Changes in income concentration: taxes or macroeconomic conditions?

Bruce, Donald ; Tuttle, M.H. ; Garrison, Charles B. 等

I. INTRODUCTION

The effects of tax policy at various points in the income distribution have received increased attention from politicians and researchers in recent years. Both major presidential candidates in the 2000 election proposed tax cuts that involved dramatically different distributional effects. Former Vice President Al Gore's plan included targeted tax cuts for the middle class; President George W Bush's plan provided a tax cut to all taxpayers regardless of their income. President Bush has been criticized for this plan, as it gives the largest tax break (at least in dollar value terms) to those at the upper end of the income distribution.

What has only recently been discussed, however, is the fact that the ultra-rich pay a much larger than proportionate share of federal income taxes. Feenberg and Poterba (2000) report that the top 0.5% of taxpayers with the largest income tax bills paid nearly one-fourth of all income taxes in 1995, a share that has increased dramatically since the early 1960s. The Joint Committee on Taxation (2001) reports that the top 1% of the income distribution will be responsible for nearly 36% of total individual income tax liability in 2001. In response to critics of his plan, President Bush's supporters have noted publicly that even though rich taxpayers would receive larger tax cuts in dollar value terms, they would contribute an even larger share of total income tax collections after his reform.

Although there is little controversy over the importance of ultra-rich taxpayers to the tax system, researchers have not reached a clear consensus as to how they react to changes in tax rates. President Bush's supporters imply that wealthy taxpayers respond to tax rate cuts by reporting more adjusted gross income (AGI), either by working more and earning more money, by reaping the benefits of a more prosperous economy, by shifting earnings into lower-tax years, or by reducing noncompliance, among other possibilities. It is not clear which (if any) of these explanations is most relevant. No consensus has arisen, primarily because this largely empirical question has not received significant attention in the literature.

Our research is a direct extension of the recent literature on the responsiveness of reported AGI to changes in top federal income and capital gains tax rates. We address these issues in a time-series econometric framework, first by using more recent data to reexamine earlier time-series results and second by departing from earlier research and implementing a vector autore-gression (VAR) technique. Results indicate that tax rate changes are responsible for much of the cyclical movements in the share of AGI that is reported by the top 0.5% of the AGI distribution but that macroeconomic conditions are at least as important. Our baseline results show that a 10% cut in the top federal marginal income tax rate would increase the top AGI share by only 2.7% to 3.1%, and a similar cut in the top capital gains tax rate would increase it by 4% to 5%.

Section II of the article discusses the motivation for our research and describes previous findings. We continue in section III with a description of our data and empirical methods, and present time-series regression results in section IV Section V includes simulations from those regressions. We discuss an alternative estimation strategy based on VAR techniques in section VI, and section VII concludes.

II. BACKGROUND AND LITERATURE REVIEW

Initiating the most recent wave of research on this topic, Feenberg and Poterba (1993) examine data from 1951 to 1990and reveal a substantial increase in the share of AGI that is reported on very high income tax returns. They conclude that this is at least partly a result of tax code changes and not a result of increased capital gains. Furthermore, they note that it is impossible to determine how much of the increase in reported income is due to different avoidance behavior, to changes in behavior (labor supply), or to changes in returns to the factors (labor and capital) that high-income taxpayers own.

Slemrod (1996) continues the dialog by noting that causes of increased inequality include skill-biased technological change, globalization, and tax changes (which might induce income creation or income shifting). Although nontax demand factors can explain much of the increased income concentration before 1985, they are not likely to be the cause of the increased concentration after the Tax Reform Act of 1986 (TRA86). Unlike Feenberg and Poterba, Slemrod uses a consistent definition of AGI over time (adjusted for the different treatment of capital gains in the time-series data). He also considers capital gains and corporate income tax rates, and his time-series regressions indicate that TRA86 is likely to be an important cause of the increased AGI concentration. However, much of it represents income shifting into lower-tax years rather than real income creation.

Goolsbee (1999) finds that the responsiveness of high-income people to tax changes is relatively modest in all time periods except the 1980s. In his analysis of a long history of tax reforms, he notes that evidence from the 1980s is not indicative of overall effects-it is the outlier decade. High elasticities around 1986 are probably biased upward due to other economic effects, most notably the increase in income inequality during the same time. Elasticity estimates from other historical tax rate changes are much smaller, though still positive. The true elasticity is probably nonzero but smaller than the 1986 estimates in the literature.

Feenberg and Poterba (2000) provide an update of the descriptive analysis from their earlier (1993) paper, including data for 1991 through 1995 and a standardized definition of AGI (as in Slemrod, 1996). In this newer article, they claim that income retiming does not explain most of the increased concentration post-TRA86 but that it is evident.

An important related issue is the ability of high-income taxpayers to shift income between the corporate and personal income tax system. As shown by Gordon and Slemrod (1998), an increase in corporate tax rates relative to personal income tax rates leads to more reported personal income and less reported corporate income, even after controlling for the use of debt financing and the level of corporate assets. However, given limited statutory changes over time to the top corporate income tax rate, controlling for this is extremely difficult in empirical work (see Slemrod, 1996).

In a similar vein, Goolsbee (2000a, 2000b) uses panel data on executive compensation to show how the line between wage and capital income has been blurred. Better stock performance increases ordinary income due to use of stock options, and stock options enhance the ability to retime income reporting, thereby overstating responsiveness to tax changes in the short run. Changing capital gains tax rates can affect options and timing of ordinary income (as executives exercise options early so that future gains are taxed as capital gains instead of ordinary income).

As an example of this, Goolsbee (2000b) finds that the higher marginal tax rates of 1993 led to a significant decline in taxable income of CEOs, and estimates that the tax rate elasticity of taxable income lies between 0 and 0.4. This is concluded to be almost entirely a short-run shift in the timing of executive compensation, however, driven mainly by the exercising of stock options in 1992. With this, Goolsbee mentions the need to include future tax rates in regressions to control for anticipation effects of tax changes. He also reveals the possibility that this group of CEOs may not be representative of the population of ultra-rich taxpayers, a point that is echoed by Feenberg and Poterba (2000).

