Essays in Semiparametric Estimation and Inference with Monotonicity Constraints PDF Download
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Author: Mengshan Xu
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Languages : en
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Author: Mengshan Xu
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Languages : en
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Author: Haitian Xie
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Languages : en
Pages : 0
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This dissertation is a collection of three essays on the econometric analysis of causal inference methods. Chapter 1 examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries. Chapter 2 examines the local linear regression (LLR) estimate of the conditional distribution function F(y|x). We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both x and y and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. Chapter 3 studies the estimation of causal parameters in the generalized local average treatment effect model, a generalization of the classical LATE model encompassing multi-valued treatment and instrument. We derive the efficient influence function (EIF) and the semiparametric efficiency bound for two types of parameters: local average structural function (LASF) and local average structural function for the treated (LASF-T). The moment condition generated by the EIF satisfies two robustness properties: double robustness and Neyman orthogonality. Based on the robust moment condition, we propose the double/debiased machine learning (DML) estimators for LASF and LASF-T. We also propose null-restricted inference methods that are robust against weak identification issues. As an empirical application, we study the effects across different sources of health insurance by applying the developed methods to the Oregon Health Insurance Experiment.
Author: Rui Wang
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Languages : en
Pages : 0
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Chapter 1: Our paper characterizes partial identification of a binary choice model when the binary dependent variable is potentially misreported. We propose two different approaches by exploiting different instrumental variables respectively. In the first approach, the instrument is assumed to only affect the true dependent variable but not misreporting probabilities. The second approach uses an instrument that only affects misreporting probabilities monotonically but does not influence the true dependent variable. Our approaches do not impose distributional assumptions over unobserved disturbances and do not assume parametric models for the misreporting process. We characterize conditional moment inequalities based on the identification results, and this approach is shown to perform more robustly than the parametric method via simulations. In an extension, we study the identification by using two instruments jointly and under one-sided misreporting. Chapter 2: The paper characterizes new point identification results of the local average treatment effect by using two instruments but requiring weaker assumptions on both instruments compared to Imbens and Angrist (1994). Imbens and Angrist (1994) require an instrument to satisfy the conditions of exclusion, monotonicity, and independence, while their results do not hold if one of the conditions fails. My paper uses two instruments; however, the first instrument is allowed to violate the exclusion restriction and the second instrument does not need to satisfy the monotonicity condition. Therefore, the first instrument can affect the outcome via both direct effects and a shift in the treatment status. My method can identify the direct effects of the first instrument via exogenous variation in the second instrument and consequently identify the local average treatment effect. An estimator for the local average treatment effect is developed, and using Monte Carlo simulations, it is shown to perform more robustly than the instrumental variable estimand.
Author: Hyungtaik Ahn
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Languages : en
Pages : 402
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Author: In Hŏ
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Category : Mathematical models
Languages : en
Pages : 138
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Author: Abhisek Banerjee
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Category : Academic theses
Languages : en
Pages : 0
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Author: Shenshen Yang
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Languages : en
Pages : 432
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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
Author: Abhisek Banerjee
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Category :
Languages : en
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Author: Jiun-Hua Su
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Category :
Languages : en
Pages : 133
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This dissertation consists of three chapters studying microeconometric methods. The first two chapters focus on models with unobserved heterogeneity, and topics include testing shape restrictions imposed by economic theory and estimating counterfactual policy effects in duration analysis. In the last chapter, predictive methods in machine learning are adapted to study model selection within the framework of utility-maximizing binary decision-making. These proposed methods are described in greater detail below. Causal inference on the individual treatment effect is fundamental in econometric analysis. In Chapter 1, I develop the concept of structural monotonicity, that is, monotonicity of a structural function in a treatment given any observable covariates and unobserved heterogeneity. Different from regression monotonicity, in which heterogeneous factors average out, structural monotonicity emphasizes the sign of ceteris paribus individual treatment effect. Since economic theory may neither detail enough potential heterogeneous factors nor elaborate on parametric structures, I consider a two-period panel data model with nonseparable time-invariant heterogeneity, and avoid imposing restrictions on the dimensionality of heterogeneity and functional form of the structural function. Structural monotonicity in this setup implies shape constraints on the joint cumulative distribution function (CDF) of outcome variables conditional on the observable treatments and covariates over some regions. These regions are parameterized by a nuisance parameter, which can be consistently estimated. According to the shape constraints on the conditional joint CDF over the estimated regions, I propose a test for structural monotonicity and validate the empirical bootstrap method. Some Monte Carlo experiments show that the proposed test can detect departures from structural monotonicity, which are not revealed by some existing tests for regression monotonicity. The presence of unobserved heterogeneity is also essential for policy effects especially in duration analysis. In Chapter 2, I propose a counterfactual Kaplan-Meier estimator that incorporates time-invariant exogenous covariates and nonseparable heterogeneity in duration models with random censoring. The over-parameterization in traditional duration analysis can be avoided because distributional features of unobserved heterogeneity are unspecified. I establish the joint weak convergence of the proposed counterfactual Kaplan-Meier estimator and the traditional Kaplan-Meier estimator under some regularity conditions. Therefore, by comparing the estimated counterfactual and original unconditional distribution of the duration variable, we can evaluate the policy effects, for example the change of duration dependence in response to an exogenous manipulation of covariates. In addition to counterfactual analysis in policy research, a better prediction may improve policy-making. In Chapter 3, I show that in a model of binary decision-making based on the prediction of a binary outcome variable, the semiparametric maximum utility estimation can be viewed as cost-sensitive binary classification. Its in-sample overfitting issue is thus similar to that of perceptron learning in the machine learning literature. To alleviate the in-sample overfitting, I apply techniques in structural risk minimization to construct a utility-maximizing prediction rule. This proposed prediction rule, in comparison to the common machine learning Lasso-logit predictor, has larger relative expected utility in some simulation results when the conditional probability of the binary outcome is misspecified. The results show that a better prediction arising from the combination of machine learning techniques and economic theory can improve policy-making.
Author: Lei Pang
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Category :
Languages : en
Pages : 76
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