This paper studies inference for the local average treatment effect in randomized controlled trials with imperfect compliance where treatment status is determined according to "matched pairs." By "matched pairs," we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Under weak assumptions governing the quality of the pairings, we first derive the limit distribution of the usual Wald (i.e., two-stage least squares) estimator of the local average treatment effect. We show further that conventional heteroskedasticity-robust estimators of the Wald estimator's limiting variance are generally conservative, in that their probability limits are (typically strictly) larger than the limiting variance. We therefore provide an alternative estimator of the limiting variance that is consistent. Finally, we consider the use of additional observed, baseline covariates not used in pairing units to increase the precision with which we can estimate the local average treatment effect. To this end, we derive the limiting behavior of a two-stage least squares estimator of the local average treatment effect which includes both the additional covariates in addition to pair fixed effects, and show that its limiting variance is always less than or equal to that of the Wald estimator. To complete our analysis, we provide a consistent estimator of this limiting variance. A simulation study confirms the practical relevance of our theoretical results. Finally, we apply our results to revisit a prominent experiment studying the effect of macroinsurance on microenterprise in Egypt.

翻译：本文研究了在随机对照试验中，针对局部平均处理效应的推断问题，其中存在不完美依从性，且处理状态根据"匹配配对"方式确定。所谓"匹配配对"，是指从目标总体中独立同分布地抽取单元，根据观测到的基线协变量进行配对，最后在每个配对内随机选择一个单元接受处理。在关于配对质量的弱假设下，我们首先推导了局部平均处理效应的常用Wald（即两阶段最小二乘）估计量的极限分布。我们进一步证明，Wald估计量极限方差的常规异方差稳健估计量通常是保守的，因为它们的概率极限（通常严格）大于极限方差。因此，我们提供了一个一致的极限方差替代估计量。最后，我们考虑利用未用于配对单元的额外观测基线协变量来提高估计局部平均处理效应的精度。为此，我们推导了一个两阶段最小二乘估计量的极限行为，该估计量除了包含配对固定效应外，还纳入了额外的协变量，并证明其极限方差总是小于或等于Wald估计量的极限方差。为完善分析，我们提供了该极限方差的一致估计量。一项模拟研究证实了我们理论结果的实际相关性。最后，我们应用我们的结果重新审视了一项研究宏观保险对埃及微型企业影响的著名实验。