On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes

Summary Besides a brief historical outline of the Gini index decomposition proposals, we compare, in a subgroups framework, the decompositions of the Gini index and of the uniformity and inequality indexes recently proposed by Zenga. The two decompositions follow a similar scheme: in both cases the overall index can be at first expressed as a weighted average of convenient “cross” measures, with their own interpretation, and afterwards it is decomposed into a within and a between term by merely distinguishing measures evaluated within the same subgroup from the ones regarding different subgroups. This procedure does not depend on an a priori definition of the within or the between term and allows their contribution to be naturally evaluated preserving the structure of the index itself. In the last section the two decompositions are applied to the Italian net household wealth provided by the 2006 central Bank of Italy sample survey on household budgets.