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On the Stock–Yogo Tables

Author

Listed:
  • Christopher L. Skeels

    (Department of Economics, The University of Melbourne, Parkville, 3010, Australia)

  • Frank Windmeijer

    (Department of Economics and IEU, University of Bristol, Bristol, BS8 1TU, UK)

Abstract

A standard test for weak instruments compares the first-stage F -statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are derived, as well as present some second-order asymptotic approximations that may be of value in the presence of multiple endogenous regressors. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalised and improved. Finally, we explore the calculation of p -values for the first-stage F -statistic weak instruments test.

Suggested Citation

  • Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    • Handle: RePEc:gam:jecnmx:v:6:y:2018:i:4:p:44-:d:182573
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    weak instruments; hypothesis testing; Stock–Yogo tables; hypergeometric functions; quadratic forms; p -values;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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