The subgroup decomposable intermediate indices of inequality

An inequality index is called subgroup decomposable if it can be expressed as a weighted sum of inequality values calculated for population subgroups plus inequality arising from differences among subgroup means. This paper derives the class of subgroup decomposable inequality indices that satisfies the Bossert–Pfingsten type intermediate inequality invariance. When the intermediate inequality equivalence concept coincides with the relative notion of inequality, the derived class becomes the Cowell–Shorrocks generalized entropy family. For comments and suggestions, we are grateful to Peter J. Lambert and two anonymous referees. We thank Chranjib Neogi for drawing the only figure of the paper.