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SPECIFICATION TESTING IN MODELS WITH MANYINSTRUMENTS

Published online by Cambridge University Press:  13 September 2010

Stanislav Anatolyev  and
Nikolay Gospodinov
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Abstract

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.

Information

Type
Brief Report
Information
Econometric Theory , Volume 27 , Issue 2 , April 2011 , pp. 427 - 441
Copyright
Copyright © Cambridge University Press 2010

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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.

References

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