Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model

We consider using the J-test procedure for the non-nested model selection problem between the spatial autoregressive (SAR) model and the matrix exponential spatial specification (MESS) model. The 2SLS and GMM methods are used to implement the J-test procedure and derive several test statistics under the GMM framework. We investigate the behavior of those J-test statistics in terms of pseudo true values. We extend the J-test procedure into the setting when error terms in the model are with unknown heteroskedasticity. Monte Carlo results suggest with strong spatial dependence the J-test statistics can have good power to distinguish the SAR and MESS models.