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Estimation and Inference with Weak, Semi-strong, and Strong Identification

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Abstract

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) in a class of models in which the parameters are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's, including maximum likelihood (ML), least squares (LS), quantile, generalized method of moments (GMM), generalized empirical likelihood (GEL), minimum distance (MD), and semi-parametric estimators. The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic size (in a uniform sense) of standard tests and CS's is established. The results are applied to the ML estimator of an ARMA(1, 1) model and to the LS estimator of a nonlinear regression model.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1773-a.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 1773.

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Length: 173 pages
Date of creation: Oct 2010
Date of revision:
Handle: RePEc:cwl:cwldpp:1773

Note: Includes supplement.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
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; Confidence set; Estimator; Identification; Nonlinear models; Strong identification; Test; Weak identification;

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References

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  1. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  2. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  4. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
  5. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
  6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  7. Donald W.K. Andrews & Xu Cheng, 2010. "Estimation and Inference with Weak, Semi-strong, and Strong Identification," Cowles Foundation Discussion Papers 1773R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2011.
  8. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  9. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
  10. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  11. Andrews, Donald W K, 2002. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 530-44, October.
  12. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  13. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
  14. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics.
  15. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  16. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  17. 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, 05.
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Citations

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Cited by:
  1. Dovonon, Prosper & Renault, Eric, 2011. "Testing for Common GARCH Factors," MPRA Paper 40224, University Library of Munich, Germany.
  2. Andrea Fracasso & Giuseppe Vittucci Marzetti, 2014. "International R&D Spillovers, Absorptive Capacity and Relative Backwardness: A Panel Smooth Transition Regression Model," International Economic Journal, Taylor & Francis Journals, vol. 28(1), pages 137-160, March.
  3. Xiaohong Chen & Maria Ponomareva & Elie Tamer, 2013. "Likelihood inference in some finite mixture models," CeMMAP working papers CWP19/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, 09.
  7. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
  8. Donald W. K. Andrews & Xu Cheng, 2011. "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure," Cowles Foundation Discussion Papers 1824, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
  10. Joachim Freyberger, 2012. "Asymptotic theory for differentiated products demand models with many markets," CeMMAP working papers CWP19/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. 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.
  12. Zhongjun Qu, 2011. "Inference and Speci?cation Testing in DSGE Models with Possible Weak Identification," Boston University - Department of Economics - Working Papers Series WP2011-058, Boston University - Department of Economics.
  13. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.

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