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SPECIFICATION TESTING IN MODELS WITH MANYINSTRUMENTS
Published online by Cambridge University Press: 13 September 2010
Abstract
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This paper studies the asymptotic validity of theAnderson–Rubin (AR) test and theJ test for overidentifyingrestrictions in linear models with many instruments.When the number of instruments increases at the samerate as the sample size, we establish that theconventional AR andJ tests are asymptoticallyincorrect. Some versions of these tests, which aredeveloped for situations with moderately manyinstruments, are also shown to be asymptoticallyinvalid in this framework. We propose modificationsof the AR and Jtests that deliver asymptotically correct sizes.Importantly, the corrected tests are robust to thenumerosity of the moment conditions in the sensethat they are valid for both few and manyinstruments. The simulation results illustrate theexcellent properties of the proposed tests.
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Footnotes
We thank the co-editor Richard Smith, tworeferees, and Bruce Hansen for very usefulcomments and suggestions. The second authorgratefully acknowledges financial support fromFQRSC and SSHRC.
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