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The robust F-statistic as a test for weak instruments

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  • Windmeijer, Frank

Abstract

For the linear model with a single endogenous variable, (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) or limited information maximum likelihood (LIML) estimator relative to a benchmark worst-case bias. We show that their methodology for the 2SLS estimator applies to a class of linear generalized method of moments (GMM) estimators with an associated class of generalized effective F-statistics. The standard robust F-statistic is a member of this class. The associated GMMf estimator, with the extension “f” for first-stage, has the weight matrix based on the first-stage residuals. In the grouped-data IV designs of Andrews (2018) with moderate and high levels of endogeneity and 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.

Suggested Citation

  • Windmeijer, Frank, 2025. "The robust F-statistic as a test for weak instruments," Journal of Econometrics, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:econom:v:247:y:2025:i:c:s0304407625000053
    DOI: 10.1016/j.jeconom.2025.105951
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    Keywords

    Instrumental variables; Weak instruments; Heteroskedasticity; Robust F-statistic; GMM;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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