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Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables

Author

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  • Russell Davidson

  • James MacKinnon

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 be written as functions of six random quantities. This leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-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

  • Russell Davidson & James MacKinnon, 2006. "Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables," Departmental Working Papers 2006-21, McGill University, Department of Economics.
    • Handle: RePEc:mcl:mclwop:2006-21
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    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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