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Maximum likelihood estimation and uniform inference with sporadic identification failure

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  • Andrews, Donald W.K.
  • Cheng, Xu

Abstract

This paper analyzes the properties of a class of estimators, tests, and confidence sets (CSs) 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 θ. This includes log likelihood, quasi-log likelihood, and least squares criterion functions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 173 (2013)
Issue (Month): 1 ()
Pages: 36-56

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Handle: RePEc:eee:econom:v:173:y:2013:i:1:p:36-56

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Web page: http://www.elsevier.com/locate/jeconom

Related research

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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  1. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
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  3. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
  4. Donald W. K. Andrews & Xu Cheng, 2011. "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure," Cowles Foundation Discussion Papers 1824R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2012.
  5. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.
  6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  7. Charles Nelson & Richard Startz, 2004. "The Zero-Information-Limit Condition and Spurious Inference in Weakly Identified Models," Working Papers UWEC-2004-03-FC, University of Washington, Department of Economics.
  8. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S135-S171, 01.
  9. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
  10. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  11. 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.
  12. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
  13. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  14. Bertille Antoine & Eric Renault, 2012. "Efficient Inference with Poor Instruments: a General Framework," Discussion Papers dp12-04, Department of Economics, Simon Fraser University.
  15. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  16. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
  17. Mehmet Caner, 2010. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 330-363.
  18. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  19. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  20. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
  21. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
  22. 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.
  23. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  24. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
  25. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics.
  26. 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.
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Citations

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Cited by:
  1. Donald W. K. Andrews & Xu Cheng, 2011. "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure," Cowles Foundation Discussion Papers 1824R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2012.
  2. 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.
  3. 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.
  4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2012. "Inference on treatment effects after selection amongst high-dimensional controls," CeMMAP working papers CWP10/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  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. 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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