Effectiveness of fiscal policy in the U.K. during the 1960-1990 time period.

Saunders, Peter J.

Abstract

This study investigates the impact of fiscal policy on the U.K. economy during the 1960 - 1990 time period. The empirical analysis is conducted within the Granger causality testing methodology. Initially the causal flows between fiscal expenditures, deficits and nominal GDP are examined. A hi-directional causal flow between expenditures and nominal GDP is established while deficits and nominal GDP are found to be statistically independent. However, the main contribution of this research lies in its emphasis on analyzing the impact of fiscal expenditures on real output and prices. The results of the trivariate analysis indicate the absence of causal flows from fiscal expenditures to real GDP while the U.K. economy's prices appear to be causally affected by these expenditures.

Introduction

One of the key postulates of standard Keynesian economic theory concerns the impact of fiscal policy on national output and the employment level. It is explicitly assumed that expansionary fiscal policy exerts a positive impact on an economy's output and level of employment. (1) This theoretical proposition has been tested empirically. One of the first serious empirical challenges to the standard view of the effectiveness of fiscal policy was presented by Andersen and Jordan (1968) in their now well known St. Louis model. Andersen and Jordan's findings cast serious doubt on the effectiveness of fiscal policy in economic stabilization. A further empirical investigation of the impact of fiscal policy on the U.S. economy was undertaken by Hafer (1982). This study was partially designed to reassess the role of fiscal policy while maintaining some of the testing framework of the original St. Louis model. The study was conducted within the Granger (1969) causality testing methodology. According to Hafer, fiscal policy has no lasting or statistically significant impact on nominal GDP growth in the U.S.

The above studies indicate that the standard postulated relationship between expansionary fiscal policy and its subsequent effect on output may not be supported by empirical evidence. However, given the importance of fiscal expenditures in economic theory and policy, further empirical research into the effects of fiscal policy is desirable. The purpose of this study is to undertake such a task. The investigation is conducted within the Granger (1969) causality testing framework. The U.K. data are analyzed to determine if fiscal expenditures and deficits have had a statistically significant causal impact on output in the U.K. The empirical evidence presented for the U.K. can supplement the U.S. studies by providing further important information on the impact of fiscal policy on an economy.

The effects of fiscal policy on an economy can be investigated by analyzing the existence and strength of empirical relationships between some measures of fiscal policy and nominal output. This is the standard approach to analyzing the effectiveness of fiscal policy [Andersen and Jordan (1968), Hafer (1982)]. Granger (1969) causality testing framework provides a useful empirical tool for such an undertaking. It allows an examination of causal relationship between any two variables, such as fiscal expenditures and nominal GNP [Hafer (1982)]. However, the standard approach to investigating the effects of expenditure changes on nominal GDP is incomplete. It only indicates the existence or absence of causal flows from fiscal expenditures to nominal GNP. Since nominal GDP comprises of the price component and the real output component, one is left guessing whether fiscal expenditures affect only real GDP, or prices, or both. Successful fiscal stabilization policy requires that fiscal expenditures impact an economy's real output and, thereby, its employment level. Consequently, the focus of an empirical investigation should be on the effects of fiscal policy on the two components of nominal output, namely prices and real output.

The present study addresses the above raised issue. Its main contribution lies in its emphasis on analyzing the impact of fiscal expenditures on real output and prices in addition to nominal output. It is the objective of this study to make meaningful comparisons to the earlier U.S. research on the effectiveness of fiscal policy in the 1960s, 1970s and 1980s. Therefore, this study is confined to investigating the impact of fiscal policy in the U.K. during the 1960-1989 time period. In order to make meaningful comparisons with the work of Hafer (1982), the Granger (1969) causality testing methodology is adopted throughout the study. In addition to investigating the appropriate causal relationships, the present study addresses the time series data stationarity and cointegration issues. For this purpose all time series data are subjected to the Dickey-Fuller (1976, 1979) stationarity tests and the Engle-Granger (1987) cointegration test. The results of these tests are reported in the following section of this study. Bivariate causality test results involving fiscal expenditures, deficits, and nominal gross domestic product are reported thereafter. However, the main focus of this study is on analyzing the impact of fiscal expenditures on prices and real gross domestic product. The results of this investigation are reported in the fourth part of the paper. Finally, overall conclusions regarding the effectiveness of fiscal expenditures on the U.K. economy are made.

