IDEAS home Printed from https://ideas.repec.org/p/shr/wpaper/10-03.html
   My bibliography  Save this paper

Income Inequality Games

Author

Listed:
  • 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.

Suggested Citation

  • Arthur Charpentier & Stephane Mussard, 2010. "Income Inequality Games," Cahiers de recherche 10-03, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke.
    • Handle: RePEc:shr:wpaper:10-03
    as

    Download full text from publisher

    File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-1003.pdf
    File Function: First version, 2010
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
    3. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    4. 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, February.
    5. 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.
    6. 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.
    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. 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.
    10. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    11. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    12. 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.
    13. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    14. 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.
    15. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    16. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    17. Francesco Devicienti, 2010. "Shapley-value decompositions of changes in wage distributions: a note," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(1), pages 35-45, March.
    18. Thon, Dominique, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    19. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
    20. Lerman, Robert I & Yitzhaki, Shlomo, 1985. "Income Inequality Effects by Income," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 151-156, February.
    21. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-1230, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. repec:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-017-9619-7 is not listed on IDEAS
    3. 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.
    4. Pauline Mornet, 2013. "A program for weakly decomposable inequality measures by population subgroups," Economics Bulletin, AccessEcon, vol. 33(3), pages 1738-1750.
    5. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    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. 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.
    8. 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.
    9. repec:spr:soinre:v:138:y:2018:i:2:d:10.1007_s11205-017-1690-5 is not listed on IDEAS
    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.
    11. 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 l'École de gestion à l'Université de Sherbrooke.
    12. 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.
    13. 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).

    More about this item

    Keywords

    Inequality; Poverty; Shapley; Source decomposition;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:shr:wpaper:10-03. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Luc Savard). General contact details of provider: http://edirc.repec.org/data/deushca.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.