Within-Between Decomposition of the Gini Index: A Novel Proposal

Abstract

The socioeconomic impact of spatial concentration has been receiving an increasing attention during the last two decades. Consequently, the necessity of effective measures of this phenomenon has increased too. This paper considers a population partitioned by subgroups and develops a decomposition of the Gini index in two components, which measure the within and the between group inequality and are also particularly effective to quantify spatial concentration. Indeed, they possess a crucial property which overcomes important issues that may arise using any Gini index decomposition in the spatial context, following a recent approach. In addition, the availability of an only-two highly informative components decomposition provides in numerous applications and several frameworks further significant advantages in the determination of the contributions to global inequality of the intra and the inter groups differences. The ability of the components to capture these phenomena is supported by a parametric bootstrap procedure. This highlights extremely high correlations between the components and two axiomatically derived benchmarks. The presentation of a case study concerning the income distribution in the Italian provinces concludes the works, the informativeness and the interpretative advantages of the proposed decomposition appear evidently.