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Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure

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Abstract

This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS's) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS's. We provide methods of constructing QLR tests and CS's that are robust to the strength of identification. The results are applied to two examples: a nonlinear binary choice model and the smooth transition threshold autoregressive (STAR) model.

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File URL: http://cowles.econ.yale.edu/P/cd/d18a/d1824-ra.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1824R.

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Length: 107 pages
Date of creation: Oct 2011
Date of revision: Oct 2012
Publication status: Published in Journal of Econometrics(March 2013), 173(1): 36-56
Handle: RePEc:cwl:cwldpp:1824r

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Asymptotic size; Binary choice; Confidence set; Estimator; Identification; Likelihood; Nonlinear models; Test; Smooth transition threshold autoregression; Weak identification;

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References

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Citations

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Cited by:
  1. Jean-Marie Dufour & Joachim Wilde, 2013. "Weak Identification in Probit Models with Endogenous Covariates," Working Papers 95, Institute of Empirical Economic Research, revised 28 Feb 2013.
  2. Tiemen Woutersen & John Ham, 2013. "Calculating confidence intervals for continuous and discontinuous functions of parameters," CeMMAP working papers CWP23/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. 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, revised Jan 2013.
  4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2013. "Inference on treatment effects after selection amongst high-dimensional controls," CeMMAP working papers CWP26/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. 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.
  6. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.

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