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On Decomposition of the Gini Index of Equality

Author

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  • Stéphane Mussard

    (GREDI, Université de Sherbrooke and Université de Perpignan)

Abstract

The purpose of this paper is to show that the Gini index of equality is: (i) subgroup decomposable throughout interpersonal comparisons; (ii) decomposable by income source; (iii) decomposable both by subgroup and income source; (iv) and decomposable in a multidimensional context permitting statistical inference on equality components. These results entail that decision makers must use the Gini index of equality decompositions since they imply necessarily the computation of the Gini index of inequality decompositions. The reverse is not true.

Suggested Citation

  • Stéphane Mussard, 2005. "On Decomposition of the Gini Index of Equality," Cahiers de recherche 05-09, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
  • Handle: RePEc:shr:wpaper:05-09
    as

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    File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0508.pdf
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    2. 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 313-329, September.
    3. 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.
    4. Kuan Xu & Lars Osberg, 2002. "The social welfare implications, decomposability, and geometry of the Sen family of poverty indices," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 35(1), pages 138-152, February.
    5. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    6. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    7. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    8. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    9. John C. H. Fei & Gustav Ranis & Shirley W. Y. Kuo, 1978. "Growth and the Family Distribution of Income by Factor Components," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(1), pages 17-53.
    10. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-547, August.
    11. Berrebi, Z M & Silber, Jacques G, 1987. "Dispersion, Asymmetry and the Gini Index of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 331-338, June.
    12. 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 107-115, February.
    13. Shlomo Yitzhaki & Robert I. Lerman, 1991. "Income Stratification And Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
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    More about this item

    Keywords

    Gini index of equality; Multi-decomposition;

    JEL classification:

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

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