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Redundancy of moment conditions in Restricted GMM Estimation

Frontiers of Economics in China-Selected Publications from Chinese Universities 2016年第3期11卷 468-497页

作者： Hailong Qian Department of Economics John Cook School of Business Saint Louis University St. Louis MO 63108 USA

Using a novel approach to calculating the rank of the difference of two asymptotic variance matrices, The author derives the necessary and sufficient conditions for an extra set of moment conditions to be redundant given a set of moment conditions in GMM estimation with general nonlinear restrictions. The necessary and sufficient conditions derived in this paper include as a special case the redundancy of moment conditions for GMM estimation without restrictions that was first derived by Breusch et al. （1999）. Therefore this paper advances the research on redundancy of moment conditions from unrestricted GMM estimation to a larger class of GMM estimation. To show their usefulness, the main results of the current paper are applied to instrumental variables estimation of linear regression models and the efficient estimation of seemingly unrelated regressions models, subject to restrictions.

关键词： GMM restricted GMM estimation moment conditions redundancyof moment conditions efficiency

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Some Properties for the Estimators in Linear Mixed Models

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 105-116页

作者： Zai-xing Li Yan Cui Wang-li Xu College of Science China University of Mining and Technology (Beijing) School of Statistics Renmin University of China

Linear mixed models （LMMs） have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.

关键词： moment conditions LMMs Consistency Asymptotical normality

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