Mind the Income Gap: Behavior of Inequality Estimators from Complex Survey Small Samples

Abstract

Income inequality measures are biased in small samples leading generally to an underestimation. After investigating the nature of the bias, we propose a biascorrection 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 lepto-kurtosis at decreasing sample sizes, confirming the non-applicability of the classical asymptotic results in small samples and suggesting the development of alternative methods of inference.