Intersecting Lorenz curves and aversion to inverse downside inequality

From Springer Nature via Jisc Publications RouterHistory: received 2019-01-22, registration 2020-09-16, accepted 2020-09-16, pub-electronic 2020-10-02, online 2020-10-02, pub-print 2021-04Publication status: PublishedFunder: University of ManchesterAbstract: This paper defines and characterizes the concept of an increase in inverse downside inequality and show that, when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting inverse downside inequality aversion often depends on the relative strengths of its aversion to inverse downside inequality and inequality aversion. For the class of linear inequality indices, of which the Gini coefficient is a member, a measure characterizing the strength of an index’s aversion to inverse downside inequality against its own inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified