Our paper focuses on the case of SUR models with spatial effects. Specifically, the problem
that we pose is testing for the presence of spatial effects in these multivariate models, considering
that one of our main interests is to deal with the question of selecting the most adequate
specification for the data. In order to do this, we obtain several tests that check for the fundamental
hypothesis of the model, including the assumption of time stability of the spatial dependence
mechanisms. We solve the discussion in a maximum-likelihood framework because this facilitates
the obtaining of appropriate tests. The second part of the paper contains a Monte Carlo experiment
in order to study the behaviour of the two most popular model selection strategies, Specific-to-
General or General-to-Specific, using the collection of tests that have been proposed.This work has been carried out with the financial support of project
ECO2009-10534/ECON of the Ministerio de Ciencia y Tecnología of the Reino de España