关于基尼系数若干问题的再研究——与部分学者商榷

A Further Study about Some Problems of the Gini Coefficient

基尼系数是测量收入不平等的一个重要指标,近年来有很多学者对此进行了深入研究,本文主要对有关学者的研究内容进行商榷与补充。首先,实际计算基尼系数应首选离散公式,并且根据具体的抽样方法选择无偏或有效的估计公式;其次,本文论证了对数正态分布下基尼系数G与标准差σ的关系式G=2Φ(σ/2)-1;再次,针对基尼系数存在的不足,改进基尼系数成为一些学者的研究重点,本文发现一些改进并没有解决基尼系数与洛伦茨曲线的非一一对应问题,并且可操作性较差,通过介绍S基尼系数和E基尼系数,本文说明了基尼系数改进的总体思路;最后,针对学者提出的“部分分布决定性定理(PD定理)”,本文论证了其推理过程中存在的问题,说明该定理是错误的。

The Gini coefficient is an important index in measuring inequality and many scholars have researched it recently. This paper mainly discusses some questions with these scholars. Firstly, calculating Gini coefficient should first use the discrete formulae and choose the best statistical inference form according to specific sample. The continuous formula in calculating Gini coefficient is improper. Secondly, we get G=2Ф（σ/√2）-1 under logarithm normal distribution. Thirdly, though Gini coefficient has some deficiencies, some modified Gini coefficients introduced by some scholars are worse in conduct and cannot identify the Lorenz curve absolutely. This paper shows the orientation by introducing S-Gini ＆ E Gini. Lastly, this paper finds a mistake in a theorem named deterministic theorem of the partial distribution （PD theorem） by its author, and explains the reason.