Asymptotic distribution theory of empirical rank-dependent measures of inequality
Working paper
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http://hdl.handle.net/11250/180931Utgivelsesdato
2005Metadata
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Sammendrag
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.
Keywords: The Lorenz curve, the Gini coefficient, rank-dependent measures of inequality,
nonparametric estimation methods, asymptotic distribution theory.