Broadly, this dissertation identifies and addresses issues that arise in experimental and observational data contexts for estimating causal effects. In particular, the three chapters in this dissertation focus on issues of consistent and efficient estimation of causal effects using methods that are robust to misspecification of a conditional model of interest. Chapter 1: Revisiting regression adjustment in experiments with heterogeneous treatment effects. Regression adjustment with covariates in experiments is intended to improve precision over a simple difference in means between the treated and control outcomes. The efficiency argument in favor of regression adjustment has come under criticism lately, where papers like Freedman (2008a,b) find no systematic gain in asymptotic efficiency of the covariate adjusted estimator. This chapter shows that, like in Lin (2013), estimating separate regressions for the control and treated groups is guaranteed to do no worse than both the simple differencein-means estimator and just including the covariates in additive fashion. This result appears to be new, and simulations show that the efficiency gains can be substantial. This chapter also talks about some important cases - applicable to binary, fractional, count, and other nonnegative responses - where nonlinear regression adjustment is consistent without any restrictions on the conditional mean functions. Chapter 2: Robust and efficient estimation of potential outcome means under random assignment. This chapter studies improvements in efficiency for estimating the entire vector of potential outcome means using linear regression adjustment with two or more assignment levels. This chapter shows that using separate regression adjustments for each assignment level is never worse asymptotically than using the subsample averages and that separate regression adjustment generally improves over pooled regression adjustment, except in the obvious case where slope parameters in the linear projections are identical across the different assignment levels. An especially promising direction is to use certain nonlinear regression adjustment methods, which we show to be robust to misspecification in the conditional means. We apply this general potential outcomes framework to a contingent valuation study which seeks to estimate the lower bound mean willingness to pay (WTP) for an oil spill prevention program in California. Chapter 3: Doubly weighted M-estimation for nonrandom assignment and missing outcomes. This chapter studies the problems of nonrandom assignment and missing outcomes, which together, undermine the validity of standard causal inference. While the econometrics literature has used weighting to address each issue in isolation, empirical analysis is often complicated by the presence of both. This chapter proposes a new class of inverse probability weighted M-estimators that deal with the two issues by combining propensity score weighting with weighting for missing data. This chapter also discusses applications of the proposed method for robust estimation of the two prominent causal parameters, namely, the average treatment effect and quantile treatment effects, under misspecification the framework's parametric components. This chapter also demonstrates the proposed estimator's viability in empirical settings by applying it to the sample of Aid to Families with Dependent Children (AFDC) women from the National Supported Work program compiled by Calonico and Smith (2017).
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