Unit Root and Cointegration Tests

Government expenditures are often used as a fiscal variable for the purposes of assessing the effectiveness of fiscal policy [Hafer (1982)]. However, budget deficits can also be used as a measure of an expansionary fiscal policy. One advantage of using deficits as an approximation of fiscal policy is that deficits measure the net benefit of fiscal expenditures (as tax revenues are subtracted from total government expenditures). Consequently, both deficits (DEF) and the U.K. government expenditures (EXPEND), expressed in nominal terms, are used as measures of fiscal policy, while the nominal gross domestic product (GDPN) is used to approximate the level of economic activity. In the trivariate section of this paper, real output is measured by real gross domestic product (GDPR) while the U.K.'s consumer price index (CPIUK) approximates the prices. (2) Quarterly data ranging from the first quarter of 1961 to the third quarter of 1989 are used in all estimations.

Statistical procedures used to investigate the effects of fiscal policy on GDPN, GDPR, and CPIUK are based upon unit root, cointegration, and Granger (1969) causality tests. The first step in data analysis must involve addressing the question of the stationarity of time series data. (3) The unit root tests outlined by Dickey and Fuller (1976, 1979) can be used to determine whether the data are stationary or not. The cointegration tests determine if there exists a long-run stable relationship between test variables. They also determine which framework should be used in any subsequent data analysis. In general, the absence of cointegration necessitates using a VAR testing framework, such as the Granger (1969) causality technique. If, on the other hand, test variables are found to be cointegrated, then vector error correction modeling may be a more appropriate tool for any further data analysis.

The stationarity testing procedure can be summarized as follows: Let [X.sub.t] and [Y.sub.t], for t = 1, 2, ..., T, be two time series data sets on two variables. Initially it is necessary to determine if these two variables are integrated of order zero, I(O). In order to investigate this proposition, the Augmented Dickey-Fuller (ADF) test is implemented. Relying upon the OLS method, the following regression is estimated for [x.sub.t]:

[x.sub.t] = a + b[X.sub.t-1] + c[x.sub.t-1] + dT. (1)

In the above equation [x.sub.t=] [X.sub.t-1] - [X.sub.t-1], [x.sub.t-1=] [X.sub.t-1] - [X.sub.t-2], and T is the trend variable. Since the test statistic does not follow the standard t-distribution, the significance tests are conducted with the help of MacKinnon (1991) test statistics (4) Finding statistically insignificant t statistics implies that the series contains unit root in its original form. This finding necessitates further stationarity testing to determine whether the first difference of the series is stationary; i.e., whether it is integrated of order one, I(1). If the resulting test coefficient is statistically significant, then the series is integrated of order one, I(1). This means that its first difference is stationary and as such it does not contain a unit root. Having completed the testing procedure for [X.sub.t], the same tests are carried out for all the remaining test variables. In the present case the test variables are: GDPN, GDPR, EXPEND, DEF, and CPIUK.

The results of the ADF tests for all variables are reported in Table 1 above. The calculated Dickey--Fuller statistics for the levels of variables are not significantly different from zero in all test cases. This means that all of the time series are not I(0). Consequently, they contain unit roots in their level forms. In order to determine the appropriate detrending procedure, all of the data were subjected to further stationarity testing. This testing involved determining whether the time series were I(1). The results of these tests are also reported in Table 1. The results imply that all time series are I(1). Therefore, the first differences of these series do not contain unit roots, and they are stationary.

Given the fact that all individual test variables are I(1), it is possible that there exists a long-run relationship among them. Cointegration tests determine whether such relationship actually exists among the time-series variables. In the present case, these test results can indicate whether fiscal policy has any long-term impact on nominal GDP. In addition to investigating the existence of long-run relationships among test variables, cointegration test results can be used to determine the subsequent specification form of all test variables.

Several cointegration testing techniques are available, inclusive of the Stock and Watson (1988) procedure, the Engle-Granger (1987) cointegration test, and Johansen's (1988) method. In all of these methods, the most stationary linear combination of the vector time-series is sought. (5) The Engle-Granger test is easy to use in a bivariate case and the interpretation of its results is straightforward. Consequently, this test is used in the present case. Lags ranging from one to four quarters are examined. Test results for the two bivariate test specifications are reported in Table 2 below.

