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SPECIFICATION TESTING IN MODELS WITH MANY INSTRUMENTS

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 the Anderson–Rubin (AR) test and the J test for overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional AR and J tests are asymptotically incorrect. Some versions of these tests, which are developed for situations with moderately many instruments, are also shown to be asymptotically invalid in this framework. We propose modifications of the AR and J tests that deliver asymptotically correct sizes. Importantly, the corrected tests are robust to the numerosity of the moment conditions in the sense that they are valid for both few and many instruments. The simulation results illustrate the excellent properties of the proposed tests.

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, two referees, and Bruce Hansen for very useful comments and suggestions. The second author gratefully acknowledges financial support from FQRSC and SSHRC.

References

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