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Income Inequality Games

  • Arthur Charpentier

    (CREM Département des Sciences Economiques - Université de Rennes I, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Stéphane Mussard

    (LAMETA - Université de Montpellier I)

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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Paper provided by HAL in its series Working Papers with number hal-00456573.

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Date of creation: 15 Feb 2010
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Handle: RePEc:hal:wpaper:hal-00456573
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  1. 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.
  2. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  3. 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.
  4. 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.
  5. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  6. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  7. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  8. 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..
  9. 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.
  10. Francesco Devicienti, 2010. "Shapley-value decompositions of changes in wage distributions: a note," Journal of Economic Inequality, Springer, vol. 8(1), pages 35-45, March.
  11. 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.
  12. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  13. Jean-Yves Duclos & Paul Makdissi & Quentin Wodon, 2005. "Poverty-Reducing Tax Reforms with Heterogeneous Agents," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 107-116, 02.
  14. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
  15. Cowell, Frank A, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 521-31, April.
  16. 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.
  17. 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.
  18. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
  19. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  20. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  21. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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