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3.2  Redistributive Effects

Table 4 shows that a range of possible comparisons exists. Another comparison (other than of distributions 1 and 2) involving the household as unit is between distributions 3 and 4 (that is, pre- and post-tax-and-transfer incomes), each of which adjusts household incomes using adult equivalence scales. Various inequality measures could then be computed. In some cases they are linked with a particular ‘social welfare function', reflecting the value judgements of an independent observer, and a degree of inequality aversion can be specified.[20] In practice it is valuable to examine results using a range of measures, thereby considering the effects of adopting different value judgements.

However, for present purposes, where the emphasis is on the various distributions rather than the precise measurement of inequality, it is sufficient to use a single inequality measure. Results are reported for the standard well-known Gini measure. This can be calculated in a variety of ways, but a convenient form is the following, where xi denotes unit i's income, is arithmetic mean, and individuals are arranged in ascending order:

Equation 3   .

The Gini inequality measures of distributions 3 and 4 are shown in the first row of Table 5. Although the adjusted household income measures are to some extent more comparable than with distributions 1 and 2, this comparison ignores the number of individuals involved.

Comparisons between two distributions of market and disposable income per adult equivalent, which allow for the differing compositions of the households, are between numbers 5 and 6 (using the individual as unit) and between 7 and 8 (using the equivalent adult as unit) in Table 4. The Gini comparisons are reported in Table 5.

The simplest comparison is of the effect of the tax and transfer system on the market and disposable incomes of those individuals who have some market income; this compares distributions 9 and 10.[21] However, this comparison would suggest some horizontal inequity in that the two individuals with market incomes of 100 (in households 1 and 4) are treated differently. This judgement clearly ignores the fact that the tax and particularly the transfer structure does not regard the two individuals as being similar, a fact which is ignored when only those with positive market incomes are considered.

Table 5 - Gini Inequality Measures
Before and after
Reduction (per cent)
3 and 4 0.1871 0.1538 0.0333 (18 %)
5 and 6 0.1405 0.1171 0.0234 (17 %)
7 and 8 0.1371 0.1125 0.0246(18 %)
9 and 10 0.2375 0.2190 0.0185(8 %)
11 and 12 0.3530 0.3269 0.0261(7 %)
11 and 13 0.3530 0.2404 0.1126(32 %)
12 and 13 0.3269 0.2404 0.0864(26 %)

Consider comparisons which allow for the allocation of indirect taxes and some items of government expenditure. Since the use of an income sharing or income allocation rule (which differs from the use of an adult-equivalence scale) is crucial, the comparisons are necessarily based on the individual as the unit of analysis. Comparisons are thus between distributions 11 and 12, between 12 and 13 and between 11 and 13. These are also reported in Table 5, along with the percentage reductions. Clearly any judgement about the redistributive effects of taxes and transfers, and of some components of government expenditure, depends crucially on which comparisons are selected.

The comparisons moving from a measure of market income to disposable income are obtained by comparing distributions 3 to 4; 5 to 6; 7 to 8; 9 to 10; and 11 to 12. The last two comparisons reveal much smaller percentage reductions in the Gini inequality measure than the first three. Of those using adult equivalence scales (the first three) the absolute Gini values differ slightly although in this case there are small differences in percentage reductions. However, in practice it is possible for the use of different income units to come to different, even opposite, conclusions about the effects of a tax change.

The allocation of some government expenditure to individuals (comparisons involving distribution 13) produces the largest reductions in inequality. This is perhaps not surprising in view of the fact that the Gini measure depends on relative incomes (as well as on the ranks of individuals), and government expenditure in this example involves relatively larger amounts going to the households with children.


  • [20]For a short introduction see, for example, Creedy (1999), and for extensive analysis, see Lambert (1992).
  • [21]There may be a temptation to include all individuals, and hence zero incomes for those not working. It is not clear why one would wish to add zero values and of course the resulting inequality measures are much higher. In the present example, the addition of 4 zeros to each of the distributions 9 and 10 produces Gini values of 0.5425 and 0.5314 respectively.
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