Within-between decomposition of the Gini index: A novel proposal

This paper considers a partitioned population and develops a decomposition of the Gini index in two components, which measure the within and the between groups inequality. Differently from the most widespread inequality measure decompositions, having a between component that compares the means of the groups, ours informs about the distance between their entire distributions. This makes the decomposition helpful in several frameworks, such as in the measurement of spatial concentration A Monte Carlo experiment supports the appropriateness of our components highlighting that they strongly correlate with two axiomatically derived benchmarks. The presentation of a case study concerning the income distribution in the Italian provinces concludes the work and stresses the informativeness of the proposed decomposition.