Inference for inequality measures: a review

In this paper we present a review of the most recent contributes of the econometric literature on comparing inequality measures, focusing in particular on Theil index and Gini index. We will start by discussing the main issue behind this bulk of literature, which is the heavy tail of the income distribution. Specifically, the severity of the inference problem responds to the exact nature of the right tail of the distribution. Attention in the literature has been given to determining the limits of conventional inference in the presence of heavy tails and, in particular, of bootstrap inference. Then we review a number of methods based on alternative parametric bootstrap and, more recently on permutations that heated in this debate in the last 10 years.