A practical guide to proper estimation and inference of the Gini index by avoiding often encountered methodological pitfalls

Abstract

The Gini index is the most widely-used measure of inequality. Unfortunately, its computation is subject to error. Researchers and practitioners often fall into common methodological pitfalls, leading to inaccurate estimates and inferences, and ultimately hindering efforts to reduce inequality and improve societal quality of life. This paper clarifies the challenges of non-parametric estimation of the Gini index more comprehensively than previous contributions, and offers robust methodological recommendations to ensure accurate estimates. Additionally, we reference a free, easy-to-use R package which, together with the clear methodological insights, enhances the real-world applicability of our findings. First, we investigate the impact of common methodological pitfalls on point estimates, providing a complete review for both infinite and finite populations. We then examine variance estimation and the performance of confidence intervals. Among other issues, the findings reveal that, when a popular regression-based variance estimator is used, the variance of the Gini index is seriously underestimated in distributions with high skewness and inequality, as often observed in real-world applications. Jackknife variance estimates and jackknife intervals, based on studentized quantiles, prove to be the most accurate approaches. The analysis employs variables with varying degrees of skewness and inequality (as both characteristics influence the potential for bias), thereby encompassing most of the situations found in empirical research.