|2008/9<br>0.336|83%|17%|
|---|---|---|

There has long been some dissatisfaction with inequality decompositions based on the conventionally applied decomposition methodology.<sup>9</sup> Elbers, Lanjouw, Mistiaen and Özler (2008) point out that the standard procedure for decomposing inequality into a between- and a within-group component fails to capture a particular feature of group differences that might be highly relevant to an assessment of their importance. Standard decomposition procedures assess the extent to which group divisions contribute to inequality by giving everyone within a group the average income of the group and then asking how much of overall inequality can be attributed to the inequality accounted for by the inequality in these group-average income levels. By comparing group-average income inequality against total inequality, the procedure in effect compares observed group differences against the extreme benchmark where each individual in the data is treated as a separate group. As a result, the proportion of between-group inequality is always rather low, in comparison with the benchmark. Furthermore, standard measures have the mathematical property that between-group inequality will increase (or more precisely - never decrease) with a greater number of groups.

Elbers et al (2008) propose a relatively minor adaptation of the conventional procedure to produce an alternative statistic that overcomes some of these issues. Suppose that a given population is divided into two groups. The approach proposed by Elbers et al (2008) compares the extent of between-group group inequality against a new benchmark, namely the extent to which these two groups are completely “separate” from each other in income terms; i.e., whether the richest person of the poorer group is poorer than the poorest person in the richer group. The standard decomposition procedure is entirely silent on this question. Yet, from the perspective of assessing the importance of, say, caste differences in a village such as Palanpur, the Elbers et al (2008) index is arguably quite relevant. If two population groups divide the income distribution into two entirely non-overlapping partitions, but there exists a high level of inequality within each of the two groups, overall between-group inequality - conventionally calculated – would be relatively low. Yet a fairly strong statement about the relevance of the contribution of groups to inequality would remain unstated; namely, that the two groups “stand apart” in income terms – they are somehow economically “excluded” from one another.<sup>10</sup> Lanjouw and Rao (2012) compared the Elbers et al (2008) statistic with standard inequality decomposition measures to study dynamics of caste-inequality in Palanpur, drawing on data covering the survey period up to 1983/4. They found that when Jatabs are compared to the rest of the village population taken as a single group, the Elbers et al (2008) statistic reveals that Jatabs in 1983/4 were 50% of the way of standing fully apart from the rest of the village, up from 39% in 1974/5 and even lower in the earlier survey years. There was clear evidence, consistent with the narrative offered above, that over the decades since the 1950s, Jatabs as a

> 9  See for example, Kanbur (2000).

> **10** Elbers et al (2008) illustrate this point with reference to South Africa.  They show that when inequality is decomposed by racial group defined in terms of a “white/non-white” classification, the conventional decomposition suggests that only about 27% of inequality is attributable to between-group differences.  Their alternative statistic, on the other hand, shows that two groups are 80% of the way towards a completely partitioned South African income distribution.

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