A General Theory of Matching Estimation

该研究项目包括两个截然不同但密切相关的项目。这两种方法都涉及在二元处理环境中估计因果效应的统计方法：单位要么接受两个水平的处理中的一个，一个人对这两个处理水平下的平均结果的差异感兴趣。在许多观察性(非随机)研究中，研究人员试图通过比较成对单位(一个治疗和一个未治疗)的结果与观察到的治疗前变量的相同相似值来估计因果影响。关键假设是，在消除了因协变量差异而导致的结果差异后，剩余的差异可以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器可能会很困难。Rosenbaum和Rubin的一篇开创性论文(Biilliska，1984)表明，在多个协变量在这些协变量的标量函数上匹配的情况下，倾向分数可以消除与协变量差异相关的所有偏差。这种方法已经得到了广泛的应用。然而，在倾向性分数未知的情况下，匹配估计器的渐近分布尚未推导出来。事实上，已经证明了基于重采样方法(例如Bootstrap)来构造置信度区间的常用方法是不有效的。研究人员将开发统计方法，使他们能够推导出匹配估计器的渐近分布，其中匹配是基于估计的倾向分数。他们将开发和利用匹配估计量的一种新的鞅表示，并表明这为它们的渐近分布提供了新的曙光。然后，调查人员将展示如何使用这种表示法来推导出匹配倾向分数的情况的渐近分布。鉴于这种匹配方法的广泛使用，这些结果将是有用的政策执行者。更广泛的影响：匹配估计器经常被用来评估公共干预的有效性。因此，用于匹配估计量的有效推理工具很可能在实证实践中产生重大影响。该项目将生产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.