Estimation with Valid and Invalid Instruments

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Determinants of R&D cooperation: Evidence from Spanish manufacturing firms (2008, unknown): “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.”
The validity of instruments revisited (2012, background): “Hahn and Hausman (2006) also look at this issue.”
Sensitivity analysis using approximate moment condition models (2018, background): “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. Bounding the norm of γ using some norm ‖·‖ then leads to the set given in equation (12), w”
Identification With Imperfect Instruments (2008, methodology): “For research on the implications of instrument invalidity in the linear model, outside the study of treatment effects, see, for example, Ashley (2009), Hahn and Hausman (2003), Berkowitz, Caner, and Fang (2008), Conley, Hansen, and Rossi (2006), and Kraay (2008).”