Including the asymmetry of the Lorenz curve into measures of economic inequality

TL;DR

This paper introduces an adjusted inequality measure that incorporates the asymmetry of the Lorenz curve, making it more sensitive to income disparities at the distribution tails compared to the Gini index.

Contribution

It proposes a new inequality measure that accounts for distributional asymmetry by weighting Lorenz curve deviations, enhancing sensitivity to income extremes.

Findings

The new measure reduces to Gini for symmetric distributions.

It is more responsive to income differences at the distribution tails.

The measure maintains desirable properties of the Gini index.

Abstract

The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by attaching weights to the distances between the Lorenz curve and the 45-degree line. The measure is equivalent to the Gini if the distribution is symmetric. The alternative measure of inequality inherits good properties from the Gini but is more sensitive to changes in the extremes of the income distribution.