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Income Inequality Games

Author Info

  • Arthur Charpentier

    ()

    (Departement des Sciences Economiques, Universite Rennes I,)

  • Stephane Mussard

    ()

    (Lameta-Cnrs Université de Montpellier I. Address: Lameta-Cnrs, Université Montpellier I, GREDI-Universite de Sherbrooke)

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://gredi.recherche.usherbrooke.ca/wpapers/GREDI-1003.pdf
File Function: First version, 2010
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Paper provided by Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke in its series Cahiers de recherche with number 10-03.

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Length: 22 pages
Date of creation: 04 Feb 2010
Date of revision:
Handle: RePEc:shr:wpaper:10-03
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Keywords: Inequality; Poverty; Shapley; Source decomposition;

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Find related papers by 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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  1. 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.
  2. 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.
  3. 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.
  4. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  5. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
  6. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  7. 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.
  8. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  9. 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.
  10. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
  11. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  12. 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.
  13. F. Chantreuil & A. Trannoy, 1999. "Inequality decomposition values : the trade-off between marginality and consistency," THEMA Working Papers 99-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  14. 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.
  15. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  16. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  17. 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.
  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. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
  20. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  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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Cited by:

  1. 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," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  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. Frank Cowell & Carlo V. Fiorio, 2009. "Inequality decomposition: a reconciliation," LSE Research Online Documents on Economics 25431, London School of Economics and Political Science, LSE Library.
  4. 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.
  5. 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.
  6. 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.
  7. Pauline Mornet, 2013. "A program for weakly decomposable inequality measures by population subgroups," Economics Bulletin, AccessEcon, vol. 33(3), pages 1738-1750.
  8. Alessandro Tampieri & Elena M. Parilina, 2014. "Stability and Cooperative Solution in Stochastic Games," CREA Discussion Paper Series 14-26, Center for Research in Economic Analysis, University of Luxembourg.
  9. 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.
  10. 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.

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