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Linking Yitzhaki's and Dagum's Gini decompositions

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  • Stéphane Mussard
  • Patrick Richard

Abstract

In this article we show that the Gini coefficient is simultaneously decomposable both by sources of income and by populations of income receivers for nonoverlapping income distributions: the so-called first-best Gini multi-decomposition. We show that this multidimensional decomposition is useful for many reasons: (i) it is related to the degree of inequality aversion of the decision maker, (ii) it is especially well suited to study inequalities between poor and nonpoor people, (iii) it enables one to measure the impact of marginal tax reforms on within- and between-group inequalities, respectively.

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File URL: http://hdl.handle.net/10.1080/00036846.2011.568410
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Economics.

Volume (Year): 44 (2012)
Issue (Month): 23 (August)
Pages: 2997-3010

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Handle: RePEc:taf:applec:44:y:2012:i:23:p:2997-3010

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  1. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  2. Stéphane MUSSARD, 2006. "Une réconciliation entre la décomposition en sous-groupes et la décomposition en sources de revenu de l'indice de Gini. La multi-décomposition de l'indicateur de Gini," Annales d'Economie et de Statistique, ENSAE, issue 81, pages 169-193.
  3. Russell Davidson, 2009. "Reliable inference for the GINI Index," Working Papers halshs-00443553, HAL.
  4. Sastry, D V S & Kelkar, Ujwala R, 1994. "Note on the Decomposition of Gini Inequality," The Review of Economics and Statistics, MIT Press, vol. 76(3), pages 584-86, August.
  5. BOSSERT, Walter & D’AMBROSIO, Conchita, 2004. "Reference Groups and Individual Deprivation," Cahiers de recherche 13-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-47, August.
  7. Jacques Silber, 1998. "On Inequality in Consumption Expenditures. The Case of Switzerland," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 134(IV), pages 545-564, December.
  8. 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.
  9. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
  10. Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
  11. Paul Makdissi & Quentin Wodon, 2001. "Poverty-Reducing and Welfare-Improving Marginal Public Price and Price Cap Reforms," Cahiers de recherche 04-04, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke, revised 2004.
  12. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
  13. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-55, June.
  14. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  15. Duclos, Jean-Yves & Makdissi, Paul & Wodon, Quentin, 2003. "Poverty-Efficient Transfer Programs: The Role of Targeting and Allocation Rules," Cahiers de recherche 0305, CIRPEE.
  16. Fields, Gary S, 1979. "Income Inequality in Urban Colombia: A Decomposition Analysis," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(3), pages 327-41, September.
  17. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-29, September.
  18. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-15, February.
  19. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  20. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May.
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Cited by:
  1. Mussini, Mauro, 2013. "On decomposing inequality and poverty changes over time: A multi-dimensional decomposition," Economic Modelling, Elsevier, vol. 33(C), pages 8-18.

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