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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 324904, 8 pages
Research Article

Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models

1School of Management, University of Chinese Academy of Sciences, Beijing 100190, China
2Institute of China’s Economic Reform and Development, Renmin University of China, Beijing 100892, China
3School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China
4School of Economics, Central University of Finance and Economics, Beijing 100081, China

Received 14 February 2014; Accepted 12 April 2014; Published 28 April 2014

Academic Editor: Chuangxia Huang

Copyright © 2014 Yi Hu et al. 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.


Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.