Comparing income distributions

In this talk, we discuss some hypothesis tests related to stochastic orders of convex or concave-type (also called second order dominance in economics). This kind of tests arises naturally in many applied disciplines such as economics, biology, reliability theory and control quality, among others. For instance, we may wonder if the distribution of wealth in a population is more even now than 10 years ago; if one financial inversion is riskier than another; if the lifetime of certain species is "significatively lower" under adverse conditions, such as pollution or stress; or if an airplane component ages with time or not.

We shall exhibit a new methodology to carry out these tests, as well as some illustrative examples focussed on the analysis of income distributions. The technique mainly consists in comparing the estimated means in ordered samples of the involved populations. The estimators which appear are functions of L-statistics and thus, in some situations, an asymptotic theory can be developed. However, in other cases computational techniques such as bootstrap are also required.

The present results are joint work with José Ramón Berrendero and Amparo Baíllo (Departamento de Matemáticas, Universidad Autónoma de Madrid).