A likelihood ratio test for spatial model selection

This paper develops a nondegenerate likelihood-ratio test for model selection between two competitive spatial econometrics models. It generalizes the test of Vuong (1989) to models with spatial near-epoch dependent (NED) data. We do not make any structural assumption on the true model specification and allow for the cases where both or one of the two competing models are mis-specified. The test is valid whether two models are nested or non-nested. As a prerequisite of the test, we first show that quasi-maximum likelihood estimators (QMLE) of spatial econometrics models are consistent estimators of their pseudo-true values and are asymptotically normal under regularity conditions. In particular, we study spatial autoregressive models with spatial autoregressive errors (SARAR) and matrix exponential spatial specification (MESS) models. We derive the limiting null distribution of the test statistic. A spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null, which is necessary to implement the test, is constructed. Monte Carlo experiments are designed to investigate finite sample performance of QMLEs for SARAR and MESS models, as well as the size and power of the proposed test. (C) 2019 Elsevier B.V. All rights reserved.