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. In the worst case, Wald-based confidence intervals always exclude the true structural parameter value. Confidence intervals based on the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. The Anderson-Rubin

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... tistic 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 and then making inference based on the Wald statistic leads to extremely poor results when the instruments are very weak. We show pre-testing leads to much better results if inference instead is based on the LM or LR statistics. * Thanks to Jiahui Wang for excellent research assistance and computer programming, to Andrew Siegel for numerous long talks, and to Paul Ruud for his discussion at the 1996 ASSA meetings. Computations were carried out using GAUSS and Matlab. GAUSS code to compute the statistics in the paper can be found on the first author's web page at http://weber.u.washington.edu/~ezivot/wpapers.htm. Financial support from the Royalty Research Fund of the University of Washington and from the National Science Foundation under grant SBR-9711301 is gratefully acknowledged. Responsibility for errors is entirely the authors'.