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Asymptotic distribution of the quintile share ratio estimator


TA Kpanzou

Abstract

The quintile share ratio (QSR) is a recently introduced measure of income in- equality, also forming part of the European Laeken indicators which cover four important dimensions of social inclusion (nancial poverty, employment, health and education). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. From the denition of the QSR, a (traditional) nonparametric estimator for it follows easily as a plug-in-type estimator. However, not much is known about the theoretical properties of this estimator. In this paper the estimator is dened and its asymptotic distribution theory derived. Using a simulation study, some nite sample properties of the limiting normal distribution are explored and reported on.

Resume. Le rapport des quintiles (QSR) est une mesure d'inegalite  introduite recemment et fait partie des indicateurs europeens couvrant quatre dimensions importantes de l'inclusion sociale, a savoir, la pauvrete, l'emploi, la sante et l'education. En 2001, le Conseil Europeen a decide que l'inegalite du revenu dans les pays membres de l'Union Europeenne devrait etre decrite par un certain nombre d'indicateurs y compris le QSR. De part sa denition, on obtient facilement un estimateur de substitution pour cette mesure d'inegalite. Cependant, tres peu est connu sur les proprietes theoriques dudit estimateur. Dans cet article nous denissons l'estimateur nonparametrique du QSR et nous donnons sa distribution limite. A travers des simulations, nous explorons la loi limite ainsi obtenue, a savoir la loi normale.

Key words: Measures of inequality; Extreme value index; Influence function; Empirical process; Condence intervals; Simulation.


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print ISSN: 2316-090X