Government expenditures and revenues: evidence from asymmetric modeling.

In this article, we examine the relationship between U.S. federal revenues and expenditures while relaxing the assumption of a symmetric adjustment process underlying the conventional cointegration and error correction model. Threshold autoregression and momentum threshold autoregression models are used to ascertain the empirical link between the two variables of the budgetary process. Our results suggest that revenues and expenditures are cointegrated and that the adjustment process of the budgetary disequilibrium is asymmetric. The application of the asymmetric error correction model indicates that revenues and expenditures respond to the long-run requirements of the budgetary balance only when the budget is worsening.

JEL Classification: E600, H600, H500, H300

1. Introduction

Examining the empirical relationship between government revenues and expenditures is a crucial step in understanding the future path of the budget deficit. Four alternative explanations have been used to describe the relationship between these variables in the budgetary process: (i) the tax-and-spend hypothesis, (ii) the spend-and-tax hypothesis, (iii) the fiscal synchronization hypothesis, and (iv) the institutional separation hypothesis. The issue of which hypothesis best describes the nature of the budgetary process has yet to be resolved in the literature. However, existing research has implicitly assumed that the state of the budget and whether or not the budget deficit (or surplus) is worsening or improving does not matter. We argue that government decision-makers may take these factors into account when determining expenditures and tax policy. As such, this article reexamines the tax-spend debate by using a more robust econometric technique that allows for asymmetry in the relationship between revenues and expenditures.

Until now, the empirical evidence on the tax-spend debate has focused almost exclusively on two conventional econometric techniques. Depending on the cointegrating properties between revenues and expenditures, these techniques are based on either variations of the unrestricted vector autoregression (UVAR) or the vector autoregression error correction model (ECM).l if, for example, the two budgetary variables are not cointegrated, then the application of causality (2) tests requires the use of stationary variables in the UVAR model. (3) On the other hand, if the two budgetary variables are cointegrated, then the application of causality tests requires an ECM specification.

It is important to note that the ECM specification implicitly assumes that the adjustment process of expenditures and revenues due to disequilibrium between the variables is strictly symmetric. Indeed, if the adjustment is asymmetric, then the symmetric adjustment implicitly assumed in the conventional techniques to ascertain causality implies model misspecification. This specification error may lead to misguided and perhaps inappropriate fiscal policy decisions. Accurate estimation of the revenue and expenditure process is especially important as changes in taxes and spending alter incentives for work, investment, and productive activity (CEA 2004). Thus, the anticipated behavioral responses of households and businesses may be better captured by more general models that allow for asymmetry in the tax-spend relationship. To this end, this article examines the existence of cointegration between revenues and expenditures and the corresponding ECM specification by using the recently developed techniques of asymmetric modeling. In particular, we employ the threshold autoregression (TAR) and momentum threshold autoregression (M-TAR) models developed by Enders and Granger (1998) and Enders and Siklos (2001). Within the context of these models, we shed new light on whether budget surpluses versus budget deficits (or an improving budget versus a worsening budget) have asymmetric effects on the dynamic behavior of expenditures and revenues.

There is an a priori rationale for modeling asymmetry in the budget and for the response of its components to disequilibrium. This rationale can be categorized into four factors. First, the fiscal policymakers may respond differently to a deviation of the deficit or surplus from its long-run trend. One would expect, for example, that the response would be more aggressive if the deficit was greater than its long-run trend than if it was less than its trend.

Second, it is widely acknowledged that there is a very close connection between the budget and the business cycle through automatic fiscal stabilizers and discretionary fiscal measures. To the extent that the business cycle is asymmetric, the associated change in the budget may also be asymmetric. (4) Some elements of tax revenues are especially sensitive to cyclical movements in the macroeconomy. (5) Sichel (1993) makes a distinction between sharp versus deep cycles because he found that many important macroeconomic variables display asymmetric adjustment paths. Thus, one cannot rule out the possibility that aggregate federal revenues and expenditures may also exhibit asymmetries. Third, taxpayers' behavioral responses to changes in either the effective tax rate or the effective tax base may produce asymmetric variations in the budget. Examples of such responses include changes in portfolio investments or changes in the related tax elasticities. These behavioral responses will probably manifest as large swings in tax revenues.

