A Simple and Effective Inequality Measure

Luke A. Prendergast and Robert G. Staudte

The American Statistician, 2018, vol. 72, issue 4, 328-343

Abstract: Ratios of quantiles are often computed for income distributions as rough measures of inequality, and inference for such ratios has 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) quantile, 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 measure 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 large sample 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.

Date: 2018
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DOI: 10.1080/00031305.2017.1366366

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