Abstract
We investigate confidence intervals and inference for the instrumental variables model with weak instruments. Wald-based confidence intervals perform poorly in that the probability they reject the null is far greater than their nominal size. In the worst case, Wald-based confidence intervals always exclude the true parameter value. Confidence intervals based on the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. The AndersonRubin statistic always has the correct size, but LM and LR statistics have somewhat greater power. Performance of the LM and LR statistics is improved by a degrees-of-freedom correction in the overidentified case. We show that the practice of “pre-testing” by looking at the significance of the first-stage regression leads to extremely poor results when the instruments are very weak.
Published Version
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