Ranking intersecting Lorenz curves

Abstract

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that focuses on changes that take place in the lower part of the income distribution and the other that focuses on changes that concern the upper part of the income distribution. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of Lorenz curves. Keywords: The Lorenz curve, partial orderings, rank-dependent measures of inequality, generalized Gini families of inequality measures, principles of transfers and mean-spread-preserving transformations.

JEL classification: D31, D63