Is There Any Rationale to the Brazilian Fiscal Policy ? *

Barro's tax smoothing hypothesis (TSH) implies that, when faced by a temporary increase in expenditure, the government should issue debt in order to spread the increase in taxes over time and minimize the welfare costs of high tax rates. Changes in the tax rate should then be unpredictable. This paper performs a test of the TSH that goes beyond the random walk tests usually done in literature. It examines the implied restrictions of the TSH on a vector autoregression (VAR) model using Brazilian data for the period 1970-94. The tests reject the hypothesis for the full sample period. For the period 198792, however, disregarding the volatility of the actual budget surplus, the TSH seems to provide a better approximation to the historical movements of Brazilian fiscal data series.


Introduction
It is hard to believe that any government, and in particular the Brazilian government, follows a debt management policy.Barro (1979) proposed a simple theory of how governments operate.Since the government has the objective of minimizing the present value of excess burden for a given present value of tax collections, it should spread the burden of raising taxes over time.Therefore, when faced with a temporary increase in expenditure it should finance the temporary difference between expenditures and revenues by issuing debt in order to reduce the welfare costs associated with high taxes.
The question of whether or not the time series properties of Brazilian fiscal data are consistent with the above observable implications has neveI' been examined before.The purpose of this papel' is to test the theory of optimal taxation over time using data for 1970-94 in order to verify if it gives a rationale to the pattern of budget deficits and taxes in Brazil over this period.The methodology used was initially developed by Campbell (1987) to analyze the optimal pattern of savings.The assumption of tax smoothing implies that the budget surplus should equal the expected present discounted value of the change in government expenditures.If the government expects a temporary increase in its expenditures, it should spread the tax burden over time in order to minimize the distortionary effects of taxes.In other terms the increase in expenditures should be financed by means of a budget deficit.li the government expects a permanent increase in its expenditures it should raise taxes immediately in order to minimize the tax rate when the higher expenditure is actually observed.Given the analogy between a consumeI' who tries to smooth consumption and a government who tries to smooth taxes, Ghosh (1995b) adapts Campbell's methodology to study the behavior of the optimal budget surplus. 1 The result that the budget surplus should equal the present discounted value of expected changes in government expenditures has two implications.First, it is possible to construct a time series for the optimal budget surplus and compare it to the actual surplus.Under the hypothesis that the government smoothes taxes these two series should differ only by sampling error.Second, as long as the government has more information about the path of future expenditure than is contained in past values of the expenditure series, the budget surplus will have this additional information and thus Granger-cause changes in government expenditures.
The papel' is organized as follows.Section 2 presents Barro's model of optimal taxation over time.Section 3 discusses Ghosh's testo It tries to derive the implications of the smoothing hypothesis for the time series behavior of budget surpluses and government expenditures.Section 4 outlines the data to be used in the empirical analysis.Section 5 applies the test to the Brazilian fiscal data.Section 6 presents the conclusions and provides some suggestions for further research.

The Model
Barro's tax smoothing model establishes that if a government must rely on distortionary taxes, the tax rate should be set on the basis of permanent (noninterest) government expenditures with transitory expenditure fiuctuations financed by issuing debt.The purpose of this section is to derive the optimal path of taxes associated with the financing of a given path for government expenditure.
The problem facing the government is: i=O where the distortionary costs are assumed proportional to the square of the tax rate and where ,8 is the government's subjective discount rate.E{-IDt} is the expectation conditional on the government's information set at time t, Dt.
The government maximizes (1) subject to its budget constraint: where B is the stock of government debt, G is government expenditure, r is a real rate of interest (which is assumed, for the sake of simplicity, to be constant over time), T is the tax rate, and Y is output.

