In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), each of which can be motivated by 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 two of the estimators under consideration, which are weight normalized, are generally preferable. Several other estimators, which are unnormalized, do not 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. We also demonstrate that, when noncompliance is one sided, certain estimators have the advantage of being based on a denominator that is strictly greater than zero by construction. This is the case for only one of the two normalized estimators, and we recommend this estimator for wider use. We illustrate our findings with a simulation study and three empirical applications. The importance of normalization is particularly apparent in applications to real data. The simulations also suggest that covariate balancing estimation of instrument propensity scores may be more robust to misspecification. Software for implementing these methods is available in Stata.

翻译：本文研究了局部平均处理效应（LATE）各类加权估计量的有限样本与大样本性质，这些估计量均可从Abadie（2003）的kappa定理推导得出。我们的分析框架假设二元处理变量与二元工具变量，且该工具变量可能仅在控制协变量后满足有效性条件。我们认为，所考虑的两个经权重归一化的估计量通常更优。其他未归一化的估计量不满足自然对数尺度不变性与平移不变性，因此在估计对数化LATE及更广义的结果变量中心化时，会对测量单位表现出敏感性。同时证明，当存在单侧不依从时，特定估计量因其分母严格大于零而具有优势——这仅适用于两个归一化估计量中的一个，我们推荐广泛采用该估计量。我们通过模拟研究与三项实证应用验证研究结论。在实际数据应用中，归一化的重要性尤为显著。模拟结果还表明，工具变量倾向得分的协变量平衡估计对模型误设可能具有更强的稳健性。Stata软件包已提供这些方法的实现程序。