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Author: Patrick F. Burauel
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Languages : en
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Author: Patrick F. Burauel
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Languages : en
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Author: Eoghan O'Neill
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Languages : en
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Author: Elias Moor
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Languages : en
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Author: Yoshiyasu Rai
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Languages : en
Pages : 112
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In Chapter 1, I study the statistical inference problem for treatment assignment policies. In typical applications, individuals with different characteristics are expected to differ in their responses to treatment. As a result, treatment assignment policies that allocate treatment based on individuals' observed characteristics can have a significant influence on outcomes and welfare. A growing literature proposes various approaches to estimating the welfare-optimzing treatment assignment policy. I develop a method for assessing the precision of estimated optimal policies. In particular, for the welfare used by \cite{KT:18} to propose estimated assignment policy, my method constructs (i) a confidence set of policies that contains the optimal policy, which maximizes the average social welfare among all the feasible policies with prespecified level and (ii) a confidence interval for the maximized welfare. A simulation study indicates that the proposed methods work reasonably well with modest sample size. I apply the method to experimental data from the National Job Training Partnership Act study. In Chapter 2, I derive the large sample properties of $M$th nearest neighbor propensity score matching estimator with a potentially misspecified propensity score model. By using the local misspecification framework, I formalize the bias/variance trade-off with respect to the choice of propensity score estimator and propose a model selection criterion that aims to minimize the estimation error. Finally, in Chapter 3 (co-authored with Taisuke Otsu), we propose asymptotically valid inference methods for matching estimators based on the weighted bootstrap. The key is to construct bootstrap counterparts by resampling based on certain linear forms of the estimators. Our weighted bootstrap is applicable for the matching estimators of both the average treatment effect and its counterpart for the treated population. Also, by incorporating a bias correction method in \cite{AI:11}, our method can be asymptotically valid even for matching based on a vector of covariates. A simulation study indicates that the weighted bootstrap method is favorably comparable with the asymptotic normal approximation by \cite{AI:06}. As an empirical illustration, we apply the proposed method to the National Supported Work data.
Author: Neng-Chieh Chang
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Languages : en
Pages : 134
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This dissertation consists of three chapters that study causal inference when applying machinelearning methods. In Chapter 1, I propose an orthogonal extension of the semiparametric difference-in-differences estimator proposed in Abadie (2005). The proposed estimator enjoys the so-called Neyman-orthogonality (Chernozhukov et al. 2018) and thus it allows researchers to flexibly use a rich set of machine learning (ML) methods in the first-step estimation. It is particularly useful when researchers confront a high-dimensional data set when the number of potential control variables is larger than the sample size and the conventional nonparametric estimation methods, such as kernel and sieve estimators, do not apply. I apply this orthogonal difference-in-differences estimator to evaluate the effect of tariff reduction on corruption. The empirical results show that tariff reduction decreases corruption in large magnitude. In Chapter 2, I study the estimation and inference of the mode treatment effect. Mean,median, and mode are three essential measures of the centrality of probability distributions. In program evaluation, the average treatment effect (mean) and the quantile treatment effect (median) have been intensively studied in the past decades. The mode treatment effect, however, has long been neglected in program evaluation. This paper fills the gap by discussing both the estimation and inference of the mode treatment effect. I propose both traditional kernel and machine learning methods to estimate the mode treatment effect. I also derive the asymptotic properties of the proposed estimators and find that both estimators follow the asymptotic normality but with the rate of convergence slower than the regular rate N^1/2, which is different from the rates of the classical average and quantile treatment effect estimators. In Chapter 3 (joint with Liqiang Shi), we study the estimation and inference of the doublyrobust extension of the semiparametric quantile treatment effect estimation discussed in Firpo (2007). This proposed estimator allows researchers to use a rich set of machine learning methods in the first-step estimation, while still obtaining valid inferences. Researchers can include as many control variables as they consider necessary, without worrying about the over-fitting problem which frequently happens in the traditional estimation methods. This paper complements Belloni et al. (2017), which provided a very general framework to discuss the estimation and inference of many different treatment effects when researchers apply machine learning methods.
