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Income inequality games

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  • Arthur Charpentier
  • Stéphane Mussard

Abstract

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, baed on the Shapley Value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that multiplicative income sources inequality games provide dual results compared with Chantreuil and Trannoy's ones. We also investigate the case of multiplicative poverty games for which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with, as in the Sen Shorrocks-Thon poverty index. We finally show in the case of additive poverty indices that the Shapley value may be equivalent to traditional methods of decomposition such as subgroup consistency and additive decompositions.
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Suggested Citation

  • Arthur Charpentier & Stéphane Mussard, 2011. "Income inequality games," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 529-554, December.
    • Handle: RePEc:kap:jecinq:v:9:y:2011:i:4:p:529-554
    DOI: 10.1007/s10888-011-9184-1
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    Cited by:

    1. Frank Cowell & Carlo Fiorio, 2011. "Inequality decompositions—a reconciliation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 509-528, December.
    2. 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.
    3. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    4. John Creedy & Nicolas Hérault, 2011. "Decomposing Inequality and Social Welfare Changes: The Use of Alternative Welfare Metrics," Melbourne Institute Working Paper Series wp2011n08, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    5. Pauline Mornet, 2013. "A program for weakly decomposable inequality measures by population subgroups," Economics Bulletin, AccessEcon, vol. 33(3), pages 1738-1750.
    6. Ogwang Tomson, 2016. "The Marginal Effects in Subgroup Decomposition of the Gini Index," Journal of Official Statistics, Sciendo, vol. 32(3), pages 733-745, September.
    7. 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.
    8. Yawo Agbényég Noglo, 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 wp-2014-151, World Institute for Development Economic Research (UNU-WIDER).
    9. Carlos Gradín, 2021. "Inequality by Population Groups and Income Sources: Accounting for Inequality Changes in Spain During the Recession," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(2), pages 481-508, June.
    10. Carlos Gradín, 2020. "Quantifying the contribution of a subpopulation to inequality an application to Mozambique," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(3), pages 391-419, September.
    11. John Creedy & Nicolas Hérault†, 2011. "Decomposing Inequality and Social Welfare Changes : The Use of Alternative Welfare Metrics," Department of Economics - Working Papers Series 1121, The University of Melbourne.
    12. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    13. Carlos Gradín, 2018. "Quantifying the contribution of a subpopulation to inequality: An application to Mozambique," WIDER Working Paper Series 60, World Institute for Development Economic Research (UNU-WIDER).
    14. Ferreira Lima, Luis Cristovao, 2013. "A Persistente Desigualdade nas Grandes Cidades Brasileiras: o Caso de Brasília [The Persistent Inequality in the Great Brazilian Cities: The case of Brasília]," MPRA Paper 50936, University Library of Munich, Germany.
    15. Pim Verbunt & Anne-Catherine Guio, 2019. "Explaining Differences Within and Between Countries in the Risk of Income Poverty and Severe Material Deprivation: Comparing Single and Multilevel Analyses," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 827-868, July.
    16. Joseph Deutsch & María Noel Pi Alperin & Jacques Silber, 2018. "Using the Shapley Decomposition to Disentangle the Impact of Circumstances and Efforts on Health Inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(2), pages 523-543, July.
    17. Ferreira Lima, Luis Cristovao, 2013. "The Persistent Inequality in the Great Brazilian Cities: The Case of Brasília," MPRA Paper 50938, University Library of Munich, Germany.
    18. Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    19. 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.
    20. 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).

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    More about this item

    Keywords

    Inequality; Poverty; Shapley; Source decomposition; Subgroup decomposition; D31; D63;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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