Asymptotic Distribution Theory of Empirical Rank-Dependent Measures of Inequity

ICER Working Paper No. 12/2006

21 Pages Posted: 24 Sep 2006

See all articles by Rolf Aaberge

Rolf Aaberge

Statistics Norway; Institute for the Study of Labor (IZA); Deaprtment of Economics

Date Written: 2006

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 is 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 [14] 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.

Suggested Citation

Aaberge, Rolf, Asymptotic Distribution Theory of Empirical Rank-Dependent Measures of Inequity (2006). ICER Working Paper No. 12/2006, Available at SSRN: https://ssrn.com/abstract=932062 or http://dx.doi.org/10.2139/ssrn.932062

Rolf Aaberge (Contact Author)

Statistics Norway ( email )

N-0033 Oslo
Norway

Institute for the Study of Labor (IZA) ( email )

P.O. Box 7240
Bonn, D-53072
Germany

Deaprtment of Economics ( email )

Norway

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