Do revenues or expenditures respond to budgetary disequilibria?

I. Introduction

The post-World War II increase in the size of the federal government has led to a number of theoretical and empirical investigations of the sources of this growth. In particular, economists have questioned whether increases in the size of the federal budget tend to be initiated by changes in expenditures followed by revenue adjustments, by the reverse sequence, or both. Friedman, for example, argues that governments adjust expenditures to the level of revenues, so that control of taxation is essential to limit growth in government [13]. Alternatively, the spend-and-tax model posits that revenues will be adjusted to finance any politically chosen level of expenditures. A third perspective, reflecting the institutional separation of allocation and taxation functions of the federal government, hypothesizes the independent determination of revenues and expenditures. The goal of this investigation is to test these three alternative theories of the budgetary process for the United States.

The tax-and-spend and the spend-and-tax models have been examined in previous studies through causality testing, initially within a conventional vector autoregression (VAR) framework [1; 4; 23; 27; 29]. We follow the more recent studies of Bohn, Jones and Joulfaian and Miller and Russek, who employed the techniques of cointegration and error correction models (ECMs) to examine this same question [5; 21; 25]. In addition, our models include GNP as a control variable. In the cointegration framework this introduces several interesting methodological issues and leads to results that are sharply different than those reported in previous studies. The presence of three variables in the system raises the possibility of more than one cointegrating vector, and we find evidence of two such vectors. We experiment with both maximum likelihood and least squares estimation of these cointegrating vectors, and establish a close correspondence between the two sets of estimates. The cointegrating equations define long run equilibrium relations, one of which is interpreted as a "budgetary equilibrium" relating expenditures and revenues, and the other describing an equilibrium between GNP and either fiscal variable. The departures from both equilibria, represented by the residuals from the cointegrating equations, are included in error correction models, to capture the responses of expenditures and revenues to each of the two disequilibria. We find that neither revenues nor expenditures responds to the budgetary disequilibrium. Instead each budgetary variable adjusts to disequilibrium in the relation between that variable and GNP. We conclude that neither the tax-and-spend nor the spend-and-tax hypotheses account for post-World War II budgetary expansion. Instead these results are consistent with the third model, based on the institutional separation of the allocation and taxation functions of government, with the expansion in revenues and expenditures each determined by long run economic growth.

II. Theoretical and Empirical Background

Several alternative models of government finance characterize the dynamic relation between expenditures and revenues. The tax-and-spend school, championed by Friedman views expenditures as adjusting, up or down, to whatever level can be supported by revenues [13]. This view implies a causal relation running from revenues to expenditures. The spend-and-tax model posits the reverse relation, with revenues responding to prior spending changes. Peacock and Wiseman see economic or political crises creating increased expenditure programs that are subsequently ratified by tax increases [26]. Barro's tax-smoothing model also implies causation running from expenditures to revenues [3].

A third model, reflecting the laws and institutions governing the U.S. budgetary process, hypothesizes the independence of revenues and expenditures. Both executive and legislative branches of government participate in the budgetary process, but lack of agreement between these two branches has undermined recent attempts to rationalize the process [30]. Within the Congress there is an institutional separation of allocation and taxation functions of government, for example, into the Appropriations and Ways and Means Committees in the House of Representatives. Despite the reform of the budget process attempted in the Congressional Budget and Impoundment Control Act of 1974, the large deficits of the post-1974 period indicate a continued absence of coordination between expenditure and revenue decisions. The Gramm-Rudman-Hollings Act was another attempt to coordinate the expenditure and taxation decisions of government, which again failed to achieve linkage between the two budget components. Hoover and Sheffrin attribute this failure to the interplay of numerous diverse interests in the context of nonparliamentary U.S. institutions [18].

