两阶段最小二乘法何时真正是局部平均处理效应？

中文摘要

线性工具变量估计量，如两阶段最小二乘（TSLS），通常被解释为在估计因果效应的非负加权平均，即局部平均处理效应（LATE）。我们考察 LATE 这一解释是否真正适用于实践中所使用的各类 TSLS 设定。我们表明，如果设定中包含协变量——大多数实证研究都是如此——那么 LATE 解释一般并不成立。相反，TSLS 估计量一般会同时反映依从者与始终接受者/从不接受者的处理效应，且始终接受者/从不接受者的某些处理效应必然被赋予负权重。我们证明，唯一具有 LATE 解释的设定是对协变量进行非参数控制的"饱和"设定；这意味着，至少在不附加额外参数假设的情况下，此类设定既是 TSLS 具有 LATE 解释的充分条件，也是必要条件。这一结果令人担忧，因为正如我们所记录的，实证研究者几乎从不以非参数方式控制协变量，也很少讨论或论证协变量参数化设定的合理性。我们将上述结论应用于十三项实证研究，发现有力证据表明：对于实践中实际使用的设定类型，TSLS 的 LATE 解释远非准确。基于理论与实证结果，我们提出了具体的实践建议。

Abstract

Abstract Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating non-negatively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general. Instead, the TSLS estimator will, in general, reflect treatment effects for both compliers and always/never-takers, and some treatment effects for the always/never-takers will necessarily be negatively weighted. We show that the only specifications that have a LATE interpretation are “saturated” specifications that control for covariates nonparametrically, implying that such specifications are both sufficient and necessary for TSLS to have a LATE interpretation, at least without additional parametric assumptions. This result is concerning because, as we document, empirical researchers almost never control for covariates nonparametrically, and rarely discuss or justify parametric specifications of covariates. We apply our results to thirteen empirical studies and find strong evidence that the LATE interpretation of TSLS is far from accurate for the types of specifications actually used in practice. We offer concrete recommendations for practice motivated by our theoretical and empirical results.