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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

    (SMU)

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 .xed number of parameters, our intuition may extend to the analytical bias correction of the panel data models with individual speci.c eects. Noting the M-estimation can nest many kinds of estimators including IV, 2SLS, MLE, GMM, and GEL, our .nding 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," Labor Economics Working Papers 22453, East Asian Bureau of Economic Research.
    • Handle: RePEc:eab:laborw:22453
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    JEL classification:

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

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