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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

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

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    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.

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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/7213/Firth_ES4.pdf
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    Bibliographic Info

    Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 17-2006.

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    Length: 42 pages
    Date of creation: Sep 2006
    Date of revision:
    Publication status: Published in SMU Economics and Statistics Working Paper Series
    Handle: RePEc:siu:wpaper:17-2006

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    Related research

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

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