Inference for Lorenz Curves

The Lorenz curve, introduced more than 100 years ago, is still one of the main tools in poverty and inequality analysis. International institutions such as the World Bank collect and publish grouped income data in the form of population and income shares for a large number of countries. These data are often used for estimation of parametric Lorenz curves which in turn form the basis for most poverty and inequality analyses. Despite the prevalence of parametric estimation of Lorenz curves from grouped data, and the existence of well-developed nonparametric methods, a rigorous statistical foundation for estimating parametric Lorenz curves has not been provided. In this paper we propose a sound statistical framework for making inference about parametric Lorenz curves for both grouped and individual data. Building on two data generating mechanisms, efficient methods of estimation and inference are proposed and a number of results useful for comparing the two methods of inference, and aiding computation, are derived. Simulations are used to assess the estimators, and curves are estimated for some example countries. We also show how the proposed methods improve upon World Bank methods and make recommendations for improving current practices.