Linear Inequality Measures and the Redistribution of Income

Abstract

A class of inequality measures that is a natural companion to the popular Lorenz curve is the class of measures that are linear in incomes. These measures, which include the Gini and S-Gini coefficients, can be interpreted as ethical means of relative deprivation feelings. Their change through the tax and benefit system can be decomposed simply as a sum of progressivity indices for individual taxes and benefits, minus an index of horizontal inequity measured by the extent of reranking in the population. These progressivity and horizontal inequity indices can also be interpreted as ethical means of perceptions of fiscal harshness and ill-performance. We furthermore derive the asymptotic sampling distribution of these classes of indices of redistribution, progressivity, and horizontal inequity, which enables their use with micro-data on a population. We illustrate the theoretical and statistical results through an application on the distribution and redistribution of income in Canada in 1981 and in 1990.