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首页> 外文期刊>Review of Income and Wealth >PARAMETRIC LORENZ CURVES AND THE MODALITY OF THE INCOME DENSITY FUNCTION
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PARAMETRIC LORENZ CURVES AND THE MODALITY OF THE INCOME DENSITY FUNCTION

机译：参数洛伦兹曲线和收入密度函数的模态

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摘要

Similar looking Lorenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz curve and the modality of its underlying income density: given a parametric Lorenz curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e., downward-sloping). The density modality of several important Lorenz curves such as the Pareto, Weibull, Singh-Maddala parametrizations and hierarchical families of Lorenz curves are discussed. A Lorenz curve performance comparison with Monte Carlo simulations and data from the UNU-WIDER World Income Inequality Database underlines the relevance of the theoretical result: curve-fitting based on criteria such as mean squared error or the Gini difference might lead to a Lorenz curve implying an incorrectly-shaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz curve.
机译：看起来类似的洛伦兹曲线可能暗示着收入密度函数完全不同，并可能导致有关不平等的错误政策含义。本文推导了Lorenz曲线与其潜在收入密度的模态之间的关系：给定参数性Lorenz曲线，则是其三阶导数的符号，它指示密度是单峰还是零峰（即向下倾斜）。讨论了一些重要的Lorenz曲线的密度模态，例如Pareto，Weibull，Singh-Maddala参数化以及Lorenz曲线的层次族。将洛伦兹曲线的性能与蒙特卡罗模拟和联合国大学发展经济学所世界收入不平等数据库中的数据进行比较，强调了理论结果的相关性：基于均方误差或基尼差等标准的曲线拟合可能导致洛伦兹曲线暗示形状不正确的密度函数。因此，在选择参数Lorenz曲线时必须考虑模态。

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