Unconditional maximum likelihood estimation of linear and log-linear dynamic models for spatial panels

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered. the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 7992.