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Transformations that minimize the Gini index of a random variable and applications
The Journal of Economic Inequality ( IF 3.6 ) Pub Date : 2021-07-26 , DOI: 10.1007/s10888-021-09508-4
Michael McAsey 1 , Libin Mou 1
Affiliation  

Let X be a continuous or discrete random variable with values in [0,M] and consider all functions (here called transformations) \(q:[0,M]\to [0,\infty )\) that are increasing and have given bounded rates \(B \le \frac {q(v)-q(u)}{v-u} \le A\) for u < v. We prove that among such transformations, there is a transformation q that minimizes the Gini index of q(X), and such a q can be chosen as piecewise linear with only two rates, namely A and B. In the motivation for the study, X represents the incomes of a population. Our results imply that among all such tax policies with fixed allowable minimum and maximum tax rates, there is a tax policy that minimizes the Gini index of the disposable incomes of the population and such a tax policy has only two brackets with the given minimum and maximum rates.



中文翻译:

最小化随机变量的基尼指数的变换和应用

X是一个连续或离散的随机变量,其值在 [0, M ] 并考虑所有函数(这里称为转换)\(q:[0,M]\to [0,\infty )\)增加并具有给定有界率\(B \le \frac {q(v)-q(u)}{vu} \le A\)对于u < v。我们证明在这样的变换中,有一个变换q使q ( X )的基尼指数最小化,并且这样的q可以选择为只有两个比率的分段线性,即AB。在研究动机中,X代表人口的收入。我们的结果表明,在所有这些具有固定可允许的最低和最高税率的税收政策中,有一项税收政策使人口可支配收入的基尼指数最小化,而这种税收政策只有两个等级,给定的最低和最高税率率。

更新日期:2021-07-27
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