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. Wald-based confidence intervals for a structural parameter perform poorly in that the probability they reject the null is far greater than their nominal size. We show that the preactice of "pre-testing" by looking at the significance of the fist-stage regression and then making inference based on the Wald statistic leads to extremely poor results when the instruments are very weak.