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Gel Criteria For Moment Condition Models

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  • Smith, Richard J.

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 are asymptotically equivalent to their efficient two-step GMM counterparts. The basis for GEL estimation is via a smoothed version of the moment indicators using kernel function weights which incorporate a bandwidth parameter. Examples for the choice of bandwidth parameter and kernel function are provided. Efficient moment estimators based on implied probabilities derived from the GEL method are proposed, a special case of which is estimation of the stationary distribution of the data. The paper also presents a unified set of test statistics for over-identifying moment restrictions and combinations of parametric and moment restriction hypotheses.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 06 (December)
Pages: 1192-1235

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Handle: RePEc:cup:etheor:v:27:y:2011:i:06:p:1192-1235_00

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References

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  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  2. Imbens, Guido W, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 359-83, July.
  3. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," Harvard Institute of Economic Research Working Papers 1736, Harvard - Institute of Economic Research.
  4. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-75, July.
  6. Smith, Richard J, 1987. "Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 665-80, October.
  7. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  8. Richard Smith, 2004. "Automatic positive semi-definite HAC covariance matrix and GMM estimation," CeMMAP working papers CWP17/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. 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 262-80, July.
  10. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  11. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-17, October.
  12. Andrew Chesher & Richard J. Smith, 1997. "Likelihood Ratio Specification Tests," Econometrica, Econometric Society, vol. 65(3), pages 627-646, May.
  13. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  14. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  15. Sargan, J D, 1980. "Some Tests of Dynamic Specification for a Single Equation," Econometrica, Econometric Society, vol. 48(4), pages 879-97, May.
  16. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(01), pages 63-82, April.
  17. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  18. Szroeter, Jerzy, 1983. "Generalized Wald Methods for Testing Nonlinear Implicit and Overidentifying Restrictions," Econometrica, Econometric Society, vol. 51(2), pages 335-53, March.
  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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Citations

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Cited by:
  1. Smith, Richard J., 2005. "Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation," Econometric Theory, Cambridge University Press, vol. 21(01), pages 158-170, February.
  2. 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(04), pages 667-709, August.
  3. Alain Guay & Jean-François Lamarche, 2008. "The Information Content of Implied Probabilities to Detect Structural Change," Cahiers de recherche 0833, CIRPEE.
  4. 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.
  5. Francesco Bravo, 2010. "Nonparametric likelihood inference for general autoregressive models," Statistical Methods and Applications, Springer, vol. 19(1), pages 79-106, March.

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