IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1824.html
   My bibliography  Save this paper

Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure

Author

Listed:

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.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1824
    Note: Includes Supplement
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1824-a.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    2. 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.
    3. 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, September.
    4. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    5. 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 119-136, Suppl. De.
    6. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    7. 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.
    8. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    9. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
    10. 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.
    11. 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.
    12. 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(2), pages 426-468, April.
    13. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    14. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    15. Nelson, Charles R. & Startz, Richard, 2007. "The zero-information-limit condition and spurious inference in weakly identified models," Journal of Econometrics, Elsevier, vol. 138(1), pages 47-62, May.
    16. Mehmet Caner, 2010. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 330-363.
    17. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    18. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    19. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    20. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    21. Bertille Antoine & Eric Renault, 2012. "Efficient Inference with Poor Instruments: a General Framework," Discussion Papers dp12-04, Department of Economics, Simon Fraser University.
    22. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    23. 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.
    24. Hansen, Bruce E., 1996. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 12(2), pages 347-359, June.
    25. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    26. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    27. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    28. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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. Young-Joo Kim & Myung Hwan Seo, 2017. "Is There a Jump in the Transition?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 241-249, April.
    3. Tiemen M. 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.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    5. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    6. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    7. Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
    8. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    9. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-Robust Inequality Analysis," Cahiers de recherche 03-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    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. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    13. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org.
    14. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.
    15. Chen, Feiyan & Ding, Feng & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 53-67.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    2. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    3. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    5. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    6. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    7. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    8. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    9. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
    10. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org.
    11. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    12. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
    13. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics.
    14. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    15. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1192-1228, December.
    16. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics.
    17. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    18. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    19. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    20. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    Asymptotic size; Binary choice; Confidence set; Estimator; Identification; Likelihood; Nonlinear models; Test; Smooth transition threshold autoregression; Weak identification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:cwl:cwldpp:1824. 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: (Matthew Regan). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.