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Second Order Bias of Quasi-MLE for Covariance Structure Models

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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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Paper provided by Concordia University, Department of Economics in its series Working Papers with number 10001.

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Date of creation: Jan 2010
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Handle: RePEc:crd:wpaper:10001

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Keywords: (Q)MLE; GMM; EL; Covariance structures;

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  1. Joseph G. Altonji & Lewis M. Segal, 1994. "Small Sample Bias in GMM Estimation of Covariance Structures," NBER Technical Working Papers 0156, National Bureau of Economic Research, Inc.
  2. 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 367-73, July.
  3. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
  4. 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.
  5. Artem Prokhorov, 2008. "On relative efficiency of Quasi-MLE and GMM estimators of covariance structure models," Working Papers 08004, Concordia University, Department of Economics.
  6. Haruhiko Ogasawara, 2004. "Asymptotic biases in exploratory factor analysis and structural equation modeling," Psychometrika, Springer, vol. 69(2), pages 235-256, June.
  7. 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.
  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.
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