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Within-group inequality: a comparison of different definitions and a new proposal of decomposition

Author

Listed:
  • Marc Fleurbaey

    (Paris School of Economics)

  • Peter Lambert
  • Domenico Moramarco

    (University of Bari)

  • VIto Peragine

    (University of Bari)

Abstract

In this paper, we compare two alternative procedures for identifying the within-group component of total inequality while decomposing total inequality into a between and a within-group term: the standard additive decomposition, which defines within-group inequality as the weighted sum of the inequality in each group, and the path-independent decomposition, which redefines the concept of within-group inequality by looking at a standardized distribution where groups have the same average income and do not overlap.We show that a decomposition of total inequality based on the former approach offers a clean measure of the between-group inequality, which is insensitive to changes in the distribution that do not alter the relative difference between the groups' averages. On the other hand, a decomposition based on the latter approach offers an unbiased measure of the within-group inequality, which is independent of the between-group component. Hence, we propose a new decomposition of the Gini index that combines the definition of between-group inequality stemming from the additive decomposition with the measure of within-group inequality at the base of the path-independent decomposition.Finally, we turn to the decomposition of the partial Lorenz ordering by exploring the implications of Lorenz between-group dominance combined with Lorenz within-group dominance. We also show the difficulty of defining sufficient conditions for two Lorenz curves not to intersect and suggest an alternative partial order based on concentration curves which do not account for the overlap between groups.

Suggested Citation

  • Marc Fleurbaey & Peter Lambert & Domenico Moramarco & VIto Peragine, 2024. "Within-group inequality: a comparison of different definitions and a new proposal of decomposition," Working Papers 673, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2024-673
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    References listed on IDEAS

    as
    1. Mauro Mussini, 2013. "A matrix approach to the Gini index decomposition by subgroup and by income source," Applied Economics, Taylor & Francis Journals, vol. 45(17), pages 2457-2468, June.
    2. Aronson, J. Richard & Lambert, Peter J., 1994. "Decomposing the Gini Coefficient to Reveal the Vertical, Horizontal, and Reranking Effects of Income Taxation," National Tax Journal, National Tax Association;National Tax Journal, vol. 47(2), pages 273-294, June.
    3. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    4. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
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    6. Peter Lambert & S. Subramanian, 2014. "Disparities in socio-economic outcomes: some positive propositions and their normative implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 565-576, October.
    7. Edward N. Wolff, 1976. "Occupational Earnings Behavior And The Inequality Of Earnings By Sex And Race In The United States," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 22(2), pages 151-166, June.
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    9. Aronson, J. Richard & Lambert, Peter J., 1994. "Decomposing the Gini Coefficient to Reveal the Vertical, Horizontal, and Reranking Effects of Income Taxation," National Tax Journal, National Tax Association, vol. 47(2), pages 273-94, June.
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    More about this item

    Keywords

    inequality; Gini coefficient; decomposition; within-group inequality;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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