Abstract

Nearest-neighbor matching is a popular nonparametric tool to create balance between treatment and control groups in observational studies. As a preprocessing step before regression, matching reduces the dependence on parametric modeling assumptions. In current empirical practice, however, the matching step is often ignored in the calculation of standard errors and confidence intervals. In this article, we show that ignoring the matching step results in asymptotically valid standard errors if matching is done without replacement and the regression model is correctly specified relative to the population regression function of the outcome variable on the treatment variable and all the covariates used for matching. However, standard errors that ignore the matching step are not valid if matching is conducted with replacement or, more crucially, if the second step regression model is misspecified in the sense indicated above. Moreover, correct specification of the regression model is not required for consistent estimation of treatment effects with matched data. We show that two easily implementable alternatives produce approximations to the distribution of the post-matching estimator that are robust to misspecification. A simulation study and an empirical example demonstrate the empirical relevance of our results. Supplementary materials for this article are available online.

摘要

最近邻匹配是一种流行的非参数工具，可在观察性研究中在治疗组和对照组之间建立平衡。作为回归之前的预处理步骤，匹配减少了对参数建模假设的依赖。然而，在当前的经验实践中，匹配步骤在计算标准误差和置信区间时经常被忽略。在本文中，我们表明，如果匹配是在没有替换的情况下完成的，并且回归模型相对于结果变量对治疗变量的总体回归函数正确指定，则忽略匹配步骤会导致渐近有效的标准误差用于匹配的协变量。但是，如果匹配是通过替换进行的，或者更重要的是，如果第二步回归模型在上述意义上被错误指定，则忽略匹配步骤的标准误差是无效的。此外，回归模型的正确规范对于使用匹配数据对治疗效果进行一致估计是不需要的。我们表明，两个易于实现的替代方案产生了匹配后估计量分布的近似值，这些估计量对错误指定具有鲁棒性。模拟研究和经验示例证明了我们结果的经验相关性。本文的补充材料可在线获取。