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

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

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    1. 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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    More about this item

    Keywords

    Third-order Stochastic Expansion; Bias Correction; M-estimation;
    All these keywords.

    JEL classification:

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

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