Bootstrap Tests for Overidentification in Linear Regression Models

Russell Davidson and James MacKinnon

Econometrics, 2015, vol. 3, issue 4, 1-39

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.

Keywords: Sargan test; Basmann test; Anderson-Rubin test; weak instruments (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Related works:
Working Paper: Bootstrap Tests for Overidentification in Linear Regression Models (2015)
Working Paper: Bootstrap Tests For Overidentification In Linear Regression Models (2014)
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