Abstract
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.
Highlights
It is a stylized fact that plenty of relationships are dynamic and nonlinear in nature and society, especially in economic and financial systems [1,2,3,4,5,6,7,8]
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
Generalized method of moments (GMM) has been widely applied for analysis for these nonlinear models since it was first introduced by Hansen [9] and gradually became a fundamental estimation method in econometrics [10]
Summary
It is a stylized fact that plenty of relationships are dynamic and nonlinear in nature and society, especially in economic and financial systems [1,2,3,4,5,6,7,8]. Nagar [16] studied the small sample properties of the general k-class estimators of simultaneous equations and gave the higher-order asymptotic expansion of the first- and secondorder moments for two-stage least squares (2SLS) estimator. Bao and Ullah [21] derived the higher-order bias and mean squared error of a large class of nonlinear estimators to order O(n−5/2) and O(n−3), respectively These papers gave the high-order bias and MSE for nonlinear estimators, they were not suitable for two-step efficient GMM estimators. Donald et al [24] examined higher-order asymptotic MSE for conditional moment restriction models. Based on this MSE, they developed moment selection criteria for two-step GMM estimator, a bias corrected version, and GEL estimators. We have to obtain it through higher-order asymptotic theory
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