Do redistributive state taxes reduce inequality?

One might imagine several different processes through which taxes affect the distribution of wages. Wage inequality might be affected only by the current tax system, only by a previous year's tax system, or by some combination of the two. To take in account of these various possibilities, I present both current and lagged coefficients. In addition, I estimate the linear sum of the lagged redistributivity coefficients, and the linear sum of all redistributivity coefficients. (8) I then present a one-tailed F-test against the null hypothesis that the sum of the coefficients is equal to or smaller than zero (which would imply that the wage distribution does not become more unequal in response to more redistributive taxes), and a one--tailed F-test against the null hypothesis that the sum of the coefficients is equal to or greater than one (which would imply that the wage distribution fully adjusts in response to taxes).

The rationale for using one-tailed F--tests, rather than the standard two-tailed tests, is that the policy outcome of interest is whether the coefficient on tax redistributivity is closer to zero or one; not whether it is precisely zero or precisely one. Any coefficient above one would mean that a rise in tax redistributivity was more than compensated for by a rise in wage inequality. Likewise, a coefficient below zero would mean that a rise in tax redistributivity led to an additional fall in wage inequality. These findings carry the same policy implications as if the coefficient had been--respectively--precisely one or precisely zero.

These null hypotheses are calculated for current taxes, lagged taxes, and both current and lagged taxes. Thus a reader whose prior was that taxes affected wage inequality immediately would focus only on the "Current taxes" F--tests, while a reader whose prior was that taxes affected wage inequality only with some lag would focus on the "Lagged taxes" F-tests. A reader who originally thought that the effect was some combination of current and lagged taxes would focus on the "Current and lagged taxes" F-tests.

Table 1 shows the results of these specifications. With between zero and six lags, the coefficient on the contemporaneous tax rate is negative, and the linear sum of the lags is always negative. The hypothesis that wage inequality does not rise in response to a rise in tax redistributivity cannot be rejected in any specification. (9)

By contrast, the null hypothesis that pre-tax inequality fully adjusts in response to taxes can be rejected in all 11 specifications, indicating that the main conclusion is not sensitive to the particular lag structure or form of the null hypothesis. This provides strong evidence that the effect of more redistributive state taxes is not undone by a subsequent rise in pre-tax inequality. This result is at odds with Feldstein and Wrobel (1998), who find--using individual-level data from 1983 and 1989--that gross wages fully adjust to changes in taxes within six years.

As Table 1 demonstrates, these results are not particularly sensitive to the number of lags of the tax redistribution variable that are included in the regression. Table 2 also presents four additional robustness checks. The first check omits the time-varying state controls, as a way of testing whether the previous results are sensitive to these controls. The second check weights states by their 2002 population, to account for the fact that wage inequality will typically be better measured in larger states, since there are more CPS observations for these states. The third check omits state fixed effects, and estimates the model using pooled ordinary least squares (OLS) (though still including year fixed effects, since these absorb most changes in federal taxes). And the fourth check estimates the model with random state effects, rather than fixed state effects.

None of these robustness checks seems to have a substantial impact on the main results. As in Table 1, none of the F-tests in Table 2 reject the hypothesis that (in sum) pre-tax inequality is unaffected by tax redistributivity, while they do tend to reject the hypothesis that wage inequality fully adjusts to a change in the level of tax redistribution. The exceptions are in columns 3 and 4: the hypothesis of full adjustment in response to the current tax rate cannot be rejected in the specifications without state effects, or with random state effects. I do not place much weight on these results, however, since a Hausman test strongly rejects the hypothesis that the random effects estimator is consistent, suggesting that the fixed effects results should be preferred. (10) Overall, the results in Table 2 provide further reassurance that the results are not driven by some idiosyncratic feature of the primary specification.

HOW DO REDISTRIBUTIVE TAXES AFFECT THE TOP AND BOTTOM OF THE INCOME DISTRIBUTION?

While the results in the previous section suggest that more redistributive taxes do not cause the distribution of gross wages to fully adjust, it is possible that a stronger impact is felt by tax reforms that affect either the bottom or top of the distribution. This could occur if either the poor or the rich were particularly sensitive to tax changes. A straightforward way to test this is to use a measure of income distribution that places more weight on one or other of the ends of the distribution. A natural choice is the S-Gini (Donaldson and Weymark, 1980), a scale-free index that allows for a flexible inequality aversion parameter, [delta], which determines the social weight to be applied to parts of the distribution.

