An examination of two-step estimators for models with lagged dependent variables and autocorrelated errors

The possible roles of the Durbin Equation and the first observation correction in improving the efficiency of parameter estimates in the lagged dependent variables-serial correlation model are examined. Unconstrained estimation of the Durbin Equation results in an estimate of ρ which is inefficient and its use in feasible generalized least squares does not provide asymptotically efficient estimates. Evidently, the first observation correction is a very important determinant of small sample properties in the present model. Asymptotically inefficient estimators which use a first observation correction frequently outperform Hatanaka's asymptotically efficient estimator in finite samples, essentially because it does not use the first observation.