All of these authors would probably agree that some tax rate responsiveness is evident, but they are not in agreement as to the relative importance of statutory rate changes to movements in the top AGI share. Slemrod and Goolsbee would likely expect to find a small elasticity of the top AGI share with respect to tax rates after controlling for other factors that influence the timing of reported taxable income. Feenberg and Poterba would seem to agree to a certain extent but would place more importance on a true behavioral response to tax rate changes. Again, the available empirical evidence has been largely inconclusive.

The goal of our research is to gather more data and use slightly varied methods to address these issues. We place relatively more emphasis on the comparative manner in which taxes and general macroeconomic conditions influence the top AGI share. Nonetheless, our analysis sheds some light on the issues of income shifting and overall revenue effects at the top end of the income distribution.

III. DATA AND EMPIRICAL METHODOLOGY

Our primary data sources are the St. Louis Federal Reserve Bank database (Federal Reserve Bank of St. Louis, 2000) and published tables in the Economic Report of the President (Council of Economic Advisors, 2000). We supplement annual data for 1960 through 1997 from these sources with the share of total AGI that is reported by the top 0.5% of the AGI distribution (hereafter top AGI share), as calculated by Feenberg and Poterba (2000).(1) We add a 1997 value to their series by using published data in Internal Revenue Service Statistics of Income Bulletins (Internal Revenue Service, 2000) to replicate their method.(2) Furthermore we use interpolation to fill in missing top AGI share data during the 1960s. All series are reported in Appendix Tables 1 and 2.

The top AGI share series uses a constant definition of AGI over time, as noted by Slemrod (1996). Figure 1 shows the trend in the top AGI share since 1960. As documented previously by Feenberg and Poterba (2000), the top AGI share was fairly stable (and actually declined by a small amount) during the 1960s and 1970s. It increased dramatically during the 1980s and, after hitting a plateau in the early 1990s, has begun to rise again. Of course, many factors may have contributed to this trend, including changes in tax rates.

To address this possibility, Figure 2 displays trends in the top federal personal income tax rate over this same time period. Despite increases in the late 1960s and early 1990s, the top rate has trended downward since 1960. Figure 3 shows a more inconsistent trend in the top capital gains tax rate. Although it has not undergone as many changes over time, those changes have been substantial. An increase of 15 percentage points during the 1970s was more than reversed during the late 1970s and early 1980s. An increase in 1987 was later erased in 1997.

Little can be gained from these figures regarding the independent effects of taxes on the top AGI share other than the apparent inverse relationship between the top income tax rate and the AGI share. There does not appear to be a strong, identifiable relationship between the AGI share and the capital gains tax rate. A multivariate statistical approach is necessary to more carefully assess any possible relationships.

Our first econometric approach builds on the methods of Slemrod (1996) by estimating ordinary least squares (OLS) time-series regressions of the top AGI share on a number of explanatory variables. Our specification mirrors Slemrod's with a few exceptions. Most important, we are able to add several years' data to the regression. We are, however, unable to include his measure of wage inequality (which, incidentally, was not statistically significant in his regressions). (3) Though this raises the possibility of omitted variable bias, our baseline results are very similar to Slemrod's (1996) as will be shown.

To allow comparison of our results with the earlier findings, we include both the top income and capital gains tax rates, as well as lead and lag differences in both tax rates, in our baseline specification. (4) This enables the interpretation of the coefficients on the tax rates themselves as above and beyond any anticipatory or reactionary effects (which are captured in the lead and lag difference variables). We also include the average corporate AAA bond rate and a real measure of the Standard & Poor 500 stock index. These two variables are intended to capture forces that affect incentives to report interest and capital gains, respectively. A constant and a linear time trend are included to account for other effects and the upward trend of some variables. Finally, the real gross domestic product (GDP) growth rate is also included to relate any macroeconomic effects from changes in aggregate income on adjusted gross income.

IV. TIME-SERIES REGRESSION RESULTS

Results from our baseline specification are largely similar to Slemrod's and are shown in Table 1. (5) We estimate the regression for three time periods: 1960-85 to get at the pre-TRA86 effects, 1960-90 to examine the impact of TRA86, and 1960-97 to include the effects of the 1990s tax rate changes. It is interesting that the most prominent tax effect comes from the capital gains rate. Increases in the capital gains rate lead to reductions in the AGI share above and beyond reactions to previous changes or anticipatory effects of future changes. The effect is largely unchanged across the three time periods and is certainly driven by the fact that our AGI share measure includes realized capital gains. Realizing accrued capital gains is perhaps one of the simplest ways these taxpayers can change their reported income amounts.

The personal income tax rate exhibits a similar yet smaller influence, but only when the later years are added. In the 1960-85 regression, the primary effect of the income tax was from anticipatory effects of rate changes. As rates were slated to fall in the next year, the AGI share fell in the current year, reflecting the shifting of earned income into the lower-tax year. None of the income tax effects are statistically significant in the 1960-90 regression. Furthermore, for 1960- 97, the negative and statistically significant coefficient on the current-year income tax rate is only slightly more than one-fourth the size of the capital gains rate coefficient (-0.039 compared with -0.144, respectively). (6)

The average corporate AAA bond rate exerts a consistently large and negative influence on the AGI share in all three regressions. One possible explanation for this result is that increases in the AAA rate might signal reduced returns in equity markets, leading taxpayers to realize fewer capital gains and report less income overall. The other controls in Table 1 have no statistically significant effect (with the exception of the time trend, which has the expected positive sign).

Fullerton's (1996) comments on Slemrod's (1996) work suggest that omitted variable bias may be an important consideration in the regression analysis. Among those factors that Fullerton recommends are the extent of computerization in the workplace, the import share of GDP, and the fraction of youth that is college-educated. Such added variables are potentially necessary to identify the independent effects of tax rates on reported AGI shares. We augment our baseline 1960-97 specification with additional variables to investigate the extent of omitted variable bias, and Table 2 presents the findings from this experiment.

