Diagnostic Testing of Finite Moment Conditions for the Consistency and Root-N Asymptotic Normality of the GMM and M Estimators*

Common econometric analyses based on point estimates, standard errors, and confidence intervals presume the consistency and the root-n asymptotic normality of the GMM or M estimators. However, their key assumptions that data entail finite moments may not be always satisfied in applications. This paper proposes a method of diagnostic testing for these key assumptions with applications to both simulated and real data sets.