Coupling the Gini and Angles to Evaluate Economic Dispersion

TL;DR

This paper introduces a novel inequality measure that emphasizes disparities at the lower end of the distribution by combining Gini and angular differences, addressing limitations of traditional mean-based metrics.

Contribution

It proposes a new inequality index that better captures inequality at the lower tail, with desirable mathematical properties and sensitivity to disparities in that region.

Findings

The index is normalized and scale-invariant.

It is sensitive to transfers at the lower end of the distribution.

The measure is weakly decomposable and possesses several desirable properties.

Abstract

Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement tool that gives more weight to inequality at the lower end of the distribution, it is based on the comparison of all value pairs and synthesizes the dispersion of the whole distribution. The differences that sum to the Gini coefficient are scaled by angular differences between observations. The resulting index possesses a set of desirable properties, including normalization, scale invariance, population invariance, transfer sensitivity, and weak decomposability.