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Pair-Based Decomposable Inequality Measures


  • Stéphane Mussard


Four axioms are introduced in order to characterize the family of pair-based decomposable inequality measures, which is embraced in the class of weakly decomposable inequality measures. Three axioms, namely, normalization by pairs, aggregation by pairs, and decomposition by pairs enable the pair-based family of inequality measures to be deduced and to be decomposed into within- and between-group components. The weights of population shares that bring out those within- and between-group estimators have the particularity to be unique and to sum to unity. By invoking the fourth axiom of symmetry by pairs, it is proved that pair-based inequality measures and their two decomposed components are U-statistics, so that, statistical information may be inferred.

Suggested Citation

  • Stéphane Mussard, 2010. "Pair-Based Decomposable Inequality Measures," Working Papers 10-15, LAMETA, Universtiy of Montpellier, revised Nov 2010.
  • Handle: RePEc:lam:wpaper:10-15

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    References listed on IDEAS

    1. Antonio Abatemarco, 2010. "Measuring inequality of opportunity through between-group inequality components," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 475-490, December.
    2. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-547, August.
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    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation


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