IDEAS home Printed from
   My bibliography  Save this article

Testing, Estimation in GMM and CUE with Nearly-Weak Identification


  • Mehmet Caner


In this article, we analyze Generalized Method of Moments (GMM) and Continuous Updating Estimator (CUE) with strong, nearly-weak, and weak identification. We show that with this mixed system, the limits of the estimators are nonstandard. In the subcase of GMM estimator with only nearly-weak instruments, the correlation between the instruments and the first order conditions decline at a slower rate than root T. We find an important difference between the nearly-weak case and the weak case. Inference with point estimates is possible with the Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests in GMM estimator with only nearly-weak instruments present in the system. The limit is the standard χ2 limit. This is important from an applied perspective, since tests on the weak case do depend on the true value and can only test simple null. We also show this in the more realistic case of mixed type of strong, weak, and nearly-weak instruments, Anderson and Rubin (1949) and Kleibergen (2005) type of tests are asymptotically pivotal and have χ2 limit.

Suggested Citation

  • Mehmet Caner, 2010. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 330-363.
  • Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:330-363
    DOI: 10.1080/07474930903451599

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. 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.
    2. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    3. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(02), pages 287-333, April.
    4. Bertille Antoine & Eric Renault, 2012. "Efficient Inference with Poor Instruments: a General Framework," Discussion Papers dp12-04, Department of Economics, Simon Fraser University.
    5. Hayakawa, Kazuhiko & Nagata, Shuichi, 2016. "On the behaviour of the GMM estimator in persistent dynamic panel data models with unrestricted initial conditions," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 265-303.
    6. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    7. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    8. Mehmet Caner, 2011. "A Pretest to Differentiate Between Weak and Nearly-Weak Instrument Asymptotics," International Econometric Review (IER), Econometric Research Association, vol. 3(2), pages 13-21, September.


    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:taf:emetrv:v:29:y:2010:i:3:p:330-363. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.