The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables
American Economic Review · 2021 · Magne Mogstad、Alexander Torgovitsky、Christopher Walters
中文摘要
实证研究者经常使用两阶段最小二乘（2SLS）将多个工具变量组合用于单一处理。当处理效应存在异质性时，纳入多个工具变量的一个常见理由是，2SLS估计量可以作为局部平均处理效应的正加权平均而被赋予因果解释。这一理由需要众所周知的单调性条件。然而，我们表明，当存在多于一个工具变量时，只有当选择行为实质上同质时，该条件才能得到满足。基于这一发现，我们考虑了在较弱的偏单调性条件下使用多个工具变量。我们刻画了在偏单调性下，2SLS估计量成为局部平均处理效应的正加权平均的实证可验证的充分必要条件。我们将这些结果应用于使用多个工具变量的大学教育回报的实证分析中。我们表明，标准的单调性条件与数据相悖。尽管如此，我们的实证检验揭示，2SLS估计量仍保留因果解释，即为遵从组中大学入学效应的正加权平均。
Abstract
Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple IVs is that the 2SLS estimand can be given a causal interpretation as a positively weighted average of local average treatment effects (LATEs). This justification requires the well-known monotonicity condition. However, we show that with more than one instrument, this condition can only be satisfied if choice behavior is effectively homogeneous. Based on this finding, we consider the use of multiple IVs under a weaker, partial monotonicity condition. We characterize empirically verifiable sufficient and necessary conditions for the 2SLS estimand to be a positively weighted average of LATEs under partial monotonicity. We apply these results to an empirical analysis of the returns to college with multiple instruments. We show that the standard monotonicity condition is at odds with the data. Nevertheless, our empirical checks reveal that the 2SLS estimate retains a causal interpretation as a positively weighted average of the effects of college attendance among complier groups. (JEL C26, I23, I26, J24, J31, R23)