Evaluating the normal approximation in econometric models

Abstract

Many models in the economics literature are estimated using generalized method of moments (GMM) and other extremum estimators that attempt to minimize an objective function with few assumptions about the underlying data. These estimates have been proven to be consistent and asymptotically normal under a range of regularity assumptions, and researchers often take these assumptions for granted when calculating standard errors and conducting inference. Using a quasi-Bayesian alternative to the standard GMM estimation procedure, we test whether asymptotic normality is actually a reasonable assumption in three well-cited papers. we use Markov chain Monte Carlo (MCMC) algorithms to sample from the quasi-posterior and find deviations from normality in all cases, though to varying extents.