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3.3  Progressivity Measures

Comparisons between distributions may also involve the use of progressivity measures. In view of the use of the standard Gini inequality measure, it is convenient to use the Kakwani (1986) progressivity measure. This reflects the disproportionality of taxation. It involves the concentration measure of tax payments, which is precisely like the Gini inequality measure, except that in ranking the units in ascending order, the rank used for tax payments is the same as that used for pre-tax incomes. For example, in comparing distributions 3 and 4, the market incomes per adult equivalent are, when ranked in ascending order, given by

[41.5, 48.1, 57.5, 100],

and the net tax paid (the effect of direct taxes and transfers) by those households is [4.16, 0, 11.5, 20].

The concentration measure of taxation is simply obtained by using the expression for the Gini measure in equation (3) above, but keeping the order as in the previous sentence. The actual Gini measure of tax payments would of course be obtained by arranging households in the order

[0, 4.16, 11.5, 20].

Another phenomenon, discussed briefly above, arises when the ranking of households or individuals changes when moving from pre-tax to post-tax incomes. Reranking can be measured by the difference between the Gini measure of post-tax incomes and the (smaller) concentration measure of post-tax incomes. These are obviously equal when there is no reranking.

In the present context, where transfer payments and some other government expenditure items are allocated, it is not possible to consider progressivity measures for all the distributions examined in Table 5. This is because in some cases there are negative effective tax payments and the basic Gini and concentration measures cannot apply for negative values. Where comparisons are possible, the results are shown in Table 6. The tax ratio shown in the final column of the table is defined as total (effective) tax payments divided by total pre-tax income.[22]

Table 6 - Progressivity Measure
Before and after Progressivity Reranking Tax ratio
3 and 4 0.2267 0.0050 0.1443
5 and 6 0.2252 0.0054 0.1135
7 and 8 0.2142 0.0060 0.1251
11 and 12 0.1950 0.0017 0.1250


  • [22]Kakwani (1986) showed that the redistributive effect (the reduction in the Gini inequality measure when moving from pre- to post-tax income) is equal to the progressivity measure multiplied by g/(1-g), where g denotes the tax ratio, less the reranking measure. This can be confirmed using the results in Tables 5 and 6.
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