Small area estimation of inequality measures using mixtures of Beta

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 reliable microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at the 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.