In this paper, we use the distributions of order statistics to define functions with the appropriate properties to represent social preferences regarding income distributions. Following the approach of Yaari (1987, 1988), this allows constructing a set of social welfare functions from which the corresponding inequality indices are derived. The obtained measures incorporate diverse normative criteria, with different degrees of preference for equality. The generalized Gini coefficients and the family of indices proposed by Aaberge (2000) are obtained as particular cases. This approach allows interpreting each inequality measure in terms of the statistics computed from a randomly selected sample and the identification of unbiased estimators of the Social Welfare Functions. It also shows that each of the families of inequality indices are obtained from the moments of the order statistics and, therefore, each of the families characterizes any income distribution with finite mean. This characterization is very useful in the case of distributions with heavy tail and pronounced positive skew that shows only a few potential moments.
The authors acknowledge the financial support provided by the Spanish Institute of Fiscal Studies and the Universidad of Málaga. Elena Bárcena acknowledges the financial support provided by the Spanish Ministry of Education through Grant ECO2012-33993. She also thanks the financial support provided by Fundación Ramón Areces, XI Concurso Nacional para la Adjudicación de Ayudas a la Investigación en Ciencias Sociales.
Parrado-Gallardo, E.M., Bárcena-Martín, E. and Imedio-Olmedo, L.J. (2014), "Inequality, Welfare, and Order Statistics", Economic Well-Being and Inequality: Papers from the Fifth ECINEQ Meeting (Research on Economic Inequality, Vol. 22), Emerald Group Publishing Limited, pp. 383-399. https://doi.org/10.1108/S1049-258520140000022012Download as .RIS
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