Further Results on the Limiting Distribution of GMM Sample Moment Conditions

In this paper, we extend the results in Hansen (1982) regarding the asymptotic distribution of GMM sample moment conditions. In particular, 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 asymptotic distribution for a given linear combination of the sample moment conditions and show how to conduct statistical inference. We demonstrate the finite-sample properties of the proposed asymptotic approximation using simulation