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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]
In the citing paper
“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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Initial conditions and moment restrictions in dynamic panel data models
Blundell, R., & Bond, S. (1995) · Working Paper Series · doi:10.1920/wp.ifs.1995.9517 · Cited by 14,755
“Following Nelson and Startz (1990a,b) and Staiger and Stock (1997) we characterise this problem of weak instruments using the concentration parameter.”
BackgroundMethodBowden, J., Davey Smith, G., & Burgess, S. (2015) · International Journal of Epidemiology · doi:10.1093/ije/dyv080 · Cited by 9,816
“With many IVs in a one-sample setting (genetic variants, exposure and outcome measured in the same participants), IV estimates (particularly those from the TSLS method) are biased in the direction of the observational association between the exposure and the outcome.(49) This bias depends on the strength of the associ…”
MethodMendelian Randomization Analysis With Multiple Genetic Variants Using Summarized Data
Burgess, S., Butterworth, A., & Thompson, S. G. (2013) · Genetic Epidemiology · doi:10.1002/gepi.21758 · Cited by 6,050
“In particular, this means that when the expected value of the F statistic is greater than 10, the bias of the causal estimate is less than 10% of the bias of the confounded observational estimate from an OLS regression analysis [Staiger and Stock, 1997].”
BackgroundA finite sample correction for the variance of linear efficient two-step GMM estimators
Windmeijer, F. A. G. (2004) · Journal of Econometrics · doi:10.1016/j.jeconom.2004.02.005 · Cited by 6,007
Frankel, J. A., & Romer, D. (1999) · American Economic Review · doi:10.1257/aer.89.3.379 · Cited by 5,593
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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