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Bootstrap tests for overidentification in linear regression models

  • Russell Davidson

    ()

    (McGill University)

  • James G. MacKinnon

    ()

    (Queen's University)

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
File Function: First version 2014
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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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  1. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
  2. Donald W.K. Andrews & Marcelo J. Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," Cowles Foundation Discussion Papers 1476, Cowles Foundation for Research in Economics, Yale University.
  3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  4. Russell Davidson & James Mackinnon, 2009. "Wild bootstrap tests for IV regression," Working Papers halshs-00443550, HAL.
  5. Russell Davidson & James G. MacKinnon, 2006. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Working Papers 1024, Queen's University, Department of Economics.
  6. 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.
  7. Russell Davidson & James G. MacKinnon, 2008. "Wild Bootstrap Tests for IV Regression," Working Papers 1135, Queen's University, Department of Economics.
  8. Russell Davidson & James Mackinnon, 2009. "Bootstrap inference in a linear equation estimated by instrumental variables," Working Papers halshs-00442713, HAL.
  9. 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.
  10. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  11. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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