Identification strength with a large number of moments
研究了广义矩估计中矩条件数量增加如何影响识别强度，允许矩条件具有异质性识别强度且数量随样本量发散，并考虑了局部误设定，发现增加矩条件数量可弥补单个矩条件的弱识别并提高收敛速度。
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.