Our first additional variable is a measure of worker productivity (see column 1 of Table 2), which may lead to increased profits and increased income reporting at the top end of the AGI distribution. We also examine the importance of globalization by adding (separately, in column 2) the international share of GDP, defined here as the sum of imports and exports divided by GDP. A third and final added variable is the percentage of the population with a college degree, intended to capture the increasing returns to schooling over time (column 3). (7) Each of these three variables may have an impact on movements in the top AGI share above and beyond changes in tax rates. As observed in Table 2, these additional variables have very little if any impact on our overall findings. Though the variables themselves are somewhat statistically significant, the tax rate coefficients are apparently not biased as a result of leaving them out.

Another important issue raised by Fullerton (1996) is that the tax rate variables do not fully capture other elements of the tax system, especially those that change as a result of major tax reforms. Econometrically speaking, TRA86 might have resulted in a structural change in the tax rate coefficients. To investigate this possibility, we create a dummy variable for the years 1987 and beyond and insert it in our baseline specification; we also interact it with all six of our tax rate variables. With the exception of the interactions of the post-1986 dummy with the lag differences of the income and capital gains tax rates, none of the new variables are individually or jointly statistically significant. More important, the inclusion of these variables does not alter the general findings from our baseline specification. (8)

To gain a better feel for the economic significance of our regression results, Table 3 presents estimated elasticities of the AGI share with respect to our tax rate variables. Our results for the top marginal income tax rate are in line with Slemrod (1996) and Goolsbee (2000b). Specifically, given our income tax rate elasticities of -0.27 to -0.31, cutting the top marginal personal income tax rate by 10% would increase the share of AGI reported by the top 0.5% of all taxpayers by only about 2.7% to 3.1%. Cutting the capital gains tax rate by 10% would have a larger effect; it would increase the top AGI share by about 4% to 5% (elasticities range from -0.41 to -0.51). Given our estimate of the top AGI share in 1997 of 12.75%, these policy changes would increase it to about 13.1% and 13.26%, respectively.

Does this increase in reported AGI share translate into an increase in the share of income taxes paid? To investigate this, we repeat our baseline regression using the share of total taxes paid as our dependent variable. As a further check, we use the tax share variable with and without capital gains taxes included. As with the top AGI share data, the source for these two data series is Feenberg and Poterba (2000). However, these data are only available for 1962 through 1995.

Results in Table 4 indicate that the top capital gains tax rate has a very similar effect on the share of taxes paid, regardless of whether or not capital gains taxes are included in the dependent variable. The corresponding tax share elasticities with respect to the capital gains tax rate are -0.284 for the specification that includes capital gains and -0.269 for the other. The top marginal income tax rate effects are very small and are not measured with a high degree of statistical precision. In other words, changes in the top marginal income tax rate are not likely to have quantitatively important effects on the share of total taxes paid by the top 0.5% of the income distribution. (9) A similar statement in the presence of changes in other tax rates below the maximum (as in President Bush's plan) is beyond the scope of this analysis.

V. SIMULATIONS

We have not yet addressed the relative importance of tax rate changes and other factors in explaining historical movements in the top AGI share during and after major tax reforms. This notion of relative importance has been the primary focus of the recent debate in the literature. Are movements in the top AGI share primarily real responses to tax rate changes, or are they mainly responses to other contemporaneous macroeconomic conditions?

To investigate this issue, we implement a forecasting strategy that estimates the baseline specification of the regressions in Table 1 from 1960 through two years prior to a major tax reform. We use these results to estimate the percentage change in the top AGI share from one year prior to a major reform to one year after in the absence of the actual tax changes (but given changes in the other variables). We then compare this predicted percentage change with the actual percentage change in the AGI share and attribute the difference to the tax reform.

Beginning with TRA86, note that the actual top AGI share in 1987 returned to the 1985 value after a spike upward in 1986. Our statistical model, however, forecasts an increase in the top AGI share in the absence of the tax reform (holding both tax rates constant) but in the presence of prevailing economic conditions. The expected increase would have been from 9.16 in 1985 to 9.65 in 1987, an increase of just over 5%. The negative effect of the capital gains rate increase in 1987 appears to have more than offset the positive stimulus of the 1986 income tax rate reduction and other macroeconomic factors.

We estimate our statistical model through 1989 to assess the relative impacts of these factors as a result of the 1991 tax changes. The actual top AGI share increased from 10.75 in 1990 to 11.05 in 1992 (an increase of about 3%). Minus any tax rate changes, we would have expected an increase of about 6.9%, from 11.32 in 1990 to 12.1 in 1992. In other words, the 1991 tax changes apparently reduced the percentage increase in the top AGI share by more than one-half.

Repeating this analysis for the 1993 tax changes, we note first that the actual change in the top AGI share from 1992 to 1994 was a reduction of about 3.2%, from 11.05% to 10.70%. If both tax rates remained unchanged, we would have expected an increase in the top AGI share of 2.6% (from 11.28% to 11.57%). Again, the tax changes during this time more than offset the stimulus from the thriving economy of the early 1990s.

These simple forecasting exercises, illustrative at best, reveal an important theme: tax rate changes have important effects on the share of AGI that is reported by the top taxpayers. Economic conditions also play a large role, but taxes can often exert a more dominant influence. To be sure, much of this response may reflect income shifting or retiming, which the present simulations only partially capture. Identifying long-term effects requires a more general approach, to which we now turn.

VI. VAR-BASED ANALYSIS

The shortcomings of OLS regression in a time-series framework are by now well established. Of particular interest to this study is the lingering possibility that our regressions have not fully captured the potential endogeneity of tax rates, which may lead to dubious OLS estimates. Specifically, tax rate changes may be enacted as a result of changes in the top AGI share. Additionally, the effects of tax changes on AGI share may extend beyond the three-year window built into our baseline specification (current values with one-year lag and lead differences). With these issues in mind, we now present a more general analysis that is based on VAR.

