ML estimation of spatially and serially correlated panels with random effects: an estimation framework and a software implementation

It is described a procedure for maximum likelihood estimation of panel models incorporating: random effects and spatial dependence in the error terms; and/or a spatially lagged dependent variable; and possibly also a serial dependence structure in the remainder of the error term. We start by sketching a taxonomy of spatial panel models, beginning with the two basic random effects (RE) specifications used in the literature: the spatial autoregressive (SAR) RE model containing a spatially lagged dependent variable and a group-specific, time-invariant component in the error term, and the spatial error (SEM) RE model, with both a group-specific component and a spatial dependence structure in the error term. Extending the SEM specification, an encompassing model allowing for serial correlation in the residuals is considered. Restrictions of the full model give rise to 18 different specifications. It is discussed an efficient implementation of the estimation procedure in R, to be added to the splm package for estimation and testing of spatial panel models, illustrating it through some well-known examples from the literature.