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Testing for Weak Instruments in Linear IV Regression
Open accessAbstract
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 this bias is small.58,59”
From Mendelian randomization (2022) · cites this paper as [58]
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Metadata
- 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
- 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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