A General Theory of Matching Estimation

这个研究项目包括两个不同但密切相关的项目。两者都涉及在二元治疗的情况下估计因果效应的统计方法：单位要么接受两个水平的治疗之一，一个是在这两个水平的治疗下的平均结果的差异。 在许多观察性（非随机）研究中，研究人员试图通过比较两个单位（一个治疗，一个未治疗）的结果来估计因果效应，观察到的治疗前变量具有相同的相似值。 关键假设是，在消除由于协变量差异导致的结局差异后，剩余差异可归因于治疗的因果效应。 如果有许多协变量，实现这样的匹配估计可能是困难的。 Rosenbaum和Rubin（Biometrika，1984）的一篇开创性论文表明，在多个协变量匹配这些协变量的标量函数的情况下，倾向评分可以消除与协变量差异相关的所有偏倚。 该方法已被广泛应用。 然而，在倾向分数未知的情况下，匹配估计量的渐近分布尚未得到。 事实上，已经表明，常用的方法来构建置信区间的基础上，如自助法是无效的。 研究人员将开发统计方法，使他们能够推导出匹配估计量的渐近分布，其中匹配是在估计的倾向得分上。 他们将开发和利用一个新的鞅表示匹配估计，并表明，这揭示了他们的渐近分布。 然后，研究人员将展示如何使用这种表示来推导倾向分数匹配情况下的渐近分布。由于这种匹配方法的广泛使用，这些结果将是有用的topractioners.broader影响：匹配估计经常被用来评估公共干预措施的有效性。因此，有效的推理工具匹配估计可能会有实质性的影响，在实证实践中。该项目将制作免费提供的软件来实施所提出的方法。

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 topractitioners.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.