Fourth, some elements of tax revenues are highly responsive to certain internal and external developments. Trade tax revenues, for example, are sensitive to the international economy, including any asymmetric variations in interest rates or exchange rates. Profit tax revenues, as another example, are sensitive to internal and external demand and supply shocks. Finally, expenditures on defense are sensitive to political developments, especially when we compare wartime spending with peacetime expenditures.

Within the public finance literature, it is often assumed that a government determines both revenues and expenditures in ways that maximize the social welfare of the society. However, four alternative hypotheses have been advanced to ascertain the nature of the causality between these variables in the budgetary process. The tax-and-spend argument proposes that changes in government revenues lead to changes in government expenditures. Friedman (1978) and Buchanan and Wagner (1978) were early proponents of this view but differed in their perspectives. Friedman argued that increasing the resources available to government by increasing tax revenues will only lead to increases in government expenditures. The Friedman version of the tax-spend hypothesis suggests that government revenues have a positive effect on government expenditures. Alternatively, Buchanan and Wagner argued that increases in government revenues may lead to decreases in government expenditures through fiscal illusion. In particular, if the government is financing expenditures by means other than direct taxation, the fiscal illusion occurs because the public pays less in direct taxation but more in the form of indirect taxation (e.g., crowding-out effects and bracket creep caused by inflation). If indirect taxation declines while direct taxation increases, this trend could reduce government expenditures.

The spend-and-tax hypothesis suggests that a government first makes expenditure decisions and then adjusts tax policy and revenues as necessary to accommodate expenditures. From a Ricardian equivalence perspective, Barro (1979) argued that increased government expenditures financed by borrowing will translate into higher future tax liability for the public. In the context of fiscal policy response to "crisis" situations, Peacock and Wiseman (1979) argued that temporary increases in government expenditures in response to such crises will lead to higher permanent taxes. Under either perspective, higher expenditures would lead to higher taxes.

Many recent studies have found that revenues and expenditures are cointegrated. The finding of cointegration implies that the standard UVAR specification is incorrectly specified, thereby casting doubt on the earlier causality test findings. (6) Numerous studies have yielded mixed results from applying the ECM as the dynamic specification for the cointegrating relationship between revenues and expenditures. For example, Bohn (1991), Mounts and Sowell (1997), Koren and Stiassny (1998), Garcia and Henin (1999), and Chang, Liu, and Caudill (2002) supported the tax-spend hypothesis whereas Jones and Joulfaian (1991) and Ross and Payne (1998) argued in favor of the spend-tax hypothesis.

Under the fiscal synchronization hypothesis, a government simultaneously chooses the desired package of spending programs and the revenues necessary to finance such spending programs. Musgrave (1966) and Meltzer and Richard (1981) are proponents of this view of the budgetary process. In addition, Miller and Russek (1989), Hasan and Sukar (1995), and Owoye (1995) found evidence to support the fiscal synchronization hypothesis. Finally, under the institutional separation hypothesis, government decisions to spend are independent from decisions to tax. Hoover and Sheffrin (1992) and Baghestani and McNown (1994) have provided evidence of this view.

Payne (2003) attributed these inconclusive results to differing methodological approaches, model specification, degrees of temporal aggregation, and time periods examined. In testing the validity of tax-spend hypotheses, this article examines the commonly used methods of symmetric cointegration and ECM. In particular, we extend the analysis to the asymmetric cointegration and ECM with the application of TAR and M-TAR models.

2. Data and the Empirical Methodology

This research utilizes the quarterly and seasonally adjusted federal government expenditures, which include transfer payments ([X.sub.t]) and federal government revenues ([R.sub.t]), to investigate the causality between government expenditures and government revenues. Note that the inclusion of transfer payments as expenditures is in keeping with the convention of national income product accounting. The data series cover the period from 1958:1 to 2003:2 and were obtained from the Bureau of Economic Analysis data base. While the political budgetary cycle might be described as an annual decision-making process, we analyze quarterly data because the collection of taxes and the disbursement of expenditures occur throughout the year. The [X.sub.t] and [R.sub.t] were transformed to natural logarithms, scaled to the natural logarithm of gross domestic product, and denoted henceforth by [x.sub.t] and [r.sub.t], respectively. Figure 1 illustrates the government expenditures ([x.sub.t]), government revenues ([r.sub.t]), and budgetary disequilibrium.

