We synthesize two recent advances in the literature on instrumental variables (IVs) estimation that test and relax the exclusion restriction. Our approach first estimates the direct effect of the IV on the outcome in a subsample for which the IV does not affect the treatment variable. Subsequently, this estimate for the direct effect is used as input for the plausibly exogenous method developed by Conley, Hansen and Rossi (2012). This two-step procedure provides a novel and informed sensitivity analysis for IV estimation. We illustrate the practical use by estimating the causal effect of (i) attending Catholic high school on schooling outcomes, and (ii) the number of children on female labour supply.

中文翻译：

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超越合理的外生

我们综合了关于工具变量（IVs）估计的文献中的两项最新进展，这些进展可以测试并放宽排除限制。我们的方法首先在不影响治疗变量的IV子样本中估计IV对结果的直接影响。随后，该直接影响的估计值被用作Conley，Hansen和Rossi（2012）开发的似乎是外生方法的输入。此两步过程为IV估计提供了一种新颖而明智的敏感性分析。我们通过估计（i）就读天主教高中对学业成绩的因果影响，以及（ii）子女人数对女性劳动力供给的因果作用，说明实际用途。