Further Results on the Limiting Distribution of GMM Sample Moment Conditions

with Nikolay Gospodinov and Raymond Kan, 2012, Journal of Business and Economic Statistics 30, pp. 494-504. [Paper and Additional Material]. In this paper, we examine the limiting behavior of 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 non-standard 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 non-standard) 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.