Bootstrap Tests for Overidentification in Linear Regression Models

Russell Davidson and James MacKinnon

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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: Anderson-Rubin test; Basmann test; Sargan test; weak instruments (search for similar items in EconPapers)
Date: 2015-12
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01456100
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Citations: View citations in EconPapers (5)

Published in Econometrics, 2015, 3 (4), pp.825--863. ⟨10.3390/econometrics3040825⟩

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Related works:
Journal Article: Bootstrap Tests for Overidentification in Linear Regression Models (2015)
Working Paper: Bootstrap Tests For Overidentification In Linear Regression Models (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01456100

DOI: 10.3390/econometrics3040825

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