  Grouped data in form of income shares have been conventionally used to
estimate income inequality due to the lack of availability of individual
records. Most prior research on economic inequality relies on lower bounds of
inequality measures in order to avoid the need to impose a parametric
functional form to describe the income distribution. These estimates neglect
income differences within shares, introducing, therefore, a potential source of
measurement error. The aim of this paper is to explore a nuanced alternative to
estimate income inequality, which leads to a reliable representation of the
income distribution within shares. We examine the performance of the
generalized beta distribution of the second kind and related models to estimate
different inequality measures and compare the accuracy of these estimates with
the nonparametric lower bound in more than 5000 datasets covering 182 countries
over the period 1867-2015. We deploy two different econometric strategies to
estimate the parametric distributions, non-linear least squares and generalised
method of moments, both implemented in R and conveniently available in the
package GB2group. Despite its popularity, the nonparametric approach is
outperformed even the simplest two-parameter models. Our results confirm the
excellent performance of the GB2 distribution to represent income data for a
heterogeneous sample of countries, which provides highly reliable estimates of
several inequality measures. This strong result and the access to an easy tool
to implement the estimation of this family of distributions, we believe, will
incentivize its use, thus contributing to the development of reliable estimates
of inequality trends.
