Likelihood approach to dynamic panel models with interactive effects

This paper considers dynamic panel models with a factor error structure that is correlated with the regressors. Both short panels (small T) and long panels (large T) are considered. With a small T, consistent estimation requires either a suitable formulation of the reduced form or an appropriate conditional equation for the first observation. Also needed is a suitable control for the correlation between the effects and the regressors. Under the factor error structure, the panel system implies parameter constraints between the mean vector and the covariance matrix. We explore the constraints through a quasi-FIML approach. The factor process is treated as parameters and it can have arbitrary dynamics under both fixed and large T. The large T setting involves incidental parameters because the number of parameters (including the time effects, the factor process, the heteroskedasticity parameters) increases with T. Even though an increasing number of parameters are estimated, we show that there is no incidental parameters bias to affect the limiting distributions; the estimator is centered at zero even scaled by the fast convergence rate of root-NT. We also show that the quasi-FIML approach is efficient under both fixed and large T, despite non-normality, heteroskedasticity, and incidental parameters. Finally we develop a feasible and fast algorithm for computing the quasi-FIML estimators under interactive effects.