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
