Inequality Decomposition Values

F. Chantreuil (1) , Alain Trannoy (2)

1 CREM - Centre de recherche en économie et management
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

This paper presents a general procedure inspired by the Shapley value for decomposing any inequality indices by factor components or by sub-populations. To do so we define an inequality game. Despite the fact that the characteristic function is not super-additive in general and that the linearity assumption of the space of inequality game does not hold, an axiomatization of the Shapley value is given in this context by using the Potential function pioneered by Hart and Mas-Colell [1989]. This result proves to be useful in illustrating a trade-off between the desirable properties of consistency and marginality. A comparison of such decomposition with the decomposition method investigated by SHORROCKS [1982] is provided in the case of factor component decomposition. Refinement of the Shapley decomposition is investigated when the set of income sources is nested. Furthermore, an application to the sub-population decomposition problem is also investigated.

Mots clés: Game Theory; Shapley Value; Income Inequality

Domaines: Economies et finances

F. Chantreuil, Alain Trannoy. Inequality Decomposition Values. Annales d'Economie et de Statistique, 2011, 101/102, pp.13-36. ⟨10.2307/41615472⟩. ⟨halshs-00656822⟩