First difference estimation of spatial dynamic panel data models with fixed effects

This paper investigates the first difference (FD) estimation of spatial dynamic panel data (SDPD) models with fixed effects using quasi-maximum likelihood (QML) approach, where both n and T are large. We show that the QML estimation for the SDPD with FD can be reduced to the direct estimation of individual effects, except for the estimation of variance parameter. After bias correction, these two approaches would yield asymptotically equivalent estimates for all parameters including the variance parameter. Our results extend the equivalence of LSDV estimate and GLS estimate of FD equation in the panel regression model to the spatial dynamic panel model, which includes the conventional dynamic panel as a special case. Our analysis highlights the importance of initial values rather than the many fixed effects in spatial panel models.