Abstract This paper studies how identification is affected in GMM estimation as the number of moment conditions increases. We develop a general asymptotic theory extending the set up of Chao and Swanson and Antoine and Renault to the case where moment conditions have heterogeneous identification strengths and the number of them may diverge to infinity with the sample size. We also allow the models to be locally misspecified and examine how the asymptotic theory is affected by the degree of misspecification. The theory encompasses many cases including GMM models with many moments (Han and Phillips), partially linear models, and local GMM via kernel smoothing with a large number of conditional moment restrictions. We provide an understanding of the benefits of a large number of moments that compensate the weakness of individual moments by explicitly showing how an increasing number of moments improves the rate of convergence in GMM.

中文翻译：

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具有大量矩的识别强度

摘要 本文研究了随着矩条件数量的增加，GMM 估计中识别如何受到影响。我们开发了一个一般渐近理论，将 Chao 和 Swanson 以及 Antoine 和 Renault 的设置扩展到矩条件具有异质识别强度的情况，并且它们的数量可能会随着样本大小而发散到无穷大。我们还允许模型局部错误指定，并检查渐近理论如何受错误指定程度的影响。该理论涵盖了许多情况，包括具有许多矩的 GMM 模型（Han 和 Phillips）、部分线性模型以及通过具有大量条件矩限制的内核平滑的局部 GMM。