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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Controlling for a covariate that is influenced by the exposure or the outcome could bias the MR effect estimate.
“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]
Selection bias can arise in MR studies if an individual's exposure and outcome values affect their participation.
“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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“The critical values of the Stock and Yogo (2005) weak instrument test statistic are 16.38 and 8.96, respectively, for the 10 and 15 percent levels (see also Staiger and Stock 1997).”
BackgroundInfluentialAsymptotic Distributions of Instrumental Variables Statistics with Many Instruments
Stock, J. H., & Yogo, M. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511614491.007 · Cited by 682 · see citing works
“Specifically, we extend the weak instrument asymptotics developed in Staiger and Stock (1997) to the case of many instruments.”
MethodSelf-citationInformal care and health care use of older adults
Houtven, C. H. V., & Norton, E. C. (2004) · Journal of Health Economics · doi:10.1016/j.jhealeco.2004.04.008 · Cited by 676 · see citing works
ECONOMETRICS IN OUTCOMES RESEARCH: The Use of Instrumental Variables
Newhouse, J. P., & McClellan, M. (1998) · Annual Review of Public Health · doi:10.1146/annurev.publhealth.19.1.17 · Cited by 678 · see citing works
Shaping Liquidity: On the Causal Effects of Voluntary Disclosure
Balakrishnan, K., Billings, M. B., Kelly, B., & Ljungqvist, A. P. (2014) · The Journal of Finance · doi:10.1111/jofi.12180 · Cited by 636 · see citing works
Corruption, economic growth, and income inequality in Africa
Gyimah‐Brempong, K. (2002) · Economics of Governance · doi:10.1007/s101010200045 · Cited by 662 · see citing works
“Tanzi (1998) and Tanzi and Davoodi (1997) investigate the effects of corruption on economic growth and government expenditures.”
BackgroundResultInfluentialVega, S. H., & Elhorst, J. P. (2015) · Journal of Regional Science · doi:10.1111/jors.12188 · Cited by 648 · see citing works
Credit Supply and the Price of Housing
Favara, G., & Imbs, J. (2015) · American Economic Review · doi:10.1257/aer.20121416 · Cited by 621 · see citing works
“as an independent variable, while Stein and Lamont (1997) include contemporaneous and lagged per capita income.”
Income Variance Dynamics and Heterogeneity
Meghir, C., & Pistaferri, L. (2003) · Econometrica · doi:10.1111/j.1468-0262.2004.00476.x · Cited by 612 · see citing works
- 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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