Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding  

作　　者：Yu-ling LI Jun WANG 

机构地区：[1]Research Center for Applied Mathematics and Interdisciplinary Sciences,Beijing Normal University,Zhuhai 519087,China [2]Yunnan Key Laboratory of Statistical Modeling and Data Analysis,Yunnan University,Kunming 650091,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第2期320-336,共17页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos.12101545);by the natural science foundation of Inner Mongolia Autonomous Region (2022MS01007)。

摘　　要：Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.

关 键 词：nonlinear models quasi likelihood estimator STABLE treatment effects unobserved confounding 

分 类 号：O212.1[理学—概率论与数理统计]