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Inequality Decomposition Values

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  • Frédéric Chantreuil
  • Alain Trannoy

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.

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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    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. Vincent Merlin & Marc Fleurbaey & Dominique Lepelley, 2012. "Introduction to the special issue on new developments in social choice and welfare theories," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 253-257, July.
    4. Luis A. Hierro & Rosario Gómez‐Álvarez & Pedro Atienza, 2014. "A Consistent Decomposition Of The Redistributive, Vertical, And Horizontal Effects Of Health Care Finance By Factor Components," Health Economics, John Wiley & Sons, Ltd., vol. 23(1), pages 117-121, January.
    5. Lucio Bertoli-Barsotti & Marek Gagolewski & Grzegorz Siudem & Barbara .Zoga{l}a-Siudem, 2023. "Equivalence of inequality indices: Three dimensions of impact revisited," Papers 2304.07479, arXiv.org.
    6. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebière, Thérèse, 2021. "Magnitude and evolution of gender and race contributions to earnings inequality across US regions," Research in Economics, Elsevier, vol. 75(1), pages 45-59.
    7. 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.
    8. Martin FOURNIER, 1999. "Décomposition de l'inégalité de revenu par source : méthode des rangs et application au cas de Taiwan version anglaise : "Inequality Decomposition by factor Component: a "rank correlation&qu," Working Papers 199920, CERDI.
    9. O. Alonso-Villar & C. Grad󸀍 & C. del R􈀍, 2013. "Occupational segregation of Hispanics in US metropolitan areas," Applied Economics, Taylor & Francis Journals, vol. 45(30), pages 4298-4307, October.
    10. Silber, Jacques, 2004. "Inequalities: theory, experiments and applications," European Journal of Political Economy, Elsevier, vol. 20(3), pages 813-821, September.
    11. Carlos Grad�n & Coral Del R�o & Olga Alonso-Villar, 2015. "Occupational Segregation by Race and Ethnicity in the United States: Differences Across States," Regional Studies, Taylor & Francis Journals, vol. 49(10), pages 1621-1638, October.
    12. Frédéric Chantreuil & Sébastien Courtin & Kevin Fourrey & Isabelle Lebon, 2019. "A note on the decomposability of inequality measures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 283-298, August.
    13. Frederic Chantreuil & Kévin Fourrey & Thérèse Rebière & Isabelle Lebon, 2020. "Decomposing US Income Inequality à la Shapley: Race Matters, but Gender Too," Working Papers hal-02552244, HAL.
    14. Ramani Gunatilaka & Duangkamon Chotikapanich, 2006. "Inequality Trends and Determinants in Sri Lanka 1980-2002: A Shapley Approach to Decomposition," Monash Econometrics and Business Statistics Working Papers 6/06, Monash University, Department of Econometrics and Business Statistics.
    15. Rodrigue Tido Takeng & Arnold Cedrick Soh Voutsa & Kévin Fourrey, 2023. "Decompositions of inequality measures from the perspective of the Shapley–Owen value," Theory and Decision, Springer, vol. 94(2), pages 299-331, February.
    16. Martin Fournier, 2000. "Inequality Decomposition by Factor Component: A New Approach Illustrated on the Taiwanese Case," Econometric Society World Congress 2000 Contributed Papers 1288, Econometric Society.
    17. Gunatilaka, Ramani., 2013. "To work or not to work? : Factors holding women back from market work in Sri Lanka," ILO Working Papers 994838403402676, International Labour Organization.
    18. repec:ilo:ilowps:483840 is not listed on IDEAS

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