Small Area Estimation of Inequality Measures using Mixtures of Beta

TL;DR

This paper develops a Bayesian hierarchical Beta mixture model for small area estimation of inequality measures, improving accuracy over standard models and providing variance approximations, with application to EU-SILC data.

Contribution

It introduces a novel Beta mixture model for small area estimation of inequality measures, addressing skewness and heavy tails, and extends analysis with variance function derivations.

Findings

Model outperforms standard Beta regression in bias, coverage, and error.

Application to EU-SILC data demonstrates practical effectiveness.

Variance functions for inequality estimators are derived.

Abstract

Economic inequalities referring to specific regions are crucial in deepening spatial heterogeneity. Income surveys are generally planned to produce reliable estimates at countries or macroregion levels, thus we implement a small area model for a set of inequality measures (Gini, Relative Theil and Atkinson indexes) to obtain microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at area level involving a Beta mixture. An application on EU-SILC data is carried out and a design-based simulation is performed. Our model outperforms in terms of bias, coverage and error the standard Beta regression model. Moreover, we extend the analysis of inequality estimators by deriving their approximate variance functions.