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Two Types of Inequality

Inequality Between Persons and Inequality Between Subgroups

New York University, New York, gj1{at}nyu.edu

Samuel Kotz

George Washington University, Washington, DC

This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ``deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

Key Words: continuous univariate distributions • two-parameter distributions • lognormal distribution • Pareto distribution • power-function distribution • Gini coefficient • Atkinson measure • Theil's MLD • coefficient of variation • Lorenz curve • decomposition of inequality measures • between component • within component

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