Bootstrap Tests For Overidentification In Linear Regression Models

James MacKinnon and Russell Davidson

No 1318, Working Paper from Economics Department, Queen's University

Abstract: Little attention has been paid to the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. We study several such tests in models estimated by instrumental variables (IV) and limited-information maximum likelihood (LIML). 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. Simulation experiments demonstrate that 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 the power properties of the bootstrap tests.

Keywords: Sargan test; Basmann test; Anderson-Rubin test; weak instruments; bootstrap P value (search for similar items in EconPapers)
JEL-codes: C10 C12 C15 C30 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2014-04
New Economics Papers: this item is included in nep-ecm and nep-ore
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https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1318.pdf First version 2014 (application/pdf)

Related works:
Journal Article: Bootstrap Tests for Overidentification in Linear Regression Models (2015)
Working Paper: Bootstrap Tests for Overidentification in Linear Regression Models (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:qed:wpaper:1318

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