Book Description

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.