[FIGURE 1 OMITTED]

We test [x.sub.t] and [r.sub.t] for their order of integration using standard unit root tests. If they are integrated of order one, it is necessary to find whether or not they are cointegrated. If [x.sub.t] and [r.sub.t] are cointegrated, then the estimated residuals resulting from this cointegration relationship should be used in the symmetric ECM. On the other hand, if the two series are not cointegrated, then the application of the causality tests requires that [x.sub.t] and [r.sub.t] should simply be converted to stationary series by first-differencing before entering the UVAR.

For purposes of unit root testing, we utilize the standard augmented Dickey and Fuller (1979, 1981), ADF, and Phillips-Perron (1988) PP tests. Table 1 presents the ADF and PP test results for the variables in both levels and first differences. The results suggest that each series has a unit root and that the first differences of [x.sub.t] and [r.sub.t] are stationary.

Since both [x.sub.t] and [r.sub.t] appear to have a unit root, it is appropriate to test for cointegration. Following Engle and Granger (1987), we estimate the cointegration relation as follows:

[r.sub.t] = [alpha] + [beta][x.sub.t] + [[epsilon].sub.t]. (1)

Note that the residuals ([[epsilon].sub.t]) recovered from Equation 1 represent the disequilibrium between [x.sub.t] and [r.sub.t] and signify the budgetary disequilibrium. In the second step, we test for cointegration based on the OLS estimate of p in the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

where [v.sub.t] ~ I.I.D(O,[[sigma].sup.2]) and the lagged values of [DELTA][??] are meant to yield uncorrelated residuals.

We reject the null hypothesis of no cointegration between [x.sub.t] and [r.sub.t] (Table 1). Thus, the budgetary disequilibrium appears to be stationary such that federal revenues and federal expenditures do not arbitrarily drift far apart from each other in the long run.

In the symmetric approach, however, we test for cointegration based on the null hypothesis of [rho] = 0 in Equation 2. (7) The key point to note is that the alternative hypothesis implicitly assumes a symmetric adjustment process around the budgetary disequilibrium, [[epsilon].sub.t] = 0. Additionally, the symmetric ECM implicitly assumes that any short-run changes in expenditures and revenues due to budgetary disequilibrium are strictly symmetric to the absolute value of the disequilibrium. If, however, the adjustment in expenditures and revenues due to the budgetary disequilibrium is asymmetric, then the symmetric adjustment process assumed by the unit root and cointegration tests and the corresponding ECM implies misspecification.

To test for cointegration that recognizes the possibility of an asymmetric ECM of the budgetary process, the TAR and M-TAR models developed by Enders and Granger (1998) and Enders and Siklos (2001) are utilized. As shown by Enders and Granger (1998), the distinction is important because tests for both unit roots and cointegration all have low power in the presence of an asymmetric adjustments process. The two-step procedure of Engle and Granger (1987) is extended to incorporate the TAR and M-TAR specifications to examine the possibility of asymmetric causality between [x.sub.t] and [r.sub.t].

The TAR model is estimated from Equations 3 and 4, while the M-TAR model is estimated from Equations 3 and 5:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

where [[??].sub.t] ~ I.I.D(O,[[sigma].sup.2]) and the lagged values of [DELTA][[??].sub.t] are meant to yield uncorrelated residuals.

The Heaviside indicator functions are denoted as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where the threshold z is endogenously determined using Chan's (1993) method. This method arranges the values, {[[??].sub.t]} for the TAR model and {[DELTA][[?].sub.t]} for the M-TAR model, in ascending order and excludes the smallest and largest 15%. The consistent estimate of the threshold is the parameter which yields the smallest residual sum of squares over the remaining 70%.

The indicator variable in Equation 4, [I.sub.t], depends on the previous period's budgetary disequilibrium ([[??].sub.t-1]). As such, Equations 3 and 4 can capture the response of the budgetary disequilibrium to positive versus negative discrepancies from the threshold. Specifically, if [[??].sub.t-1] is above the long-run balance position, which amounts to the positive phase of the budgetary disequilibrium, the adjustment is [[rho].sub.1][[??].sub.t-1] and if [[??].sub.t-1] is below the long-run balance position, which amounts to the negative phase of the budgetary disequilibrium, the adjustment is [[rho].sub.2][[??].sub.t-1]. In applying the TAR model, it is possible to examine whether the positive phase of the budgetary disequilibrium (e.g., surpluses) has different effects on the behavior of expenditures and revenues than does the negative phase of budgetary disequilibrium (e.g., deficits).

