Maximum Likelihood and GMM Estimation of Dynamic Panel Data Models with Fixed Effects

This paper considers inference procedures for two types of dynamic linear panel data models with fixed effects (FE). First, it shows that the closures of stationary ARMAFE models can be consistently estimated by Conditional Maximum Likelihood Estimators and it derives their asymptotic distributions. Then it presents an asymptotically equivalent Minimum Distance Estimator which permits an analytic comparison between the CMLE for the ARFE(1) model and the GMM estimators that have been considered in the literature. The CMLE is shown to be asymptotically less efficient than the most efficient GMM estimator when N tends to infinity but T is fixed. Under normality some of the moment conditions become asymptotically redundant and the CMLE attains the Cramer-Rao lowerbound when T tends to infinity as well. The paper also presents likelihood based unit root tests. Finally, the properties of CML, GMM, and Modified ML estimators for dynamic panel data models that condition on the initial observations are studied and compared. It is shown that for finite T the MMLE is less efficient than the most efficient GMM estimator.