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)

中文翻译：

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多工具变量两阶段最小二乘的因果解释

经验研究人员通常使用两阶段最小二乘法 (2SLS) 将多个工具变量 (IV) 组合在一起进行单一治疗。当治疗效果异质时，包含多个 IV 的常见理由是 2SLS 估计值可以作为局部平均治疗效果 (LATE) 的正加权平均值进行因果解释。这种证明需要众所周知的单调性条件。然而，我们表明，对于不止一种工具，只有在选择行为有效同质的情况下才能满足这一条件。基于这一发现，我们考虑在较弱的部分单调性条件下使用多个 IV。我们将 2SLS 估计的经验可验证充分和必要条件描述为部分单调性下 LATE 的正加权平均值。我们将这些结果应用于使用多种工具对大学回报的实证分析。我们表明标准单调性条件与数据不一致。尽管如此，我们的实证检验表明，2SLS 估计保留了因果解释，作为编译器群体中大学出勤率影响的正加权平均值。（JEL C26、I23、I26、J24、J31、R23）