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

• Main Author: KIM, Kyoo-il
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2006
• Subjects: Third-order Stochastic Expansion; Bias Correction; M-estimation; Econometrics
• 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
• Institution: Singapore Management University

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.