Cointegration test results indicate that the two sets of test variables are not cointegrated. This means that there exists no long-run relationship between either measure of fiscal policy and nominal GDP. Stated simply, fiscal policy has no long-run impact on U.K.'s nominal output. Cointegration tests analyzed together with unit root tests provide one additional important information. From a statistical point of view, establishing that all of the tests variables are I(1), and finding no evidence of cointegration necessitates that the first differences of levels be used for all subsequent econometric tests. Consequently, this estimation form is used thereafter. The results also indicate that a VAR estimation form, such as the Granger (1969) method, can be deployed in the data analysis.

Bivariate Causality Test Results

Given the estimation results reported above, the Granger (1969) testing methodology is adopted to investigate causal relationships under investigation. The standard procedure for Granger (1969) causality testing requires estimating the following equations:

[X.sub.t] = [a.sub.0] + [J.summation over (j=1)] [b.sub.j][X.sub.t - j] + [I.summation over (i=1)] [c.sub.i] [Y.sub.t - 1] + [[epsilon].sub.t] (2)

[Y.sub.t] = [a.sub.1] + [J.summation over (j=1)] [b.sub.j][Y.sub.t - j] + [I.summation over (i=1)] [c.sub.1] [X.sub.t - i] + [[zeta].sub.t] (3)

and testing [H.sub.0] that [c.sub.i] = 0 and [c.sub.1] = 0 for i = 1,2, ... , I. Under this standard causality testing procedure, the researcher must decide on the lag structure of the two test variables. The lag selection can be based upon an arbitrary decision about appropriate lag length [Sims (1972), and many others]. Alternatively, a statistical criterion such as Hsiao's (1979 and 1981) minimum final prediction error (FPE) can be used to guide researchers in selecting the appropriate lag structure. Arbitrary lag selection techniques in causality testing are subject to serious criticism on at least two grounds. First, when relatively short sample sizes are used, investigating longer lags can cause serious loss of the degrees of freedom problem. Consequently, there may be a tendency to select relatively short lags regardless of any existing theoretical considerations. Second, the lag selection itself may have an overriding influence on the implications of causality tests. In fact, the results of causality tests may be directly determined by a particular lag structure chosen in each test. This point is noted by several authors [Thornton and Batten (1985), Saunders (1988)]. Consequently, it may be more appropriate to examine all of the relevant lags and select the lag structure which is based upon a statistical criterion rather than just an ad hoc choice.

Hsiao's (1979 and 1981) minimum FPE criterion overcomes both of the above mentioned difficulties. It is particularly suited for studies involving relatively short sample periods, such as the present case. Under this method the optimum lag structure is determined by minimizing the FPE. The FPE is calculated as (SEE) (2). (T + K)/T. SEE is the standard error of the regression, T indicates the number of observations, and K stands for the number of parameters. The estimation procedure involves several statistical steps whose main purpose is to search for the specification yielding minimum FPEs in each phase of causality testing. (6)

The minimum FPE causality testing method was applied to equations (2) and (3). In equation (2), the optimum lag length of X (GDPN) was first determined in the absence of the lagged values of Y (EXPEND). For this purpose lags ranging from one to twelve quarters were examined. The optimum lag length of X (GDPN) was found to be four. Having determined the optimum lag length of X, this length was retained while lagged values of Y (EXPEND) were introduced one by one to minimize the FPE. This resulted in the selection of two lags for Y (EXPEND). The same procedure was followed for equation (3) where the roles of X and Y were reversed. This resulted in the selection of twelve and one lags for EXPEND and GDPN. Once the minimum FPEs are obtained, the causality implications are straightforward. If the minimum FP[E.sub.x] without the lagged values of Y is greater than that with the lagged values of Y, then the causality flows from Y to X. Similarly if the minimum FP[E.sub.y] without the lagged values of X exceeds the minimum FPE with these lagged values, then the causality runs from X to Y. A bi-directional causality is said to exist if X causes Y and Y causes X. The same testing procedure was used when fiscal policy was approximated by DEF. Finally, X and Y can also be found to be statistically independent. This occurs when adding lagged values in bivariate testing specifications does not decrease the minimum FPEs obtained under the univariate tests.

