A Simulation Study on FIML Covariance Matrix

In econometric models, estimates of the asymptotic covariance matrix of FIML coefficients are traditionally computed in several different ways: with a generalized least squares type matrix; using the Hessian of the concentrated log-likelihood; using the outer product of the first derivatives of the log-likelihoods; with some suitable joint use of Hessian and outer product. The different alternative estimators are asymptotically equivalent in case of correct model's specification, but may produce large differences in the numerical application to small samples. The behaviour of the different estimators of the covariance matrix in standardizing or normalizing FIML estimated coefficients in the small samples is investigated in this paper. Monte Carlo experiments are performed on several small-medium size models, and some systematic behaviours are evidenced.