Between-Group Pigou-Dalton Transfers

This paper introduces the concept of Pigou-Dalton transfers between populations of income receivers. Gini's mean difference and Dagum's Gini index between populations are axiomatically derived in order to gauge the impact of within- and between-group Pigou-Dalton transfers on Dagum's measure. We show its sensitiveness for any given transfer in the sense that inequality-reducing transfers are captured when transfers occur from higher-income donors to lower-income recipients, which belong to two distinct populations. Accordingly, we point out the implications of between-group transfers on: the ordering of multivariate majorization, the multivariate stochastic dominance in the sense of multivariate Lorenz ordering and zonotope inclusions, the Gini decomposition, and on the use of the generalized entropy index.