本项目研究平均处理效应（ATE）的半参数和非参数估计问题。当非混淆性假定不成立时，广泛使用的非参数匹配方法不能得到ATE的相合估计。此时，处理变量存在内生性，所以我们需要诉诸工具变量方法。当工具变量为离散型随机变量时，我们只能识别局部ATE，但局部ATE的含义因工具变量的选取而异，不能进行外推预测。当工具变量为连续型变量时，我们则可以利用无穷处识别方法，识别和估计全局的ATE。无穷处识别方法下ATE的半参数或非参数估计方法主要有两种：样本选择模型方法和边际处理效应方法，其中样本选择模型方法又可分解为斜率系数的估计和截距项的估计。本项目研究的主要内容包括：（1）提出样本选择模型斜率系数的一种新的更有效的半参数估计量；（2）解决样本选择模型截距项半参数估计量的窗宽选取难题；（3）提出样本选择模型截距项的新的非参数估计量；（4）证明边际处理效应模型下ATE的非参数估计量的相合性和渐近正态性。

This project study semiparametric and nonparametric estimation of average treatment effect (ATE). The widely used nonparametric matching approach cannot consistently estimate ATEs if the unconfoundedness assumption is violated. The treatment assignment is endogenous in this case, therefore we need resort to the instrumental variable method. When the instrumental variable is discretely distributed, only local ATEs are identified. The local ATEs, however, are useless in extrapolating and predicting, because their implications vary with the instrumental variables. In contrast, when the instrumental variable is continuously distributed, we can (point) identify and estimate global ATEs by the identification-at-infinity approach. There are two methods for semiparametrically or nonparametrically estimating ATEs under the identification-at-infinity: sample selection model method and marginal treatment effect method. Furthermore, the sample selection model method can be decomposed into estimation of slopes and estimation of the intercept. The main contents of this study are as following. (1) We propose a new, more efficient semiparametric estimator for slopes of the sample selection model. (2) We resolve the difficulty of bandwidth selection in semiparametric estimation of the intercept of the sample selection model. (3) We propose a new nonparametric estimator for the intercept of the sample selection model. (4) We establish consistency and asymptotic normality of the nonparametric ATE estimator under the marginal treatment effect model.