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Open AccessArticle

Bootstrap Tests for Overidentification in Linear Regression Models

by Russell Davidson 1,2,† and James G. MacKinnon 3,*,†
1
Department of Economics and CIREQ, McGill University, Montréal, Québec H3A 2T7, Canada
2
AMSE-GREQAM, Centre de la Vieille Charité, 13236 Marseille cedex 02, France
3
Department of Economics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Kerry Patterson
Econometrics 2015, 3(4), 825-863; https://doi.org/10.3390/econometrics3040825
Received: 13 July 2015 / Revised: 24 November 2015 / Accepted: 24 November 2015 / Published: 9 December 2015
(This article belongs to the Special Issue Recent Developments of Specification Testing)
We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight mutually independent random variables and two nuisance parameters. The distributions of the statistics are shown to have an ill-defined limit as the parameter that determines the strength of the instruments tends to zero and as the correlation between the disturbances of the structural and reduced-form equations tends to plus or minus one. This makes it impossible to perform reliable inference near the point at which the limit is ill-defined. Several bootstrap procedures are proposed. They alleviate the problem and allow reliable inference when the instruments are not too weak. We also study their power properties. View Full-Text
Keywords: Sargan test; Basmann test; Anderson-Rubin test; weak instruments Sargan test; Basmann test; Anderson-Rubin test; weak instruments
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Davidson, R.; MacKinnon, J.G. Bootstrap Tests for Overidentification in Linear Regression Models. Econometrics 2015, 3, 825-863.

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