具有内生变量的部分线性模型研究

Research on Partially Linear Models With Endogenous Variables

在线性模型中变量内生性的处理已经有了许多很成熟的方法,但在非参数模型中变量内生性的处理则要困难得多。直接运用工具变量来处理非参数模型中变量的内生性将会遇到所谓的"病态回归问题",从而无法得到函数的一致估计。为此,文章提出采用非参数控制函数法来解决部分线性模型中的变量内生性问题,并且还推导了估计量的一致性和大样本性质。通过数值模拟计算,对比了非参数控制函数法和传统控制函数法在处理部分线性模型中变量内生性的效果,结果显示,非参数控制函数法在拟合优度上的表现优于传统的控制函数法。在实证部分的研究发现,家庭背景对考生的高考成绩有显著的正效应。特别对于低收入家庭而言,家庭收入的增长能够使得孩子的高考成绩有较大的提高。

There are a number of well-established approaches to the variable endogeneity in linear models,but it is much more difficult to deal with variable endogeneity in nonparametric models.Using instrumental variables to handle the variable endogeneity in nonparametric models will encounter the so-called"ill-condition regression",so that a consistent estimation of the function cannot be obtained.In view of this,the paper proposes the method of using a nonparametric control function to solve the problem of variable endogeneity in partial linear models,and also derives the consistency of estimators and large sample properties.And then,through numerical simulation,the paper compares the effects of nonparametric control function method and traditional control function method in dealing with variable endogeneity in partial linear model.The results show that the performance of nonparametric control function method in goodness of fit is superior to that of traditional control function method.The empirical part of the research finds that family background has a significant positive effect on the scores of college entrance examination candidates,and that especially for low-income families,the increase of family income can greatly improve students’college entrance examination scores.