Bivariate causality test results for both test specifications inclusive of causality implications are reported in Table 3 above. The results indicate the existence of feedback in the case of EXPEND and GDPN. Simply stated, this means that although fiscal expenditures "Granger-cause" GDPN, so does GDPN "Granger-cause" EXPEND. These results indicate that although fiscal policy has causal impact on GDPN, at the same time GDPN growth has causal impact on fiscal expenditures." These results are in contrast to those reported by Hafer (1982) for the United States economy for the comparable time period. Hafer found no causal impact of high-employment expenditures on nominal output in the U.S. In fact, Hafer found these two variables to be statistically independent. When high-employment government surplus was used to approximate fiscal policy, Hafer found a unidirectional causation from GNP to this variable. It is clear that the results of the present study indicating a bi-directional causality between expenditures and nominal output differ from those reported by Hafer (1982). This difference in causality test results may well be due to the lag selection method used in causality testing. Hafer relied upon an arbitrary lag selection in his causality tests. As mentioned previously, this lag selection may affect test results.

When fiscal policy is approximated by deficits, the two time series are statistically independent. This implies that no statistically significant relationship exists between deficits and nominal GDP in the U.K. Theoretical explanation of the bivariate test results is readily available. In the Keynesian framework, fiscal expenditures lead to increases in nominal gross domestic product. At the same time, it is possible to postulate that increased nominal gross domestic product leads to higher fiscal expenditures. This effect is due to higher tax revenues being collected from an increased GDPN. These revenues can then be used to finance further government expenditures. Consequently, the existence of a bi-directional causality between EXPEND and GDPN has a sound theoretical basis.

Trivariate Analysis

The above results give an indication of causal flows between fiscal expenditures and nominal output of the U.K. economy. However, they give no indication which component of nominal output is affected by fiscal expenditures. As explained previously, this issue is perhaps even more important than determining the existence of a causal flow between fiscal expenditures and nominal output. The key question concerning the effectiveness of fiscal policy must be asked in the context of whether this policy affects real output or prices, rather than just nominal output. If only prices are affected, then the key postulate of the Keynesian economic theory would be in serious doubt.

In order to examine the effects of fiscal expenditures on the two components of GDPN, the trivariate testing framework is appropriate. The main advantage of trivariate modeling lies in its ability to examine causal flows between three test variables in one combined model. Ram (1984) outlines the extension of Hsiao's (1979 and 1981) minimum FPE causality testing procedure into a trivariate format. Ram's technique involves calculating the univariate and bivariate equations and their use as the building process for the final trivariate forms? In the present case the following trivariate equations were estimated:

GDP[R.sub.1] = [a.sub.0] + [b.sub.1]GDP[R.sub.t - 1] + [3.summation over (j=1)] [c.sb.j]CPIU[K.sub.t-j] + [d.sub.1]EXPEN[D.sub.-1] + [[epsilon].sub.t] (6)

CPIU[K.sub.t] = [[alpha].sub.0] + [3.summation over (j=1)] [[beta].sub.j]CPIU[K.sub.t - j] + [[gamma].sub.1] GDP[R.sub.t - 1] + [6.summation over (i=1)] [[delta].sub.i]EXPEN[D.sub.t - 1] + [[xi].sub.t] (9)

The results of the estimations of the above equations as well as the univariate and bivariate estimations are reported in Table 4 below.

Table 4 reports estimation results of all the equations necessary for the trivariate analysis of the data. The causality implications are outlined in the last column of this table. The arrow indicates the direction of causality. Causality inferences are based upon the comparisons of the FPEs from the bivariate and the trivariate specifications. The results are striking, as there is no evidence of causal flow from fiscal expenditures to real gross domestic product. The addition of the lagged EXPEND variable to the GDPR equation [equation (6)] increases the minimum FPE from 16.5699 [equation (5)] to 16.6949 [equation (6)]. This means that fiscal expenditures have no causal impact on real gross domestic product. At the same time it appears that EXPEND "Granger-cause" CPIUK. This is evident from the comparison of FPEs of equations (8) and (9). The inclusion of the lagged EXPEND variable in equation (9) leads to a reduction in the FPEs from 0.8787 [equation (8)] to 0.8452 [equation (9)]. Consequently, a causal flow is established from EXPEND to CPIUK.

Having established a causal flow from EXPEND to CPIUK, it would certainly be of interest to determine the direction and the size of expenditures' impact on CPIUK. An examination of the coefficients of the lagged EXPEND term in equation (9) gives a broad indication of this impact. The results of the estimates of equation (9) are reported in Table 5 below. As is evident from this table, all of the coefficients have a positive sign. This means that expenditures exert positive influence over prices. Furthermore, it seems that the impact of the expenditures is statistically significant from the second quarter until the fifth quarter, declining thereafter. This means that there is approximately a one quarter impact lag. Judging by the size of coefficients of the lagged values of EXPEND, it appears that expenditures have an important and sizable impact on prices in the U.K.

