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Income inequality games

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Author Info

  • 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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File URL: http://hdl.handle.net/10.1007/s10888-011-9184-1
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Bibliographic Info

Article provided by Springer in its journal The Journal of Economic Inequality.

Volume (Year): 9 (2011)
Issue (Month): 4 (December)
Pages: 529-554

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Handle: RePEc:kap:jecinq:v:9:y:2011:i:4:p:529-554

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Web page: http://springerlink.metapress.com/link.asp?id=111137

Related research

Keywords: Inequality; Poverty; Shapley; Source decomposition; Subgroup decomposition; D31; D63;

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References

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  1. Paul Makdissi & Jean-Yves Duclos & Quentin Wodon, 2002. "Poverty-Reducing Tax Reforms with Heterogeneous Agents," Cahiers de recherche 02-09, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke, revised 2003.
  2. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
  3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  4. Mercedes Sastre & Alain Trannoy, 2002. "Shapley inequality decomposition by factor components: Some methodological issues," Journal of Economics, Springer, vol. 9(1), pages 51-89, December.
  5. Casilda Lasso de la Vega & Ana Urrutia, 2008. "The ‘Extended’ Atkinson family: The class of multiplicatively decomposable inequality measures, and some new graphical procedures for analysts," Journal of Economic Inequality, Springer, vol. 6(2), pages 211-225, June.
  6. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  7. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  8. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
  9. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  10. Cheng, Yuk-shing & Li, Sung-ko, 2006. "Income inequality and efficiency: A decomposition approach and applications to China," Economics Letters, Elsevier, vol. 91(1), pages 8-14, April.
  11. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  12. Chantreuil, F. & Trannoy, A., 1999. "Inequality Decomposition Values: the Trade-Off Between Marginality and Consistency," Papers 99-24, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  13. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  14. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  15. Jonathan Morduch & Terry Sicular, 2002. "Rethinking Inequality Decomposition, With Evidence from Rural China," Economic Journal, Royal Economic Society, vol. 112(476), pages 93-106, January.
  16. Thon, Dominique, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-39, December.
  17. Cowell, Frank A, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 521-31, April.
  18. Lerman, Robert I & Yitzhaki, Shlomo, 1985. "Income Inequality Effects by Income," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 151-56, February.
  19. Francesco Devicienti, 2008. "Shapley-Value Decompositions of Changes in Wage Distributions: A Note," LABORatorio R. Revelli Working Papers Series 80, LABORatorio R. Revelli, Centre for Employment Studies.
  20. Shorrocks, Anthony F, 1983. "The Impact of Income Components on the Distribution of Family Incomes," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 311-26, May.
  21. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
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Citations

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Cited by:
  1. Frank A Cowell & Carlo V. Fiorio, 2009. "Inequality Decomposition - A Reconciliation," STICERD - Distributional Analysis Research Programme Papers 100, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. 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.
  3. 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'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  4. 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.
  5. Pauline Mornet, 2013. "A program for weakly decomposable inequality measures by population subgroups," Economics Bulletin, AccessEcon, vol. 33(3), pages 1738-1750.
  6. 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.
  7. 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.

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