However, the M-TAR model, estimated using Equations 3 and 5, allows the adjustment to depend on the previous period's change in [[??].sub.t-1]. This model is especially valuable when the adjustment is believed to exhibit more momentum in one direction than the other. In particular, it is possible to examine whether the positive phase of the changes in budgetary disequilibrium has a different effect on the behavior of expenditures and revenues than does the negative phase.

In both models, the null hypothesis of no cointegration can be tested by the restriction [[rho].sub.1] = [[rho].sub.2] = 0, while the null hypothesis of symmetry can be tested by the restriction [[rho].sub.1] = [[rho].sub.2].

3. Empirical Results

Having established that [x.sub.t] and [r.sub.t] are I(1) in their level form, the long-run relationship is estimated and reported in Table 1. Next, the residuals [[??].sub.t] are used to jointly estimate Equations 3 and 4 in the form of the TAR model and Equations 3 and 5 for the M-TAR model. The results of the TAR and M-TAR models are reported in Table 2.

As reported in the second column of Table 2, the estimates of [[rho].sub.1] and [[rho].sub.2] from the TAR model satisfy the stationarity (convergence) conditions. More importantly, the [[PHI].sup.*](T) = 8.81 for the null hypothesis of [[rho].sub.1] = [[rho].sub.2] = 0 was compared to the 5% (1%) critical values of 7.08 (9.51) given by Enders and Siklos (2001). Therefore, we reject the null hypothesis of no cointegration, [[rho].sub.1] = [[rho].sub.2] = 0, at the 5% significance level. Since the budgetary disequilibrium is stationary and [x.sub.t] and [r.sub.t] are cointegrated, it is possible to test the null hypothesis of symmetric adjustment, [[rho].sub.1] = [[rho].sub.2]. Based on the standard F-statistic = 2.45 (p = 0.12), the null hypothesis of symmetry is not rejected. Thus, asymmetry is not established in the TAR model.

The third column of Table 2 reports the point estimates of [[rho].sub.1] and [[rho].sub.2] as estimated by the M-TAR model. Based on the [[PHI].sup.*](M) = 11.43 for [[rho].sub.1] = [[rho].sub.2] = 0, we reject the null hypothesis of no cointegration. The matching 5% (1%) critical values are 6.86 (9.29) as reported in Enders and Siklos (2001). Thus, the budgetary disequilibrium is stationary and [x.sub.t] and [r.sub.t] are cointegrated. Next, it is possible to test the null hypothesis of symmetric adjustment, [[rho].sub.1] = [[rho].sub.2]. Based on both the F-statistic = 7.28 for the null hypothesis, [[rho].sub.1] = [[rho].sub.1], we reject symmetric adjustment in the case of the M-TAR model (p = 0.01). Given [absolute value of [[rho].sub.1]] < [absolute value of [[rho].sub.2]], the adjustment toward the balance position tends to persist more when the budget is improving and reverts more quickly when the budget is worsening. Therefore, the speed of adjustment when the budget is worsening is higher than when the budget is improving.

Having established cointegration between [x.sub.t] and [r.sub.t] as well as asymmetric adjustment in the budgetary disequilibrium with the M-TAR model, it is possible to estimate the asymmetric version of the ECM. (8) The asymmetric version of the ECM, then, replaces the single symmetric error-correction term with two asymmetric components of the error correction terms as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

where [u.sub.12t] ~ I.I.D(0,[[sigma].sup.2]), and [[??].sub.t-1] = [r.sub.t-1] - [??] - [??][x.sub.t-1], and [I.sub.t] takes the form given in Equation 5.

The results obtained from the asymmetric ECM are reported in Table 3. The t-statistics for the error correction terms indicate that revenues and expenditures adjust to budgetary disequilibrium only if the previous period's change in [[??].sub.t-1] < t. That is, revenues and expenditures respond to a worsening in the budget but not to an improving budget. Note that the response of revenues to a worsening in the budget is much larger (in absolute terms) than the response of expenditures. These results from the asymmetric ECM confirm the findings of the M-TAR model on the speed of adjustment.

Finally, the F-statistics concerning short-run causality indicate that revenues are not Granger-caused by expenditures and that expenditures are not Granger-caused by revenues. These findings again suggest the lack of significant short-run causal effects running from revenues to expenditures and from expenditures to revenues. However, the coefficient on the error correction term when the budget is worsening is significant in the revenue and expenditure equations.

