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

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  • Mehmet Caner

Abstract

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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 29 (2010)
Issue (Month): 3 ()
Pages: 330-363

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Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:330-363

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Related research

Keywords: Empirical process; Rate of convergence; Triangular central limit theorem;

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Cited by:
  1. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University.
  2. Bertille Antoine & Eric Renault, 2012. "Efficient Inference with Poor Instruments: a General Framework," Discussion Papers dp12-04, Department of Economics, Simon Fraser University.
  3. 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.
  4. Mehmet Caner, 2011. "A Pretest to Differentiate Between Weak and Nearly-Weak Instrument Asymptotics," International Econometric Review (IER), Econometric Research Association, Econometric Research Association, vol. 3(2), pages 13-21, September.

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