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Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Russell Davidson

    (McGill University)

Abstract

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that all the test statistics--Student's t,Anderson-Rubin, Kleibergen's K, and likelihood ratio (LR)--can bewritten as functions of six random quantities. This leads to a number ofinteresting results about the properties of the tests under weak-instrumentasymptotics. We then propose several new procedures for bootstrapping the threenon-exact test statistics and a conditional version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, K and conditional LR have excellent performance under the null, and LR also performs very well. However, power considerations suggest that the conditional LR test, bootstrapped using this new procedure when the sample size is not large, is probably the method of choice.

Suggested Citation

  • James G. MacKinnon & Russell Davidson, 2006. "Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables," Working Paper 1024, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1024
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1024.pdf
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    References listed on IDEAS

    as
    1. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," Harvard Institute of Economic Research Working Papers 2048, Harvard - Institute of Economic Research.
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    7. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series 948, The University of Melbourne.
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    12. 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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    More about this item

    Keywords

    anderson-rubin test; weak instruments; bootstrap test; conditional LR test; wald test;
    All these keywords.

    JEL classification:

    • 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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