Valid confidence intervals and inference in the presence of weak instruments

We investigate confidence intervals and inference for the instrumental variables model with weak instruments. Confidence intervals based on inverting the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. Performance of the LM and LR statistics is improved by a degrees-of-freedom correction in the overidentified case. The practice of 'pre-testing' by looking at the significance of the first-stage regression and then making inference based on the LM or LR statistics leads to better results than pre-testing and using the Wald statistic.