A test to select between spatial weighting matrices

There exist a number of ways of selecting the best spatial weighting matrix in a spatial regression framework. But these methods all work under the assumption that there is only one matrix in the final model and they simply aim to pick the best one. We propose an encompassing tests which allows for the possibility that the final preferred model may have two or more spatial weighting matrices. We validate the proposed test through a Monte Carlo study. We then illustrate the test by applying it to a two-equation simultaneous system determining sovereign bond ratings and spreads for two groups comprising northern and Southern Euro-area countries.