Likelihood approach to dynamic panel models with interactive effects

This paper studies dynamic panel models with a factor error structure that is correlated with the regressors. Both short panels (small ������) and long panels (large ������) are considered. A dynamic panel forms a simultaneous-equation system, and under the factor error structure, there exist constraints between the mean and the covariance matrix. We explore the constraints through a quasi-FIML (full information maximum likelihood) approach. The quasi-FIML approach does not estimate individual effects, even if they are fixed constants, thus circumventing the incidental parameters problem in the cross-sectional dimension. The factor process is treated as parameters and it can have arbitrary dynamics. We show that there is no incidental parameters bias, for fixed or large ������, and that the estimator is centered at zero even when scaled by the fast convergence rate of root-������������. We also study the efficiency of the quasi-FIML estimator. Finally, we develop a feasible and fast algorithm for computing the quasi-FIML estimators under interactive effects.