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Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency

Author

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  • Kyoo il Kim

    () (School of Economics and Social Sciences, Singapore Management University)

Abstract

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equation in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies that at least in terms of the third order stochastic expansion, we cannot improve on the simple one-step bias correction by using the bias correction of moment equations. Though the result in this paper is for a fixed number of parameters, our intuition may extend to the analytical bias correction of the panel data models with individual specific effects. Noting the M-estimation can nest many kinds of estimators including IV, 2SLS, MLE, GMM, and GEL, our finding is a rather strong result.

Suggested Citation

  • Kyoo il Kim, 2006. "Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency," Working Papers 17-2006, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:17-2006
    as

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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/7213/Firth_ES4.pdf
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    References listed on IDEAS

    as
    1. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    2. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    3. 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.
    4. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    5. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," UWO Department of Economics Working Papers 20028, University of Western Ontario, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Third-order Stochastic Expansion; Bias Correction; M-estimation;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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