A variance stabilizing transformation for the Gini concentration ratio

Abstract

In this paper we propose a new variance stabilizing transformation for the sample Gini concentration ratio. Our purpose is to improve inferences based on this sample inequality index, by yielding more reliable confidence intervals even for small sample sizes. In fact, those based on the asymptotic Normality of the Gim ratio are typically inaccurate because of the skewness of its finite sample distribution, which converges to Normality too slowly. The proposal is developed in a non-parametric setting but it is very easy to implement since it relies upon a linear approximation of the standard deviation of the Gini index. Finally, the better performance of confidence intervals elicited from the new variance stabilizing transformation is assessed through Monte Carlo experiments under the most common models for the income distribution.