01':
(1 where lowercase letters denote corresponding variables expressed as a fraction of the GDP, and where n is the rate of growth of output (which is also assumed to be constant for the sake of analytic convenience).Solving the optimization problem (1), subject to (2) and ( 3), yields the optimal tax rate in each period: where R = (1 + n)/(l + r), and where í' Therefore, taxes are proportional to the present discounted value of government expenditure plus the effective real interest cost of servicing the initial debt.Assuming the government's subjective discount rate, {3, is equal to its effective interest rate, R (so that í' is equal to unity) , the optimality condition (4) establishes that taxes should equal the expected present value of government expenditure and not just government expenditure in the current period.
One implication of (4) is that optimally set tax rates should follow a random walk: 00 (5) i=O Since the right-hand si de of ( 5) is an expectational error, it should be unpredictable based on information available in period t -1 01' earlier.Thus, (5) states that under tax smoothing, tax rates should follow a random walk.Barro (1981) and Sahasakul (1986) used this random walk property to test whether governments have tried to smooth taxes.Barro found that US public debt issue responds positively to temporary increases in governrnent expenditures but responds negatively to temporary increases in aggregate output.Sahasakul made a joint test of the hypotheses of uniform taxation over time and the reliability of a specific forecasting equation for the permanent government spending variable.The joint hypotheses imply that only permanent government spending and initial public debt determine the marginal tax rates.Since there are other variables in the current information set that help to determine the marginal tax rate (temporary defense purchases, the general price leveI, and a time trend), he rejects the tax smoothing hypothesis.Although Barro and Sahasakul carne to different condusions, their econometric analyses require that government spending and aggregate output be empirically decomposed into permanent and temporary components.So, whether or not their empirical finding is valid depends upon the specification of variables and equations in their construction of the temporary or permanent components of the series.Trehan and Walsh (1988) argued that if expenditures are nonstationary, taxes will also be nonstationary even in the absence of smoothing.Therefore, in order to find support to the smoothing hypothesis one should check if the difference between tax receipts and net of interest expenditures is nonstationary.The authors' empirical tests, however, showed that this difference is stationary for the United States for 1890-1928, implying rejection of the tax smoothing hypothesis.Huang and Lin (1993) focused on the budget surplus instead of the tax rate.They derived and tested the restrictions imposed by the tax smoothing hypothesis on the process of the budget deficit (surplus), government expenditure, and aggregate output using a vector autoregression (VAR).They concluded that the tax smoothing hypothesis provides a good approximation for US fiscal data from 1929 to 1988.

