Income inequality measures are biased in small samples leading generally to an underestimation. After investigating the nature of the bias, we propose a bias-correction framework for a large class of inequality measures comprising Gini Index, Generalized Entropy and Atkinson families by accounting for complex survey designs. The proposed methodology is based on Taylor's expansions and Generalized Linearization Method, and does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of the suggested correction has been carried out using data taken from EU-SILC survey. Results show a noticeable bias reduction for all measures. A bootstrap variance estimation proposal and a distributional analysis follow in order to provide a comprehensive overview of the behavior of inequality estimators in small samples. Results about estimators distributions show increasing positive skewness and leptokurtosis at decreasing sample sizes, confirming the non-applicability of classical asymptotic results in small samples and suggesting the development of alternative methods of inference.
翻译:收入不平等措施一般在导致低估的小型抽样中存在偏差。在调查偏差的性质之后,我们建议为一大批不平等措施提供一个偏差纠正框架,其中包括基尼指数、通用的Entropy和Atkinson家庭,其中考虑到复杂的调查设计。拟议方法以泰勒的扩张和普遍线性化方法为基础,并不要求对收入分配作任何参数假设,而且非常灵活。对建议的更正进行基于设计的业绩评价时使用了欧盟-SILC调查的数据。结果显示所有措施都有明显的偏差减少。结果显示所有措施都有明显的偏差减少。一个靴子间差异估计建议和分配分析随后进行,以便全面概述小样本中不平等估计者的行为。关于估计者分布的结果显示,在抽样规模缩小时,正值和浸水管病增加,证实在小样本中经典的无症状结果不适用,并建议开发其他推论方法。