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Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality

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Abstract

A major aim of most income distribution studies is to make comparisons of income inequality across time for a given country and/or compare and rank different countries according to the level of income inequality. However, most of these studies lack information on sampling errors, which makes it difficult to judge the significance of the attained rankings. The purpose of this paper it to derive the asymptotic properties of the empirical rank-dependent family of inequality measures. A favourable feature of this family of inequality measures is that it includes the Gini coefficients, and that any member of this family can be given an explicit and simple expression in terms of the Lorenz curve. By relying on a result of Doksum (1974) it is easily demonstrated that the empirical Lorenz curve, regarded as a stochastic process, converges to a Gaussian process. Moreover, this result forms the basis of the derivation of the asymptotic properties of the empirical rank-dependent measures of inequality.

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  • Rolf Aaberge, 2005. "Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality," Discussion Papers 402, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:402
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    1. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
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    9. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    10. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
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    12. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    13. Aaberge, Rolf, 2008. "Erratum to "Axiomatic characterization of the Gini coefficient and Lorenz curve orderings" [J. Econ. Theory 101 (2001) 115-132]," Journal of Economic Theory, Elsevier, vol. 140(1), pages 1-1, May.
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    Cited by:

    1. Francesco Andreoli, 2013. "Inference for Inverse Stochastic Dominance," Working Papers 295, ECINEQ, Society for the Study of Economic Inequality.
    2. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    3. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    4. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.
    5. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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