The Likelihood Ratio Test of Common Factors under Non-Ideal Conditions

The Spatial Durbin model occupies an interesting position in Spatial Econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we can obtain the Likelihood Ratio test of Common Factors (LRCOM). This test has good properties if the model is correctly specified, as shown in Mur and Angulo (2006). However, as far as we know, there is no literature in relation to the behaviour of the test under non-ideal conditions, which is the purpose of the paper. Specifically, we study the performance of the test in the case of heteroscedasticity, non-normality, endogeneity, dense weighting matrices and non-linearity. Our results offer a positive view of the Likelihood Ratio test of Common Factors, which appears to be a useful technique in the toolbox of spatial econometrics.