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Inequality Decomposition Values


  • Frédéric Chantreuil
  • Alain Trannoy


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.

Suggested Citation

  • Frédéric Chantreuil & Alain Trannoy, 2011. "Inequality Decomposition Values," Annals of Economics and Statistics, GENES, issue 101-102, pages 13-36.
  • Handle: RePEc:adr:anecst:y:2011:i:101-102:p:13-36

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    References listed on IDEAS

    1. Maurice Salles, 2005. "Social Choice," Post-Print halshs-00337075, HAL.
    2. Antoinette Baujard & Herrade Igersheim & Thomas Senne, 2011. "The Political Supply in the 2007 French Presidential Elections: An Analysis Based on Experimental Data," Annals of Economics and Statistics, GENES, issue 101-102, pages 149-186.
    3. Boniface Mbih & Xingyu Zhao, 2011. "No-Show Paradoxes under Parliamentary Agendas," Annals of Economics and Statistics, GENES, issue 101-102, pages 127-147.
    4. Maurice Salles, 2005. "The launching of ‘social choice and welfare’ and the creation of the ‘society for social choice and welfare’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 557-564, December.
    5. Nicolas Gravel & Benoît Tarroux, 2011. "Freedom-Based Measurement of Living Standard," Annals of Economics and Statistics, GENES, issue 101-102, pages 37-69.
    6. Fabrice Barthelemy & Mathieu Martin, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections," Annals of Economics and Statistics, GENES, issue 101-102, pages 87-106.
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    16. Fleurbaey,Marc & Salles,Maurice & Weymark,John A. (ed.), 2008. "Justice, Political Liberalism, and Utilitarianism," Cambridge Books, Cambridge University Press, number 9780521640930, March.
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    Cited by:

    1. Chantreuil, Frédéric & Lebon, Isabelle, 2015. "Gender contribution to income inequality," Economics Letters, Elsevier, vol. 133(C), pages 27-30.
    2. Isabelle Lebon & Jean-Pascal Guironnet & Frédéric Gavrel & Frédéric Chantreuil, 2016. "La contribution des écarts de rémunération entre les femmes et les hommes à l’inégalité des rémunérations dans la fonction publique : une approche par la décomposition des inégalités," Économie et Statistique, Programme National Persée, vol. 488(1), pages 151-168.
    3. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.

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