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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.

Suggested Citation

  • Stéphane Mussard & Patrick Richard, 2008. "Linking Yitzhaki’s and Dagum’s Gini Decompositions," Working Papers 08-13, LAMETA, Universtiy of Montpellier, revised Jul 2008.
  • Handle: RePEc:lam:wpaper:08-13

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    References listed on IDEAS

    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    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.
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    4. 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.
    5. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    6. 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 327-341, September.
    7. 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," Annals of Economics and Statistics, GENES, issue 81, pages 169-193.
    8. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, 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 584-586, August.
    10. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    11. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    12. Duclos, Jean-Yves & Makdissi, Paul & Wodon, Quentin, 2003. "Poverty-Efficient Transfer Programs: The Role of Targeting and Allocation Rules," Cahiers de recherche 0305, CIRPEE.
    13. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-547, August.
    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, 2006. "Reference groups and individual deprivation," Economics Letters, Elsevier, vol. 90(3), pages 421-426, March.
    16. 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.
    17. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, Oxford University Press, vol. 93(2), pages 321-324.
    18. 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, August.
    19. 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.
    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.
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    Cited by:

    1. Mussard, Stéphane & Pi Alperin, Maria Noel, 2011. "Poverty growth in Scandinavian countries: A Sen multi-decomposition," Economic Modelling, Elsevier, vol. 28(6), pages 2842-2853.
    2. Ogwang Tomson, 2016. "The Marginal Effects in Subgroup Decomposition of the Gini Index," Journal of Official Statistics, De Gruyter Open, vol. 32(3), pages 733-745, September.
    3. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.
    4. Mussini, Mauro, 2013. "On decomposing inequality and poverty changes over time: A multi-dimensional decomposition," Economic Modelling, Elsevier, vol. 33(C), pages 8-18.

    More about this item

    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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