This research project encompasses two distinct but closely related projects. Both deal with statistics methods for estimating causal effects in settings with binary treatments: units either receive one of two levels of a treatment, and one is interested in the difference in average outcomes under these two levels of the treatment. In many observational (non-randomized) studies, researchers attempt to estimate causal effects by comparing outcomes for pairs of units, one treated and one not treated, with identical similar values for observed pre-treatment variables. The key assumption is that after eliminating differences in outcomes due to differences in covariates, the remaining differences can be attributed to the causal effect of the treatment. Implementing such matching estimators can be difficult if there are many covariates. A seminal paper by Rosenbaum and Rubin (Biometrika, 1984) shows that in settings with multiple covariates matching on a scalar function of these covariates, the propensity score, can eliminate all biases associated with differences in covariates. This method has been widely applied. In settings where the propensity score is unknown, however, the asymptotic distribution for the matching estimator has not been derived. In fact, it has been shown that commonly used methods for constructing confidence intervals based on resampling methods such as the bootstrap are not valid. The researchers will develop statistical methods that allow them to derive the asymptotic distribution for matching estimators where the matching is on the estimated propensity score. They will develop and exploit a new martingale representation for matching estimators, and show that this sheds new light on their asymptotic distribution. The investigators will then show how to use this representation to derive the asymptotic distribution for the case of matching on the propensity score. Given the widespread use of this matching method, these results will be useful to practitioners.
Broader Impacts: Matching estimators are often used to evaluate the effectiveness of public interventions. As a result, valid inferential tools for matching estimators are likely to have substantial impact in empirical practice. This project will produce freely available software to implement the proposed methods.
