The Marginal Effects in Subgroup Decomposition of the Gini Index

In this article, we derive the elasticity of the Gini index with respect to changes in subgroup incomes for subgroups that are characterized by significant income separation. The resulting elasticity, which is structurally similar to that of the empirically popular Lerman and Yitzhaki's (1985) elasticity for Gini income-source decomposition, entails easy and transparent computations. Some possible checks for income separation are described and an illustrative example using Canadian data is provided. The advantages of the proposed methodology over the Shapley value approach to Gini subgroup decomposition are stated.