Minimum distance estimation of parametric Lorenz curves based on grouped data
针对世界银行等机构发布的分组收入数据，提出两种参数洛伦兹曲线的有效估计与推断方法，并通过模拟和实例证明其优于现有做法，为不平等分析提供更严谨的工具。
The Lorenz curve, introduced more than 100 years ago, remains as one of the main tools for analysis of inequality. 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 inequality analyses. Despite the prevalence of parametric estimation of Lorenz curves from grouped data, and the existence of well-developed nonparametric methods, a formal description of rigorous methodology for estimating parametric Lorenz curves from grouped data is lacking. We fill this gap. Building on two data generating mechanisms, efficient methods of estimation and inference are described; several 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.