW1.501.581.221.991.531.912.001.98
SER0.630.640.770.700.940.430.750.68
SSR47.114.017.5
Note: The dependent variable is the after-tax real rate of interest on U.S. three-month Treasury bills, except in equation (5), where it is the pretax real rate; f-statistics are in parentheses; R2 is the adjusted coefficient of determination; DW is the Durbin-Watson statistic; SER is the standard error of the regression; and SSR is the sum of squared residuals. An MA(1) moving average error specification is used to correct for autocorrelation.
Note: The dependent variable is the after-tax real rate of interest on U.S. three-month Treasury bills, except in equation (5), where it is the pretax real rate; f-statistics are in parentheses; R2 is the adjusted coefficient of determination; DW is the Durbin-Watson statistic; SER is the standard error of the regression; and SSR is the sum of squared residuals. An MA(1) moving average error specification is used to correct for autocorrelation.

If one considers the theoretical grounds stated above—that the stock of debt influences the level of the interest rate—it would also imply that changes in the stock of debt influence changes in the interest rate. This is seen in equation (4), where all the variables are in the form of changes from the same quarter a year ago, and the distributed lag of the change in the debt ratio is a significant explanatory factor. The change in the debt ratio is equivalent to the moving average of the deficit normalized to income. This version of the deficit is in fact a significant explanatory variable, with the right sign. However, it explains the change in the real interest rate, not the level of the rate, which is what previous researchers were (inappropriately) looking for.

This model was also tried with government consumption included as an additional explanatory variable, following the reasoning of Barth and others (1989, p. 20). The government debt variable remained significant, and government consumption itself proved to be insignificant.

In view of the gradual lagged incorporation of the influence of the debt in interest rates, a causality test has to be carefully designed for this variable. Recent past values of the dependent variable will already have incorporated most of the influence of the more distant past changes in the debt ratio.2 However, if causality is considered in the sense of a variable providing information to predict the interest rate three years in the future, then the debt ratio passes a Granger-type causality test by a large margin.3

The time period for equations (1) through (5) was chosen objectively. These equations cover the entire period for which data on the cyclically adjusted debt ratio have been published by the U.S. Bureau of Commerce. Equations (6) through (8) look at shorter time periods. A Chow test rejects structural stability in the sample by a relatively small margin.4 However, a comparison of the coefficients in equations (6) and (7) indicates that the main source of instability is in the response to the monetary variable. This accords with numerous findings that there has been a stronger liquidity effect in the post-1979 period.

In this 1979 to 1988 subperiod, the t-statistic on the debt variable declines to where it is just barely significant at the 95 percent level of confidence. This is not a function of the time period chosen but rather the shortness of the period. I found that a similar reduction in significance occurred in any ten-year subperiod chosen within the 1958 to 1988 sample. The debt ratio is a slowly changing variable with relatively little variance over short periods of time, and therefore a regression covering a short period is not able to detect the significance of its effect. This probably explains Evans’s (1989) claim that the stock of debt is not a significant determinant of interest rates. He tested its influence over the very short period 1981 to 1986, when the change in the debt ratio was unidirectional and smooth. It was rising rapidly at a relatively steady rate, making it difficult to distinguish from a simple time trend. Equation (8) covers a long enough period to include both increases and decreases in the debt ratio, and it once again shows a highly significant effect of the debt ratio on the real interest rate.

II. Conclusions

A Keynesian theory with well-defined microfoundations would not in fact predict that interest rates are a function of the current government deficit or surplus. The interest rate is the rate on a large stock of assets, and it is determined by the demand versus the supply of that stock, rather than by the flow of additions to the stock. This would imply that the government debt relative to income is the variable that should be used to test the effect of fiscal deficits on interest rates.

The results described above provide strong confirmation of Tanzi’s (1985) finding that a higher government debt contributes to significantly higher interest rates. It was found that this variable remains significant over a wide variety of specifications of a reduced-form interest rate equation. It appears to be the missing link in the explanation of the effect of government fiscal policies on interest rates.

APPENDIX Data Definitions and Sources

This Appendix identifies and defines the data sources used.

Debt

Cyclically adjusted U.S. government debt at par value as a percent of GNP was used (based on middle expansion trend GNP). Data were taken from the U.S. Department of Commerce’s Survey of Current Business (March 1986, August 1988, and March 1989).

Saving

Data used comprised personal saving as a percent of GNP; Citibase GPSAV/GNP.

Profits

Corporate profits including capital cost allowance (CCA) and inventory valuation adjustment (IVA) as a percent of GNP were used; Citibase GPJVA/GNP.

Expected Inflation

Data comprised the six-month horizon semiannual Livingston survey of expected CPI increase, provided by the Federal Reserve Bank of Philadelphia. Omitted quarters are obtained by straight-line interpolation.

Money Ratio

The ratio was obtained from the monetary base (adjusted for reserve requirement changes, by the Federal Reserve Bank of St. Louis) as a percent of GNP; Citibase FMBASE/GNP.

Real Interest Rate

The three-month Treasury bill rate (FYGM3 from Citibase) was converted to an after-tax real rate. The tax rate is the variable RTPMARG from Data Resources, Inc; calculated as the nominal rate times 1-RTPMARG minus the expected inflation rate.

REFERENCES

Peter S. Spiro is Head of the Economic Forecasts Section of the Ontario Hydro Corporation. He holds graduate degrees in Economics from the University of Toronto and the University of Chicago. The author would like to thank Paul Evans, Vito Tanzi, and Peter Howitt for comments on earlier versions of this work.

Using the cyclically adjusted debt improves the fit, but debt remains quite significant even when unadjusted data are used.

In view of the lagged effect of the debt on interest rates, Barro and Sala i Martin’s (1990) model is not well specified. They included the lagged value of the dependent variable as an explanatory variable, which makes the debt variable appear to be insignificant. The previous period’s lagged value includes most of the earlier influence of the debt. Barro and Sala i Martin used stock prices as a variable explaining interest rates. Stock prices are also used by Spiro (1989, pp. 74–80), with no effect on the significance of the debt variable.

The dependent variable was first predicted by a constant term and its own past value three years before. The sum of squared residuals (SSR) from this regression was contrasted with one where the dependent variable is predicted by the former plus the value of the debt ratio three years before. The improvement in predictability was substantial. The difference in the two equations was F(l,121) = 14.8, versus a critical value of about 3.9.

F(16,124) = 3.34, versus a critical value of about 2.2.

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