Estimation of fixed effects panel regression models with separable and nonseparable space–time filters

This paper considers a quasi-maximum likelihood estimation for a linear panel data model with time and individual fixed effects, where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable. We first consider both separable and nonseparable space–time filters for the stable model. The separable space–time filter is subject to a parametric restriction which results in relative computational simplicity. In contrast to the spatial econometrics literature, we expose economic restrictions imposed by the separable space–time filter model and explore computational tractability of the nonseparable filter model. Throughout this paper, the effect of initial observations is taken into account, which results in an exact likelihood function for estimation. This is important when the span of time periods is short. We then investigate spatial unstable cases, where we propose to apply a “spatial differencing” to all variables in the regression equation as a data transformation, which may eliminate unstable or explosive spatial components in order to achieve a robust estimator. For estimates of the parameters in both the regression part and the disturbance process, they are nT-consistent and asymptotically centered normal regardless of whether T is large or not and whether the process is stable or not.