Sitthiyot Thitithep, Holasut Kanyarat
Department of Banking and Finance, Faculty of Commerce and Accountancy, Chulalongkorn University, Bangkok, Thailand.
Department of Chemical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, Thailand.
PLoS One. 2023 Jun 23;18(6):e0287546. doi: 10.1371/journal.pone.0287546. eCollection 2023.
Given that an excellent performance of any parametric functional form for the Lorenz curve that is based on a single country case study and a limited range of distribution must be treated with great caution, this study investigates the performance of a single-parameter functional form proposed by Paul and Shankar (2020) who use income data of Australia to show that their functional form is superior to the other existing widely used functional forms considered in their study. By using both mathematical proof and empirical data of 40 countries around the world, this study demonstrates that Paul and Shankar (2020)'s functional form not only fails to fit the actual observations well but also is generally outperformed by the other popular functional forms considered in their study. Moreover, to overcome the limitation of the performance of a single-parameter functional form on the criterion of the estimated Gini index, this study employs a functional form that has more than one parameter in order to show that, by and large, it performs better than all popular single-parameter functional forms considered in Paul and Shankar (2020)'s study. Thus, before applying any functional form to estimate the Lorenz curve, policymakers should check if it could describe the shape of income distributions of different countries through the changes in parameter values and yield the values of the estimated Gini index that are close to their observed data. Using a functional form that does not fit the actual observations could adversely affect inequality measures and income distribution policies.
鉴于基于单个国家案例研究和有限分布范围的任何洛伦兹曲线参数函数形式的出色表现都必须谨慎对待，本研究调查了保罗和尚卡尔（2020年）提出的单参数函数形式的表现，他们使用澳大利亚的收入数据表明他们的函数形式优于他们研究中考虑的其他现有的广泛使用的函数形式。通过数学证明和全球40个国家的实证数据，本研究表明，保罗和尚卡尔（2020年）的函数形式不仅不能很好地拟合实际观测值，而且在他们的研究中通常也不如其他流行的函数形式。此外，为了克服单参数函数形式在估计基尼系数标准方面的性能限制，本研究采用了一种具有多个参数的函数形式，以表明总体而言，它的表现优于保罗和尚卡尔（2020年）研究中考虑的所有流行的单参数函数形式。因此，在应用任何函数形式来估计洛伦兹曲线之前，政策制定者应检查它是否可以通过参数值的变化来描述不同国家的收入分配形状，并得出接近其观测数据的估计基尼系数值。使用不适合实际观测值的函数形式可能会对不平等度量和收入分配政策产生不利影响。
