Small Area Estimation of Relative Inequality Indices using Mixtures of Beta

The paper aims at proposing a small area estimation strategy for the Theil Index, an entropy-based inequality measure. Specifically, we have developed an area-level model of its relative index, i.e. Theil index over its maximum, which has more manageable support between 0 and 1. Classical proposals in area-level context for measures defined on the unit interval are mostly based on proportions modelling and show limitations when dealing with asymmetric heavy-tailed data, such as in our case. We propose a Hierarchical Bayes model with alternative likelihood assumptions based on a particular Beta mixture, providing a more flexible framework.