Semiparametric estimation of average treatment effect through a random coefficient dummy endogenous variable model  

作　　者：ZHOU YaHong WANG LiMing HE XiaoDan 

机构地区：[1]School of Economics,Shanghai University of Finance and Economics,Key Laboratory of Mathematical Economics (SUFE) [2]School of Statistics and Management,Shanghai University of Finance and Economics [3]School of Economics,Shanghai University of Finance and Economics

出　　处：《Science China Mathematics》2014年第11期2415-2428,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(GrantNo.71171127);the Construction Program of Elaborate Course for Advanced Econometrics Ⅱ of ShanghaiUniversity of Finance and Economics

摘　　要：This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations:an outcome equation and a decision equation.Given the linear restriction in outcome and decision equations,Chen(1999) provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen's estimator by relaxing the linear index into a nonparametric function,which greatly reduces the risk of model misspecification. A two-step approach is proposed:the first step uses a nonparametric regression estimator for the decision variable,and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore,we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations：an outcome equation and a decision equation.Given the linear restriction in outcome and decision equations,Chen（1999） provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen＇s estimator by relaxing the linear index into a nonparametric function,which greatly reduces the risk of model misspecification. A two-step approach is proposed：the first step uses a nonparametric regression estimator for the decision variable,and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore,we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.

关 键 词：random-coefficient model endogenous variable model SYMMETRY 

分 类 号：O212.1[理学—概率论与数理统计] TP13[理学—数学]