Test Procedures
This section presents Ghosh's approach (1995b) to test the theory of optimal taxation over time.It will be used to analyze Brazilian fiscal policy in the next section.There are several reasons that justify this choice.
First, the test goes beyond the random walk tests oftax smoothing models.Since tax smoothing is only one of many possible explanations for tax rates following a random walk, it is important to try to test all of the time series implications of the optimal tax path.
Second, the tax smoothing hypothesis is tested directly without any empirical pre-decomposition of data into permanent and temporary components.Therefore, it avoids any specification errar derived from inappropriate data decomposi tion.
Third, when the government runs a budget deficit it is (potentially) motivated by two considerations: tax tilting and tax smoothing.Tax smoothing is the intertemporal substitution of taxes in order to give them a relatively fiat time profile.Tax tilting occurs when the burden of taxation is shifted either toward 01' away from the present, depending on the government's subjective discount rate, but in a manner which is consistent with intertemporal solvency.If the ratio between government expenditure and GDP is constant over time, there is no tax smoothing component of budget deficits.However, a tax tilting component may existo When f3 < R, the government has a high discount rate reI ative to the market interest rate.It runs large deficits early on and increases taxes over time to serve its accumulating debt.In this case, r is less than unity.When f3 > R, the government has a low discount rate relative to the market interest rate.It chooses relatively high rates early on in order to build up a stock of assets, and plans to lower taxes over time.If the ratio between government expenditure and GDP follows a perfect cycle, and if f3 = R, there is no tax tilting motive for budget deficits but there would be a strong tax smoothing motive.Ghosh's method distinguishes between these two motivations. 2The primary focus of the analysis is on the tax smoothing component of the budget deficits.Therefore, the long-term trend in the public saving does not matter, but only the short run dynamics of the budget deficits around their trend.Intertemporal solvency constraint is, then, imposed.Therefore, it is necessary initially to remove the tax tilting component.After that it is possible to identify correctly the consumption smoothing component of the tax rate with which the model is concerned.
The procedure is as follows.
First, the budget surplus is defined as Using ( 2) and ( 4) we have: Expression ( 6) embodies all the implications of optimal intertemporal tax smoothing.The budget surplus is equal to the expected present discounted value of changes in government expenditure.Assuming that the government expects a future increase in its expenditures, waiting to raise taxes would result in relatively large tax rates and distortionary cost.The optimal strategy requires that the government raise taxes immediately in order to minimize the distortion in any period.Because taxes increase prior to the rise in expenditures, the government runs a larger budget surplus (smaller deficit).Expression (6) gives the optimal budget surplus, and it is going to be written hereafter as SU R; .
Is Ther.Any Rationale to the Brazilian Fiscal Policy?
The tax smoothing hypothesis is then tested by comparing the optimal budget surplus to the actual budget surplus.In order to do so, it is first necessary to create the right hand side of (6a).The difficulty is that the path of the government expenditure may depend on institutional and political factors that are not completely known by the econometrician.However, if the government has more information about the path of future expenditure than is contained in lagged values of tlgt, the budget surplus, which is equal to the expected future changes in g, will contain this additional information.Thus, the first implication of the tax smoothing hypothesis is that the budget surplus should Granger-cause subsequent changes in government expenditure. 3he estimation proceeds as follows.To create the optimal budget surplus it is necessary to calculate the expected present discounted value of changes in government expenditure, where the expectation is conditional on information available at time t.According to Campbell (1987), the following umestricted vector autoregression (VAR) model in tlgt and SU Rt is estimated, where SU Rt is the actual tax smoothing component of the budget surplus defined as SU Rt = (1h)rt -[gt + (r -n)bt ]: (7) or Zt = WZt-l + U t , where Z = [tlgt, SU Rt]', 'li is the transition matrix of the VAR, and U t is a white noise errors vector.A first order VAR is used because, as will be seen soon, one lag suits better the Brazilian data.
However, it is possible to generalize this expression for higher order VARs just stacking the lagged variables.The optimal forecast of Zt k periods ahead, given {Zt, Zt-l' .. -}, should satisfy EtZt+k = w k Zt for k 2: 1.Using this formula, (6a) can be translated into the following expression: 00 Since tlgt and SU Rt are both stationary, the infinite sum in (8) converges to: (9) Assurning that gt is I(l) its first difference will be stationary, and since the budget surplus is a discounted sum of !:l.gt (by expression ( 6)), it will also be stationary.
Once the optimal budget surplus series SU Rt has been calculated, a number of tests may be performed.First, as observed previously, the model predicts that the budget surplus should Granger-cause changes in government expenditure.This provides a simple test of the model.8econd, a more formal test of the model can be done rewriting equation (9) as: (10) If the null hypothesis is correct, the weight ..\1 on !:l.gt should be zero and the weight ..\2 on SU Rt should be unity.If the VAR has an order higher than 1, the coeilicient on the contemporaneous budget surplus (SU Rt) should be unity and the coeilicients on all other variables should be zero. 4hird, the above VAR model can also be used for informally evaluating the performance of the tax smoothing hypothesis.SU RI is the "theoretical" budget surplus, that is, the optimal VAR forecast of the present value of future growth rates of government expenditures.8ince SU Rt is included in the current information set, according to (6), under the tax smoothing hypothesis SU RI should differ from SU Rt only by sampling error.Therefore, the plausibility of the tax smoothing hypothesis can be informally evaluated by comparing the predicted surplus, SU RI, to the actual surplus, SU Rt.
Fourth, the variances and the sample correlation between SU Rt and SU Rt should be compared.If the variance of the optimal budget surplus is larger than the variance of the actual (tax smoothing) budget surplus, the actual surplus has not changed enough to smooth taxes in face of shocks to expenditures.
Finally, it is necessary to explain how the tax tilting parameter is calculated.80 far it has been assumed that the government does no tax tilting, that is, , = 1.However, now it is necessary to estimate, in order to elirninate the tax tilting component of the actual data on the budget surplus.When I is different from unity the tax smoothing component of the budget surplus can be defined as: (11) As argued previously, the optimal budget surplus series will be an I(O) processo Under the null hypothesis that the actual tax smoothing component of the surplus is equal to the optimal budget surplus, the actual budget surplus is also I(O).This means that the left hand side of equation ( 11

