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

作     者：ZHOU YaHong WANG LiMing HE XiaoDan 

作者机构：School of EconomicsShanghai University of Finance and EconomicsKey Laboratory of Mathematical Economics (SUFE) School of Statistics and ManagementShanghai University of Finance and Economics School of EconomicsShanghai University of Finance and Economics 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第11期

页      面：2415-2428页

核心收录：

学科分类：02[经济学] 07[理学] 08[工学] 070103[理学-概率论与数理统计] 071102[理学-系统分析与集成] 0711[理学-系统科学] 0202[经济学-应用经济学] 020208[经济学-统计学] 0714[理学-统计学（可授理学、经济学学位）] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 081103[工学-系统工程] 

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 

主　　题：模型参数估计 治疗效果 随机系数 平均 渐近正态分布 培训项目 分布自由 模型假设 

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 *** 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.