Abstract In Instrumental Variables (IV) estimation, the effect of an instrument on an endogenous variable may vary across the sample. In this case, IV produces a local average treatment effect (LATE), and if monotonicity does not hold, then no effect of interest is identified. In this paper, I calculate the weighted average of treatment effects that is identified under general first-stage effect heterogeneity, which is generally not the average treatment effect among those affected by the instrument. I then describe a simple set of data-driven approaches to modeling variation in the effect of the instrument. These approaches identify a Super-Local Average Treatment Effect (SLATE) that weights treatment effects by the corresponding instrument effect more heavily than LATE. Even when first-stage heterogeneity is poorly modeled, these approaches considerably reduce the impact of small-sample bias compared to standard IV and unbiased weak-instrument IV methods, and can also make results more robust to violations of monotonicity. In application to a published study with a strong instrument, the preferred approach reduces error by about 19% in small (N ≈ 1, 000) subsamples, and by about 13% in larger (N ≈ 33, 000) subsamples.

中文翻译：

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具有异质效应的乐器：偏差、单调性和局部性

摘要 在工具变量 (IV) 估计中，工具对内生变量的影响可能因样本而异。在这种情况下，IV 产生局部平均处理效果 (LATE)，如果单调性不成立，则不会识别出感兴趣的效果。在本文中，我计算了在一般第一阶段效应异质性下识别的处理效应的加权平均值，这通常不是受仪器影响的那些的平均处理效应。然后，我描述了一组简单的数据驱动方法，用于对仪器效果的变化进行建模。这些方法确定了一个超局部平均治疗效果 (SLATE)，它比 LATE 更重地通过相应的仪器效果对治疗效果进行加权。即使第一阶段的异质性建模不佳，与标准 IV 和无偏弱仪器 IV 方法相比，这些方法大大减少了小样本偏差的影响，并且还可以使结果对违反单调性更加稳健。在使用强大的仪器应用于已发表的研究时，首选方法将小 (N ≈ 1, 000) 子样本的误差减少了约 19%，并将较大 (N ≈ 33, 000) 子样本的误差减少了约 13%。