4. Conclusion

Our article relaxes the implicit assumption of a symmetric adjustment process underlying the conventional cointegration and ECM when examining the relationship between revenues and expenditures. We suggest that the behavior of budgetary disequilibrium and changes in federal government expenditures and revenues due to the level as well as the changes in the budgetary disequilibrium is asymmetric. The new specifications of the TAR and M-TAR models developed by Enders and Granger (1998) and Enders and Siklos (2001) are used to ascertain the empirical links between the two variables of the budgetary process.

In testing the validity of the various tax-spend hypotheses, we took a closer look at the common methodology of symmetric cointegration and ECM. Additionally, we extended the analysis to the asymmetric cointegration and asymmetric ECM by utilizing the recently developed TAR and M-TAR asymmetric models. With the application of the M-TAR model, our findings suggest that federal government revenues and expenditures are cointegrated and the adjustment process of the budgetary disequilibrium is asymmetric. The point estimates suggest the speed of adjustment when the budget is worsening is higher than when it is improving. Moreover, the results obtained from the asymmetric ECM suggest that revenues and expenditures respond to a worsening of the budget, but not to an improving budget.

Under the symmetric and asymmetric ECMs, we found that revenues are not Granger-caused by expenditures and that expenditures are not Granger-caused by revenues in the short run. These findings suggest the lack of significant short-run causal effects running from revenues to expenditures or expenditures to revenues. Furthermore, the results of the asymmetric ECM suggest that revenues and expenditures respond to the long-run requirements of the budgetary balance only when the budget is worsening. Finally, to the extent that the deficit is corrected only when it is worsening, one would question the sustainability of the current path of fiscal policy. A noteworthy feature of the current fiscal policy is the feasibility of adjusting both expenditures and revenues via an increase in expenditures along with a tax cut to stimulate the economy. Obviously, the projected increase in expenditures, for example, Medicare and Medicaid, would cause the deficit to grow dramatically in the long run. To finance such a growing deficit, public debt is expected to follow. Without sufficiently high economic growth, the public debt would grow relative to national income and eventually the government would be forced to increase taxes. More importantly, higher public borrowing would leave less national savings available to finance private sector investment.

Appendix

Results of the Symmetric ECM

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (A2)

Parameter                                    [DELTA][x.sub.t]

[[alpha].sub.0]                                0.0003 [1.93]
[[alpha].sub.1]                                0.1670 [2.28] *
[[alpha].sub.2]                                0.2715 [3.77] **
[[beta].sub.1]                                 0.0095 [0.17]
[[beta].sub.2]                                 0.0544 [1.00]

Error Correction Term

  [delta]                                      0.0564 [3.02] **
  [Q.sub.LB] {4, 8}                            {0.53, 0.14}
  Null hypothesis                    F [statistic.sub.(2, 173)] = 0.50
    that [DELTA][r.sub.t] does not     [[chi square].sub.(2)] = 1.00
    Granger-cause [DELTA][x.sub.t]

Parameter                                       Parameter

[[alpha].sub.0]                                [[??].sub.0]
[[alpha].sub.1]                                [[??].sub.1]
[[alpha].sub.2]                                [[??].sub.2]
[[beta].sub.1]                                 [[??].sub.1]
[[beta].sub.2]                                 [[??].sub.2]

Error Correction Term

  [delta]                                         [psi]
  [Q.sub.LB] {4, 8}                         [Q.sub.LB] {4, 8}
  Null hypothesis                    Null hypothesis
    that [DELTA][r.sub.t] does not     that [DELTA][x.sub.t] does not
    Granger-cause [DELTA][x.sub.t]     Granger-cause [DELTA][r.sub.t]

Parameter                                    [DELTA][r.sub.t]

[[alpha].sub.0]                                 0.0006 [2.94] **
[[alpha].sub.1]                                -0.0791 [1.05]
[[alpha].sub.2]                                 0.1639 [2.19] *
[[beta].sub.1]                                 -0.1956 [1.94]
[[beta].sub.2]                                  0.0750 [0.76]

Error Correction Term

  [delta]                                      -0.0798 [3.11] **
  [Q.sub.LB] {4, 8}                            {0.85, 0.70}
  Null hypothesis                    F [statistic.sub.(2, 173)] = 2.01
    that [DELTA][r.sub.t] does not     [[chi square].sub.(2)] = 4.02
    Granger-cause [DELTA][x.sub.t]

The absolute values of t statistics are in square brackets ([]). The
estimates of the ECM are specified in Equations A1 and A2. [delta] and
[psi] are the coefficients on the error-correction terms in Equations
A1 and A2, respectively. [Q.sub.LB] is the Ljung-Box statistic with
probability values for order 4, 8 in braces ({}), respectively.

