矩约束模型的最优矩条件选取方法

中国管理科学 ›› 2014, Vol. 22 ›› Issue (7): 26-33.

矩约束模型的最优矩条件选取方法

胡毅¹, 王美今², 汪寿阳³

1. 中国科学院大学管理学院, 北京 100190;
2. 中山大学岭南学院, 广东广州 510275;
3. 中国科学院数学与系统科学研究院, 北京 100190

收稿日期:2013-07-16 修回日期:2014-02-18 出版日期:2014-07-20 发布日期:2014-07-24
作者简介:胡毅（1985-），男（汉族），湖北荆州人，中国科学院大学管理学院，讲师，研究方向：计量经济学模型及其在经济管理中的应用。
基金资助:
国家自然科学基金资助项目（71301160）；中国博士后科学基金资助项目（2012M520420）

Choosing the Optimal Moments in Moment Restriction Models

HU Yi¹, WANG Mei-jin², WANG Shou-yang³

1. School of Management, University of Chinese Academy of Sciences, Beijing 100190, China;
2. Lingnan College, Sun Yat-sen University, Guangzhou 510275, China;
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2013-07-16 Revised:2014-02-18 Online:2014-07-20 Published:2014-07-24

摘要/Abstract

摘要： 大量经济、金融以及企业管理等领域研究对象的行为特征可以通过矩约束模型来刻画。然而，该模型中参数的估计对矩条件的选取非常敏感。如何选取最优的矩条件，进而得到更准确的参数估计和更精确的统计推断，是实证研究面临的重要问题。本文从估计量均方误差（MSE）最小的角度，研究了一般矩约束模型两步有效广义矩（GMM）估计的最优矩条件选取方法。首先，利用迭代的方法，推导出两步有效GMM估计的高阶MSE，然后通过Nagar分解，求出了两步有效GMM估计量的近似MSE。接着，基于近似MSE表达式，给出了两步有效GMM估计矩条件选取准则的一般理论，即定义了最优的矩条件，提出了两步有效GMM估计的最优矩条件选取准则，并证明了选取准则的渐近有效性。模拟结果表明，本文提出的矩条件选取方法能够很好地改善两步有效GMM估计量的有限样本表现，降低估计量的有效样本偏差。本研究为实证研究中面临的矩条件选择问题提供了理论依据。

关键词: 矩约束模型, GMM估计, 高阶MSE, 近似MSE, 选取准则

Abstract: Many behavior characteristics in the area of economics, finance and business management can be depicted by moment restriction models. Nevertheless, the parameters estimation in these models is sensitive to the selection of moments. How to choose the optimal moments, and then get more accurate parameter estimation and statistical inference is a crucial problem in empirical research. A method is proposed in this paper to select moments for two-step generalized method of moments (GMM) estimators in moment restriction models with many moments. The basic idea of this method is choosing moments such that the MSE of the GMM estimator is smallest. Firstly, iterative techniques are used to derive the higher order mean squared error (MSE) for two-step GMM, and obtain the approximate MSE for the estimators using Nagar decomposition. Then the optimal selection criterion is proposed and the asymptotic efficiency is shown. Monte Carlo simulations indicate that the proposed selection criterion could improve the finite sample properties of two-step GMM, and reduce the finite sample bias of two-step GMM, significantly. This research provides a theoretical basis for selection of moments in empirical studies.

Key words: moment restriction models, generalized method of moments, higher order MSE, approximate MSE, selection criterion

中图分类号:

F224.0

胡毅, 王美今, 汪寿阳. 矩约束模型的最优矩条件选取方法[J]. 中国管理科学, 2014, 22(7): 26-33.

HU Yi, WANG Mei-jin, WANG Shou-yang. Choosing the Optimal Moments in Moment Restriction Models[J]. Chinese Journal of Management Science, 2014, 22(7): 26-33.

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