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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.

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  • 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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    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. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, October.
    5. 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.
    6. 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.
    7. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
    8. 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.
    9. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    10. 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.
    11. 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.
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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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