A Simple and Effective Inequality Measure

TL;DR

This paper introduces a simple, robust, and interpretable inequality measure based on ratios of symmetrically chosen quantiles, offering advantages over traditional methods like the Gini coefficient.

Contribution

It proposes a new inequality measure using quantile ratios, with properties like robustness, distribution-free inference, and convexity, improving upon traditional inequality metrics.

Findings

The measure is applicable to all positive income distributions.

It allows robust estimation and confidence intervals.

The inequality curve satisfies a median-based transference principle.

Abstract

Ratios of quantiles are often computed for income distributions as rough measures of inequality, and inference for such ratios have recently become available. The special case when the quantiles are symmetrically chosen; that is, when the p/2 quantile is divided by the (1-p/2), is of special interest because the graph of such ratios, plotted as a function of p over the unit interval, yields an informative inequality curve. The area above the curve and less than the horizontal line at one is an easily interpretable coefficient of inequality. The advantages of these concepts over the traditional Lorenz curve and Gini coefficient are numerous: they are defined for all positive income distributions, they can be robustly estimated and distribution-free confidence intervals for the inequality coefficient are easily found. Moreover the inequality curves satisfy a median-based transference principle and are convex for many commonly assumed income distributions.