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Instrumental Variables Regression with Weak Instruments
Open accessAbstract
This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).
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“In either of these situations, controlling for such a covariate could bias the MR effect estimate.55–57”
From Mendelian randomization (2022) · cites this paper as [57]
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“Another type of bias that can arise in MR studies that cannot be easily corrected for is selection bias64 In an MR study, an example of selection bias would be if an individual’s exposure and outcome values affected their participation.57”
From Mendelian randomization (2022) · cites this paper as [57]
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Vandenbussche, H., & Zanardi, M. (2010) · European Economic Review · doi:10.1016/j.euroecorev.2010.01.003 · Cited by 168
“23 Although critical values for the weak identification test have not been tabulated for non i.i.d. errors, the rule of thumb of Staiger and Stock (1997) is that the F-statistic should be at least 10 for weak identification not to be considered a problem.”
BackgroundCo-invention networks and inventive productivity in US cities
Breschi, S., & Lenzi, C. (2016) · Journal of Urban Economics · doi:10.1016/j.jue.2015.12.003 · Cited by 171
FDI and credit constraints: Firm-level evidence from China
Héricourt, J., & Poncet, S. (2008) · Economic Systems · doi:10.1016/j.ecosys.2008.07.001 · Cited by 174
“F-statistics are consistently above 10, verifying the Staiger and Stock (1997) ‘‘rule of thumb’’.”
BackgroundModel Uncertainty in Sociological Research: An Application to Religion and Economic Growth
Young, C. (2009) · American Sociological Review · doi:10.1177/000312240907400303 · Cited by 166
A Robust Test for Weak Instruments in Stata
PFLUEGER, C. E., & Wang, S. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500113 · Cited by 173
“Staiger and Stock (1997) and Stock and Yogo (2005) proposed widely used pre tests for weak instruments under the assumption of conditionally homoskedastic, serially uncorrelated model errors.”
Early teen marriage and future poverty
Dahl, G. B. (2010) · Demography · doi:10.1353/dem.0.0120 · Cited by 173
Is there a Causal Effect of High School Math on Labor Market Outcomes?
Joensen, J. S., & Nielsen, H. S. (2009) · The Journal of Human Resources · doi:10.1353/jhr.2009.0004 · Cited by 168
Where do biospheric values come from? A connectedness to nature perspective
Martin, C., & Czellar, S. (2017) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2017.04.009 · Cited by 171
“This caused the first-stage F-statistic (Tables 4a and 4b) to be smaller than the recommended minimum value of 10 (Staiger & Stock, 1997) in several of our models.”
Background
Metadata
- Authors
- Staiger, D., & Stock, J.
- ORCID
- Staiger, Douglas
- Venue
- National Bureau of Economic Research
- Publisher
- National Bureau of Economic Research
- Published
- 1994-01
- OpenAlex
- W3122531453
- Cited by
- 5,302
- References
- 0
- Citations by year
- 2026: 39 · 2025: 51 · 2024: 42 · 2023: 41 · 2022: 73 · 2021: 242 · 2020: 254 · 2019: 246 · 2018: 248 · 2017: 286 · 2016: 328 · 2015: 343 · 2014: 345 · 2013: 336 · 2012: 337
- Type
- report
- Language
- en
- Open access
- green
- doi.org
- Locations
- National Bureau of Economic Research (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
- Keywords
- weak instruments, instrumental variable regression, asymptotic distribution, two-stage least squares, limited information maximum likelihood, endogeneity, returns to education, t-statistic
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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