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GEL Criteria for Moment Condition Models

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  • Richard Smith

Abstract

GEL methods which generalize and extend previous contributions are defined and analysed for moment condition models specified in terms of weakly dependent data. These procedures offer alternative one-step estimators and tests that areasymptotically equivalent to their efficient two-step GMM counterparts. The basisfor GEL estimation is via a smoothed version of the moment indicators usingkernel function weights which incorporate a bandwidth parameter. Examples forthe choice of bandwidth parameter and kernel function are provided. Efficient momentestimators based on implied probabilities derived from the GEL method areproposed, a special case of which is estimation of the stationary distribution of thedata. The paper also presents a unified set of test statistics for over-identifyingmoment restrictions and combinations of parametric and moment restriction hypotheses.

Suggested Citation

  • Richard Smith, 2004. "GEL Criteria for Moment Condition Models," CeMMAP working papers 19/04, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:19/04
    DOI: 10.1920/wp.cem.2004.1904
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    References listed on IDEAS

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    1. Smith, Richard J., 2005. "Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation," Econometric Theory, Cambridge University Press, vol. 21(1), pages 158-170, February.
    2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    3. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    4. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    5. Szroeter, Jerzy, 1983. "Generalized Wald Methods for Testing Nonlinear Implicit and Overidentifying Restrictions," Econometrica, Econometric Society, vol. 51(2), pages 335-353, March.
    6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    7. Sargan, J D, 1980. "Some Tests of Dynamic Specification for a Single Equation," Econometrica, Econometric Society, vol. 48(4), pages 879-897, May.
    8. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    9. 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.
    10. Richard J Smith, 1987. "Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 665-680.
    11. 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.
    12. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    13. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    14. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(1), pages 63-82, April.
    15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
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    1. Kabderian Dreyer, Johannes & Sharma, Vivek & Smith, William, 2023. "Warm-glow investment and the underperformance of green stocks," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 546-570.

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