On the size distortion of tests after an overidentifying restrictions pretest
Article first published online: 2 JUN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Journal of Applied Econometrics
Volume 27, Issue 7, pages 1138–1160, November/December 2012
How to Cite
Guggenberger, P. and Kumar, G. (2012), On the size distortion of tests after an overidentifying restrictions pretest. J. Appl. Econ., 27: 1138–1160. doi: 10.1002/jae.1251
- Issue published online: 27 NOV 2012
- Article first published online: 2 JUN 2011
- Manuscript Revised: 22 MAR 2011
- Manuscript Received: 5 APR 2010
In the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two-stage hypothesis test that uses a test of overidentifying restrictions (OR) in the first stage. We derive a lower bound for the asymptotic size of the two-stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 − εP, where εP is the pretest nominal size, for a parameter space that allows for local non-exogeneity of the instruments but rules out weak instruments. Copyright © 2011 John Wiley & Sons, Ltd.