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Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification

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  • Guggenberger, Patrik
  • Smith, Richard J.

Abstract

The 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 as in Stock and Wright (2000, Econometrica 68, 1055–1096) when identification may be weak. The paper makes two main contributions. First, 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. Second, 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 identification. 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.This paper is a revision of Guggenberger's job market paper “Generalized Empirical Likelihood Tests under Partial, Weak, and Strong Identification.†We are thankful to the editor, P.C.B. Phillips, and three referees for very helpful suggestions on an earlier version of this paper. Guggenberger gratefully acknowledges the continuous help and support of his adviser, Donald Andrews, who played a prominent role in the formulation of this paper. He thanks Peter Phillips and Joseph Altonji for their extremely valuable comments. We also thank Vadim Marner for help with the simulation section and John Chao, Guido Imbens, Michael Jansson, Frank Kleibergen, Marcelo Moreira, Jonathan Wright, and Motohiro Yogo for helpful comments. Aspects of this research have been presented at the 2003 Econometric Society European Meetings; York Econometrics Workshop 2004; Seminaire Malinvaud; CREST-INSEE; and seminars at Albany, Alicante, Austin (Texas), Brown, Chicago, Chicago GSB, Harvard/MIT, Irvine, ISEG/Universidade Tecnica de Lisboa, Konstanz, Laval, Madison (Wisconsin), Mannheim, Maryland, NYU, Penn, Penn State, Pittsburgh, Princeton, Rice, Riverside, Rochester, San Diego, Texas A&M, UCLA, USC, and Yale. We thank all the seminar participants. Guggenberger and Smith received financial support through a Carl Arvid Anderson Prize Fellowship and a 2002 Leverhulme Major Research Fellowship, respectively.

Suggested Citation

  • Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
  • Handle: RePEc:cup:etheor:v:21:y:2005:i:04:p:667-709_05
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    References listed on IDEAS

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    1. 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, January.
    2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    3. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1192-1235, December.
    4. 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.
    5. 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 777-787, October.
    6. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
    7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    9. 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.
    10. Mehmet Caner, 2010. "Exponential Tilting with Weak Instruments: Estimation and Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(3), pages 307-325, June.
    11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    13. 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 518-529, October.
    14. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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