Correct (and Incorrect) Inference with a Single Instrumental Variable: Practical Takeaways from the Weak Instruments Literature
Journal of Economic Perspectives · 2026 · David S. Lee、Jack Porter
中文摘要
大多数经验经济学家都遇到过工具变量可能“弱”的警告，但其潜在问题——什么使工具变量变弱、为何弱性会扭曲推断、以及该如何应对——却不那么广为人知。本文针对单一内生回归元与单一工具变量这一常见的恰好识别情形，对弱工具变量问题提供了一个易懂的介绍。我们解释了为何通常的两阶段最小二乘t比率及其“±1.96倍标准误”置信区间会产生错误推断，正如仅同方差标准误在误差存在异方差时那样。随后，我们描述了实用且对弱工具变量稳健的解决方案——包括Anderson-Rubin与tF方法——无论工具变量的真实强度如何，这些方法都能给出有效的置信区间；我们还提供了一些宜忌事项，特别是为何在此设定下流行的“F大于10”规则没有理论依据。
Abstract
Most empirical economists have encountered the warning that instrumental variables can be “weak,” but the underlying issues—what makes an instrument weak, why weakness distorts inference, and what to do about it—are less widely understood. This article offers an accessible introduction to the weak instruments problem for the common just-identified case of a single endogenous regressor and a single instrument. We explain why the usual two-stage least squares t-ratio and its “±1.96 times the standard error” confidence interval can yield incorrect inferences, much as homoskedasticity-only standard errors do when errors are not homoskedastic. We then describe practical, robust-to-weak-instrument solutions—including the Anderson-Rubin and tF methods—that deliver valid confidence intervals whatever the instrument's true strength, and we offer some do's and don'ts, notably why the popular “F greater than 10” rule has no theoretical justification in this setting.