A note on budget deficits and interest rates: evidence from a small open economy.

I. Introduction

The interplay between budget deficits and other economic variables is of great importance to economic policy makers. It is therefore of great concern how macroeconomic policy actions affect budget deficits and how these actions determine the course of economic activity. A related aspect of the argument concerns the links between budget deficits and interest rates. Using annual data of the Greek economy, this paper explores the sensitivity and robustness of the Keynesian and Ricardian equivalence paradigms.(1) Most studies testing the Keynesian proposition and the Ricardian equivalence hypothesis are based on United States data. Hence, there is a need for further investigation of this issue using data from other countries with different structures.

The empirical evidence on the linkages between government deficits and interest rates has been mixed. For example, Feldstein [13], Zahid [26], Cebula [5; 6], Laumas [19], Abell [1], Miller and Russek [21], Due [9], Raynold [23] argue in favor of the Keynesian proposition (the conventional view) of a positive relationship between government deficits and interest rates. On the other hand, Barro [3], Hoelscher [15], Evans [11; 12], and Darrat [7] refute the Keynesian proposition, supporting the view either that government deficits negatively influence interest rates, or that interest rates and deficits follow independent paths.

This paper examines the cointegratedness of the time series and estimates the implied Error-Correction interest rate model. Moreover, the paper uses a number of basic diagnostic and specification tests in order to investigate the robustness, consistency and stability of the Error-Correction Model (ECM). In the next section, several issues relating to data and specification are discussed. Section III presents the empirical findings and section IV considers the main conclusions.

II. Data, Specification

In constructing the interest rate equation, we have taken into account previous empirical work concerning the relationship between budget deficits and interest rates. We have adopted Sim's view [25] and have included in the analysis additional economic variables which have a significant influence on and are influenced by budget deficits and interest rates. The exclusion of these variables from our interest rate model could lead to biased and spurious results. Based on the economic modelling of previous studies examining the links between budget deficits and interest rates, the following interest rate regression equation is considered:(2)

[INTR.sub.t] = [a.sub.0] + [a.sub.1][RGNP.sub.t] + [a.sub.2] [UNML.sub.t] + [a.sub.3] [INFL.sub.t]

+ [a.sub.4] [BDEF.sub.t] + [a.sub.5] [M.sub.t] + [a.sub.6] [GE.sub.t] + [a.sub.7] [GT.sub.t] + [u.sub.t](1)

where [a.sub.0], [a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4], [a.sub.5], [a.sub.6], [a.sub.7], are parameters; INTR is the average nominal interest rate on one year yield bonds and treasury bills; RGNP is the real Gross National Product; the unemployment rate series (UNML) is the annual average of the seasonally adjusted monthly unemployment rates; INFL is the inflation rate calculated by the CPI (Consumer Price Index); BDEF is the actual budget deficit in real terms; M is the narrowly defined money stock [M.sub.1] in real terms; GE is current government expenditure on goods and services in real terms; GT is current government transfers in real terms; u is a white noise disturbance term; and t stands for time. We obtain BDEF, M, GE and GT by dividing the nominal data by the CPI.(3)

In accordance with Barro [2; 3] and other advocates of the Ricardian equivalence hypothesis, we decompose government spending into permanent and transitory components.(4) As Seater [24, 175] pointed out, this decomposition is very important, otherwise "both the deficit and debt variables may have elements of simultaneity bias in them." When the budget deficit is included in an interest rate regression, and at the same time excluding government purchases, this may introduce omitted variable bias. It is possible for statistical results to ascribe to budget deficits effects that should actually be ascribed to government purchases.

Therefore, when testing the validity of Keynesian and Ricardian equivalence paradigms and properly specifying the interest rate regression (1), we decompose total government spending into permanent and temporary purchases and introduce the GE and GT series. With no decomposition of government spending, it is possible that "the deficit may proxy for transitory purchases and have a significant coefficient even if Ricardian equivalence actually holds" [24, 182].

III. Integration, Cointegration and ECM

Recent empirical work has suggested that the components of several economic variables usually contain stochastic elements, thus a misspecification of trend elements may produce incorrect tests. Therefore, we apply unit root and cointegration tests using both deterministic and non-deterministic trends. The investigation of the model covers the time periods 1950-1993, 1954-1993 and 1958-1993 in order for the statistical results to be reliable and robust. The entire period of 1950-1993 was chosen because there has consistently been a deficit in the State Budget since 1950.

Before exploring cointegration, the first step is to perform tests for stationarity in order to look for the existence of unit roots in the time series under study. A variable is said to be stationary if its mean, variance and covariance are all invariant with respect to time. Augmented Dickey-Fuller (ADF) tests of the type given by regressions (3) and (4) were conducted. As reported in Table I, the ADF tests demonstrated that the null hypothesis of a unit root cannot be rejected for the levels of all series. Applying first differences, the computed ADF tests suggested that the null hypothesis should be rejected for the individual series and that the variables INTR, RGNP, UNML, INFL, BDEF, M, GE and GT are integrated to order one I (1).

