Estimation of income inequality from grouped data

TL;DR

This paper evaluates the use of the generalized beta distribution of the second kind (GB2) to improve income inequality estimates from grouped data, outperforming traditional nonparametric bounds across extensive datasets.

Contribution

It demonstrates that the GB2 distribution provides more accurate income inequality estimates from grouped data than nonparametric methods, with practical implementation in R.

Findings

GB2 outperforms nonparametric bounds in accuracy

The method is effective across diverse countries and periods

Implementation in R is accessible and reliable

Abstract

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.