A note on the relationship between top income shares and the Gini coefficient

Abstract

When a very top group of the income distribution, infinitesimal in numbers, owns a finite share S of total income, the Gini coefficient G can be approximated by G⁎(1 − S)+S, where G⁎ is the Gini coefficient for the rest of the population. We provide a simple formal proof for this expression, give a general formula of the relationship when the top group is not infinitesimal, and offer two applications as illustrations.