The Hausman Test and Weak Instruments

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The impact of a Hausman pretest on the size of a hypothesis test: The panel data case (2010, background): “Furthermore, variants of Hausman pretests are still being developed in the theoretical literature, see e.g. Hahn et al. (2009).”
THE IMPACT OF A HAUSMAN PRETEST ON THE ASYMPTOTIC SIZE OF A HYPOTHESIS TEST (2009, methodology): “Dhrymes (2008) provides alternatives to Hausman pretests based on estimators of the correlation between the structural and reduced form errors.”
OLS and IV estimation of regression models including endogenous interaction terms (2019, methodology): “51), is not robust to weak instruments (Staiger and Stock, 1997; Hahn et al., 2011). In the case of weak instruments, however, one can still test Assumption 2 exploiting a weak instrument robust version of the Hausman test proposed by Hahn et al. (2011). In the case of exact identication, i.”