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Econometrics 2015, 3(4), 825-863; doi:10.3390/econometrics3040825

Bootstrap Tests for Overidentification in Linear Regression Models

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
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Kerry Patterson
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)
View Full-Text   |   Download PDF [580 KB, uploaded 9 December 2015]   |  

Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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