IDEAS home Printed from https://ideas.repec.org/p/bri/uobdis/16-679.html
   My bibliography  Save this paper

On the Stock-Yogo Tables

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.bristol.ac.uk/efm/media/workingpapers/working_papers/pdffiles/dp16679.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    5. 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.
    6. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-180, January.
    7. 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.
    8. 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.
    9. 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.
    10. Skeels, Christopher L., 1995. "Instrumental Variables Estimation in Misspecified Single Equations," Econometric Theory, Cambridge University Press, vol. 11(3), pages 498-529, June.
    11. 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.
    12. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, October.
    13. 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.
    14. 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.
    15. Peter C. B. Phillips, 2017. "Reduced forms and weak instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 818-839, October.
    16. 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.
    17. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    18. 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.
    19. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    20. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    26. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2021. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 307-324, January.
    2. Ansink, Erik & Wijk, Louise & Zuidmeer, Frederiek, 2022. "No clue about bioplastics," Ecological Economics, Elsevier, vol. 191(C).
    3. Ahmad, Syedah & Lensink, Robert & Mueller, Annika, 2020. "The double bottom line of microfinance: A global comparison between conventional and Islamic microfinance," World Development, Elsevier, vol. 136(C).
    4. d'Este, Rocco & Einiö, Elias, 2021. "Beyond Black and White: The Impact of Asian Peers on Scholastic Achievement," Economics of Education Review, Elsevier, vol. 83(C).
    5. Felfe, Christina & Lalive, Rafael, 2018. "Does early child care affect children's development?," Journal of Public Economics, Elsevier, vol. 159(C), pages 33-53.
    6. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.
    7. Cesa-Bianchi, Ambrogio & Thwaites, Gregory & Vicondoa, Alejandro, 2020. "Monetary policy transmission in the United Kingdom: A high frequency identification approach," European Economic Review, Elsevier, vol. 123(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics.
    3. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    4. Poskitt, D.S. & Skeels, C.L., 2007. "Approximating the distribution of the two-stage least squares estimator when the concentration parameter is small," Journal of Econometrics, Elsevier, vol. 139(1), pages 217-236, July.
    5. D.S. Poskitt & C.L. Skeels, 2002. "Assessing Instrumental Variable Relevance:An Alternative Measure and Some Exact Finite Sample Theory," Department of Economics - Working Papers Series 862, The University of Melbourne.
    6. Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    7. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 29(1), pages 117-131.
    8. 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.
    9. Phillips, Garry D. A., 2000. "An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 97(2), pages 345-364, August.
    10. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    11. Dufour, J.M., 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    12. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
    13. Iglesias Emma M., 2011. "Constrained k-class Estimators in the Presence of Weak Instruments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-13, September.
    14. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    15. Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2021. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 307-324, January.
    16. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    17. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    18. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2006. "Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1707-1727.
    19. Russell Davidson & James G. MacKinnon, 2014. "Confidence sets based on inverting Anderson–Rubin tests," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 39-58, June.
    20. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bri:uobdis:16/679. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Vicky Jackson (email available below). General contact details of provider: https://edirc.repec.org/data/sebriuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.