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Valid Confidence Regions and Inference in the Presence of Weak Instruments

Eric Zivot (), Charles 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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