任何第一阶段都无法检测的问题：线性IV中的函数形式污染
What No First Stage Can Detect: Functional-Form Contamination in Linear IV
- Ashoka University（阿肖卡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究证明线性IV中第一阶段诊断无法检测函数形式污染，该污染同时偏误估计量并夸大强度，提出定向检验和修正估计量，两个应用证实了问题。
AI中文摘要：
应用工具变量（IV）实践报告第一阶段F统计量，现在通常为Sanderson和Windmeijer（2016）的条件F，并将大值解读为解释第二阶段的许可。我们证明，没有任何第一阶段诊断能提供这种许可。对于标量工具、标量处理变量以及线性进入的协变量，2SLS估计量分解为一个饱和设定会针对的信号，以及一个污染项，即工具倾向中的曲率与协变量水平函数之间的协方差。相同的干扰项同时出现在两个项中，因此它使估计量产生偏误，并同时夸大报告的强度。当工具与协变量近似共线时，信号消失，强度被人为制造。当强度是真实的时，曲率仍通过结果变量使估计量产生偏误，而第一阶段数字无法触及该路径。我们证明，工具、处理变量和协变量联合分布的任何泛函都无法检测这第二种偏误，并给出一个基于简化式回归的定向检验、一个修正估计量以及一个可报告的污染份额。两个应用展示了这些模式。丈夫的保险工具（Olson, 1998）的条件F超过36,000，但修正线性收入控制后估计值增加了一倍以上。Nunn和Wantchekon（2011）的工具在灵活加入地理变量后失去了大部分第一阶段强度。
英文摘要：
Applied instrumental variables (IV) practice reports a first-stage F, now often the conditional F of Sanderson and Windmeijer (2016), and reads a large value as license to interpret the second stage. We show that no first-stage diagnostic can provide it. With a scalar instrument, a scalar treatment, and covariates entered linearly, the 2SLS estimand splits into a signal that a saturated specification would target and a contamination, the covariance between curvature in the instrument propensity and a covariate level function. The same nuisance sits in both terms, so it biases the estimand and inflates the reported strength at once. When the instrument is nearly collinear with the covariates the signal vanishes and the strength is manufactured. When the strength is honest the curvature still biases the estimand through the outcome, where no first-stage number reaches it. We prove that no functional of the joint distribution of instrument, treatment, and covariates can detect this second bias, and we give a directed test built from reduced-form regressions, a corrected estimator, and a reportable contamination share. Two applications show the modes. A husband's insurance instrument (Olson, 1998) has a conditional F above 36,000, yet correcting a linear income control more than doubles the estimate. The instrument of Nunn and Wantchekon (2011) loses most of its first stage once geography enters flexibly.
