Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency
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...
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2006
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| Online Access: | https://ink.library.smu.edu.sg/soe_research/901 https://ink.library.smu.edu.sg/context/soe_research/article/1900/viewcontent/Firth_ES4.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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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