The Data
The data on expenditures and on revenues are from Anuário Estatístico do Brasil, several issues.Since the tax smoothing hypothesis is tested using expenditures other than interest payments, interest payments (also from Anuário Estatístico do Brasil) are subtracted from expenditures when the VAR is estimated.The tax tilting parameter test, however, uses the government expenditure including real interest rate payments.Given that the data on expenditures includes payments of nominal interest on public debt, the actual series differs from the theoretical one.As seigniorage is an important source of revenue to the Brazilian government, it is added to tax revenues .It is calculated as t::..B t , where Bt is the monetary base (end-of-the-year values) extracted from Boletim do Banco Central, several issues.All data are annual series for the period 1970-94.All variables are divided by GDP.5 5 Some could argue that there are too fe10 observations to make the regressions meaningful.The tax smoothing test requires a series of expenditures excluding interest payments and the tax tilting estimate requires a series of expenditures including interest payments.Since it 10as possible to obtain the two different series of expenditures only for the period after 1970, the span of the data used is really short.The estimations, however, 10ere also performed using data from 1947-94, where the series from 1947-92 toas kindly provided by João Victor Issler.As the main conclusions do not change, only the results for the period 1970-94 are presented since the variables used match the theoretical modelo  -4.20 for the 5% and 1 % significance leveIs, respectively.Tests for two unit roots, not shown here, reject the null hypothesis for alI three series.

Empirical Results
For SU R, the nonconstant specification was used.CriticaI values are -1.95 and -2.62 for the 5% and 1 % significance leveIs, respectively.*represents rejection of the null of a unit root at the 5% significance leveI.
As previously observed, as long as 9t follows an 1(1) process, its first difference will be stationary, and from (6), the budget surplus, which is the discounted value of a stationary series, will also be stationary.Therefore, one implication of the model is that SU Rt should be stationary, even if 9t is noto The unit root test on 9t cannot reject the null of nonstationarity.The null of a unit root in SU Rt, on the other hand, can be rejected at the 5% leveI.
The regression of [9t + (r -n )btl on Tt, therefore, results in a coeflicient not significantly different from unity.A value of (lh) equal to 1 is consistent with the theoretical model, that is, there is no tax tilting component to the budget surplus.The budget surplus movements associated with the tax tilting motive are not included in the analysis. 6n order to choose the lag length for the VAR, the Schwarz criteria is evaluated (table 2).7 The optimallag length is 1.Lagrange multiplier tests for serial correlation of second order indicate that one lag is sufficient to guarantee that the residuaIs are white noise.For the first equation (!:lgt) the test statistic is 2.55 with a p-value equal to 0.11.For the second equation (SU Rt) the test statistic is 1.96 with a p-value equal to 0.17.Although the actual budget has been almost six times as large as would have been necessary for tax smoothing, the two series now become positively correlated.In other terms, for this subperiod the model explains better the budget surplus movements though not necessarily the magnitudes of those movements.The theoretical budget surplus generally does not match the tax smoothing component of the budget surplus , indicating absence of evidence supporting the tax smoothing hypothesis.Till 1983 the actual surpluses are positive, indicating taxes greater than expenditures, while the optimal surpluses are nega tive.In other terms, the government was rUillling a surplus when the optimal, in order to smooth taxes, would be to run a deficit.After 1983, the reverse happens.The optimal surpluses are mostly positive and the actual surpluses are mostly negative.If, however, attention is focused on the period 1987-92, disregarding the magnitude of actual fiows, i.e., the volatility of the actual budget surpluses, the two senes follow each other movements. 9It is important to observe that the results for the 1987-92 period are based only on the visual impression conveyed by the picture, and confirmed by the standard deviation ratios and the correlation coeflicients.There are no suflicient observations to perform a formal testo Once again, during this period actual and predicted budget surpluses still do not move closely together but at least they follow partly the same movements.

