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Income Inequality Games

  • Arthur Charpentier
  • Stéphane Mussard

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://www.lameta.univ-montp1.fr/Documents/DR2010-01.pdf
File Function: First version, 2010
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Paper provided by LAMETA, Universtiy of Montpellier in its series Working Papers with number 10-01.

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Length: 21 pages
Date of creation: Jan 2010
Date of revision: Jan 2010
Handle: RePEc:lam:wpaper:10-01
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  1. Udo Ebert, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Working Papers V-325-10, University of Oldenburg, Department of Economics, revised May 2010.
  2. Mercedes Sastre & Alain Trannoy, 2002. "Shapley inequality decomposition by factor components: Some methodological issues," Journal of Economics, Springer, vol. 77(1), pages 51-89, December.
  3. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  5. Jonathan Morduch & Terry Sicular, 1998. "Rethinking Inequality Decomposition, with Evidence from Rural China," Harvard Institute of Economic Research Working Papers 1831, Harvard - Institute of Economic Research.
  6. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  7. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  8. Duclos, Jean-Yves & Makdissi, Paul & Wodon, Quentin, 2002. "Poverty-Reducing Tax Reforms with Heterogeneous Agents," Cahiers de recherche 0202, Université Laval - Département d'économique.
  9. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
  10. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  11. 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," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 211-225, June.
  12. 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.
  13. 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..
  14. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  15. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  16. 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.
  17. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  18. Anthony F. Shorrocks, 1983. "The Impact of Income Components on the Distribution of Family Incomes," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 311-326.
  19. 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.
  20. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
  21. 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.
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