[TABULAR DATA FOR TABLE I OMITTED]

Cointegration is the statistical approach which tests for the existence of long-run equilibrium relationships among non-stationary variables which are integrated to the same order. We chose the cointegration methodology of Johansen [17; 18] because it employs the well-established likelihood ratio statistics. According to Gonzalo [14], the Johansen maximum likelihood procedure for cointegration is a better technique than single equation methods or alternative multivariate methods. Tests for cointegration are presented in Table II. In determining the number of cointegrating vectors r, we use the maximum eigenvalue statistic, [Lambda] max. The null hypothesis to be tested is whether there can be r cointegrating vectors among the variables of the interest rate model (1).

Using either a linear deterministic trend or a no deterministic trend in the data, and if the order of the underlying VAR model is one- or two-year lag respectively, the LR-tests are statistically significant across the entire period 1950-1993, and the intervals 1954-1993 and 1958-1993, thus rejecting the null hypothesis of noncointegration. The series INTR follows a stable and strong long-run relationship with the group of the system variables. Given that the Johansen [TABULAR DATA FOR TABLE II OMITTED] cointegration technique indicated the existence of more than one cointegrating vector, one may ask: which is better, to have one or many cointegrating vectors among the variables which compose the interest rate model (1)? The existence of many cointegrating vectors may indicate that the system under examination is stationary in more than one direction and hence more stable. Dickey, Jansen and Thornton [8, 22], in a lucid paper examining the strategy of cointegration techniques and the significance of cointegration tests, argue that "the more cointegrating vectors there are, the more stable the system . . . it is desirable for an economic system to be stationary in as many directions as possible."

According to Engle and Granger [10], cointegrated variables must have an ECM representation. Cointegration analysis is quite popular because it provides a formal background for testing and estimating long-run equilibrium relationships among economic variables. On the other hand, in recent years the ECM strategy has gained popularity in applied economics, because it provides an answer to the problem of spurious correlation. Given that the linear combination [INTR.sub.t] - [a.sub.0] - [a.sub.1] [RGNP.sub.t] - [a.sub.2] [UNML.sub.t] - [a.sub.3] [INFL.sub.t] - [a.sub.4] [BDEF.sub.t] - [a.sub.5] [M.sub.t] - [a.sub.6] [GE.sub.t] - [a.sub.7] [GT.sub.t] is stationary, the variables can be expressed by an ECM representation of the following type:

[Delta][INTR.sub.t] = [[Gamma].sub.1][Delta][RGNP.sub.t] + [[Gamma].sub.2][Delta][UNML.sub.t] + [[Gamma].sub.3][Delta][INFL.sub.t] + [[Gamma].sub.4][Delta][BDEF.sub.t]

+ [[Gamma].sub.5][Delta][M.sub.t] + [[Gamma].sub.6][Delta][GE.sub.t] + [[Gamma].sub.7][Delta][GT.sub.t] + [[Delta].sub.1][EC.sub.-1] + [[Epsilon].sub.t] (2)

where [Delta] is the difference operator, t stands for time, and [[Epsilon].sub.t] is a white noise error term obeying all the usual classical assumptions. ECM model (2) is nested within equation (1) and can be estimated by OLS. In ECM representation (2), short-run dynamics are captured by the first differences of the variables and long-run dynamics are reflected through the one-lagged error-correction term [EC.sub.-1]. The regressor [EC.sub.-1] corresponds to the lagged value of the residuals from regression model 1, and we expect [[Delta].sub.1] [less than] 0. The coefficients [[Gamma].sub.1], [[Gamma].sub.2], [[Gamma].sub.3], [[Gamma].sub.4], [[Gamma].sub.5], [[Gamma].sub.6], [[Gamma].sub.7] are short-run parameters measuring the immediate impact of independent variables on [Delta]INTR, and the parameter [[Delta].sub.1] is the long-run parameter providing long-run effects. In this way, the parameters contain predictions about the short- and long-run dynamics of ECM formulation (2). Notice that ECM model (2) does not contain an intercept term because the error-correction term [EC.sub.-1] already includes an estimate of it.

