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Bootstrap Tests for Overidentification in Linear Regression Models

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  • Russell Davidson

    (Department of Economics and CIREQ, McGill University, Montréal, Québec H3A 2T7, Canada
    AMSE-GREQAM, Centre de la Vieille Charité, 13236 Marseille cedex 02, France
    These authors contributed equally to this work.)

  • James G. MacKinnon

    (Department of Economics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Russell Davidson & James G. MacKinnon, 2015. "Bootstrap Tests for Overidentification in Linear Regression Models," Econometrics, MDPI, vol. 3(4), pages 1-39, December.
    • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:4:p:825-863:d:60287
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    References listed on IDEAS

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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. So Much Good Reading........
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-10-09 04:21:00

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    4. Kiviet, Jan F. & Kripfganz, Sebastian, 2021. "Instrument approval by the Sargan test and its consequences for coefficient estimation," Economics Letters, Elsevier, vol. 205(C).
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    More about this item

    Keywords

    Sargan test; Basmann test; Anderson-Rubin test; weak instruments;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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