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 limiting behavior of the usual Wald (i.e., two-stage least squares) estimator of the local average treatment effect. We show further that the conventional heteroskedasticity-robust estimator of its limiting variance is generally conservative in that its limit in probability is (typically strictly) larger than the limiting variance. We therefore provide an alternative estimator of the limiting variance that is consistent for the desired quantity. 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 the 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. We use our results to revisit a prominent experiment studying the effect of macroinsurance on microenterprise in Egypt.

翻译：本文研究在治疗状态根据“匹配对”确定的不完全依从随机对照试验中，局部平均治疗效应的推断问题。所谓“匹配对”，是指从目标总体中独立同分布地抽样个体，根据观测到的基线协变量进行配对，然后在每一对中随机选取一个个体接受治疗。在控制配对质量的弱假设下，我们首先推导了局部平均治疗效应的常用Wald估计量（即两阶段最小二乘估计量）的极限行为。进一步证明，其极限方差的标准异方差稳健估计量通常是保守的，因为它的概率极限（通常严格）大于极限方差。因此，我们提供了一个与目标量一致的极限方差替代估计量。最后，我们考虑使用未用于配对的额外观测基线协变量来提高局部平均治疗效应的估计精度。为此，我们推导了包含额外协变量和配对固定效应的两阶段最小二乘估计量的极限行为，并证明其极限方差始终小于或等于Wald估计量的极限方差。为完成分析，我们给出了该极限方差的一致估计量。模拟研究证实了我们理论结果的实际相关性。我们利用研究结果重新审视了埃及关于宏观保险对微观企业影响的著名实验。