GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS
GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS
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DOI：
10.1017/s0266466600166010
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发表时间：
2000-12
影响因子：
0.8
通讯作者：
M. Carrasco;J. Florens
中科院分区：
文献类型：
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作者：
M. Carrasco;J. Florens
本文提出了广义矩法程序的一个版本，它既处理了矩条件数目有限的情况，也处理了矩条件连续体的情况。通常，力矩条件由一个索引参数索引，该参数在一个区间内接受其值。要最小化的目标函数是希尔伯特空间中矩条件的范数。证明了估计量是一致的和渐近正态的。通过最小化与协方差相关的再现核希尔伯特空间中矩条件的范数得到最优估计量。我们给出了一种简单的方法来计算这个估计量。最后，我们研究了使用过度识别限制的规范测试的性质。本文的结果在出现连续矩条件的许多情况下是有用的。例子包括连续时间回归模型的有效估计，满足条件矩限制的截面模型，以及标量扩散过程。
This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically normal. The optimal estimator is obtained by minimizing the norm of the moment conditions in the reproducing kernel Hilbert space associated with the covariance. We show an easy way to calculate this estimator. Finally, we study properties of a specification test using overidentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models that satisfy conditional moment restrictions, and scalar diffusion processes.