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 withinand between-group PigouDalton 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 higherincome 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. Key-words and phrases : Between-group Gini, Between-group Transfers, Entropy, PigouDalton, Within-group Transfers. JEL Codes : D31, D63. ∗This paper was partly done when Stéphane Mussard was post-doctoral researcher at CEPS/INSTEAD Luxembourg and when he visited the University of Sherbrooke and GRÉDI, which are greatly acknowledged. He is also greatly indebted to the Minsitère de la Recherche du Luxembourg and GRÉDI for financial support. A part of this paper beneficiated from Marc Fleurbaey’s and Charles Horvath’s comments, which are greatly acknowledged. The usual disclaimer applies. †CEPS/INSTEAD Luxembourg, GRÉDI Université de Sherbrooke and GEREM Université de Perpignan. Address : Département des Sciences Economiques, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France, E-mail : [email protected]