Credible Two-Stage Least Squares Inference With Possibly-Flawed Instruments

Two-stage least squares (2SLS) is commonly used to obtain consistent structural parameter inferences and asymptotically-valid inference results where one or more explanatory variables is – due to endogeneity, measurement error, etc.– correlated with the model error term. But the validity of 2SLS rests on an assumption that each of the instruments used is itself is unflawed – i.e., uncorrelated with the model error. Here we finesse the untestability of this assumption by quantifying the sensitivity of any particular 2SLS inference result to failures of this assumption. Our results make it feasible to determine which 2SLS inference results are robust to instrument flaws and which are not, thereby making it possible to obtain ‘credible’ 2SLS inferences.