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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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    1. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(5), pages 707-743, October.
    2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    3. Richardson, David H & Wu, De-Min, 1971. "A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators," Econometrica, Econometric Society, vol. 39(6), pages 973-981, November.
    4. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    5. Sanderson, Eleanor & Windmeijer, Frank, 2016. "A weak instrument F-test in linear IV models with multiple endogenous variables," Journal of Econometrics, Elsevier, vol. 190(2), pages 212-221.
    6. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    7. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413.
    8. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    9. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    10. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2014. "Generating Functions And Short Recursions, With Applications To The Moments Of Quadratic Forms In Noncentral Normal Vectors," Econometric Theory, Cambridge University Press, vol. 30(2), pages 436-473, April.
    13. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," CeMMAP working papers CWP14/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Phillips, Peter C.B. & Gao, Wayne Yuan, 2017. "Structural inference from reduced forms with many instruments," Journal of Econometrics, Elsevier, vol. 199(2), pages 96-116.
    15. Knight, John L., 1982. "A note on finite sample analysis of misspecification in simultaneous equation models," Economics Letters, Elsevier, vol. 9(3), pages 275-279.
    16. Peter C. B. Phillips, 2016. "Inference in Near-Singular Regression," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 461-486, Emerald Group Publishing Limited.
    17. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    18. Hillier, Grant H & Kinal, Terrence W & Srivastava, V K, 1984. "On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation," Econometrica, Econometric Society, vol. 52(1), pages 185-202, January.
    19. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-180, January.
    20. Skeels, Christopher L., 1995. "Instrumental Variables Estimation in Misspecified Single Equations," Econometric Theory, Cambridge University Press, vol. 11(3), pages 498-529, June.
    21. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    22. Nelson, C.R. & Startz, R., 1990. "More on the Exact Small Sample Distribution of the Instrumental Variable Estimator: A Reply to Maddala and Jeong," Discussion Papers in Economics at the University of Washington 90-29, Department of Economics at the University of Washington.
    23. Peter C. B. Phillips, 2017. "Reduced forms and weak instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 818-839, October.
    24. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(2), pages 222-240, April.
    25. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    26. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
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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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