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Generalized empirical likelihood estimators and tests under partial, weak and strong identification

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Author Info
Patrik Buggenberger
Richard Smith () (Institute for Fiscal Studies and University of Cambridge)

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Abstract

The principal purpose of this paper is to describe the performance of generalized empirical likelihood (GEL) methods for time series instrumental variable models specified by nonlinear moment restrictions when identification may be weak. The paper makes two main contributions. Firstly, we show that all GEL estimators are first-order equivalent under weak identification. The GEL estimator under weak identification is inconsistent and has a nonstandard asymptotic distribution. Secondly, the paper proposes new GEL test statistics, which have chi-square asymptotic null distributions independent of the strength or weakness of identification. Consequently, unlike those for Wald and likelihood ratio statistics, the size of tests formed from these statistics is not distorted by the strength or weakness of iden- tification. Modified versions of the statistics are presented for tests of hypotheses on parameter subvectors when the parameters not under test are strongly identified. Monte Carlo results for the linear instrumental variable regression model suggest that tests based on these statistics have very good size properties even in the presence of conditional heteroskedasticity. The tests have competitive power properties, especially for thick tailed or asymmetric error distributions.

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Publisher Info
Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP08/03.

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Length: 54 pp.
Date of creation: Jul 2003
Date of revision:
Handle: RePEc:ifs:cemmap:08/03

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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Mehmet Caner, 2005. "Exponential Tilting with Weak Instruments: Estimation and Testing," Econometrics 0509017, EconWPA. [Downloadable!]
  2. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  3. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01. [Downloadable!] (restricted)
    Other versions:
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    Other versions:
  5. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September. [Downloadable!] (restricted)
  6. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    Other versions:
  7. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October. [Downloadable!] (restricted)
  8. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
  9. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  10. Frank Kleibergen, 2001. "Testing Parameters in GMM without assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute. [Downloadable!]
  11. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
  12. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  13. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
  14. Richard Smith, 2004. "GEL Criteria for Moment Condition Models," CeMMAP working papers CWP19/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," NBER Technical Working Papers 0302, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Patrik Guggenberger, 2006. "Finite-Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator, accepted for publication, Econometric Reviews," UCLA Economics Online Papers 371, UCLA Department of Economics. [Downloadable!]
  4. Mehmet Caner, 2005. "Nearly Singular design in gmm and generalized empirical likelihood estimators," Working Papers 211, University of Pittsburgh, Department of Economics, revised Jan 2005. [Downloadable!]
    Other versions:
  5. Vadim Marmer & Taisuke Otsu, 2009. "Optimal Comparison of Misspecified Moment Restriction Models," Cowles Foundation Discussion Papers 1724, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. Paul Levine & Luis F. Martins & Vasco J. Gabriel, 2006. "Robust Estimates of the New Keynesian Phillips Curve," Department of Economics Discussion Papers 0206, Department of Economics, University of Surrey. [Downloadable!]
  7. Stefan Boes, 2004. "Empirical Likelihood in Count Data Models: The Case of Endogenous Regressors," Working Papers 0404, University of Zurich, Socioeconomic Institute. [Downloadable!]
  8. Mehmet Caner, 2005. "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Fixed and Many Moment Asymptotics," Econometrics 0509018, EconWPA. [Downloadable!]
    Other versions:
  9. Yoon-Jae Whang, 2004. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Cowles Foundation Discussion Papers 1453, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  10. Patrik Guggenberger, 2005. "Monte-carlo evidence suggesting a no moment problem of the continuous updating estimator," Economics Bulletin, Economics Bulletin, vol. 3(13), pages 1-6. [Downloadable!]
  11. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  12. Leandro M. Magnusson, 2008. "Inference in Limited Dependent Variable Models Robust to Weak Identification," Working Papers 0801, Tulane University, Department of Economics, revised Apr 2009. [Downloadable!]
  13. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  14. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Applications of Subsampling, Hybrid, and Size-Correction Methods," Cowles Foundation Discussion Papers 1608, Cowles Foundation, Yale University. [Downloadable!]
  15. G. Forchini, 2005. "Some Properties of Tests for Possibly Unidentified Parameters," Monash Econometrics and Business Statistics Working Papers 21/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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