Researchers have long recognized the power of VARs in forecasting macroeconomic time series. The VAR approach offers a number of advantages and disadvantages. (10) First, the VAR approach is something of a theory-free approach. All series in the model are permitted to be endogenous, and each is affected by the current values and lags of all variables in the system. Furthermore, given the usual difficulty of finding proper instruments, one VAR strength is its ability to deal with endogeneity concerns.

The VAR certainly carries with it a number of disadvantages, however. First, it removes our ability to estimate lead (i.e., anticipatory) effects of tax rates on the AGI share. Second, VARs are not able to properly handle cointegrated or nonstationary data. To address this issue, a vector error correction model (VECM) is employed because most of the data in the sample period are nonstationary and also share long-run relationships. However, VECM results are often sensitive to the ordering of the variables in the system; therefore we examine the robustness of our findings to a number of different ordering schemes in the analysis that follows. Finally, behavioral attributes, such as the elasticities obtained from earlier OLS estimates, are not obtainable. As an added advantage, though, the use of VECMs can dramatically improve the efficiency of the estimates. (11)

Perhaps the greatest advantage of the VECM approach in our framework is the ability to more cleanly assess the combined short-run and long-run effects of a shock to one variable in the system on all other variables in the system. For example, the VECM allows us to examine the effects of tax rate changes on all other variables, including the top AGI share, over time. We focus on forecast error variance decomposition (FEVD) results that reveal the relative power of shocks to each variable in explaining the total variance of the top AGI share.

As previously mentioned, results are sensitive to the ordering of variables. Several VECM orderings are estimated, and FEVD results appear in Table 5, as discussed in the Appendix. The capital gains and marginal income tax rates are assumed to drive changes in real GDP (12) the corporate AAA rate, and the AGI share and are placed first in the orderings. Variables that are first in any ordering will not be affected by contemporaneous shocks to any of the other variables. Variables placed further down in the ordering will be affected by contemporaneous shocks to variables that enter before it, but not by those further down in the ordering. Thus, the AGI share is placed after the tax rates in all orderings, since the primary contention here is that tax rates have contemporaneous and lagged effects on reporting behavior. In all estimates, the income and capital gains tax rates are always first and second, but they are moved between the two positions as robustness checks.

The baseline ordering (panel A of Table 5) places real GDP before the AGI share. Our rationale is that changes in real GDP will have intraperiod effects on AGI share as owners of capital experience changes in profitability. AGI share will then have interperiod effects through public savings, wealth, and consumption. Panel B reverses the ordering of tax rates. This reversal will not alter the effect of real output on AGI share but will change the effect of tax rates. When the corporate AAA rate replaces real GDP, the corporate AAA rate comes before AGI share in the ordering. Any changes in rates of return or interest income this period will affect AGI in the same period.

Table 5 presents FEVD estimates from a number of ordering schemes. The entries for all panels represent the percentage of the variance of the top AGI share that is accounted for by a one-standard-deviation change (or shock) in each of the variables. One theme is apparent in panels A and B. The economic significance of the tax rate elasticities from the time-series regressions is supported by the FEVD results. Specifically, a shock to the top capital gains tax rate explains approximately 25% of the variation in AGI share after five years. The results also support the relative insignificance of the top marginal income tax rate in the full-period baseline model, as it explains about one-2Oth of the variation in AGI share over the same period. Furthermore, the effects of the tax rates on the top AGI share are not limited to the first year or two after a tax rate shock-- tax rate changes continue to have lasting impacts beyond the short-term shifting effects found in earlier research.

When we allow AGI share to respond contemporaneously (panels A and B), real GDP has a sizable effect. When the ordering is changed to allow the AGI share to respond with a lag (panel C), the importance of real GDP is severely diminished. Its ability to explain variations in AGI shares falls by more than one-half, from around 54% to practically 26%.

We now turn to panel D of Table 5, where the corporate AAA rate replaces real GDP in our baseline ordering. Again, the results support the tax rate effects from the regression estimates. The importance of the capital gains rate has increased, and in this specification explains nearly three-fourths of the variation in the AGI share after five years. Also, the ability of shocks to the income tax rate to explain AGI variation remains economically insignificant. At most, innovations in the top marginal rate account for just over 2% of the variation over the same five-year period. The corporate AAA rate explains only a small amount of the variation in the AGI share, though. This contradicts the earlier regression estimates that found the AAA rate to be an economically and statistically significant determinant of the top AGI share.

Next, we turn to the impulse response functions (IRFs) from the four VECMs. IRFs show the current and future effects on the top AGI share of a one-standard-deviation shock in each of the other variables. Although the FEVD results tell how much explanatory power each variable has for the innovations of a specific variable, the IRFs provide a visual clue as to the directional response of the AGI share.

Figures 4, 5, 6, and 7 display the results of our IRF analysis. As predicted by the regression estimates, the capital gains rate generally has a negative effect on the AGI share and real GDP has a positive effect. The economically insignificant results for the top marginal income tax rate from the FEVD are supported in these figures. Its effect after five years is practically zero. Also, the AGI share has a positive effect on itself.

Figure 7 presents IRFs for the fourth ordering, where the corporate AAA rate replaces real GDP. Recall that the income tax rate explained less than 5% of the variation in AGI share in this specification. The IRFs reveal that the income tax rate has generally no effect on the AGI share. As with the regression findings, the capital gains rate and the corporate AAA rate have negative impacts on the AGI share.

To summarize the VECM analysis, real GDP appears to be the main determinant of AGI share for the top 0.5%. The top capital gains tax rate is also very important, but the income tax rate plays a small role (if any at all). Real GDP explains slightly more than half of the variation in AGI share when the AGI share is allowed to vary contemporaneously. The top capital gains tax rate explains slightly more than one-fourth of the variation in the top AGI share. Finally, our measure of interest rates plays a small role, but it is more important than the top federal marginal income tax rate.

