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Linking Yitzhaki’s and Dagum’s Gini Decompositions

  • Stéphane Mussard

    ()

    (Lameta, Université Montpellier I)

  • Patrick Richard

    ()

    (GREDI, Département d'économique, Université de Sherbrooke)

In this article we show that the Gini coefficient is simultaneously decomposable both by sources of income and by populations of income receivers for non-overlapping 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 non-poor people, (iii) it enables one to measure the impact of marginal tax reforms on within- and between-group, respectively.

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File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0821.pdf
File Function: First version, 2008
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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 08-21.

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Length: 20 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:shr:wpaper:08-21
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  1. Paul Makdissi & Quentin Wodon, 2007. "Poverty-Reducing and Welfare-Improving Marginal Public Price and Price Cap Reforms," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 683-698, 08.
  2. Duclos, Jean-Yves & Makdissi, Paul & Wodon, Quentin, 2003. "Poverty-Efficient Transfer Programs: The Role of Targeting and Allocation Rules," Cahiers de recherche 0305, CIRPEE.
  3. 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.
  4. Russell Davidson & Emmanuel Flachaire, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00175929, HAL.
  5. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  6. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-55, June.
  7. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May.
  8. 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.
  9. Russell Davidson, 2007. "Reliable Inference For The Gini Index," Working Papers halshs-00353856, HAL.
  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. 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.
  12. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  13. 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.
  14. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
  15. BOSSERT, Walter & D’AMBROSIO, Conchita, 2004. "Reference Groups and Individual Deprivation," Cahiers de recherche 13-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  16. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-47, August.
  17. 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.
  18. 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.
  19. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  20. 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.
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