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普通最小二乘法是进行回归分析最常用的基本方法,但该方法要求满足若干经典假设,对于小样本或在与收入相关回归分析的参数估计中易受奇异值、高收入群体的影响。本文试图利用基尼加权回归弥补以上不足。基尼加权回归可分为参数方法与非参数方法两类,参数方法基于样本残差的基尼平均差最小原则对参数进行估计;非参数方法则是直接由两点间的斜率加权得到。基尼加权回归分析可以进行参数假设检验并定义拟合优度,其中的假设检验在实际应用中采用Jackknife重抽样方法估计方差。文中提出的样本拓展基尼平均差算法,弥补了现有算法对样本数据只能提供近似计算的不足,极大地简化了相应的计算公式。本文利用我国2015年省域截面数据、1994—2015年总量时间序列数据分别讨论入境旅游收入对收入基尼系数的影响,发现使用基尼加权回归的结果不仅符合理论预期,而且可以通过不平等厌恶参数的变化反映入境旅游收入对不同群体收入公平性的影响。
Abstract：The method of ordinary least squares( OLS) is one of the most common one for regression analysis. OLS relies on several classical assumptions,and estimators are affected easily by extreme values,high income groups in regression analysis with related to income or small sample size. This paper promotes the weighted Gini regression as an alternative way,which consists of parameter estimating and non-parameter estimating. Parameter estimator is based on minimum of Gini mean difference of sample residues; nonparameter estimator comes from weighted value of slopes. Hypothesis test and R-squared calculating are carried in weighted Gini regression,resampling Jackknife technology is used to estimate variance for hypothesis test. It promotes a new algorithm of sample extend Gini mean difference,which can cover the shortage of approximate treatment of sample data. It discusses about how inbound tourism receipt influences income Gini coefficients by using 2015 provincial cross-sectional data and 1994—2015 total time series data in China. The results from weighted Gini regression line with expectations of relationship between variables,and they can reflect effects of inbound tourism receipt on income equity of different groups by changing inequality preference.
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(1)基尼教授1912年给出的计算公式为1/2n(n-1)n∑i=1n∑j=1|xi-xj|,即n个不同个体两两收入差距的平均值。
(1)这里的符号Cov与通常的协方差定义不同,可以看作是双变量二维分布列仅主对角线上不为0的特例,即双变量之间具有一一映射关系,Yitzhaki(1996)将其对应于(xi,yi)的双变量分布列。如不特别指出,本文的双变量协方差都隐含存在这种一一映射。
(2)他们将不平等厌恶参数ν-1直接换为ν,因而取值范围ν>-1。
(1)当不按变量值从小到大排序时,(Fi,Li)就不构成洛伦兹曲线,称为集中曲线。但同样可以得到类似的协方差公式,只是不再具有非负性。
(1)其中在x取值未排序的情况下Cov(e,ω(xi))=∑ixj}]pipj,I为示性函数。分布列平方的数学期望就是e的方差,U统计量方差估计参见Olkin和Yitzhaki(1992)。
(1)Yitzaki(1983)证明了拓展基尼平均差是不平等厌恶参数ν的增函数,由定义当ν=1为不平等中性时可得Г(1)=0。因此当0<ν<1为偏好不平等时Г(ν)<0,当ν>1为厌恶不平等时Г(ν)>0。
(2)限于篇幅,本文未给出估计结果,有兴趣读者可向作者索取。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2018.09.009
中图分类号:F124;O212.1
引用信息:
[1]戴平生.基尼加权回归分析:概念、方法及应用[J].统计研究,2018,35(09):103-114.DOI:10.19343/j.cnki.11-1302/c.2018.09.009.
2018-09-25
2018-09-25