School of Economics, Henan University, Kaifeng, Henan, China.
PLoS One. 2022 Jun 24;17(6):e0267828. doi: 10.1371/journal.pone.0267828. eCollection 2022.
This paper discusses the first moment, i.e., the mean income point, of income density functions and the estimation of single-parametric Lorenz curves. The mean income point is implied by an income density function and associated with a single-parametric Lorenz function. The boundary of the mean income point can show the flexibility of a parametric Lorenz function. I minimize the sum of squared errors in fitting both grouped income data and the mean income point and identify the best parametric Lorenz function using a large panel dataset. I find that each parametric Lorenz function may do a better job than others in fitting particular grouped data; however, a zero- and unit-modal single-parametric Lorenz function is identified to be the best of eight typical optional functions in fitting most (666 out of 969) observations of a large panel dataset. I perform a Monte Carlo simulation as a robustness check of the empirical estimation.
本文讨论了收入密度函数的第一矩，即均值收入点，以及单参数洛伦兹曲线的估计。均值收入点由收入密度函数隐含，并与单参数洛伦兹函数相关联。均值收入点的边界可以显示参数洛伦兹函数的灵活性。我通过最小化拟合分组收入数据和均值收入点的平方和误差，使用大型面板数据集确定最佳参数洛伦兹函数。我发现每个参数洛伦兹函数在拟合特定分组数据方面可能都比其他函数表现更好；然而，在拟合大型面板数据集的大多数（969 个观测值中的 666 个）观测值时，一个零模态和单位模态的单参数洛伦兹函数被确定为八个典型可选函数中最佳的函数。我进行了蒙特卡罗模拟，以检验实证估计的稳健性。
