A simple method for estimating the Lorenz curve

TL;DR

This paper introduces a straightforward method to estimate the Lorenz curve using the Gini index and income shares, avoiding complex error minimization, and demonstrates its effectiveness across diverse country data.

Contribution

It proposes a simple, closed-form approach for estimating the Lorenz curve from limited data, enhancing practical applicability in low-data scenarios.

Findings

Estimated Lorenz curves closely match actual data.

Gini index estimates are nearly identical to observed values.

Method performs well across countries with different income inequality levels.

Abstract

Given many popular functional forms for the Lorenz curve do not have a closed-form expression for the Gini index and no study has utilized the observed Gini index to estimate parameter(s) associated with the corresponding parametric functional form, a simple method for estimating the Lorenz curve is introduced. It utilizes 3 indicators, namely, the Gini index and the income shares of the bottom and the top in order to calculate the values of parameters associated with the specified functional form which has a closed-form expression for the Gini index. No error minimization technique is required in order to estimate the Lorenz curve. The data on the Gini index and the income shares of 4 countries that have different level of income inequality, economic, sociological, and regional backgrounds from the United Nations University-World Income Inequality Database are used to illustrate how the simple method works. The overall results indicate that the estimated Lorenz curves fit the actual observations practically well. This simple method could be useful in the situation where the availability of data on income distribution is low. However, if more data on income distribution are available, this study shows that the specified functional form could be used to directly estimate the Lorenz curve. Moreover, the estimated values of the Gini index calculated based on the specified functional form are virtually identical to their actual observations.