On the size distortion of tests after an overidentifying restrictions pretest

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 lowe...

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Bibliographic Details
Published inJournal of applied econometrics (Chichester, England) Vol. 27; no. 7; pp. 1138 - 1160
Main Authors Guggenberger, Patrik, Kumar, Gitanjali
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.11.2012
John Wiley & Sons
Wiley Periodicals Inc
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Summary: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 — ε P , where ε P is the pretest nominal size, for a parameter space that allows for local non-exogeneity of the instruments but rules out weak instruments.
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ISSN:0883-7252
1099-1255
DOI:10.1002/jae.1251