Next Article in Journal
Testing for the Equality of Integration Orders of Multiple Series
Previous Article in Journal
Subset-Continuous-Updating GMM Estimators for Dynamic Panel Data Models
Article Menu

Export Article

Open AccessArticle
Econometrics 2016, 4(4), 48;

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

Department of Economics, Michigan State University, 486W Circle Dr, East Lansing, MI 48824, USA
Academic Editor: Marc S. Paolella
Received: 21 September 2016 / Revised: 15 November 2016 / Accepted: 23 November 2016 / Published: 8 December 2016
Full-Text   |   PDF [917 KB, uploaded 8 December 2016]


This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations 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. This finding suggests that the comparison between the one-step bias correction and the method of correcting the moment equations or the fully-iterated bias correction should be based on the stochastic expansions higher than the third order. View Full-Text
Keywords: third-order stochastic expansion; bias correction; M-estimation third-order stochastic expansion; bias correction; M-estimation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Supplementary material


Share & Cite This Article

MDPI and ACS Style

Kim, K.I. Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency. Econometrics 2016, 4, 48.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Econometrics EISSN 2225-1146 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top