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The β Family of Inequality Measures

Working Paper 2013-289

Abstract

This paper introduces and analyses, both normatively and statistically, a new class of inequality measures. This class generalizes and comprises different well-known families of inequality measures as particular cases. The elements of this new class are obtained by weighting local inequality evaluated through the Bonferroni curve. The weights are the density functions of the beta distributions over [0,1]. Therefore, the weights are not necessarily monotonic. This allows us to choose the inequality measures that are more or less sensitive to changes that could take place in any part of the distribution. As a consequence of the different weighting schemes attached to the indexes, the elements of the class introduce very dissimilar value judgements in the measurement of inequality and welfare. The possibility of choosing the index that focuses on a specific percentile, and not necessarily on the extremes of the distribution, is one of the advantages of our proposal.

Authors: Luis José Imedio Olmedo, Encarnación M. Parrado Gallardo, Elena Bárcena Martín.

Keywords: Lorenz curve, Bonferroni curve, preference distributions, inequality aversion, beta distribution
JEL: C10, D31, I38