According to the Keynesian proposition the parameters [[Gamma].sub.4], [[Gamma].sub.6], [[Gamma].sub.7] should be positive. In Table III, we present statistical results for ECM representation (2). The empirical findings support the Keynesian proposition and raise doubt about the Ricardian equivalence hypothesis. The coefficients of [Delta]RGNP, [Delta]UNML, [Delta]INFL, [Delta]BDEF, [Delta]M, [Delta]GE have the correct sign and are significantly different from zero. The coefficient of [Delta]GT is statistically insignificant.(5) The t-ratio for the [EC.sub.-1] term is significant even at the 1 percent level. In general, the robustness of the statistical results is not altered when the sample range is varied, indicating a positive and significant effect of [Delta]BDEF and [Delta]GE on [Delta]INTR. Under the Keynesian proposition, a rise in the deficit causes the issuance of government bonds in order to cover the deficit. The income from interest gained makes bondholders feel wealthier, thereby increasing their consumption expenditure and consequently the aggregate demand. However, more consumption implies less savings. This causes the expected interest rate to rise in order to restore equilibrium between national savings and investment.

The insignificance attached to [Delta]GT may be attributed to the close correlation between budget deficits and transfer payments, in that budget deficits and temporary purchases usually move together. If budget deficits constitute a better measure of temporary spending than the [Delta]GT series, then it is possible that the [Delta]BDEF series may enter the ECM model with a significant coefficient, and the [Delta]GT series with an insignificant one. This is why the significance attached to the [Delta]BDEF series is the same, regardless of whether the [Delta]GT series is dropped from the system.

[TABULAR DATA FOR TABLE III OMITTED]

The diagnostic and specification test findings indicate that ECM representation (2) is correctly specified. The Chow test is used to examine the structural stability of ECM model (2). Choosing 1971, 1974 and 1977 as the sample breaking dates, the F-statistics confirm that the estimated values of the parameters yield a stable solution which is not sensitive to changes in the sample range. The RESET (Regression Specification Test) statistics reveal no serious omission of variables, indicating the correct specification of the model. The ARCH (AutoRegressive Conditional Heteroskedasticity) tests suggest that the errors are homoskedastic and independent of the regressors. The BG (Breusch-Godfrey) tests reveal no significant serial correlation in the disturbances of the error term. The JB (Jarque-Bera) statistics suggest that the disturbances of the regressions are normally distributed. The White F-statistics show the absence of simultaneity bias in the estimates.

In addition, we apply the CUSUM (Cumulative Sum) of squares test which is described by Brown, Durbin and Evans [4].(6) The CUSUM test gives a plot of the cumulative sum of squared residuals together with two critical lines. If the cumulative sum moves outside the region defined by the two critical lines, the test suggests parameter instability. In Figure 1, the computed CUSUM of squares test has been applied to examine parameter constancy of the ECM estimates in the 1950-1993 and 1958-1993 time intervals. In all cases, the null hypothesis of parameter stability cannot be rejected at the 5 percent level of significance.

Overall, the statistical results of Chow, RESET, ARCH, BG, JB, CUSUM of squares and White tests are significant and robust. In this sense, our empirical evidence is in agreement with the rationale of the Keynesian proposition, i.e., a positive effect of budget deficits on the interest rate.

IV. Conclusions

This paper has examined the relationship between budget deficits and interest rates by specifying the appropriate system variables based on the economic modelling of previous studies. The object of the paper was to empirically test the Keynesian proposition and the Ricardian equivalence hypothesis by using annual data of the Greek economy. The acceptability of a theory becomes more significant if the theory is tested empirically in countries of different sizes and economic structures.

The study has employed a methodological framework based on cointegration analysis, ECM strategy, specification and diagnostic tests. The ECM model estimates indicate the existence of a short- and long-run relationship between the interest rate and the budget deficit. The t-ratio for the Error-Correction term [EC.sub.-1] is statistically significant even at the 1 percent level. Although the regressor [Delta]GT has an insignificant coefficient, whether [Delta]GT is excluded from the system or not, the variables [Delta]RGNP, [Delta]UNML, [Delta]INFL, [Delta]BDEF, [Delta]GE and [Delta]M carry a statistically significant coefficient, different from zero. The specification and diagnostic tests yield satisfactory results which are consistent with the empirical framework of the Keynesian proposition.

George A. Vamvoukas Athens University of Economics and Business, Athens, Greece

The author gratefully acknowledges helpful comments and suggestions from an anonymous referee.

1. Seater [24] provides a detailed analysis of the theoretical and empirical evidence regarding the Keynesian and Ricardian equivalence paradigms.

2. The specification of our interest rate equation is based upon the research work of Hoelscher [15; 16], Evans [11; 12], Barro [3], Zahid [26], Laumas [19], Darrat [7], Cebula [5; 6] and Due [9].

3. The statistical data are taken from the Ministry of Finance, the Statistical Service of the Ministry of Labour, the Bank of Greece and the National Statistical Service of Greece. The UMNL for the period 1950-1959 is calculated by taking into account the results of the population censuses for the years 1951 and 1961. From 1950-1957 the data for INTR refer to the general interest rate for long-term loans to manufacturing and mining.

