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.

Application of Hybrid Subgroup Decomposition Method to Gas Cooled Thermal Reactor Problem

In this paper, a newly developed hybrid subgroup decomposition method is tested in a 1D problem characteristic of gas cooled thermal reactors (GCR). The new method couples an efficient coarse-group eigenvalue calculation with a set of fine-group transport source iterations to unfold the fine-group flux. It is shown that the new method reproduces the fine-group transport solution by iteratively solving the coarse-group quasi transport equation. The numerical results demonstrate that the new method applied to 1D GCR problem is capable of achieving high accuracy while gaining computational efficiency up to 5 times compared to direct fine-group transport calculations.

A Convenient Method of Decomposing the Gini Index by Population Subgroups

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.

Measuring and Explaining Economic Inequality

This chapter proposes a new class of inequality indices based on the Gini coefficient (or index). The properties of the indices are studied and are found to be regular, relative, and to satisfy the Pigou-Dalton transfer principle. A subgroup decomposition is performed, and the method is found to be similar to the one used by Dagum when decomposing the Gini index. The theoretical results are illustrated by case studies, using Cameroonian data.