The area under the Lorenz Curve, L(p), represents the proportion of total income going to the bottom fraction p of a population with individual income y and mean income [mu]. If the cumulative density function of the population is F(y) and the pth quantile of income is [F.sup.-1](p), the Lorenz Curve is

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

The S-Gini is, therefore, given by the formula

[4] [SG.sub.[delta]] = 1 - [delta]([delta] - 1)[[integral].sup.1.sub.0] [(1 - p).sup.[delta]-2] L(p)d(p).

A consistent estimator for the S-Gini, where [y.sub.1:n] [less than or equal to] [y.sub.2:n] [less than or equal to] ... [less than or equal to] [y.sub.n:n] are the order statistics for income of n individuals, is

[5] [SG.sub.[delta]] = 1 - 1/[mu][n.sup.[delta] [n.summation over (i=1)][((n - i + 1).sup.[delta]] - [(n - i).sup.[delta]])[y.sub.i:n],

where [delta] [less than or equal to] 1, the S-Gini is undefined. For 1 < [delta] < 2, the index places more weight on the top of the distribution, while for > 2, the index places progressively more weight on the bottom of the distribution. When [delta] = 2, the S-Gini is identical to the Gini coefficient. For a more detailed discussion of the properties of the S-Gini, see Lambert (1993), Barrett and Donald (2002), and Zitikis and Gastwirth (2002).

Therefore it is straightforward to use the S-Gini to develop alternative measures of the redistributive effect of taxation, weighting the top and bottom of the distribution differently. In the second section, estimates were presented for a redistribution measure based on the Gini coefficient. Where [R.sub.[delta]] is a redistribution measure based on the S-Gini:

[6] [R.sub.2] = [[bar.SGB].sub.2] - [[bar.SGB].sub.2] = [bar.GB] - [bar.GA].

Here, I present four alternative measures of redistributive effect; two that place more weight than the Gini-derived measure on the top of the income distribution:

[7] [R.sub.1.25] = [[bar.SGB].sub.1.25] - [[bar.SGA].sub.1.25];

[8] [R.sub.15] = [[bar.SGB].sub.1.5] - [[bar.SGA].sub.1.5].

And two that place more weight than the Gini-derived measure on the bottom of the income distribution:

[9] [R.sub.2.5] = [[bar.SGB].sub.2.5] - [[bar.SGA].sub.2.5];

[10] [R.sub.3.5] = [[bar.SGB].sub.3.5] - [[bar.SGA].sub.3.5].

Summary statistics for each measure are presented in Appendix Table 1.

In each instance, I estimate the impact on the corresponding pre-tax S-Gini coefficient, with current redistribution and six lags of redistribution as the independent variables of interest. For example, in the case of the redistribution measure where [delta] = 1.25, I estimate the equation:

[11] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The interpretation of [beta] is, therefore, analogous to the second section. If [beta] = 1, then a tax system that has the mechanical effect of reducing the [S-Gini.sub.[delta]] leads to a behavioral change that increases the [S-Gini.sub.[delta]] by the same amount, while if [beta] = 0, the redistributive effect of taxation, as measured by the change in the [S-Gini.sub.[delta]], has no impact on the distribution of gross wages.

Table 3 shows the results using the four alternative redistribution indices. While the effect of tax-induced redistribution on current wages appears to be slightly stronger at the top of the distribution, there is little difference between the four specifications. As with the Gini-derived redistribution measure ([delta] = 2), the hypothesis that wage inequality does not rise in response to more redistributive taxes is not rejected in any specification. However, the null hypothesis that pre-tax inequality fully adjusts in response to taxes can be rejected in all 12 specifications. This provides evidence that states that impose a heavier tax burden on the rich do not see a sudden rise in top wage incomes, and similarly that states that impose a heavier tax burden on the poor do not see a sudden rise in wages towards the bottom of the distribution.

MIGRATION, INCOME, AND POST-TAX INEQUALITY