Further Results on the Limiting Distribution of GMM Sample Moment Conditions
研究了广义矩方法（GMM）样本矩条件的极限行为，指出其渐近分布中存在一个重要的不连续性，推导了退化情况下的加权卡方分布，并提出了一个秩检验来指导使用标准还是非标准渐近框架。
In this article, we examine the limiting behavior of generalized method of moments (GMM) sample moment conditions and point out an important discontinuity that arises in their asymptotic distribution. We show that the part of the scaled sample moment conditions that gives rise to degeneracy in the asymptotic normal distribution is T -consistent and has a nonstandard limiting distribution. We derive the appropriate asymptotic (weighted chi-squared) distribution when this degeneracy occurs and show how to conduct asymptotically valid statistical inference. We also propose a new rank test that provides guidance on which (standard or nonstandard) asymptotic framework should be used for inference. The finite-sample properties of the proposed asymptotic approximation are demonstrated using simulated data from some popular asset pricing models.