Valid Confidence Regions and Inference in the Presence of Weak Instruments

Eric Zivot (), Charles R. Nelson and Richard Startz ()

Working Papers from University of Washington, Department of Economics

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 paremeter value. Confidence intervals based on the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. The Anderson-Rubin 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 ccase. 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.

Date: 1996-02
Note: June 1996 version

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Working Paper: Valid Confidence Regions and Inference in the Presence of Weak Instruments (1996)
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