Author: Michael Pollmann
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Languages : en
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This dissertation explores the estimation of causal effects in settings with non-standard data. In the first chapter, the treatments are not directly assigned to outcome units but instead occur in the same geographic space. In the second chapter, responses to hypothetical questions describing both the treated and control state are used to learn about the effects of a treatment on real behavior (outcomes). In the third chapter, treatments are assigned according to a randomized experiment but outcomes are heavy-tailed, such that semiparametric approaches are useful to improve efficiency and robustness. The first chapter considers settings where the treatments causing the effects of interest are not directly associated with specific units for which we measure outcomes, but rather occur in the same geographic space. Many events and policies (treatments), such as opening of businesses, building of hospitals, and sources of pollution, occur at specific spatial locations, with researchers interested in their effects on nearby individuals or businesses (outcome units). However, the existing treatment effects literature primarily considers treatments that could experimentally be assigned directly at the level of the outcome units, potentially with spillover effects. I approach the spatial treatment setting from a similar experimental perspective: What ideal experiment would we design to estimate the causal effects of spatial treatments? This perspective motivates a comparison between individuals near realized treatment locations and individuals near counterfactual (unrealized) candidate locations, which is distinct from current empirical practice. I derive standard errors based on this design-based perspective that are straightforward to compute irrespective of spatial correlations in outcomes. Furthermore, I propose machine learning methods to find counterfactual candidate locations and show how to apply the proposed methods on observational data. I study the causal effects of grocery stores on foot traffic to nearby businesses during COVID-19 shelter-in-place policies. I find a substantial positive effect at a very short distance. Correctly accounting for possible effect "interference" between grocery stores located close to one another is of first order importance when calculating standard errors in this application. The second chapter is co-authored with B. Douglas Bernheim, Daniel Björkegren, and Jeffrey Naecker. We explore methods for inferring the causal effects of treatments on choices by combining data on real choices with hypothetical evaluations. We propose a class of estimators, identify conditions under which they yield consistent estimates, and derive their asymptotic distributions. The approach is applicable in settings where standard methods cannot be used (e.g., due to the absence of helpful instruments, or because the treatment has not been implemented). It can recover heterogeneous treatment effects more comprehensively, and can improve precision. We provide proof of concept using data generated in a laboratory experiment and through a field application. The final chapter is co-authored with Susan Athey, Peter J. Bickel, Aiyou Chen, and Guido W. Imbens. We develop new semiparametric methods for estimating treatment effects. We focus on a setting where the outcome distributions may be heavy-tailed, where treatment effects are small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent experimentation in tech companies. We propose using parametric models for the treatment effects, as opposed to parametric models for the full outcome distributions. This leads to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for this setting, and propose efficient estimators. In the case with a constant treatment effect one of the proposed estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to (minus) the second derivative of the log of the density of the potential outcomes. Our analysis also results in an extension of Huber's model and trimmed mean to include asymmetry and a simplified condition on linear combinations of order statistics, which may be of independent interest.
Author: Claudia Luise Charlotte Noack
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Languages : en
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Author: Holger Lutz Kern
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ISBN: 9780549841968
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Languages : en
Pages : 181
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This dissertation contains three independent essays, each applying statistical methods for causal inference in observational studies to central topics in comparative political behavior.
Author: Kevin Xinkai Guo
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Languages : en
Pages : 0
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This thesis describes three research projects in causal inference, all related to the problem of contrasting the average counterfactual outcomes on two sides of a binary decision. In the first project, we discuss estimation of the average causal effect in a randomized control trial. Here, we find that statisticians find themselves in a kind of statistical paradise: a simple model-based procedure delivers correct confidence intervals even if the experimental participants are not randomly sampled and mis-specified models are used. In the second project, we consider the problem of testing for a treatment effect using observational data with no hidden confounders. Conceptually, this is no different from a rather complicated RCT, and one might expect that a return to statistical paradise is possible. Unfortunately, this is not the case: we show that even intuitively reasonable uses of correct models may still yield misleading conclusions. The final project looks at observational data with unobserved confounding and gives methods for computing bounds on average causal effects. Here, we discover some never-before-seen robustness properties unique to the partially-identified setting.
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.
