AI 中文总结
研究基于洛伦兹曲线曲率构建不平等和社会分层指数族，探讨其公理及α = 0时的形式，通过世界银行数据研究指数值及排名变化，分析与其他指数的相关性，发现曲率指数与比较指数有偏差，基于消费国家偏差较小。
AI 中文摘要
我们基于洛伦兹曲线的曲率构建了一个连续的不平等和社会分层指数族。我们研究了该指数族的不平等公理，发现只有在所谓的分层厌恶参数α设为0时才满足这些公理，其他情况下无法严格满足。α = 0时，指数有非常简单的封闭形式且值易于近似。我们研究了该指数在世界银行不平等数据上的值，以及随着α变化，众多国家排名如何改变。还计算并分析了与其他常见指数的斯皮尔曼和肯德尔等级相关矩阵。我们发现曲率指数与比较指数始终存在偏差，基于消费的国家比基于收入的国家偏差小。
英文摘要
We construct a continuous family of inequality and social stratification indices based on the curvature of the Lorenz curve. We study the inequality axioms of the family and find that they are satisfied only with the so-called stratification-aversion parameter $α$ set to 0 -- in all other cases, these constraints cannot be satisfied in a strict sense. With $α= 0$, the index has a very simple closed form and its value can be easily approximated. We study the values of the index on World Bank inequality data and see how the rankings across a wide selection of countries change as $α$ is varied. Spearman and Kendall rank-correlation matrices with other common indices are also computed and analyzed. We find the curvature index to deviate consistently from the comparison indices, albeit less so for consumption- than income-based countries.
Commentsv1: 37 pages, 10 figures, 2 tables