In the absence of a balanced budget requirement, there is no legal constraint forcing either budgetary variable to adjust to the other. Buchanan and Wagner argue that government spending grows through deficit financing, which disguises the cost of government programs [8; 9]. Tax rate changes are accompanied by intense political debate and controversy over economic impact and income distributional issues, which politicians would prefer to avoid. To the extent that major tax rate changes are infrequent, year-to-year changes in tax revenues will be dominated by fluctuations in macroeconomic activity. On the expenditures side secular growth in population and incomes increases the demand for public services [6]. Expenditure levels respond to economic growth, rather than taxation decisions. This combination of institutional, political, and economic forces results in levels of expenditures and revenues determined largely by long term growth and macroeconomic fluctuations.

Previous empirical studies of U.S. expenditures and revenues at the federal level have produced conflicting evidence on the tax-and-spend and spend-and-tax hypotheses. None have explicitly considered the third model of the budgetary process. Conclusions from the empirical studies are sensitive to the sample period under investigation, the degree of temporal aggregation, the inclusion or exclusion of macroeconomic controls, and the choice of econometric methodology. Every VAR model surveyed here employs first differences of relevant variables. Anderson, Wallace and Warner, using a VAR on annual, post-World War II data in real terms, and including macroeconomic controls, find that expenditure changes lead revenue changes [1]. Extending the sample period back to 1929, and using only a dummy variable to capture macroeconomic effects, Manage and Marlow reverse the conclusion of Anderson, Wallace, and Warner, finding either uni-directional causality from revenues to expenditures or bidirectional causality, depending upon the number of lags in the VAR [23]. To reconcile these results, Ram examines both longer period annual (1929-83) and shorter period quarterly (1947-83) data, and produces results largely consistent with Manage and Marlow, with causality running from revenues to expenditures, and some evidence of feedback following World War II [27]. However, Ram's omission of macroeconomic controls prevents a clear rejection of Anderson, Wallace, and Warner's conclusions.

Von Furstenberg, Green, and Jeong examine these relations using quarterly data for 1954-82 [29]. Controlling for macroeconomic activity, they find evidence that total expenditures lead taxes, without feedback, as is consistent with Anderson, Wallace, and Warner. Blackley uses longer term annual data (1929-82) and finds causality in the opposite direction [4]. When GNP changes are introduced as a control variable, he finds block causality from GNP and revenues to expenditures, but he is unable to establish significant individual effects of either revenues or GNP on expenditures. He also finds a significant contemporaneous relation between GNP changes and revenue changes, but no lagged effect. Blackley's results again demonstrate the sensitivity of causality results to the inclusion of macroeconomic controls, and they leave open the possibility that GNP changes are the driving force behind budgetary changes.

An independent strand of research, not directly concerned with the issue of causality, has established that federal revenues and expenditures are cointegrated [28; 2]. One implication of this result is that the VARs in differences used in the above studies are misspecified, casting doubt on the causality inferences drawn there [12]. Building on their own evidence of cointegration, Bohn, Jones and Joulfaian and Miller and Russek construct bivariate error correction models between revenues and expenditures to examine causality relations [5; 21; 25]. Jones and Joulfaian, using annual U.S. data from 1792 to 1860, find that both revenues and expenditures responded to budgetary disequilibrium. Miller and Russek find the same result for post-World War II data. Given the importance of controlling for macroeconomic activity demonstrated in the VAR studies, the results from these two ECMs can only be tentative.

In an innovative analysis of causal linkages between revenues and expenditures, Hoover and Sheffrin identify episodes of taxation or expenditure policy changes and isolate two periods of fixed policy regimes [18]. This classification of periods allows more precise inferences concerning the sources of fiscal changes. During one of the fixed regime periods, cointegration is found between revenues and expenditures, but no association between the two fiscal variables is found during the other fixed policy episode.

Bohn introduces GNP as a scaling factor, constructing bivariate cointegrating equations between expenditure/GNP and revenue/GNP ratios [5]. Using data from 1790 to 1988, cointegration is found between these two ratios, and the deficit (relative to GNP) is also stationary. However, over the post-Korean War period, our study period, the revenue/GNP ratio contains no unit roots, precluding the findings of cointegration between the two ratios. This, therefore, provides the groundwork for a three-variable model, with GNP as the macroeconomic control variable.(1) On theoretical grounds, we also argue that the use of GNP as a scaling factor clouds Bohn's interpretation that deficits are corrected by future spending or tax changes. Autonomous changes in spending, for example, could lead to GNP changes that indirectly cause budget-balancing adjustments in revenues. To consider the independent adjustments of revenues and expenditures to budgetary shocks, GNP must be entered as separate control variable in the cointegrating equation.

