Recent research has demonstrated the importance of flexibly controlling for covariates in instrumental variables estimation. In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), motivated by Abadie's (2003) kappa theorem and offering the requisite flexibility relative to standard practice. 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 weighting 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, which clearly document the sensitivity of unnormalized estimators to how the outcome variable is coded. We implement the proposed estimators in the Stata package kappalate.

翻译：近期研究表明，在工具变量估计中灵活控制协变量具有重要意义。本文基于阿巴迪(2003)的卡帕定理，研究局部平均处理效应各类加权估计量的有限样本与大样本性质，并相较于标准实践提供了必要的灵活性。我们认为，所考虑的两种经权重归一化的估计量通常更优。其他若干未归一化的估计量不满足自然对数尺度不变性和平移不变性，因此在以对数形式估计局部平均处理效应时对测量单位敏感，且普遍对结果变量的中心化处理敏感。我们还证明，当不依从性为单侧时，特定加权估计量具有优势——其分母通过构造严格大于零。在两种归一化估计量中仅有一种满足此条件，我们建议广泛使用该估计量。通过模拟研究和三项实证应用，我们清晰地展示了未归一化估计量对结果变量编码方式的敏感性。我们已在Stata软件包kappalate中实现了所提出的估计量。