VII. CONCLUSIONS

It appears that tax rates are quite important in explaining movements over time in the share of national AGI that is reported by the top 0.5% of all taxpayers. Our time-series regression analysis suggests that taxes and macroeconomic conditions both play important roles in explaining the top AGI share. However, the top capital gains tax rate is more important than the top marginal income tax rate. Specifically, cutting the top marginal personal income tax rate by 10% would increase the top AGI share by only about 2.7% to 3.1%, whereas cutting the capital gains tax rate by 10% would increase it by about 4% to 5%.

These changes, though statistically significant and economically important, are quantitatively quite small. In fact, our preferred estimates of the elasticities of the top AGI share with respect to income and capital gains tax rates are -0.27 and -0.48, respectively. Simulations of major tax reforms shed additional light on the importance of these effects and suggest that statutory tax rate changes have important effects on the top AGI share. Beginning with TRA86, the actual top AGI share was the same in 1987 as it was in 1985, but our forecast in the absence of tax rate changes would have been an increase of just over 5%. Tax rate effects were exactly offset by other factors. Regarding the 1991 tax rate changes, the actual top AGI share increased by about 3% between 1990 and 1992, but according to our results, it would have increased by about 6.9% if tax rates remained constant. Finally, our analysis of the 1993 tax rate changes indicates that the top AGI share, which fell by about 3.2% from 1992 to 1994, wo uld have actually increased by about 2.6% over this period without changes in tax rates.

The possibility remains that a time-series regression approach is inappropriate, however, due primarily to questions of stationarity and tax rate endogeneity. Results from VECMs echo the regression results and indicate that tax rates have substantial effects on immediate changes in the top AGI share but that macroeconomic swings have even larger effects. Again, the top capital gains tax rate is far more important than the top marginal income tax rate in explaining movements in the top AGI share. Even if they are only the result of income shifting or other timing effects, transitory movements in the top AGI share are at least partially driven by tax rate changes.

APPENDIX: VECM METHODOLOGY AND INTERMEDIATE RESULTS

We begin by using likelihood ratio tests to determine the appropriate lag length, such that our estimated model residuals are void of significant autocorrelation (Charemza and Deadman, 1995). The test results for VARs of various lag lengths are shown in Table A3, and indicate that the optimal lag length is 3 for both specifications. However, an analysis of these results in conjunction with estimated residuals suggests that the optimal lag length for models containing real GDP should instead be 5.

Finally, we use Johansen tests to determine whether cointegration exists between the variables and, if it does, the appropriate number of cointegrating equations for the VECMs. The cointegrating equation(s) is used to ensure stationarity of all variables in the model while maintaining the long-run relationships that may exist, because differencing the data can destroy these relationships. Note that (nonstationary) real GDP is substituted for (stationary) real GDP growth. This is acceptable in the Johansen procedure, but it adds an additional cointegrating restriction in the VECM. The additional cointegrating vector is not due to the existence of an additional long-run relationship, nor does it provide any additional information. Using real GDP in levels allows us to include the effects of aggregate income, while possibly reducing the number of econometric restrictions. Table A5 gives the results of the Johansen tests, which suggest that we cannot reject the null hypothesis of two cointegrating equations in t he presence of the real GDP and two when using the corporate AAA bond rate.

We then use augmented Dickey-Fuller tests with one lag to determine whether stationarity exists in the variables. Results, shown in Table A4, indicate that we fail to reject the null hypothesis of a unit root for all variables. Stationarity exists when first differences are taken. Therefore, all variables are integrated of order one.

TABLE A1

Time-Series Data

 Share of taxes Total taxes
 Top AGI Share of paid, less paid
Year share taxes paid capital gains ($billions) T(t) C(t)

1960 7.55 -- -- -- 91.00 25.00
1961 7.50 -- -- -- 91.00 25.00
1962 7.07 16.0 15.4 7.46 91.00 25.00
1963 6.79 17.3 16.7 8.52 91.00 25.00
1964 7.64 17.9 17.1 8.23 77.00 25.00
1965 7.50 16.9 16.2 8.60 70.00 25.00
1966 7.28 16.9 16.2 9.92 70.00 25.00
1967 7.70 17.5 17.7 11.27 70.00 25.00
1968 8.11 17.5 16.4 13.39 75.30 26.90
1969 7.41 15.6 14.7 14.32 77.00 27.50
1970 6.36 14.2 13.8 12.62 71.80 32.21
1971 6.67 15 14.5 12.89 70.00 34.25
1972 6.81 15.1 14.4 15.54 70.00 36.50
1973 6.35 13.9 13.4 15.25 70.00 36.50
1974 6.28 14.3 14 18.10 70.00 36.50
1975 6.18 14.5 14.3 17.53 70.00 36.50
1976 6.10 14.4 14.3 20.36 70.00 39.88
1977 6.26 14.5 14.2 23.53 70.00 39.88
1978 6.19 13.9 13.7 26.28 70.00 39.88
1979 7.03 14.8 14.5 33.27 70.00 28.00
1980 7.00 14.2 13.9 35.53 70.00 28.00
1981 7.18 13.3 13.1 38.68 69.10 20.00
1982 7.83 14.5 14.2 42.88 50.00 20.00
1983 9.62 15.6 15.4 44.80 50.00 20.00
1984 8.79 16.7 16 50.52 50.00 20.00
1985 9.34 17.3 16.5 58.34 50.00 20.00
1986 12.19 20.3 18.3 71.33 50.00 20.00
1987 9.34 19.5 18.1 76.93 38.50 28.00
1988 11.92 22.1 20.6 89.66 28.00 28.00
1989 10.90 19.7 18.5 89.56 28.00 28.00
1990 10.75 19.7 18.8 93.30 28.00 28.00
1991 10.53 20.5 19.7 95.37 28.00 28.93
1992 11.05 21.9 21.1 104.99 31.00 28.93
1993 10.63 23.3 22.4 118.81 39.60 29.19
1994 10.70 23 22 125.99 39.60 29.19
1995 11.30 24.2 23 143.22 39.60 29.19
1996 12.10 -- -- -- 39.60 29.19
1997 12.75 -- -- -- 39.60 20.00