The error correction models employed in these four studies lead to a different interpretation of causality relations than that based on the earlier vector autoregressions. Causal linkages may arise either through the lagged differences (the short run dynamics) or the error correction terms [15]. Since the error correction terms capture each variable's response to disequilibria, the latter source of causal linkages becomes the central focus in investigations involving cointegrated series.

All four studies that examine cointegration between revenues and expenditures find support for the existence of long run budgetary equilibrium, and conclude that either expenditures or revenues (or both) adjust to correct departures from disequilibrium.(2) The contention of this paper is that this conclusion is false. Although we also find evidence of cointegration between the fiscal variables, our conclusions concerning fiscal adjustments are fundamentally different. We find that neither revenues nor expenditures responds to budgetary disequilibrium, but rather both variables adjust to their respective long run relations with GNP.

It should, however, be noted that, in light of potential sources of model misspecification uncovered by the above-cited studies, our study will utilize the methodology of cointegration and ECMs, with GNP included as a macroeconomic control variable.

III. Data

Depending upon the objectives of the study, alternative definitions of budgetary variables may be appropriate. In analyses of macroeconomic impacts of fiscal changes, Eisner argues that fiscal policy must be measured in terms of real changes in government debt(3) [11]. McCallum's original work on the sustainability of deficits calls for the adjustment of standard measures of revenues and expenditures for interest payments and seignorage, as in Hamilton and Flavin's empirical analysis [24; 17]. Subsequent considerations of the government's intertemporal budget constraint by Trehan and Walsh and Hakkio and Rush employ conventional measures of expenditures and revenues [28; 16]. The formal analysis of the government's budget constraint holds equivalently with all variables expressed in nominal values, real terms, or relative to GNP, so that the choice of deflator in related empirical analysis is made on statistical grounds [5].

The issue in this study is one of political economy, concerning the adjustments of expenditures and revenues to budgetary disequilibria. Questions of effects of fiscal policies or of sustainability of deficits are not the concern of the present paper, and the related issues of variable definitions do not apply here. For present purposes the appropriate budgetary concepts are those measures that are of interest to politicians and the focus of political discussions. From this perspective nominal values of total expenditures and total revenues, unadjusted for interest payments, seignorage, or depreciation in the value of the debt, are the variables of interest [14]. Accordingly, we define revenues and expenditures on the National Income and Products Accounts basis, and nominal GNP is employed as a macroeconomic control variable. It should be noted that, in order to be consistent with the existing studies, the tests and estimations reported here were repeated with all three series in real terms. As described below, conversion to real magnitudes did not alter the substantive results based on nominal values.

To focus on the formation of budgetary policy under contemporary institutions, tests and estimations are based on quarterly data from 1955.1 through 1989.4. This thirty-five year period is sufficiently long to establish the cointegration properties of the system, without the problems inherent in combining vastly different episodes of fiscal policy over a longer sweep of history. The 1955.1 starting date is also consistent with the studies of von Furstenberg, Green and Jeong, and Hoover and Sheffrin, and excludes those episodes of taxation and expenditure policy changes related to the Korean War [29; 18].

In their original form, revenues, expenditures, and GNP all exhibit strong evidence of heteroscedasticity. Rescaling the budget series by GNP provides one solution to this problem. However, as mentioned already, over the post-Korean War period of this study, the revenue/GNP ratio contains no unit roots, precluding the finding of cointegration between the two ratios. As an alternative strategy to eliminate heteroscedasticity, all three series are transformed to logarithms.

