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Inequality decomposition values: the trade-off between marginality and efficiency

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  • Frédéric Chantreuil

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - CNRS - Centre National de la Recherche Scientifique)

  • Alain Trannoy

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

Abstract

This paper presents a general procedure for decomposing income inequality measures by income sources. The methods of decomposition proposed are based on the Shapley value and extensions of the Shapley value of transferable utility cooperative games. In particular, we find that Owen's value can find an interesting application in this context.We show that the axiomatization by the potential of Hart and Mas-Colell remains valid in the presence of the domain restriction of inequality indices. We also examine the properties of these decomposition rules and perform a comparison with Shorrocks' decomposition rule properties.

Suggested Citation

  • Frédéric Chantreuil & Alain Trannoy, 2013. "Inequality decomposition values: the trade-off between marginality and efficiency," Post-Print halshs-00733401, HAL.
  • Handle: RePEc:hal:journl:halshs-00733401
    DOI: 10.1007/s10888-011-9207-y
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00733401
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    References listed on IDEAS

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    6. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    7. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    8. Theil, Henri, 1979. "The measurement of inequality by components of income," Economics Letters, Elsevier, vol. 2(2), pages 197-199.
    9. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    10. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    Citations

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    Cited by:

    1. Sebastian Leitner, 2015. "Drivers of wealth inequality in euro area countries," Working Paper Reihe der AK Wien - Materialien zu Wirtschaft und Gesellschaft 137, Kammer für Arbeiter und Angestellte für Wien, Abteilung Wirtschaftswissenschaft und Statistik.
    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. SOLOGON Denisa & VAN KERM Philippe & LI Jinjing & O'DONOGHUE Cathal, 2018. "Accounting for Differences in Income Inequality across Countries: Ireland and the United Kingdom," LISER Working Paper Series 2018-01, LISER.
    4. Deutsch, Joseph & Dumas, Audrey & Silber, Jacques, 2013. "Estimating an educational production function for five countries of Latin America on the basis of the PISA data," Economics of Education Review, Elsevier, vol. 36(C), pages 245-262.
    5. DEUTSCH Joseph & PI ALPERIN Maria Noel & SILBER Jacques, 2016. "Disentangling the impacts of circumstances and efforts on health inequality: the case of Luxembourg," LISER Working Paper Series 2016-07, LISER.
    6. Mike Brewer & Liam Wren-Lewis, 2016. "Accounting for Changes in Income Inequality: Decomposition Analyses for the UK, 1978–2008," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 289-322, June.
    7. John E. Roemer & Alain Trannoy, 2013. "Equality of Opportunity," Cowles Foundation Discussion Papers 1921, Cowles Foundation for Research in Economics, Yale University.
    8. Peter Lambert, 2013. "From the editor of Rediscovered Classics," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 131-132, June.
    9. John E. Roemer & Alain Trannoy, 2016. "Equality of Opportunity: Theory and Measurement," Journal of Economic Literature, American Economic Association, vol. 54(4), pages 1288-1332, December.
    10. Ben-Shahar Danny & Sulganik Eyal, 2009. "Fair Depreciation: A Shapley Value Approach," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-18, April.
    11. Peter Lindner, 2015. "Factor decomposition of the wealth distribution in the euro area," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(2), pages 291-322, May.
    12. repec:ebl:ecbull:eb-17-00446 is not listed on IDEAS
    13. Jurgen Faik & Uwe Fachinger, 2013. "The decomposition of well-being categories: An application to Germany," Working Papers 307, ECINEQ, Society for the Study of Economic Inequality.
    14. Marco Ranaldi, 2018. "On the Measurement of Functional Income Distribution," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01379229, HAL.
    15. A. Palestini & G. Pignataro, 2013. "A multi-factor inequality approach to a transfer scheme: the case of Common Agricultural Policy," Working Papers wp891, Dipartimento Scienze Economiche, Universita' di Bologna.
    16. Chantreuil, Frédéric & Lebon, Isabelle, 2015. "Gender contribution to income inequality," Economics Letters, Elsevier, vol. 133(C), pages 27-30.
    17. Noglo, Yawo Agbenyegan, 2014. "Monetary inequality among households in Togo: An illustration based on the decomposition of the Gini coefficient using the Shapley value approach," WIDER Working Paper Series 151, World Institute for Development Economic Research (UNU-WIDER).
    18. Carlos Gradín, 2017. "Occupational segregation by race in South Africa after apartheid," WIDER Working Paper Series 073, World Institute for Development Economic Research (UNU-WIDER).
    19. Briec, Walter & Mussard, Stéphane, 2014. "Efficient firm groups: Allocative efficiency in cooperative games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 286-296.
    20. Marco Ranaldi, 2016. "On the Measurement of Functional Income Distribution," Documents de travail du Centre d'Economie de la Sorbonne 16051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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