* Significant at 5%.

** Significant at 1%.

Received December 2003; accepted June 2005.

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(1) Payne (2003) provides a survey of the empirical literature on the relationship between government expenditures and revenues.

(2) Throughout this article, we use the term causality in the context of Granger causality. That is, a variable X "causes" a variable Y if knowledge of the history of X explains movements in Y.

(3) Obtaining stationarity is often accomplished by first-differencing the variables.

(4) a For example, see Neftci (1984), Terasvirta and Anderson (1992), Sichel (1993), Potter (1995), Ramsey and Rothman (1996), Bradley and Jansen (1997), and Enders and Siklos (2001).

(5) Personal income, sales, and corporate income taxes are examples of tax revenues that are sensitive to the cyclical movements in the macroeconomy. For example, see Holcombe and Sobel (1995); Sobel and Holcombe (1996); Nelson, Cornia, and MacDonald (1998); Haonan and Dunn (2000); and Rider (2002).

(6) Throughout the empirical literature, most of the early work has applied the UVAR models using the relevant budgetary variables. Prominent papers by von Furstenberg, Green, and Jeong (1985, 1986); Anderson, Wallace, and Warner (1986); Joulfaian and Mookerjee (1991); and Islam (2001) found evidence of causality running from expenditures to revenues. In contrast, other notable papers, such as those by Blackley (1986) and Ram (1988a, b), found causality running from revenues to expenditures, whereas Manage and Marlow (1986) found support for the fiscal synchronization hypothesis.

(7) See Appendix for estimation results from symmetric error correction model.

(8) Based on the AIC, the M-TAR model fits the data better than the TAR model.

Bradley T. Ewing, * James E. Payne, ([dagger]) Mark A. Thompson, ([double dagger]) and Omar M. Al-Zoubi ([section])

* Rawls College of Business, Texas Tech University, Lubbock, TX 79409-2101, USA; E-mail [e-mail]; corresponding author.

([dagger]) Department of Economics, Illinois State University, Normal, IL 61790, USA; E-mail [e-mail].

([double dagger]) Institute for Economic Advancement, University of Arkansas at Little Rock, Little Rock. AR 72204-1099, USA; E-mail [e-mail].

([section]) Department of Economics, Texas Tech University, Lubbock, TX 79409, USA; E-mail [e-mail].

Table 1. Augmented Dickey-Fuller and Phillips-Perron Unit Root
Test Results

Variable                   ADF         PP

[r.sub.t]                - 1.87      -1.74
[DELTA][r.sub.t]         -15.48 *   -15.48 *
[x.sub.t]                 -0.9       -0.93
[DELTA][x.sub.t]          -7.15 *   -12.47 *
Cointegrating equation
  [r.sub.t] = 0.14 +
    0.83[x.sub.t] +
    [[??].sub.t]          -3.88 *    -3.37 *

Variable [r.sub.t] denotes the ratio of the logarithmic transformation
of federal government revenues to the logarithmic transformation of
gross domestic product, [x.sub.t] denotes the ratio of the logarithmic
transformation of federal government expenditures to the logarithmic
transformation of gross domestic product, and [DELTA] denotes the first
difference operator. Both the ADF and PP unit root tests are estimated
with constant and trend terms. The t statistics for the constant and
the slope coefficient of the cointegrating equation are 11.92 and
58.61, respectively. Lag length is determined by Akaike Information
Criterion.

* Null hypotheses of a unit root is rejected at 5% significance level
or less.

