A Convenient Method of Decomposing the Gini Index by Population Subgroups

Abstract

We propose a convenient method of estimating the within-group, between-group, and interaction components of the overall traditional Gini index from the estimated parameters of underlying "trick regression models" involving known forms of heteroscedasticity related to income. Two illustrative examples involving both real and artificial data are provided. The issue of appropriate standard error of the subgroup decomposition is also discussed.

The Marginal Effects in Subgroup Decomposition of the Gini Index

“…In this regard, accuracy considerations necessitate the re-ranking of the incomes in each bootstrap/jackknife subsample in accordance with the ranking rules described in Section 2, which is computationally intensive but should not be overly difficult if the empirical researcher has access to an appropriate ranking subroutine. Shao and Tu (1995) explain the bootstrap and jackknife methodologies in general and Ogwang (2014) explains the calculation of jackknife standard errors in the subgroup decomposition of the Gini index.…”

“…As already mentioned above, the approach developed by Ogwang (2014) also enables the isolation of the contributions of the various subgroups to the overall Gini index. In light of the computational convenience associated with Ogwang's approach, it makes sense to exploit the approach for the purposes of Gini elasticity analysis.…”

“…To see how the contributions to the overall Gini index of the income-receiving units in the lower quintiles could be negative, we refer to Ogwang's (2014) analytical results, which indicate that the within-group Ginis are always positive whereas the between-group and interaction pseudo-Ginis can be positive or negative.…”

“…To facilitate the exposition of the Gini subgroup decomposition elasticities, it is helpful to provide a brief overview of the nature of the contributions of the subgroups to the overall Gini index, as presented in Ogwang's (2014) article, from which the marginal effects are then derived in this article.…”

“…In a recent article, Ogwang (2014) developed a convenient method of decomposing the Gini index by population subgroups where the subgroups may be formed by gender, race, occupation, region, and so on. The advantage of Ogwang's approach is that the overall Gini index is simultaneously decomposed into the traditional within-group, between-group, and interaction (overlapping) components as well as decomposed by the contributions of the various subgroups to overall inequality.…”