论文标题
在线性模型中测试仪器强度后推断治疗效果
Inferring Treatment Effects After Testing Instrument Strength in Linear Models
论文作者
论文摘要
IV研究中的一种常见做法是检查仪器强度，即其与治疗的关联，并与回归有关。如果F统计量高于一定的阈值，通常为10，则认为该仪器可满足三个核心IV假设之一，并用于测试治疗效果。但是，在许多情况下，对治疗效果的推断没有考虑到先验的强度测试。在本文中，我们表明，不考虑这种预测试可能会严重扭曲测试统计量的分布，并提出一种纠正这种失真的方法，从而产生有效的推断。我们方法中的一个关键见解是将F检验构图为随机凸优化问题，并利用选择性推断的最新方法。我们证明我们的方法提供条件和边缘I型错误控制。我们还将方法扩展到弱仪器设置。最后，我们重新分析了有关教育对赚取的影响的研究，我们表明，不考虑预测试的情况可以极大地改变有关教育影响的原始结论。
A common practice in IV studies is to check for instrument strength, i.e. its association to the treatment, with an F-test from regression. If the F-statistic is above some threshold, usually 10, the instrument is deemed to satisfy one of the three core IV assumptions and used to test for the treatment effect. However, in many cases, the inference on the treatment effect does not take into account the strength test done a priori. In this paper, we show that not accounting for this pretest can severely distort the distribution of the test statistic and propose a method to correct this distortion, producing valid inference. A key insight in our method is to frame the F-test as a randomized convex optimization problem and to leverage recent methods in selective inference. We prove that our method provides conditional and marginal Type I error control. We also extend our method to weak instrument settings. We conclude with a reanalysis of studies concerning the effect of education on earning where we show that not accounting for pre-testing can dramatically alter the original conclusion about education's effects.
