The paper shows that matching without replacement on propensity scores produces estimators that generally are inconsistent for the average treatment effect of the treated. To achieve consistency, practitioners must either assume that no units exist with propensity scores greater than one-half or assume that there is no confounding among such units. The result is not driven by the use of propensity scores, and similar artifacts arise when matching on other scores as long as it is without replacement.

翻译：本文显示,在不替换适应性分数的情况下进行匹配会产生估计值,而这些估计值一般与被治疗者的平均治疗效果不一致。 为了实现一致性,执业者必须假设不存在任何单位的倾向性分数大于一半或假定这些单位之间没有混乱。结果不是因使用偏好分数而驱动的,而是在与其他分数进行匹配时出现类似的文物,只要没有替换。