The robust F-statistic as a test for weak instruments
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 benchma...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2025
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| Summary: | 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. |
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