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.Comment: 29 pages, 5 figures. Submitted for publicatio
