Matrix Spatial Specification models

In this paper we study a family of linear regression models with spatial dependence in the errors and in the dependent variable. The spatial dependence is modeled by arbitrary matrix functions Vn and Mn respectively, indexed by a scalar parameter and, eventually, by two (possibly distinct) weight matrices, D and W. We define the quasi maximum likelihood estimator and study its asymptotic properties under non-Gaussian errors. We use the results on the general model to define a wide class of spatial models, defined as matrix transformations of a given weight matrix. This family is large enough to encompass some popular models used in the spatial econometric literature, such as SARAR and MESS models. By defining broad families of models, where matrix transformations are associated to distribution functions, we provide some insights into the difference between specifications, with emphasis on advantages and shortcomings as well as on interpretation of the parameters and correspondences between models.