The estimation of a family of measures of economic inequality

Abstract This paper shows that a broad class of measures of inequality (including those of Herfindahl and Theil) can be readily (and accurately) estimated from grouped data. The methods are similar to those developed earlier by the author for estimating the Gini index. The results are illustrated by estimating Thiel's index from tax data and show that the standard textbook grouping method of assuming that all incomes in any class are at the mid-point can lead to serious error in the resulting estimate of inequality.