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.Comment: 28 pages, 7 figures, 2 tables, 2 pages of supplementary materia