Concluding Remarks
The purpose of the papel' was to test Barro's theory of optimal taxation over time, in order to verify if it provides a rationale to the pattern of budget deficits and taxes in Brazil over the period 1970-94.The assumption of tax smoothing implies that the budget surplus should equal the expected present discounted value of the change in government expenditures.Therefore, it is possible to construct a time series for the optimal budget surplus.
Under the hypothesis that the governrnent smoothes taxes, the optimal budget surplus and the actual surplus should differ only by sampling error.Summarizing, and following Otto (1992), there are four implications of the model: 9 lJ, instead, the raw (undetrended) actual budget surplus [SURt=Tt-gt-(T-n)btl is compared to the optimal budget surplus the results are exactly the same, and the movements during 1987-92 are most clearly observed.The correlation coefficient between the actual and optimal surplus increases to 0,5.Since only (a) is confirmed, it is possible to conclude that the Brazilian government was not able to smooth taxes over the period 1970-94.However, over the period 1987-92, disregarding the volatility of the actual budget surplus, the mo deI tracks budget surplus movements better.Therefore, maybe the tax smoothing approach would offer a reasonable explanation of how the government operated after 1987, although it seems a poor explanation when the whole period is considered.It is worth it to observe that this conclusion is based only in the visual inspection of figure 1.There are not enough observations to formally test the mode!.
Another possibility is that the tax smoothing approach does not explain why the Brazilian economy has been experiencing large budget deficits for several years or, in other terms, it does not provide a rationale to the Brazilian fiscal policy at ali.The tax smoothing could be taken as a normative benchmark and it is still necessary to find an explanation of observed deviations from tax smoothing.It provides a theory of public debt and budget deficits which views the government as a "benevolent social planner" who maximizes the utility of the representative agent when in fact debt issue would be better explained as the outcome of a confiict between groups with different interests (see, for example, Cukierman & Meltzer, 1989, Persson & Svensson, 1989and Alesina & Tabellini, 1990).
) is I(O).If Tt and [gt + (r -n)btl are I(l), (11) defines a cointegrating regression and (1h) can be obtained by regressing [gt + (r -n)btl and Tt.(1h) can also be obtained as the cointegrating vector of the cointegration regression between [gt + (r -n)btl and Tt• should equal zero, and À2 should equal 1.This is equivalent to a simple condition on the VAR transition matrix W. Given that SUR; =[10]Rw [I-Rw]-lZt, andSUR t = [Ol]Zt, SUR; = SURtif[10]Rw[I-Rw]-1 = [01].Post-multiplying by [I -Rw] and adding [Ol]Rw yields:[10]Rw + [Ol]Rw = [01] 01' [l1]Rw = [01]Thus, the sum of the elements of the first column of Rw should be zero and the sum of the elements of the second column of Rw should be 1.Since R is approximately equal to 1, the sum of the elements of the first column of W should be approximately equal to zero, or 'ljJl + 'ljJ3 ~ O, and the sum of the elements of the second column of W should be approximately dose to 1, or 'ljJ2 + 'ljJ4 ~ 1. 8 According to table 3, 'ljJl + 'ljJ3 = 0.574, which is significantly different from zero [X11) = 11.36], and 'ljJ2 + 'ljJ4 = 0.796 which issignificantly different from one [X11) = 38.71].The performance of the model is next evaluated by comparing the theoretical surplus SU R; with the actual (detrended) budget surplus, SU Rt = (1h)Tt -[gt + (rn)b t ].The relation between SU R; and SU Rt is SUllmarized by the correlation coefficients and the standard deviation ratios of the two series, which are reported in table 5.The two series have a negative correlation coefficient of -0.684 for the period 1970-94.Besides, actual budget movements have been two times as large as would have been necessary for tax smoothing.If, however, attention is focused on the period 1987-92, although the standard deviation ratio increases, the tax-smoothing model tracks much better budget surplus movements.
The government's intertemporal budget constraint states that the present value of government expenditures must equal the present value of tax revenues, net of initial indebtedness: Table 1 reports augmented Dickey-Fuller statistics on 9t (expenditures excluding interest payments), 9; (expenditures including interest payments), Tt (tax revenues plus seigniorage), and SU Rt (budget surplus).
Notes: The number of lagged terms was chosen to ensure that the errors are uncorrelated.For g, g*, and T, a constant and a time trend were included.CriticaI values are -3.53 and

Table 3
reports the VAR coefficients.It is possible to verify if the budget surplus Granger-cause changes in the government expenditures by evaluating the coefficient of SU Rt-l in the equation for !:lgt.This coefficient is not statistically significant.
Table4presents formal Granger causality tests (which are just F-tests that all coefficients on lagged budget surplus in the government expenditure are jointly zero).Lags from 2 to 4 are used in order to check the robustness of the results.For none of the lags it is possible to reject the null of no Granger causality, so the data is inconsistent with the most basic implication of the tax smoothing behavior.: Tests that SU Rt Granger-causes D..gt . Note

Table 5
Summary statistics of theoretical and actual (detrended) surplus