Table 2. Estimates for the Budgetary Disequilibrium: TAR
and M-TAR models

                                                    Models

Parameters                                   TAR             M-TAR

[[rho].sub.1]                           -0.0745 [1.92]   -0.0836 [2.33]
[[rho].sub.2]                           -0.2337 [4.28]   -0.2874 [4.25]

Threshold                               -0.0066          -0.0011

  [[rho].sub.1] = [[rho].sub.2]
    = 0 (1)                              8.81            11.43
  [[rho].sub.1] = [[rho].sup.2.sub.2]    2.45 (0.12)      7.28 (0.01)
  AIC                                   -8.8769          -8.8846
  [Q.sub.LB] {4, 81}                    {0.88, 0.54}     {0.88, 0.59}

The TAR model is estimated by using Equations 3 and 4. The M-TAR model
is estimated by using Equations 3 and 5. The absolute values of t
statistics corresponding to the point estimate of [[rho].sub.1] and
[[rho].sub.2] are in square brackets ([]) . The critical values at 5%
(1%) level of significance are: 7.08 (9.51) for TAR model and 6.86
(9.29) for M-TAR model, as Enders and Siklos (2001) reported.
[Q.sub.LB] is the Ljung-Box statistics with probability values for
order 4, 8 in braces ({}), respectively. (1) Entries represent the
sample values of ([[PHI].sup.*] (T) and [[PHI].sup.*] (M), respectively
(see Enders and Siklos [2001]). (2) Entries are the sample F statistic
for the null hypothesis, [[rho].sub.1] = [[rho].sub.2], and
significance levels are in parentheses.

Table 3. Results of the Asymmetric ECM

Parameter                                    [DELTA][x.sub.t]

[[alpha].sub.0]                                0.0003 [2.24] *
[[alpha].sub.1]                                0.1869 [2.52] *
[[alpha].sub.2]                                0.2667 [3.72] **
[[beta].sub.1]                                -0.0130 [0.23]
[[beta].sub.2]                                 0.0374 [0.68]

Error Correction Term

  [[rho].sub.1]                                0.0409 [1.95]
  [[rho].sub.2]                                0.1123 [2.82] **
  [Q.sub.LB] {4, 8}                            {0.54, 0.12}
  Null hypothesis                    F [statistic.sub.(2, 173)] = 0.30
    that [DELTA][r.sub.t] does not     [[chi square].sub.(2)] = 0.59
    Granger-cause [DELTA][x.sub.t]

Parameter                                       Parameter

[[alpha].sub.0]                                [[??].sub.0]
[[alpha].sub.1]                                [[??].sub.1]
[[alpha].sub.2]                                [[??].sub.2]
[[beta].sub.1]                                 [[??].sub.1]
[[beta].sub.2]                                 [[??].sub.2]

Error Correction Term

  [[rho].sub.1]                                [[??].sub.1]
  [[rho].sub.2]                                [[??].sub.2]
  [Q.sub.LB] {4, 8}                         [Q.sub.LB] {4, 8}
  Null hypothesis                    Null hypothesis
    that [DELTA][r.sub.t] does not     that [DELTA][x.sub.t] does not
    Granger-cause [DELTA][x.sub.t]     Granger-cause [DELTA][r.sub.t]

Parameter                                     [DELTA][r.sub.t]

[[alpha].sub.0]                                 0.0005 [2.37] *
[[alpha].sub.1]                                -0.0321 [0.42]
[[alpha].sub.2]                                 0.1992 [2.65] **
[[beta].sub.1]                                 -0.2372 [2.35] *
[[beta].sub.2]                                  0.0850 [0.87]

Error Correction Term

  [[rho].sub.1]                                -0.0474 [1.66]
  [[rho].sub.2]                                -0.1966 [3.63] **
  [Q.sub.LB] {4, 8}                             {0.77, 0.63}
  Null hypothesis                    F [statistic.sub.(2, 173)] = 2.92
    that [DELTA][r.sub.t] does not      [[chi square].sub.(2)] = 5.83
    Granger-cause [DELTA][x.sub.t]

ECM estimates are in the form of Equations 6 and 7. The absolute
values of t statistics are in square brackets ([]) The [I.sub.t]
function takes the form of Equation 5. [[rho].sub.1] and [[rho].sub.2]
are the coefficients on the error-correction terms in the
[DELTA][x.sub.t] equation; that is, the coefficients on [I.sub.t]
[[epsilon].sub.t-1] and (1 - [I.sub.t])[[epsilon].sub.t-1],
respectively. [[??].sub.1] and [[??].sub.2] are the coefficients on
the error-correction terms in the [DELTA][r.sub.t] equation; that is,
the coefficients on [I.sub.t][[epsilon].sub.t-1] and
(1 - [I.sub.t])[[epsilon].sub.t-1], respectively. [Q.sub.LB] is the
Ljung-Box statistic with probability values for order 4, 8 in braces
({}), respectively.

* Significant at 5%.

** Significant at 1%.