Measuring Inequality: Using the Geometric Mean/Arithmetic Mean Ratio

Since unambiguous ranking of income distributions according to their degree of inequality is not always possible, choice of inequality measure must rest on the appropriateness of particular measures for particular substantive problems. This article provides a complete account of one measure of inequality, δ, defined, for x > 0, as the ratio of the geometric mean to the arithmetic mean-a measure that is closely linked to the sense of distributive justice. Its properties are summarized, and formulas reported for the effects of transfers and of location changes. Analytic expressions for δ for three classical probability distributions-the Pareto, Lognormal, and Rectangular families-are provided, and δ's behavior in within-family comparisons discussed. The measure δ's behavior in between-family comparisons is explored using a new procedure for bounding the zones of ambiguity in inequality comparisons. Finally, a newly obtained decomposition formula for δ is reported.