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The Robust F-Statistic as a Test for Weak Instruments

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  • Frank Windmeijer

Abstract

Montiel Olea and Pflueger (2013) proposed the effective F-statistic as a test for weak instruments in terms of the Nagar bias of the two-stage least squares (2SLS) estimator relative to a benchmark worst-case bias. We show that their methodology applies to a class of linear generalized method of moments (GMM) estimators with an associated class of generalized effective F-statistics. The standard nonhomoskedasticity robust F-statistic is a member of this class. The associated GMMf estimator, with the extension f for first-stage, is a novel and unusual estimator as the weight matrix is based on the first-stage residuals. As the robust F-statistic can also be used as a test for underidentification, expressions for the calculation of the weak-instruments critical values in terms of the Nagar bias of the GMMf estimator relative to the benchmark simplify and no simulation methods or Patnaik (1949) distributional approximations are needed. In the grouped-data IV designs of Andrews (2018), where the robust F-statistic is large but the effective F-statistic is small, the GMMf estimator is shown to behave much better in terms of bias than the 2SLS estimator, as expected by the weak-instruments test results.

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  • Frank Windmeijer, 2023. "The Robust F-Statistic as a Test for Weak Instruments," Papers 2309.01637, arXiv.org.
    • Handle: RePEc:arx:papers:2309.01637
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    1. Melvin Stephens Jr. & Dou-Yan Yang, 2014. "Compulsory Education and the Benefits of Schooling," American Economic Review, American Economic Association, vol. 104(6), pages 1777-1792, June.
    2. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    3. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    4. José Luis Montiel Olea & Carolin Pflueger, 2013. "A Robust Test for Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 358-369, July.
    5. Frank Windmeijer, 2019. "Two-stage least squares as minimum distance," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-9.
    6. Paul A. Bekker & Jan van der Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267, August.
    7. Keith Finlay & Leandro M. Magnusson, 2009. "Implementing weak-instrument robust tests for a general class of instrumental-variables models," Stata Journal, StataCorp LP, vol. 9(3), pages 398-421, September.
    8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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