 Corporate Real GDP Real S&P
Year AAA rate growth 500

1960 4.41 0.59 256.50
1961 4.35 6.27 301.03
1962 4.33 4.12 279.53
1963 4.26 5.23 309.62
1964 4.41 5.11 355.29
1965 4.49 8.48 377.94
1966 5.13 4.42 355.30
1967 5.51 2.35 371.62
1968 6.18 4.97 382.56
1969 7.03 1.92 361.39
1970 8.04 -0.14 291.87
1971 7.39 4.41 328.23
1972 7.21 7.16 349.79
1973 7.44 4.02 325.84
1974 8.57 -2.15 230.52
1975 8.83 2.59 219.39
1976 8.43 4.56 245.78
1977 8.02 5.02 222.33
1978 8.73 6.55 203.00
1979 9.63 1.37 200.94
1980 11.94 -0.12 212.20
1981 14.17 1.23 209.24
1982 13.79 -1.63 184.13
1983 12.04 7.55 237.40
1984 12.71 5.60 228.93
1985 11.37 3.99 258.41
1986 9.02 2.82 319.81
1987 9.38 4.44 376.84
1988 9.71 3.70 337.73
1989 9.26 2.60 395.12
1990 9.32 0.46 394.12
1991 8.77 0.85 427.60
1992 8.14 4.01 461.34
1993 7.22 2.55 489.17
1994 7.96 4.08 488.75
1995 7.59 2.16 562.77
1996 7.37 4.06 683.34
1997 7.26 6.05 873.43

Source: The top AGI share and both of the share of taxes paid series are
based on Feenberg and Poterba (2000). The total taxes paid series, which
is the total for the top 0.5% of the income distribution, is calculated
using the share of taxes paid (including capital gains) and national
total income tax values from IRS-SOI bulletins. All other series are
drawn from the Federal Reserve Bank of St. Louis (2000) and the 2000
Economic Report of the President (Council of Economic Advisors, 2000).
See the text for details.

TABLE A2

Descriptive Statistics

 Top AGI Real GDP Real S&P Corporate
 share T(t) C(t) growth 500 AAA rate

Mean 8.49 59.83 28.13 3.40 344.96 8.14
Median 7.59 70.00 28.00 4.01 327.03 8.03
Maximum 12.75 91.00 39.88 8.47 873.43 14.17
Minimum 6.10 28.00 20.00 -2.14 184.13 4.25
SD 2.06 19.56 5.92 2.43 139.6 2.60

 Labor
 productivity Schooling

Mean 79.35 15.74
Median 80.62 16.05
Maximum 107.35 23.90
Minimum 48.65 7.70
SD 16.52 5.11

TABLE A3

Likelihood Ratio Test Results

 C(t), T(t), real GDP, C(t), T(t), corporate
 AGI share likelihood AAA rate, AGI share
Lag length ratio test likelihood ratio test

1 230.26 167.15
2 28.93 26.73
3 32.26 * 30.38 *
4 16.89 17.79
5 21.00 20.72
6 10.05 23.33

* Optimal lag length as suggested by the tests.

TABLE A4

Augmented Dickey-Fuller Test Results

Variable Test statistic 5% critical value

Top AGI share 1.505 -1.950
T(t) -1.691 -1.950
C(t) -0.555 -1.950
Real GDP 3.881 -1.950
Corporate AAA rate -0.186 -1.950

TABLE A5

Johansen Test Results


Eigenvalue Trace statistic 5% critical value

A: Capital gains rate, income tax
 rate, real GDP, AGI share

0.850 106.456 54.64
0.679 39.574 34.55
0.384 13.016 18.17
0.094 0.909 3.74

B: Capital gains rate, income tax
 rate, corporate AAA rate, AGI
 share

0.750 86.966 54.64
0.523 39.774 34.55
0.347 14.561 18.17
0.001 0.0503 3.74

 Hypothesized number of
Eigenvalue cointegrating equations

A: Capital gains rate, income tax
 rate, real GDP, AGI share

0.850 None
0.679 At most 1
0.384 At most 2
0.094 At most 3

B: Capital gains rate, income tax
 rate, corporate AAA rate, AGI
 share

0.750 None
0.523 At most 1
0.347 At most 2
0.001 At most 3

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

TABLE 1

Baseline Regression Results

 1960-85 1960-90

Variable Coefficient SE Coefficient

T(t) 0.005 0.039 -0.032
T(t + 1) - T(t) 0.038 0.015 0.004
T(t) - T(t - 1) 0.017 0.030 0.023
C(t) -0.141 0.012 -0.154
C(t + 1) - C(t) 0.020 0.022 0.038
C(t) - C(t - 1) 0.054 0.022 0.034
Corp. AAA bond rate -0.146 0.063 -0.491
Real S&P 500 index 0.001 0.003 -0.002
Real GDP growth 0.051 0.031 -0.006
Time trend 0.104 0.079 0.178
Constant 10.377 4.193 16.102
Adj. [R.sup.2] 0.870

 1960-90 1960-97

Variable SE Coefficient SE

T(t) 0.048 -0.039 0.021
T(t + 1) - T(t) 0.029 -0.006 0.019
T(t) - T(t - 1) 0.026 0.012 0.018
C(t) 0.018 -0.144 0.016
C(t + 1) - C(t) 0.041 0.017 0.039
C(t) - C(t - 1) 0.054 0.024 0.047
Corp. AAA bond rate 0.094 -0.379 0.105
Real S&P 500 index 0.004 -0.001 0.002
Real GDP growth 0.029 0.010 0.029
Time trend 0.084 0.131 0.041
Constant 5.716 15.563 2.327
Adj. [R.sup.2] 0.869 0.913

Notes: Entries are OLS coefficients and Newey-West standard errors. T(t)
and C(t) represent, respectively, the top marginal federal income and
capital gains tax rates in year t.

