Mind the income gap: bias correction of inequality estimators in small-sized samples

Abstract

Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains. 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 index families by accounting for complex survey designs. The proposed methodology is based on Taylor’s expansions and does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using data taken from the EU-SILC survey, showing a noticeable bias reduction for all the measures. Lastly, a small area estimation exercise shows the risks of ignoring prior bias correction in a basic area-level model, determining model misspecification