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Linking Yitzhaki’s and Dagum’s Gini Decompositions

  • Stéphane Mussard
  • Patrick Richard

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 within- and between-group Gini elasticities, which gauge the impact of global transfers on within- and between-group inequalities, respectively.

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File URL: http://www.lameta.univ-montp1.fr/Documents/DR2008-13.pdf
File Function: First version, 2008
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Paper provided by LAMETA, Universtiy of Montpellier in its series Working Papers with number 08-13.

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Length: 18 pages
Date of creation: Jul 2008
Date of revision: Jul 2008
Handle: RePEc:lam:wpaper:08-13
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  1. Bossert, Walter & D'Ambrosio, Conchita, 2006. "Reference groups and individual deprivation," Economics Letters, Elsevier, vol. 90(3), pages 421-426, March.
  2. 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.
  3. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
  4. 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.
  5. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
  6. 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.
  7. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
  8. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-55, June.
  9. 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.
  10. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  11. 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.
  12. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-47, August.
  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. 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.
  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. 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.
  17. 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.
  18. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  19. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May.
  20. 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.
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