Flexible Small Area Estimation of Theil Index using Mixtures of Beta

The aim of the paper is to propose a small area estimation model for Theil Index, an entropy-based measure used to quantify economic inequality, industrial concentration and, in general, the disparity related to economic phenomena. We developed an area-level model of its relative index, i.e. Theil index over its maximum, which has a more manageable support between 0 and 1. Classical proposals in area-level context for measures on (0,1) are mostly based on proportions modelling and show limitations when dealing with asymmetric heavy-tailed data, such as in our case. We propose a model with alternative distributional assumptions based on a particular Beta mixture with unconstrained mean modeling, estimated under a Hierarchical Bayes approach. An application to ITSILC income data is provided, showing that our proposal yields a more flexible framework in comparison with Beta regression with unmatched sampling and linking models.