内生性线性回归模型估计方法的改进

Improvement of Estimation Method for Endogenous Linear Regression Model

线性回归模型的内生性问题导致参数估计量有偏且不一致。工具变量法作为解决内生性问题的经典方法,在实践中却经常因为难以找到理想的工具变量而无法实现。Gaussian Copula方法通过Copula函数度量内生解释变量与随机误差项的相关性,无须借助工具变量即可修正内生性问题,但是以内生解释变量的非正态性为假设前提。文章基于贝叶斯理论利用最大后验方法估计模型参数,提出一种改进的Gaussian Copula方法,放松了对于内生解释变量分布的假定;同时,通过蒙特卡罗模拟验证了所提方法的有效性;最后,应用提出的方法估计了中国农村居民教育收益率。

Endogeneity of linear regression models results in biased and inconsistent estimators.As a classical method to solve endogeneity,instrumental variable method often fails to be realized in practice because it is difficult to find the ideal instru-mental variable.The Gaussian Copula method measures the correlation between endogenous explanatory variables and random er-ror terms through the Copula function and can correct the endogeneity problem without using instrumental variables,but the non-normality of endogenous explanatory variables is assumed as the premise.Based on Bayesian theory,this paper uses maxi-mum posterior method to estimate model parameters and proposes an improved Gaussian Copula method,which relaxes the as-sumption of endogenous explanatory variable distribution.At the same time,the effectiveness of the proposed method is verified by Monte Carlo simulation.Finally,the proposed method is applied to estimate the educational return rate of Chinese rural residents.