Semiparametric inference on Gini indices of two semicontinuous populations under density ratio models

TL;DR

This paper develops semiparametric methods to estimate and compare Gini indices of two semicontinuous populations, improving efficiency over existing nonparametric approaches and applicable to real-world economic data.

Contribution

It introduces maximum empirical likelihood estimators for Gini indices under a density ratio model for semicontinuous data, with proven asymptotic properties and practical advantages.

Findings

Proposed estimators are more efficient than existing methods.

Simulation studies confirm the superiority of the new estimators.

Applications to real data demonstrate practical utility.

Abstract

The Gini index is a popular inequality measure with many applications in social and economic studies. This paper studies semiparametric inference on the Gini indices of two semicontinuous populations. We characterize the distribution of each semicontinuous population by a mixture of a discrete point mass at zero and a continuous skewed positive component. A semiparametric density ratio model is then employed to link the positive components of the two distributions. We propose the maximum empirical likelihood estimators of the two Gini indices and their difference, and further investigate the asymptotic properties of the proposed estimators. The asymptotic results enable us to construct confidence intervals and perform hypothesis tests for the two Gini indices and their difference. We show that the proposed estimators are more efficient than the existing fully nonparametric estimators. The proposed estimators and the asymptotic results are also applicable to cases without excessive zero values. Simulation studies show the superiority of our proposed method over existing methods. Two real-data applications are presented using the proposed methods.