Income inequality is a persistent topic of public and political debate. In this context, the focus often shifts from the national level to a more detailed geographical level. In particular, inequality between or within local communities can be assessed. In this article, the estimation of inequality within regions, that is, between households, is considered at a regionally disaggregated level. From a methodological point of view, a small area estimation of the Gini coefficient is carried out using an area-level model linking survey data with related administrative data. Specifically, the Fay-Herriot model is applied using a logit-transformation followed by a bias-corrected back-transformation. The uncertainty of the point estimate is assessed using a parametric bootstrap procedure to estimate the mean squared error. The validity of the methodology is shown in a model-based simulation for the point estimator as well as for the uncertainty measure. The proposed methodology is illustrated by estimating model-based Gini coefficients for spatial planning regions in Germany, using survey data from the Socio-Economic Panel and aggregate data from the 2011 Census. The results show that intra-regional inequality is more diverse than a consideration only between East and West suggests.

中文翻译：

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应用德国空间规划区域估算区域内不平等

收入不平等是公众和政治辩论的一个持久话题。在这种情况下，重点往往从国家层面转移到更详细的地理层面。特别是，可以评估当地社区之间或内部的不平等。在本文中，区域内部（即家庭之间）的不平等估计是在区域分解水平上考虑的。从方法论的角度来看，基尼系数的小区域估计是使用区域级模型将调查数据与相关行政数据联系起来进行的。具体来说，Fay-Herriot 模型使用一个 logit 变换，然后是一个偏差校正的反向变换来应用。点估计的不确定性使用参数自举程序进行评估，以估计均方误差。该方法的有效性在点估计器和不确定性测量的基于模型的模拟中得到体现。通过使用社会经济面板的调查数据和 2011 年人口普查的汇总数据，估算德国空间规划区域基于模型的基尼系数，说明了拟议的方法。结果表明，区域内的不平等比仅在东西方之间的考虑所暗示的更加多样化。