Inequality foundations of concentration measures: an application to the Hannah-Kay indices

Abstract

In this paper we provide a connection between concentration and inequality by showing that the inequality measures consistent with the whole class of Hannah-Kay concentration indices are the general entropy inequality indices. We isolate the inequality component underlying the concentration measures, obtaining an explicit additive decomposition of the change in concentration into the change in its two components: inequality and the number of firms. This relationship proves to be valid for the whole class of Hannah-Kay concentration indices, and embodies as particular cases other previously found in the literature. Finally, our proposed decomposition is shown by means of an empirical example, which illustrates the sources of a change in sectoral concentration between two points in time.