Essays on nonparametric and semiparametric identification and estimation

This dissertation consists of three chapters in econometric theory, with a focus on identification and estimation of treatment effect in semi-parametric and nonparametric models, when there exists endogeneity problem. These methods are applied on policy and program evaluation in health and labor economics. \indent In the first chapter, I examine the common problem of multiple missing variables, which we refer to as multiple missingness, with non-monotone missing pattern and is usually caused by sub-sampling and a combination of different data sets. One example of this is missingness in both the endogenous treatment and outcome when two variables are collected via different stages of follow-up surveys. Two types of dependence assumptions for multiple missingness are proposed to identify the missing mechanism. The identified missing mechanisms are used later in an Augmented Inverse Propensity Weighted moment function, based on which a two-step semiparametric GMM estimator of the coefficients in the primary model is proposed. This estimator is consistent and more efficient than the previously used estimation methods because it includes incomplete observations. We demonstrate that robustness and asymptotic variances differ under two sets of identification assumptions, and we determine sufficient conditions when the proposed estimator can achieve the semiparametric efficiency bound. This method is applied to the Oregon Health Insurance Experiment and shows the significant effects of enrolling in the Oregon Health Plan on improving health-related outcomes and reducing out-of-pocket costs for medical care. The method proposed here provides unbiased and more efficient estimates. There is evidence that simply dropping the incomplete data creates downward biases for some of the chosen outcome variables. Moreover, the estimator proposed in this paper reduced standard errors by 6-24% of the estimated effects of the Oregon Health Plan. \indent The second chapter is a joint work with Sukjin Han. In this chapter, we consider how to extrapolate the general local treatment effect in a non-parametric setting, with endogenous self-selection problem and lack of external validity. For counterfactual policy evaluation, it is important to ensure that treatment parameters are relevant to the policies in question. This is especially challenging under unobserved heterogeneity, as is well featured in the definition of the local average treatment effect (LATE). Being intrinsically local, the LATE is known to lack external validity in counterfactual environments. This chapter investigates the possibility of extrapolating local treatment effects to different counterfactual settings when instrumental variables are only binary. We propose a novel framework to systematically calculate sharp nonparametric bounds on various policy-relevant treatment parameters that are defined as weighted averages of the marginal treatment effect (MTE). Our framework is flexible enough to incorporate a large menu of identifying assumptions beyond the shape restrictions on the MTE that have been considered in prior studies. We apply our method to understand the effects of medical insurance policies on the use of medical services. \indent In the third chapter, I investigate the partial identification bound for treatment effect in a dynamic setting. First, I develop the sharp partial identification bounds of dynamic treatment effect on conditional transition probabilities when the treatment is randomly assigned. Then I relax the randomization assumption and gives partial identification bounds, under a conditional mean independence assumption. Using MTR and MTS assumptions, this bound is further tightened. These bounds are used on estimating labor market return of college degree in a long term, with data from NLSY79.Economic