On the size distortion of tests after an overidentifying restrictions pretest

• Published in: Journal of applied econometrics (Chichester, England) Vol. 27; no. 7; pp. 1138 - 1160
• Main Authors: Guggenberger, Patrik, Kumar, Gitanjali
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2012; John Wiley & Sons; Wiley Periodicals Inc
• Subjects: Applied economics; Asymptotic methods; Econometric models; Econometrics; Empirical evidence; Employment; Estimators; Hypotheses; Hypothesis; Hypothesis testing; Inference; Instrumental variables; Linear models; Mathematical vectors; Model testing; Monte Carlo simulation; Null hypothesis; Parametric models; Pretests; Random variables; Size; Studies
• ISSN: 0883-7252; 1099-1255
• DOI: 10.1002/jae.1251

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.