On the whole, the trivariate analysis' results reported in Table 4 cast serious doubt on the conventional wisdom concerning the impact of fiscal policy on an economy's output. They indicate that the primary causal effect of fiscal expenditures is on prices while the economy's real output is unaffected. As such, they give no comfort to the Keynesian position regarding the benefits of fiscal expenditures. The test results can be interpreted by focusing on the U.K. economy's aggregate demand and supply curves. It appears that fiscal expenditures only affect the position of the aggregate demand curve while leaving the real aggregate supply curve unchanged. Hence, they indicate the existence of a vertical short-run aggregate supply curve. Given the above scenario, any increases in the aggregate demand curve would only affect the price level leaving the real output unchanged.

On the whole, the results of this study indicate that throughout the 1960-1990 time period, there is no evidence of a causal impact of fiscal expenditures on the U.K.'s economy real output. However, empirical evidence does indicate that the price level is causally impacted by these expenditures. Therefore, it would appear that fiscal expenditures have no statistically significant impact on real output. At the same time they do seem to lead to increased inflationary pressures. This last point is clearly evident from the examination of the relevant coefficients in equation (9).

Overall Conclusions

This paper investigates the effects of fiscal expenditures on the U.K. economy during the 1960-1990 time period. For this purpose quarterly data ranging from the first quarter of 1961 to the third quarter of 1989 are analyzed. One of the objectives of the present paper is to be able to make meaningful comparisons with the U.S. research on the effectiveness of fiscal policy during the comparable time period. The present research is motivated by Hafer's (1982) work in particular, and the Federal Reserve Bank of St. Louis earlier research on the effectiveness of fiscal policy in the U.S. during the comparable time period. In order to make comparisons with Hafer's work, Granger (1969) causality testing methodology is adopted throughout the present study.

The present study relies in its methodology on well established principles of the time-series analyses, including unit root and cointegration testing. Consequently, all of the data are initially subjected to unit root and cointegration tests. All data are found to be integrated of order one, I(1). This result allows a further investigation of the impact of fiscal policy on the U.K.'s output within the cointegration testing framework. Cointegration tests reveal important information about the long run relationship between fiscal policy, as approximated by deficits and expenditures, and nominal output growth (measured by nominal GDP). These test results indicate the absence of any long run relationship between these variables. Therefore, it is fair to conclude that in the long run, fiscal policy has had no statistically significant impact on the growth of nominal GDP in the U.K.

Given the results of cointegration tests, the Granger (1969) causality methodology is adopted in all subsequent empirical tests. In particular, Hsiao's (1979 and 1981) minimum FPE causality testing method is utilized in all test cases. This method offers several important advantages over conventional arbitrary lag selection causality testing techniques. For example, the minimum FPE procedure alleviates some of the problems associated with the effects of lag selection on causality implications. It also allows an investigation of the entire lag range rather then an arbitrarily selected lag specification.

Initially the paper addresses the issue of causal flows between fiscal expenditures and nominal gross domestic product. This standard approach to analyzing the impact of fiscal policy on an economy yields interesting results. When deficits are used as a measure of fiscal policy, then deficits and nominal GDP are found to be statistically independent. However, approximating fiscal policy by government expenditures yields different empirical results. In this case, a bi-directional causal flow between these two variables is established. This means that although fiscal expenditures do have some causal impact on nominal output, so does nominal output growth impact fiscal expenditures. The theoretical explanation of this result evolves around the relationship between the nominal output growth, tax receipt increases, and subseqaent expenditure increases.

The main contribution is presented in the trivariate section of the paper. The purpose of the trivariate analysis is to examine the existence and the strength of causal flows between fiscal expenditures, real gross domestic product, and the consumer price index. The main objective of this analysis is to find out if fiscal expenditures affected the U.K. economy's real output, or its prices, or both. The results of trivariate causality tests are striking. They indicate the absence of causal flows from fiscal expenditures to real gross domestic product while the consumer price index appears to be causally affected by these expenditures. Simply stated, this means that while fiscal expenditures have no impact on real output, they appear to cause price changes. This empirical evidence casts serious doubt on the cornerstone of Keynesian economic theory: the assumption that expansionary fiscal policy leads to an expansion in real output and subsequent reduction in unemployment. From an economic policy point of view, it appears that there is some doubt about using fiscal policy for the purposes of economic stabilization.