TABLE 2

Extensions to the Baseline Specification, 1960-97

 (1) (2)

Variable Coefficient SE Coefficient

T(t) -0.039 0.020 -0.044
T(t + 1)- T(t) -0.007 0.019 -0.003
T(t) - T(t -1) 0.014 0.020 0.021
C(t) -0.135 0.032 -0.149
C(t + 1) - C(t) 0.023 0.040 0.050
C(t) - C(t - 1) 0.022 0.044 0.061
Corp. AAA bond rate -0.361 0.134 -0.392
Real S&P 500 index 0.000 0.002 0.000
Real GDP growth 0.020 0.035 0.035
Time trend 0.183 0.172 0.047
Constant 17.015 4.584 14.844
Productivity -0.037 0.120
Globalization 0.561
Schooling
Adj. [R.sup.2] 0.910

 (2) (3)

Variable SE Coefficient SE

T(t) 0.019 -0.040 0.017
T(t + 1)- T(t) 0.018 -0.007 0.019
T(t) - T(t -1) 0.014 0.014 0.019
C(t) 0.016 -0.122 0.023
C(t + 1) - C(t) 0.049 0.035 0.042
C(t) - C(t - 1) 0.047 0.028 0.047
Corp. AAA bond rate 0.108 -0.336 0.120
Real S&P 500 mdcx 0.002 0.001 0.002
Real GDP growth 0.033 -0.002 0.032
Time trend 0.065 -0.054 0.141
Constant 2.216 11.991 4.227
Productivity
Globalization 0.329
Schooling 0.370 0.275
Adj. [R.sup.2] 0.915 0.914

Notes: Entries are OLS coefficients and Newey-West standard errors. T(t)
and C(t) represent, respectively, the top marginal federal income and
capital gains tax rates in year t.

TABLE 3

Tax Rate Elasticities

 Baseline Baseline Baseline Productivity
Variable 1960-85 1960-90 1960-97 1960-97

T(t) 0.038 -0.228 -0.272 -0.274
T(t + 1) - T(t) -0.006 -0.001 0.001 0.001
T(t) - T(t - 1) -0.003 -0.004 -0.002 -0.002
C(t) -0.467 -0.510 -0.479 -0.448
C(t + 1) - C(t) 0.000 -0.001 0.000 0.000
C(t) - C(t - 1) -0.001 -0.001 0.000 0.000

 Globalization Schooling
Variable 1960-97 1960-97

T(t) -0.310 -0.282
T(t + 1) - T(t) 0.001 0.001
T(t) - T(t - 1) -0.003 -0.002
C(t) -0.493 -0.406
C(t + 1) - C(t) -0.001 -0.001
C(t) - C(t - 1) -0.001 0.000

Notes: T(t) and C(t) represent, the top marginal federal income and
capital gains tax rates in year t. Bold represents significance at the
5% level. Italics represent significance at the 10% level.

TABLE 4

Time-Series Regressions with Tax Shares

 Tax Share Including Tax Share
 Excluding
 Full Capital Gains Full Capital
 Gains
 1962-95 1962-95

Variable Coefficient SE Coefficient

T(t) -0.005 0.028 0.005
T(t + 1) - T(t) -0.004 0.022 0.027
T(t) - T(t - 1) -0.038 0.038 -0.037
C(t) -0.172 0.023 -0.156
C(t + 1) - C(t) 0.006 0.026 -0.018
C(t) - C(t - 1) 0.047 0.060 0.019
Corp. AAA bond rate -0.950 0.093 -0.841
Real S&P 500 index 0.004 0.002 0.004
Real GDP growth -0.012 0.055 -0.024
Time trend 0.308 0.043 0.284
Constant 23.171 2.600 20.914
Adj. [R.sup.2] 0.935

 Tax Share Excluding
 Full Capital Gains
 1962-95

Variable SE

T(t) 0.024
T(t + 1) - T(t) 0.033
T(t) - T(t - 1) 0.033
C(t) 0.028
C(t + 1) - C(t) 0.038
C(t) - C(t - 1) 0.059
Corp. AAA bond rate 0.128
Real S&P 500 index 0.003
Real GDP growth 0.050
Time trend 0.053
Constant 2.378
Adj. [R.sup.2] 0.926

Notes: Entries are OLS coefficients and Newey-West standard errors. T(t)
and C(t) represent, respectively, the top marginal federal income and
capital gains tax rates in year t.

TABLE 5

FEVD Results for the Top AGI Share


A: Ordering: C(t), T(t), real GDP,
 AGI share

Period C(t) T(t) Real GDP
1 18.447 1.393 25.199
2 13.886 1.484 41.247
3 18.731 1.138 41.751
4 16.578 7.397 52.061
5 24.267 5.129 54.376

B: Ordering: T(t), C(t), real GDP,
 AGI share

Period T(t) C(t) Real GDP
1 2.998 16.842 25.199
2 2.433 12.937 41.247
3 1.742 18.128 41.751
4 6.035 17.941 52.061
5 3.933 25.462 54.376

C: Ordering: C(t), T(t), AGI share,
 real GDP

Period C(t) T(t) AGI share
1 18.447 1.393 80.158
2 13.886 1.484 56.916
3 18.731 1.138 58.511
4 16.578 7.397 51.710
5 24.267 5.129 43.873

D: Ordering: C(t), T(t), Corporate
 AAA rate, AGI share

Period C(t) T(t) Corporate AAA rate
1 47.756 0.0483 1.853
2 37.637 0.437 13.958
3 53.452 0.348 10.722
4 60.513 3.627 10.622
5 72.547 2.246 6.586


A: Ordering: C(t), T(t), real GDP,
 AGI share

Period AGI share
1 54.959
2 43.381
3 38.377
4 23.962
5 16.227

B: Ordering: T(t), C(t), real GDP,
 AGI share

Period AGI share
1 54.959
2 43.381
3 38.377
4 23.962
5 16.227

C: Ordering: C(t), T(t), AGI share,
 real GDP

Period Real GDP
1 0.0000
2 27.712
3 21.617
4 24.313
5 26.730

D: Ordering: C(t), T(t), Corporate
 AAA rate, AGI share

Period AGI share
1 50.342
2 47.966
3 35.476
4 25.236
5 18.620

Notes: Entries represent the share of the variance in the top AGI share
that is caused by a one-standard-deviation shock to that particular
variable. T(t) and C(t) represent the top marginal federal income and
capital gains tax rates in year t.

