Maximum Likelihood Estimation of Dynamic Linear Panel Data Models with Fixed Effects

In this paper we consider inference procedures for two types of dynamic linear panel data models with fixed effects. First, we show that the closure of the stationary ARMA panel model with fixed effects can be consistently estimated by the First Difference Maximum Likelihood Estimator and we derive its large N, fixed T, as well as its large T, arbitrary N asymptotic distributions. These results allow us to formulate two simple likelihood based unit root tests which use the table of the standard normal distribution. We also establish the asymptotic properties of the Modified ML Estimator for the conditional AR(1) panel model with fixed effects under various asymptotic plans. Then we show that when N tends to infinity but T is fixed, the FDMLE does not attain the (generalised) Cramer-Rao lowerbound for the stationary AR(1) panel model with fixed effects and is asymptotically less efficient than the Random Effects MLE. However, when T tends to infinity, the FDMLE, the Fixed Effects MLE, the REMLE are asymptotically equivalent to the Modified MLE and the Within ML (or LSDV) Estimator, i.e. under normality some of the moment conditions implicitly exploited by the first three estimators become asymptotically redundant.