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18%, the statutory tax rate (the capital average tax rate is computed before the dividend
allowance is applied). The proposed tax cuts are compared by using aggregate indices of lia-
bility progression and redistributive effect on income distribution. Tax-progressivity indices
as Kakwani (1976), K, and Suits (1977), S, are measures of liability progression. Values
of the progressivity indices for each tax cut reveal T2,2 as the most progressive one followed
by T3_,3. Similar results can be inferred considering a measure of residual progression. The
redistributive effect of PIT on income distribution is measured by the Redistributive Effect
or Reynolds-Smolensky index, RE = Gx - Gx-T , where Gx and Gx-T are the Gini indices of
pre-tax and post-tax income respectively. Results reveals, again, that T2,2 increases income
redistribution the most, whereas T1,1 is the least redistributive tax cut.

Next, the differential distributional effects of linear tax cuts are also compa-

red in terms of Lorenz dominance by representing concentration curves of tax-payments
(or post-tax income) against the cumulated shares of pre-tax income recipients. To test
whether T2,2 is more liability progressive than T1,1 or T3,3 we only need to prove that the
concentration curves C T1,1 or C T3,3 dominate C T2,2, which implies that the distance between
curves is positive for each decile of the income distribution. In a similar way, T2,2 has a
greater redistribution on income with respect to T1,1 or T3,3 if the difference, LV2,2 - LV1,1 or
LV3,3 - LV1,1, is always positive through income distribution, where LV1,1, LV2,2 and LV3,3
are the income post-tax distributions. The redistributive profile of PIT reforms T2_,2 and T3_,3
with respect to T1,1 is represented in Figure 2.

These results bear out the theoretical ones described in Section 3 indicating a clear Lorenz
dominance order T₂,₂ >- T₃,₃ >- T₁,1 for residual progression. Similar results on liability
progression, not reproduced here, are obtained for tax concentration curves.

The analysis of local differential effects on the income distribution can also be based on
the absolute increase of post-tax income that a particular tax-payer obtains from each reform.
To analyze how different taxes affect local inequality, the average gain is computed for a set

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