On the size distortion of tests after an overidentifying restrictions pretest

Patrik Guggenberger, Gitanjali Kumar

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5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1138-1160
Number of pages23
JournalJournal of Applied Econometrics
Volume27
Issue number7
DOIs
StatePublished - Nov 1 2012

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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