A Simple and Effective Inequality Measure

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.
Comment: 20 pages, 9 figures