Inequality Decomposition Analysis and the Gini Coefficient Revisited

When the Gini coefficient of income inequality is decomposed into between-groups and within-groups contributions, a troublesome and little understood residual term arises if the subgroup income ranges overlap. Graphical analysis is used to provide a solid understanding of this residual term as a sub-area of the Lorenz diagram. The analysis enables a clearer statement than was previously available of the Gini's appealing properties and of its overlapping limitations. In particular, between-group, within-group, and overlapping components of inequality can all now be accounted for straightforwardly on the Lorenz diagram. This affords a path to the understanding of the effects previously regarded as obscure, and a positive role is found for the Gini coefficient in certain types of inequality decomposition analysis.