IV. Unit Root and Cointegration Tests Results

With the addition of GNP to the system, it is necessary to re-examine the unit root and cointegration features of the series. As a precondition for cointegration, the individual series on revenues, expenditures and GNP are tested for a common order of integration. Based on the augmented Dickey-Fuller (ADF) tests with the critical values from MacKinnon, Table I presents evidence that each series is integrated of order one; that is, each series is I(1) in the notation of Engle and Granger [10; 22; 12]. The equations for the tests on the levels include an intercept and time trend term, to allow a deterministic trend under the alternative. In testing for a unit root in the first differences, only the intercept is included. All test equations also include four augmented lags, where the adequacy of the lag length is checked with tests for serial correlation using the Lagrange multiplier [[Chi].sup.2]-statistic.

Cointegration is tested using Johansen's maximum likelihood procedure based on the error correction representation [19]:

[Delta][z.sub.t] = [summation of] [[Gamma].sub.j][Delta][z.sub.t - j] where j = 1 to k + [Pi][z.sub.t - 1] + [Mu] (1)

where [z.sub.t] is the 3 x 1 vector of I(1) processes.(4) The rank of [Pi] (r) equals the number of cointegrating TABULAR DATA OMITTED vectors, which is tested by the maximum eigenvalue and trace statistics, with critical values from Johansen and Juselius [20].

Table I. Unit Root Test: 1955.1-1989.4

Variable                     ADF

R                           -2.72
X                           -1.83
Y                           -2.54
[Delta]R                    -5.61(***)
[Delta]X                    -4.25(***)
[Delta]Y                    -4.72(***)

Notes: R and X are the logarithms of nominal federal government revenues and
expenditures, respectively. Y is the logarithm of nominal GNP. The ADF
statistics are compared with the critical values from MacKinnon [22].
Asterisks indicate significance levels (*** significant at the 1%, **
significant at the 5%, and * significant at the 10% level).

In applying the Johansen procedure, four lagged [z.sub.t]'s are included as conditioning variables. A constant term should be included either along with the conditioning variables or in the coingrating vector(s), depending on whether or not the individual series contain deterministic trends. Examining the time trend term in the ADF unit root test equations, the evidence on this question is not decisive. Consequently, we perform tests and estimations based on both specifications, finding all inferences are substantially the same under the two alternatives. As reported in Table II both the maximum eigenvalue and trace tests reject the null hypothesis of one or fewer cointegrating vectors. The evidence from the specification without deterministic trend is somewhat stronger in this regard, rejecting the null of one or fewer cointegrating vectors at the 5% level with the maximum eigenvalue test, and at the 1% level with the trace test. Rejection of this same hypothesis is at the 10% level for both tests from the deterministic trend model. In either case these tests support the existence of two cointegrating vectors in this system.

The maximum likelihood estimates of the two cointegrating vectors in the form reported in Table II are difficult to interpret. The second vector, for example, implies a negative relation between revenues and expenditures. However, the nonuniqueness of these vectors can be exploited to aid in the interpretation of their estimates. In particular, any linear transformation of the cointegrating vectors is also a cointegrating vector [20]. In the case of the three-variable system with two cointegrating vectors, there exist transformations of the original vectors that eliminate one of the three variables from each cointegrating equation. This construction allows, without loss of any information, the examination of the independent responses of each fiscal variable, first, to budgetary disequilibria and, second, to departures from their respective long run relations with GNP.

Table III. Least Squares and Maximum Likelihood Estimates of Cointegrating
Vectors

Rows   Estimators   Expenditures   Revenues     GNP   Constant     ADF

        ML                -1         1.092       0      -0.287
        ML-Trend          -1         1.085       0
1       OLS               -1         1.077       0      -0.351   -4.67(***)
        ML               0.916        -1         0       0.263
        ML-Trend         0.922        -1         0
2       OLS              0.924        -1         0       0.349   -4.64(***)
        ML                -1           0      1.115     -2.397
        ML-Trend          -1           0      1.118
3       OLS               -1           0      1.122     -2.454   -4.49(***)
        ML                 0          -1      1.021     -1.932
        ML-Trend           0          -1      1.031
4       OLS                0          -1      1.040     -1.939   -3.98(***)

Notes: Reported are least squares (OLS) and linearly transformed maximum
likelihood estimates, without deterministic trend (ML) and with trend
(ML-Trend). ADF refers to the augmented Dickey-Fuller cointegration test
statistics compared with the critical values from MacKinnon [22]; the ADF test
equations include the first four augmented terms. Asterisks indicate
significance levels (*** significant at the 1%, ** significant at the 5%, and
* significant at the 10% level).

