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Second Order Bias of Quasi-MLE for Covariance Structure Models

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Abstract

Several recent papers (e.g., Newey et al., 2005; Newey and Smith, 2004; Anatolyev, 2005) derive general expressions for the second-order bias of the GMM estimator and its first-order equivalents such as the EL estimator. Except for some simulation evidence, it is unknown how these compare to the second-order bias of QMLE of covariance structure models. The paper derives the QMLE bias formulas for this general class of models. The bias -- identical to the EL second-order bias under normality -- depends on the fourth moments of data and remains the same as for EL even for non-normal data so long as the condition for equal asymptotic efficiency of QMLE and GMM derived in Prokhorov (2009) is satisfied.

Suggested Citation

  • Artem Prokhorov, 2010. "Second Order Bias of Quasi-MLE for Covariance Structure Models," Working Papers 10001, Concordia University, Department of Economics.
    • Handle: RePEc:crd:wpaper:10001
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    References listed on IDEAS

    as
    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. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    3. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318, Elsevier.
    4. Prokhorov, Artem, 2009. "On relative efficiency of quasi-MLE and GMM estimators of covariance structure models," Economics Letters, Elsevier, vol. 102(1), pages 4-6, January.
    5. Clark, Todd E, 1996. "Small-Sample Properties of Estimators of Nonlinear Models of Covariance Structure," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 367-373, July.
    6. Satorra, Albert & Neudecker, Heinz, 1994. "On the Asymptotic Optimality of Alternative Minimum-Distance Estimators in Linear Latent-Variable Models," Econometric Theory, Cambridge University Press, vol. 10(5), pages 867-883, December.
    7. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413.
    8. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
    9. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    10. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    11. Haruhiko Ogasawara, 2004. "Asymptotic biases in exploratory factor analysis and structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 235-256, June.
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    More about this item

    Keywords

    (Q)MLE; GMM; EL; Covariance structures;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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