On the whole, the empirical evidence on the effectiveness of fiscal policy in the U.K. during the 1960-1990 time period is similar to that reported by Hafer (1982) and the earlier empirical research undertaken by Andersen and Jordan (1968) for the U.S. It appears that just as in the U.S., fiscal policy was not an effective tool of economic stabilization during the comparable period under investigation. Such policy may not have had any of the postulated benefits. It may, in fact, have worsened the economic situation by causing inflationary pressures.

REFERENCES

Andersen, L. C., and Jordan, J. L. (1968), "Monetary and Fiscal Actions: A Test of Their Relative Importance in Economic Stabilization." Review, Federal Reserve Bank of St. Louis, November, 11-24.

Dickey, D. A., and Fuller, W. A. (1979), "Distribution of the Estimators for Autoregressive Time Series with Unit Root." Journal of the American Statistical Association, 74, 427-31.

Dickey, D. A., Jansen, D. W., and Thornton, D. L. (1991), "A Primer on Cointegration with an Application to Money and Income." Review, Federal Reserve Bank of St. Louis, March/ April, 58-78.

Engle, R. F., and Granger, C.W.J. (1987), "Cointergration and Error Correction: Representation, Estimation and Testing." Econometrica, 55, 251-76.

Fuller, W. A. (1976), Introduction to Statistical Time Series. New York: John Wiley and Sons.

Granger, C. W. J. (1969), "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods." Econometrica, 37, 424-38.

Hafer, R. W. (1982), "The Role of Fiscal Policy in the St. Louis Equation." Review, Federal Reserve Bank of St. Louis, 64, 17-22.

Hsiao, C. (1979), "Autoregressive Modeling of Canadian Money and Income Data." Journal of the American Statistical Association, 74, 553-60.

Hsiao, C. (1981), "Autoregressive Modeling and Money-Income Causality Detection." Journal of Monetary Economics, 7, 85-106.

International Monetary Fund, International Financial Statistics, various issues.

Johansen, S. (1988), "Statistical Analysis of Cointegrating Vectors." Journal of Economic Dynamics and Control, 12, 231-54.

Keynes, J. M. (1936), The General Theory of Employment, Interest, and Money. London: MacMillan.

MacKinnon. (1991), "Critical Values for Cointegration Tests." in R.F. Engle and C.W.J. Granger (eds.), Long Run Economic Relations. Oxford: Oxford University Press.

Ram, R. (1984), "Causal Ordering Across Inflation and Productivity in the Post-War United States." Review of Economics and Statistics, 66, 472-77.

Saunders, P. J. (1988), "Causality of the U.S. Agricultural Prices and the Money Supply: Further Empirical Evidence." American Journal of Agricultural Economics, 70, 588-96.

Sims, C. W. (1972), "Money, Income, and Causality." American Economic Review, 62, 540-52.

Stock, J. H., and Watson, M. W. (1988), "Variable Trends in Time Series." Journal of Economic Perspectives, 2147-74.

Thornton, D. L. and Batten, D. S. (1985), "Lag-Length Selection and Tests of Granger Causality between Money and Income." Journal of Money, Credit, and Banking, 17, 164-78.

U.K. Department of Employment, Central Statistical Office.

NOTES

(1.) Expansionary effects of fiscal policy are well documented in economic literature. Therefore, there is no need to describe them in detail. Their origins can be traced to the work of J.M. Keynes (1936).

(2.) The data on fiscal expenditures were obtained from the Department of Employment, Central Statistical Office, whereas the remaining data were obtained from various issues of International Financial Statistics, printed by the International Monetary Fund.

(3.) Time series data are often nonstationary. This means that their mean and variance depend on time. Essentially, nonstationary time series data exhibit a trend. This trend must be removed before any estimations are undertaken.

(4.) MacKinnon (1991) test statistics are similar to the original Dickey-Fuller (1976) t-statistics. The main difference lies in the fact that MacKinnon included a much larger set of observations in the calculations. Consequently, the MacKinnon approach allows calculations of critical Dickey-Fuller values for any sample size.

(5.) For a detailed explanation of the differences among these procedures, see Dickey, Jansen, and Thornton (1991).

(6.) The minimum FPE causality testing procedure is well documented in economic literature. Consequently, little would be gained by a detailed explanation of all statistical steps involved in causality testing. Interested readers are referred to Hsiao (1979 and 1981) for a detailed analysis of this procedure.

