IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/18-10.html

Optimal significance tests in simultaneous equation models

Author

Listed:
  • Theodore W Anderson

    (Institute for Fiscal Studies and Stanford)

Abstract

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level.

Suggested Citation

  • Theodore W Anderson, 2010. "Optimal significance tests in simultaneous equation models," CeMMAP working papers CWP18/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:18/10
    as

    Download full text from publisher

    File URL: http://cemmap.ifs.org.uk/wps/cwp1810.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    Full references (including those not matched with items on IDEAS)

    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. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    2. Hebous, Shafik & Zimmermann, Tom, 2014. "Revisiting the Narrative Approach of Estimating Fiscal Multipliers," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100408, Verein für Socialpolitik / German Economic Association.
    3. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    4. Xu Cheng & Winston Wei Dou & Zhipeng Liao, 2022. "Macro‐Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models," Econometrica, Econometric Society, vol. 90(2), pages 685-713, March.
    5. Tito Belchior Silva Moreira & Benjamin Miranda Tabak & Mario Jorge Mendonça & Adolfo Sachsida, 2016. "An Evaluation of the Non-Neutrality of Money," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-20, March.
    6. 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.
    7. Russell Davidson & James G. MacKinnon, 2015. "Bootstrap Tests for Overidentification in Linear Regression Models," Econometrics, MDPI, vol. 3(4), pages 1-39, December.
    8. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2019.
    9. Sunghoon Chung, 2012. "Environmental Regulation and the Pattern of Outward FDI: An Empirical Assessment of the Pollution Haven Hypothesis," Departmental Working Papers 1203, Southern Methodist University, Department of Economics.
    10. 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.
    11. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
    12. Prosper Dovonon & Alastair Hall & Frank Kleibergen, 2018. "Inference in Second-Order Identified Models," CIRANO Working Papers 2018s-36, CIRANO.
    13. MacKinnon, James G., 2023. "Fast cluster bootstrap methods for linear regression models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 52-71.
    14. Philipp Ketz & Adam McCloskey & Jan Scherer, 2025. "Numerical Analysis of Test Optimality," Papers 2512.19843, arXiv.org.
    15. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2010. "Estimation uncertainty in structural inflation models with real wage rigidities," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2554-2561, November.
    16. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Jackknife Lagrange multiplier test with many weak instruments," STICERD - Econometrics Paper Series 613, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    17. Johannes W. Ligtenberg, 2023. "Inference in clustered IV models with many and weak instruments," Papers 2306.08559, arXiv.org, revised Oct 2025.
    18. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    19. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, IZA Network @ LISER.
    20. Noel Johnson & Courtney LaFountain & Steven Yamarik, 2011. "Corruption is bad for growth (even in the United States)," Public Choice, Springer, vol. 147(3), pages 377-393, June.

    More about this item

    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:ifs:cemmap:18/10. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.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.