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Testing for Weak Instruments in Linear IV Regression

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Stock, James H., Yogo, Motohiro·2005·Identification and Inference for Econometric Models
DOI 10.1017/cbo9780511614491.006
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Abstract

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 the given instruments are weak. INTRODUCTION Standard treatments of instrumental variables (IV) regression stress that for instruments to be valid they must be exogenous. It is also important, however, that the second condition for a valid instrument, instrument relevance, holds, for if the instruments are only marginally relevant, or “weak,” then first-order asymptotics can be a poor guide to the actual sampling distributions of conventional IV regression statistics. At a formal level, the strength of the instruments matters because the natural measure of this strength – the so-called concentration parameter – plays a role formally akin to the sample size in IV regression statistics. Rothenberg (1984) makes this point in his survey of approximations to the distributions of estimators and test statistics.

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  • The recent literature on weak instruments argues for LIML's better performance in finite samples compared to 2SLS and two-step efficient GMM.

    “The recent literature on weak instruments argues for LIML s better performance in nite samples compared to 2SLS and two-step e¢ cient GMM (Baum et al., 2007; Stock and Yogo, 2005).”

    From Fertility Transitions in Developing Countries: Convergence, Timing, and Causes (2019) · cites this paper as Stock and Yogo, 2005

    The Conclusions (page unavailable) say LIML is far superior to 2SLS under weak instruments, specifically in coverage rates. Section 3.5 (page unavailable) also finds LIML-based tests more robust, but the copy does not establish a comparison with two-step efficient GMM. The claim therefore extends beyond the comparison this paper supports. (LLM, conf=0.88)

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Research works printed but not linked: 14

  1. Anderson, T.W. (1974): "An Asymptotic Expansion of the Distribution of the Limited Information Maximum Likelihood Estimate of a Coefficient in a Simultaneous Equation System," Journal of the American Statistical Association, 69, 565 -573.
  2. Bound, J., D.A. Jaeger, and R.M. Baker (1995): "Problems with Instrumental Variables Estimation when the Correlation Between the Instruments and the Endogenous Explanatory Variable is Weak," Journal of the American Statistical Association 90, 443 -450.
  3. Bowden, R. and D. Turkington (1984): Instrumental Variables. Cambridge: Cambridge University Press.
  4. Götze, F. (1991): "On the Rate of Convergence in the Multivariate CLT," Annals of Probability, 19, 724 -739.
  5. Hall, A., G.D. Rudebusch and D. Wilcox (1996): "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review 37, 283 - 298.
  6. Jensen, D.R. and L.S. Mayer (1975): "Normal-Theory Approximations to Tests of Linear Hypotheses," Annals of Statistics, 3, 429 -444.
  7. Kunitomo, N. (1980): "Asymptotic Expansions of the Distributions of Estimators in a Linear Functional Relationship and Simultaneous Equations," Journal of the American Statistical Association, 75, 693-700.
  8. Muirhead, R.J. (1978): "Latent Roots and Matrix Variates: A Review of Some Asymptotic Results," Annals of Statistics, 6, 5-33.
  9. -------(1982): Aspects of Multivariate Statistical Theory. New York: Wiley.
  10. -------(1990b): "The Distribution of the Instrumental Variables Estimator and its t- ratio when the Instrument is a Poor One," Journal of Business 63, 5125 -5140.
  11. Rothenberg, T.J. (1983): "Asymptotic Properties of Some Estimators in Structural Models," in S. Karlin, T. Amemiya, and L. Goodman, eds., Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press.
  12. Sargan, D. (1975): "Asymptotic Theory and Large Models," International Economic Review, 16, 75 -91.
  13. Shea, J. (1997): "Instrument Relevance in Multivariate Linear Models: A Simple Measure," Review of Economics and Statistics 79, 348 -352.
  14. Stock, J.H., J.H. Wright, and M. Yogo (2002): "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business and Economic Statistics, 20, 518 -529.

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Authors
Stock, J. H., & Yogo, M.
Affiliations
Harvard University (US)
ORCID
Yogo, Motohiro
Venue
Identification and Inference for Econometric Models
Publisher
Cambridge University Press
Published
2005-06-17
Pages
80-108
DOI
10.1017/cbo9780511614491.006
OpenAlex
W3124259699
Cited by
7,211
References
0
Citations by year
2026: 405 · 2025: 440 · 2024: 438 · 2023: 431 · 2022: 444 · 2021: 472 · 2020: 447 · 2019: 422 · 2018: 399 · 2017: 402 · 2016: 353 · 2015: 418 · 2014: 350 · 2013: 377 · 2012: 330
FWCI
131.84
Type
book chapter
Language
en
Open access
Licence
www.cambridge.org/core/terms (unspecified, 1713 d)
Locations
  • Cambridge University Press eBooks (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
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, concentration parameter, critical values

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