In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie's (2003) kappa theorem. Our framework presumes a binary treatment and a binary instrument, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which is weight normalized, is preferable in many contexts. Several other estimators, which are unnormalized, do not generally satisfy the properties of scale invariance with respect to the natural logarithm and translation invariance, thereby exhibiting sensitivity to the units of measurement when estimating the LATE in logs and the centering of the outcome variable more generally. On the other hand, when noncompliance is one-sided, certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. To reconcile these findings, we demonstrate that when the instrument propensity score is estimated using an appropriate covariate balancing approach, the resulting normalized estimator also shares this advantage. We use a simulation study and three empirical applications to illustrate our findings. In two cases, the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both.

翻译：本文研究了局部平均处理效应（LATE）的多种加权估计量的有限样本与渐近性质，其中若干估计量基于Abadie（2003）的kappa定理。我们的分析框架假设二元处理变量与二元工具变量，且工具变量仅在对附加协变量进行条件调整后可能有效。我们认为，在众多情境下，经过权重归一化的Abadie估计量更具优势。其他若干未归一化的估计量通常不满足自然对数尺度不变性与平移不变性，因此在对LATE进行对数估计时对测量单位敏感，且更一般地对结果变量的中心化处理敏感。另一方面，当非依从性表现为单侧形式时，某些未归一化估计量因分母远离零而具有优势。为调和这些发现，我们证明：若采用适当的协变量平衡方法估计工具变量倾向得分，所得归一化估计量同样具备这一优势。我们通过模拟研究与三项实证应用对上述结论进行阐释。在两项案例中，未归一化估计值出现明显不合理现象，表现为符号、量级或两者同时"错误"。