Table III reports the resulting bivariate vectors normalized for expenditures and revenues for both the deterministic trend and the no-trend specifications. To check the robustness of these bi-variate vectors, Table III also reports the least squares estimates of the bivariate vectors based on the Engle-Granger cointegration test [12]. As suggested by the significant ADF cointegration test statistics, these bivariate vectors are all stationary, confirming the conclusion reached based on the Johansen procedure. In addition, comparing the linearly transformed bivariate vectors with those from the Engle-Granger procedure, there is a remarkable correspondence between the two sets of estimates, whether the deterministic trend or the no-trend specification is used in the maximum likelihood procedure. The error correction models presented in the following section include the residuals from these bivariate cointegrating equations as error correction terms.

Before proceeding further, it is important to note that the cointegrating vectors relating (the logarithms of) each fiscal variable and GNP are apparently close to (1, -1), which would imply that deflating revenues and expenditures by GNP would yield stationary series. Likelihood ratio tests of this restriction reject the hypothesis for the expenditures-GNP relation, but this restriction cannot be rejected for the relation between revenues and GNP(5) [20]. Rescaling expenditures by GNP, while excluding GNP as an additional variable, would introduce an inappropriate restriction. Rescaling both fiscal series by GNP would transform one to stationarity, leaving the other nonstationary, precluding the possibility of cointegration between the transformed budgetary series. Clearly, with our data rescaling by GNP is an inappropriate modeling strategy.

An alternative rescaling is to deflate all series by the GNP deflator. Again two cointegrating vectors exist among the three real series, with the hypothesis of one or fewer vectors rejected at the 2.5% level by the maximum eigenvalue test.(6) Bivariate tests again find cointegration between all three pairs of series, with coefficients close to those reported in Table III. The inferences concerning cointegration are the same for real and nominal representations of these three series.

V. Error Correction Models

Cointegration is a necessary and sufficient condition for the representation of the series in an ECM [12]. Within an ECM Granger-causality can arise from two sources [15]. Short run dynamics in the ECM are captured by the lagged differences, and conventional tests of causality may be based on the significance of these terms. More interesting for our purposes, however, are the potential effects through the error correction terms, representing departures from long run equilibria. In the context of the alternative hypotheses of the budget process, of particular interest are the adjustments of revenues and expenditures to budgetary disequilibrium.

The nonuniqueness of multiple cointegrating vectors provides some flexibility in the construction of the ECMs. Our particular interest here is in examining the responses of revenues and expenditures to budgetary disequilibrium. The appropriate normalization of the cointegrating vectors for this investigation is in the form produced by the bivariate least squares estimations. The ECM equation for expenditures, therefore, contains one error correction term measuring budgetary disequilibrium, and one error correction term capturing departures from the equilibrium relation between GNP and expenditures. Similarly, the two error correction terms in the revenues equation represent budgetary disequilibrium and departures from equilibrium in the GNP-tax function.(7) The size and statistical significance of the coefficients on the budgetary disequilibrium term in each error correction equation measure the tendenciew of each fiscal variable to restore budgetary equilibrium.

Table IV reports the OLS regression estimates of both expenditures and revenues equations of the ECM in unrestricted form--allowing lags one through four on the differences of all variables--and specifications omitting insignificant terms. Arguing that GNP is determined by factors additional to fiscal policy variables, we do not attempt to specify an equation for GNP. The estimations in Table IV are also repeated with the three series expressed in real terms. The inferences based on Table IV are robust to this model change.

