Instrumental Variables Regression with Weak Instruments
Abstract
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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Following the rule of thumb suggested by Staiger and Stock (1997), we do not accept the null of weak instruments.
“Hence, following the rule of thumb suggested by Staiger and Stock (1997), we do not accept the null of weak instruments.”
From Fertility Transitions in Developing Countries: Convergence, Timing, and Causes (2019) · cites this paper as Staiger and Stock (1997)
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- Authors
- Staiger, D., & Stock, J. H.
- Affiliations
- Dartmouth College (US)
- National Bureau of Economic Research (US)
- ORCID
- Staiger, Douglas
- Venue
- Econometrica
- Publisher
- JSTOR
- Published
- 1997-05
- Volume
- 65
- Issue
- 3
- Pages
- 557
- ISSN
- 0012-9682 (ISSN-L)
- OpenAlex
- W2165144879
- Cited by
- 7,081
- References
- 0
- Citations by year
- 2026: 458 · 2025: 398 · 2024: 405 · 2023: 329 · 2022: 395 · 2021: 363 · 2020: 347 · 2019: 362 · 2018: 329 · 2017: 348 · 2016: 365 · 2015: 311 · 2014: 304 · 2013: 283 · 2012: 305
- FWCI
- 34.83
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Econometrica (publishedVersion)
- 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, partial correlation
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