Matching methods are widely used for causal inference in observational studies. Among them, nearest neighbor matching is arguably the most popular. However, nearest neighbor matching does not generally yield an average treatment effect estimator that is $\sqrt{n}$-consistent (Abadie and Imbens, 2006). Are matching methods not $\sqrt{n}$-consistent in general? In this paper, we study a recent class of matching methods that use integer programming to directly target aggregate covariate balance as opposed to finding close neighbor matches. We show that under suitable conditions these methods can yield simple estimators that are $\sqrt{n}$-consistent and asymptotically optimal.

翻译：在观察研究中,匹配方法被广泛用于因果推断。 其中,最近的邻居匹配可以说是最受欢迎的方法。 但是,最近的邻居匹配通常不会产生平均治疗效果估计值,即$\sqrt{n}$- constanticent(Abadie and Imbens, 2006) 。 总的来说,匹配方法是不是没有 $\sqrt{n}$- concistic? 在本文中,我们研究了最近一类匹配方法,它们使用整数编程直接针对总共共差平衡而不是寻找近邻匹配值。 我们显示,在适当条件下,这些方法可以产生简单的估算值,即$\sqrt{n}$- concisticent和无现时最佳。