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Bootstrap tests for overidentification in linear regression models

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Author Info

  • Russell Davidson

    ()
    (McGill University)

  • James G. MacKinnon

    ()
    (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.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1318.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1318.

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Length: 41 pages
Date of creation: Apr 2014
Date of revision:
Handle: RePEc:qed:wpaper:1318

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Related research

Keywords: Sargan test; Basmann test; Anderson-Rubin test; weak instruments; bootstrap P value;

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References

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  1. Russell Davidson & Emmanuel Flachaire, 2000. "The Wild Bootstrap, Tamed at Last," Econometric Society World Congress 2000 Contributed Papers 1413, Econometric Society.
  2. Russell Davidson & James Mackinnon, 2009. "Bootstrap inference in a linear equation estimated by instrumental variables," Working Papers halshs-00442713, HAL.
  3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  4. Donald W.K. Andrews & Marcelo Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," NBER Technical Working Papers 0299, National Bureau of Economic Research, Inc.
  5. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
  6. Russell Davidson & James G. MacKinnon, 2007. "Wild Bootstrap Tests For Iv Regression," Departmental Working Papers 2007-14, McGill University, Department of Economics.
  7. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  8. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
  9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  1. So Much Good Reading........
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-10-08 23:21:00

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