(1.) This data series is available online at www.nber. org/~taxsim/.

(2.) A comparison of our estimates with those in Feenberg and Poterba (2000) yielded nearly identical top AGI shares.

(3.) Slemrod (1996) included this variable to account for nontax factors regarding the increased inequality in the return to labor in recent decades. We address some of these factors in the extensions to our baseline specification.

(4.) Many of the top 0.5% of the AGI distribution do not actually face the top marginal tax rate due to the alternative minimum tax or deduction/exemption phase-outs, but it strikes us that they are likely to respond more quickly to the top rate as an effective signaling mechanism. Furthermore, the measurement of an effective tax rate for this group would be difficult without micro data.

(5.) To allow for the possibility of autocorrelation, we present consistent standard errors using the method of Newey and West (1987).

(6.) It is somewhat surprising that these results are virtually unchanged in the absence of the lag and lead differences in the tax rate variables.

(7.) Our intent with this variable is to capture the increased return to schooling in the economy, but we recognize that it is a weak proxy. Nonetheless, it may have important implications for the top AGI share regressions and the extent of proxy bias appears to be minimal.

(8.) A full set of results from this exercise is available on request from the authors.

(9.) Though not the focus of this research, our time-series data permit an investigation of the related question of how tax rate changes affect total income tax receipts from the top 0.5%. A replication of our baseline regression using this as the dependent variable does not reveal statistically significant evidence of a high-income Laffer curve; cutting the top marginal income tax rate would not yield increases in tax revenue from this group.

(10.) For additional details, see Charemza and Dead-man (1997), Enders (1995), or Harris (1994).

(11.) Additional details and background statistics for our VECM approach are provided in the Appendix.

(12.) For econometric reasons detailed in the Appendix, real GDP in levels is used in place of the growth rate.

REFERENCES

Charemza, W. W., and D. F. Deadman. New Directions in Econometric Practice. 2nd ed. New York: Edward Elgar, 1997.

Council of Economic Advisors. Economic Report of the President. Washington, DC: U.S. Government Printing Office, 2000.

Enders, W. Applied Econometric Time Series. New York: Wiley, 1995.

Federal Reserve Bank of St. Louis. Federal Reserve Economic Data (FRED [R]). 2000. Available online at www.stls.frb.org/fred.

Feenberg, D. R., and J. M. Poterba. "Income Inequality and the Incomes of Very High-Income Taxpayers: Evidence from Tax Returns," in Tax Policy and the Economy Vol. 7, edited by J. Poterba. Cambridge, MA: MIT Press, 1993, 145-77.

_____. "The Income and Tax Share of Very High Income Households, 1960-1995." National Bureau of Economic Research Working Paper No. 7525, 2000.

Fullerton, D. "High-Income Families and the Tax Changes of the 1980s: The Anatomy of Behavioral Response--Comment," in Empirical Foundations of Household Taxation, edited by M. Feldstein and J. Poterba. Chicago: University of Chicago Press, 1996, 189-92.

Goolsbee, A. "Evidence on the High-Income Laffer Curve from Six Decades of Tax Reform." Brookings Papers on Economic Activity 2,1999, 1-47.

_____. "Taxes, High-Income Executives, and the Perils of Revenue Estimation in the New Economy." American Economic Review, 90(2), 2000a, 271-75.

_____. "What Happens When You Tax the Rich? Evidence from Executive Compensation." Journal of Political Economy, 108(2), 2000b, 352-78.

Gordon, R. H., and J. Slemrod. "Are 'Real' Reponses to Taxes Simply Income Shifting between Corporate and Personal Tax Bases?," in Does Atlas Shrug? The Economic Consequences of Taxing the Rich, edited by J. Slemrod. Cambridge, MA: Harvard University Press, 1998, 240-80.

Harris, R. Using Cointegration Analysis in Econometric Modeling. London: Prentice Hall, 1994.

Internal Revenue Service Statistics of Income Division. SOI Bulletin, Spring 2000. Washington, DC: U.S. Government Printing Office, 2000.

Joint Committee on Taxation. Distribution of Certain Federal Tax Liabilities by Income Class for Calendar Year 2001 (JCX-2-01). February 27, 2001.

Newey, W. K., and K. D. West. "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica, 55, 1987, 703-8.

Slemrod, J. "High-Income Families and the Tax Changes of the 1980s: The Anatomy of Behavioral Response," in Empirical Foundations of Household Taxation, edited by M. Feldstein and J. Poterba. Chicago: University of Chicago Press, 1996, 169-89.

RELATED ARTICLE: ABBREVIATIONS

AGI: Adjusted Gross Income

FEVD: Forecast Error Variance Decomposition

GDP: Gross Domestic Product

IRF: Impulse Response Function

OLS: Ordinary Least Squares

TRA86: Tax Reform Act of 1986

VAR: Vector Autoregression

VECM: Vector Error Correction Model

DONALD BRUCE, M. H. TUTTLE, and CHARLES B. GARRISON *

* We thank Cezar Botel, Tricia Coxwell, Jean Gauger, Mohammed Mohsin, Matthew Murray, seminar participants at the University of Tennessee, and two anonymous referees for helpful comments and discussion on an earlier draft. This paper is dedicated to the memory of Charles B. Garrison, who passed away unexpectedly during its formative stages.

Bruce: Assistant Professor, Department of Economics, and Research Assistant Professor, Center for Business and Economic Research, 100 Glocker Building, University of Tennessee, Knoxville, TN 37996. Phone 1-865-974-6088, Fax 1-865-974-3100, E-mail dbruce@utk.edu

Tuttle: Graduate Assistant, Department of Economics, 505A Stokely Management Center, University of Tennessee, Knoxville, TN 37996. Phone 1-865-974-3303, Fax 1-865-974-4601, E-mail tuttle00@utk.edu

Garrison: Deceased. At the time of writing, associated with the Economics Department at the University of Tennessee.