Gini Curve and Top Incomes

Abstract

An income inequality index number, which assigns a single numerical value to the income distribution, cannot summarize the complete information in the distribution. We propose a family of inequality index curves, which includes curves generated by popular inequality index numbers (e.g. the top income shares, the Gini coefficient, the single parameter Gini coefficient, the Palma ratio, and the Hoover index). The family has two advantages: (1) The family has an axiomatic foundation based on the weighted expected utility theory. (2) Each curve in the family contains the full information of the income distribution. Complementing the previous empirical studies based on the top income shares, we use the family of inequality index curves and micro level data to show that the bottom and middle income people in the U.S. became more equally relatively poor (not just relatively poorer) from 1990 to 2010.