Optimality of Two-stage Estimator in Panel Models

This paper is concerned with the parameter estimation in the panel models. The exact ex pression of the covariance matrix of two-stage estimator is obtained. Some necessary and sufficient conditions for the superiority of two-stage estimator over within estimator and the least squares under the mean squared error criterion are established. In particular, we obtain a sample sufficient condition for the superiority of the two-stage estimator over the within estimator. In general, two-stage estimator is better than the within estimator for medium sample size. Similar results hold also for the between estimator and the least squares estimator.