Inequality Decomposition Values

Frédéric Chantreuil and Alain Trannoy

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Abstract: 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.

Keywords: Game Theory; Shapley Value; Income Inequality (search for similar items in EconPapers)
Date: 2011-01
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Citations: View citations in EconPapers (14)

Published in Annales d'Economie et de Statistique, 2011, 101/102, pp.13-36. ⟨10.2307/41615472⟩

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Related works:
Journal Article: Inequality Decomposition Values (2011)
Working Paper: Inequality decomposition values (1997)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00656822

DOI: 10.2307/41615472

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