(7.) Bivariate tests do not rule out the possibility that other variables, such as the money supply may have impact on nominal output. However, investigating other possible variables which may impact nominal GDP is beyond the scope of this paper. Its focus is only on investigating the influence of fiscal policy on nominal output in the U.K. Bivariate causality tests are well suited to provide this information while not ruling out any other influences on nominal GDP in the U.K.

(8.) For a further discussion of this procedure inclusive of a detailed outline of causality implications, see Ram (1984).

Peter J. Saunders, Professor, Department of Economics, College of Business, Central Washington University, 400 East University Way, Ellensburg, WA 98926-7486, Tel.: 509-963-1266, e-mail: saunders@cwu.edu

Table 1

Augmented Dickey-fuler (Adf) Test Results For Gdpn, Expend,
Cpiuk, Gdpr, and Def.

Variable Test Results

GDPN (1) 1.14
GDPN (2) -6.08 *
EXPEND (1) -1.97
EXPEND (2) -10.10 *
CPIUK (1) -1.95
CPIUK (2) -5.54 *
GDPR (1) -1.07
GDPR (2) -7.90
DEF (1) -2.74
DEF (2) -12.87 *

(1) ADF test results for the levels of variables.

(2) ADF test results for the first differences of variables.

* Indicates statistical significance at the five-percent level.

Table 2

Engle-granger Cointegration Test Results for Gdpn and Expend,
and GDPN and DEF

 Test Test Test Test
 Results Results Results Results
Variables (1 Lag) (2 Lags) (3 Lags) (4 Lags)

GDPN and EXPEND -2.01 -1.67 0.98 -0.39
GDPN and DEF -3.66 -2.38 -1.07 -1.52

* Critical MacKinnon statistics are -4.47 and -3.87 at the one- and
five-percent levels of significance.

Table 3

Causality Testing by Computing Final Pediction Errors (FPEs)
for Gdpn and Expend, and Gdpn and Def. *

 Independent
Dependent Variable Variable FPE Causality Impications

GDPN(4) 6.5784
GDPN(4) EXPEND(2) 6.3450 6.57846>6.6450
 EXPEND=>GDPN
EXPEND(12) 0.8200
EXPEND(12) GDPN(1) 0.7423 0.8200>0.7423
 GDPN=>EXPEND
GDPN(4) DEF(1) 6.6360 6.5784<6.6360
 DEF [not equal to] GDPN
DEF(11) 0.7402
DEF(11) GDPN(3) 0.7408 0.7402<0.7408
 GDPN [not equal to] DEF

* Numbers in parentheses are lags for minimum FPEs.

Table 4

Trivariate Results of The Minimum FPE Casality Testing
Procedure for Gdpr, Cpiuk, and Expend *

 First Second
 Controlled Manipulated Manipulated
 (Dependent) (Independent) (Independent)
Equation Variable Variable Variable

(4) GDPR(1)
(5) GDPR(1) CPIUK(3)
(6) GDPR (1) CPIUK(3) EXPEND(1)

(7) CPIUK(3)
(8) CPIUK(3) GDPR(1)
(9) CPIUK(3) GDPR(1) EXPEND(6)

 Causality
Equation FPEs Implications

(4) 16.4104
(5) 16.5699
(6) 16.6949 16.5699<16.6949
 EXPEND x GDPR
(7) 0.9018
(8) 0.8787
(9) 0.8452 0.8787>0.8452
 EXPEND=>CPIUK

* Numbers in parentheses in columns 2, 3, and 4 are lags for minimum
FPEs.

Table 5

Estimates of Equation (9) *

 Coefficients
Statistics Variables (lags) (t statistics)

[R.sup.2] = 0.423 CPIUK (-1) -0.075 (-0.746)
S.E. of regression = 0.876 CPIUK (-2) 0.113 (1.144)
F = 7.120 CPIUK (-3) 0.115 (1.172)
 GDPR (-1) 0.047 (2.192)
 EXPEND (-1) 0.143 (1.401)
 EXPEND (-2) 0.267 (2.234)
 EXPEND (-3) 0.461 (4.160)
 EXPEND (-4) 0.461 (3.987)
 EXPEND (-5) 0.345 (2.655)
 EXPEND (-6) 0.217 (1.680)

* Single digit numbers in parentheses indicate the number of lags of
test variables; other numbers in parentheses are t statistics.