The robust F-statistic as a test for weak instruments

Journal article

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.

Authors: Windmeijer, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Econometrics
• Volume: 247
• Article number: 105951
• Publication date: 2025-01-27
• Acceptance date: 2025-01-02
• DOI: 10.1016/j.jeconom.2025.105951
• EISSN: 1872-6895
• ISSN: 0304-4076
• Language: English
• Keywords: heteroskedasticity; weak instruments; GMM; instrumental variables; robust F-statistic