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On the Stock-Yogo Tables

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  • Christopher L. Skeels
  • Frank Windmeijer

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 that determines these critical values. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalized and improved. Of independent interest, our analysis makes contributions to the theory of confluent hypergeometric functions and the theory of ratios of quadratic forms in normal variables. A by-product of our developments is an expression for the distribution function of the non-central chi-squared distribution that we have not been able to find elsewhere in the literature. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test.

Suggested Citation

  • Christopher L. Skeels & Frank Windmeijer, 2016. "On the Stock-Yogo Tables," Bristol Economics Discussion Papers 16/679, School of Economics, University of Bristol, UK, revised 25 Nov 2016.
    • Handle: RePEc:bri:uobdis:16/679
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    Cited by:

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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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