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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Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number
402.
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods D - Microeconomics
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Yitzhaki, Shlomo, 1983.
"On an Extension of the Gini Inequality Index,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-28, October.
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