The restricted ECM estimates in columns 3 and 4 of Table IV pass a series of diagnostic tests including serial correlation (based on the inspection of the autocorrelation functions of the residuals as well as the reported insignificant Lagrange multiplier [[Chi].sup.2]-statistics) and omitted variables such as a time trend and other lags. In addition, recursive estimation has been utilized to investigate parameter constancy of the restricted ECM estimates based on the cusum of squares test of stability. This test, developed by Brown, Durbin and Evans, is based on a standardized one-step-ahead prediction of errors from recursive regressions and is designed to test the null hypothesis TABULAR DATA OMITTED that the regression parameters vector of the recursive regressions are identical [7]. The calculated cusum of squares together with the 5% critical value boundaries are plotted for both the restricted estimates of the revenues equation and expenditures equation. In both cases, the null hypothesis of parameter constancy cannot be rejected at the 5% or lower level of significance.(8)

The most important finding from the ECM estimates in Table IV is the lack of statistical significance of the budgetary disequilibrium terms in each equation. Neither revenues nor expenditures adjust to correct budgetary disequilibrium. In terms of adjustments to long run equilibrium, neither the tax-and-spend model nor the spend-and-tax view is supported by these results. Both revenues and expenditures adjust to correct disequilibria in their respective relations to GNP.

Of secondary interest are the causality results implied by the lagged difference terms. The short run dynamics are characterized by a unidirectional causation, with expenditures significantly affected by lagged changes in revenues, but revenues are unaffected by lagged changes in expenditures. GNP changes enter significantly into the revenues equation but appear to play no significant role in the short run movements of expenditures.

VI. Conclusion

This study has examined three alternative models of the federal budgetary process. In addition to the tax-and-spend and the spend-and-tax models, we have presented an alternative perspective, reflecting the institutional separation of allocation and taxation functions of the federal government.

Consistent with the work of Bohn, Jones and Joulfaian and Miller and Russek, we find strong support for the existence of a long run relation between revenues and expenditures of the U.S. federal government [5; 21; 25]. Based on the error correction model estimates, however, neither revenues nor expenditures respond to budgetary disequilibria, leading to rejection of both the tax-and-spend and the spend-and-tax models of the budgetary process. The adjustment to equilibrium takes place through movements in the two budgetary variables towards their long run relations with GNP. These results are consistent with the third model, reflecting the institutional separation of allocation and taxation functions of government, with the expansion in revenues and expenditures each determined by long run economic growth.

1. Both ratios appear to be trended over the 1955-89 sample period, and tests for unit roots against trend stationarity reject the unit root hypothesis at the 1% level for both series. Testing against the alternative of stationarity about a constant, the unit root hypothesis is again rejected at the 10% level for revenues/GNP, but not for expenditures/GNP.

2. Budgetary equilibrium, in this context, does not imply a balanced budget, unless the cointegrating equation relating revenues and expenditures has an intercept of zero and coefficient equal to one. Bohn finds this restriction compatible with his data [5].

3. According to Eisner this adjustment of the conventional measure of the deficit is still far from ideal, and he suggests additional corrections towards a measure of the change in the real net assets of federal, state, and local governments [11].

4. This formulation, with a one-period lag on the vector of levels, is algebraically equivalent to Johansen's equation, where the levels are lagged k periods.

5. These tests were performed on the bivariate models which include the constant term in the cointegrating vector. The chi-squared test statistic for the (1, -1) restriction on the cointegrating vector relating expenditures and GNP is 8.43 (one degree of freedom), which is significant at the 1% level. The corresponding test statistic for revenues and GNP is 0.47, which is not significant at any reasonable level.

6. The maximum eigenvalue test statistics under the hypothesis of one or fewer vectors are 17.12 for the trend model and 19.69 for the no-trend version. Trace statistics under this same hypothesis are 17.78 and 31.03 for the trend and no-trend specifications, respectively.

7. The space spanned by the original two cointegrating vectors estimated by maximum likelihood has dimension equal to 2. However, an infinity of cointegrating vectors can be generated by linear transformations of these two vectors. Although three such vectors are created for insertion into the error correction models, they do not form a linearly independent set.

8. This evidence of structural stability contradicts Hoover and Sheffrin's finding of two dissimilar subperiods. Methodological and data definition differences could account for the differences between the two sets of results [18].

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