Estimation with Valid and Invalid Instruments

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Asymptotic properties of the Hahn-Hausman test for weak-instruments (2005, background): “Hahn and Hausman (2002, 2003) suggest that tests based on these statistics will reject if one or the other of the conditions for instrument validity fail, that is, if the instruments are weak and/or if they are endogenous.”
Determinants of R&D cooperation: Evidence from Spanish manufacturing firms (2008, background): “Secondly, assuming the existence of invalid instruments, Hahn and Hausman (2005) find that the 2SLS has a smaller finite sample bias and MSE than the OLS under a wide range of conditions.”
Sensitivity analysis using approximate moment condition models (2018, result): “This form of misspecification has previously been considered in a number of papers, including Hahn and Hausman (2005), Conley, Hansen, and Rossi (2012), and Andrews, Gentzkow, and Shapiro (2017), among others.”
The validity of instruments revisited (2012, background): “Hahn and Hausman (2006) also look at this issue.”
Minimizing Sensitivity to Model Misspecification (2018, methodology): “2 b (h, β, γ) = 1 Varγ (Δ(A, β) − Eβ [h(Y ) | A]), (36)”