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.

翻译：针对特定区域的经济不平等对于深化空间异质性研究至关重要。收入调查通常设计为在国家或宏观区域层面提供可靠估计，因此我们采用一套不平等度量指标（基尼系数、相对泰尔指数和阿特金森指数）建立小区域模型，以获取微观区域估计值。考虑到不平等估计量是定义在单位区间上且具有偏态和厚尾分布，我们提出一种基于贝塔混合的贝叶斯层次区域模型。基于欧盟收入与生活条件统计数据进行应用研究，并开展设计模拟检验。我们的模型在偏差、覆盖率和误差方面均优于标准贝塔回归模型。此外，我们通过推导不平等估计量的近似方差函数，扩展了相关分析维度。