A Robust LM Test for Spatial Error Components

This paper presents a modified LM test of spatial error components, which is shown to be robust against distributional misspecifications and spatial layouts. The proposed test differs from the LM test of Anselin (2001) by a term in the denominators of the test statistics. This term disappears when either the errors are normal, or the variance
of the diagonal elements of the product of spatial weights matrix and its transpose is zero or approaching to zero as sample size goes large. When neither is true, as is often
the case in practice, the effect of this term can be significant even when sample size is large. As a result, there can be severe size distortions of the Anselins LM test, a phenomenon revealed by the Monte Carlo results of Anselin and Moreno (2003) and further confirmed by the Monte Carlo results presented in this paper. Our Monte Carlo results also show that the proposed test performs well in general.