Testing for Weak Instruments in Linear IV Regression

Stock, James; Yogo, Motohiro

doi:10.3386/t0284

Cited by 1,842Advanced Causal Inference TechniquesMonetary Policy and Economic ImpactSpatial and Panel Data Analysis

Testing for Weak Instruments in Linear IV Regression

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Stock, James, Yogo, Motohiro·2002·National Bureau of Economic Research

DOI 10.3386/t0284

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Abstract

Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions.But what, precisely, are weak instruments, and how does one detect them in practice?This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors.We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given instruments are weak.A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.

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As a general rule, if the first-stage F-statistic is greater than 10, the level of weak instrument bias is small.
“As a general rule, if the first-stage F-statistic is greater than 10, the level of this bias is small.58,59”
From Mendelian randomization (2022) · cites this paper as [58]

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Authors: Stock, J., & Yogo, M.
Affiliations: National Bureau of Economic Research (US)
ORCID: Yogo, Motohiro
Venue: National Bureau of Economic Research
Publisher: National Bureau of Economic Research
Published: 2002-11
DOI: 10.3386/t0284
OpenAlex: W2110153620
Cited by: 1,842
References: 32
Citations by year: 2026: 122 · 2025: 184 · 2024: 168 · 2023: 101 · 2022: 112 · 2021: 75 · 2020: 96 · 2019: 54 · 2018: 85 · 2017: 42 · 2016: 65 · 2015: 66 · 2014: 93 · 2013: 106 · 2012: 88
Type: report
Language: en
Open access: green
doi.org
Locations: National Bureau of Economic Research (publishedVersion)
Funders: National Science Foundation (9730489, 0214131)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
Keywords: weak instruments, instrumental variable regression, critical values

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