Gini Variance Estimation of Grouped Data

ABSTRACT We propose a jackknife variance estimator for the Gini Index based on grouped data. It only requires access to group means and counts, and is computationally fast, modifying an existing algorithm that exploits the Gini's connection with regression modelling. After reviewing the group‐level point estimator, we discuss its asymptotic normality and our jackknife's consistency. We then conduct a multiplicative random effects simulation, comparing the jackknife's results to those of an off‐the‐shelf method for variance estimation in this setting. The jackknife is more stable across within‐group variations and more closely approximates the true group‐level variance, although cases of extreme inequality may require very high sample sizes to achieve desired accuracy. We conclude with thoughts for future research.