4. Seater [24] provides a complete analysis on this point.

5. According to the Ricardian equivalence, government spending, permanent and transitory, may have a positive effect on the interest rate, but the interest rate level is independent of the budget deficit level, i.e., [[Gamma].sub.4] = 0, see Barro [2; 3] and Evans [11; 12].

6. The CUSUM of squares test is based on the test statistic

[Mathematical Expression Omitted]

where s is the standard error of the regression fitted to all i sample points and [Mathematical Expression Omitted] is the squared recursive residuals. The mean value line, giving the expected value of this test statistic under the hypothesis of parameter stability, is

E([s.sub.t]) = (t - k)/(n - k)

which goes from zero at t = k to unity at t = n.

References

1. Abell, John D., "The Deficits during the 1980s: An Empirical Investigation." Journal of Macroeconomics, Winter 1990, 81-96.

2. Barro, Robert J., "Output Effects of Government Purchases." Journal of Political Economy, June 1981, 1086-121.

3. -----, "Government Spending, Interest Rates, Prices, and Budget Deficits in the United Kingdom, 1701-1918." Journal of Monetary Economics, September 1987, 221-47.

4. Brown, R. L., J. Durbin and J. M. Evans, "Techniques for Testing the Constancy of Regression Relationship over Time." Journal of the Royal Statistical Society, 1975, 2, 149-92.

5. Cebula, Richard J., "Federal Government Budget Deficits and Interest Rates: A Brief Empirical Note." Southern Economic Journal, July 1988, 206-10.

6. -----, "An Empirical Analysis of Federal Budget Deficits and Interest Rates Directly Affecting Savings and Loans." Southern Economic Journal, July 1993, 28-35.

7. Darrat, Ali F., "Structural Federal Deficits and Interest Rates: Some Causality and Cointegration Tests." Southern Economic Journal, October 1990, 752-59.

8. Dickey, David A., Dennis W. Jansen and Daniel L. Thornton. "A Primer on Cointegration with an Application to Money and Income," in Cointegration for the Applied Economist, edited by Bhaskara B. Rao. London: The Macmillan Press Ltd., 1994.

9. Dua, Pami, "Interest Rates, Government Purchases, and Budget Deficits: A Forward-Looking Model." Public Finance Quarterly, October 1993, 470-78.

10. Engle, Robert F., and Clive W. J. Granger, "Cointegration and Error-Correction: Representation, Estimation and Testing." Econometrica, March 1987, 251-76.

11. Evans, Paul, "Do Budget Deficits Raise Nominal Interest Rates?" Journal of Monetary Economics, September 1987, 281-300.

12. -----, "Are Government Bonds Net Wealth? Evidence for the United States." Economic Inquiry, October 1988, 551-66.

13. Feldstein, Martin, "Government Deficits and Aggregate Demand." Journal of Monetary Economics, January 1982, 1-20.

14. Gonzalo, J., "Five Alternative Methods of Estimating Long-Run, Equilibrium Relationships." Journal of Econometrics, January 1994, 203-33.

15. Hoelscher, Gregory P., "Federal Borrowing and Short Term Interest Rates." Southern Economic Journal, July 1983, 319-33.

16. -----, "New Evidence on Deficits and Interest Rates." Journal of Money, Credit and Banking, February 1986, 1-17.

17. Johansen, Soren, "Statistical Analysis of Cointegration Vectors." Journal of Economic Dynamics and Control, December 1988, 231-54.

18. -----, "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive, Models." Econometrica, November 1991, 1551-80.

19. Laumas, Gurcharan S., "Anticipated Federal Budget Deficits, Monetary Policy and the Rate of Interest." Southern Economic Journal, October 1989, 375-82.

20. Mackinnon, J. G. "Critical Values for Cointegration Tests in Long-Run Economic Relationships," in Readings in Cointegration, edited by R. F. Engle and C. W. J. Granger. Oxford: Oxford University Press, 1991.

21. Miller, Stephen M. and Frank S. Russek, "The Temporal Causality Between Fiscal Deficits and Interest Rates." Contemporary Policy Issues, July 1991, 12-23.

22. Osterwald-Lenum, Michael, "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics." Oxford Bulletin of Economics and Statistics, August 1992, 461-72.

23. Raynold, Prosper, "The Impact of Government Deficits When Credit Markets Are Imperfect: Evidence from the Interwar Period." Journal of Macroeconomics, Winter 1994, 55-76.

24. Seater, John J., "Ricardian Equivalence." Journal of Economic Literature, March 1993, 142-90.

25. Sims, Christopher A., "Macroeconomics and Reality." Econometrica, January 1980, 1-48.

26. Zahid, Kahn H., "Government Budget Deficits and Interest Rates: The Evidence Since 1971, Using Alternative Deficit Measures." Southern Economic Journal, January 1988, 725-31.