Two special spatial weight matrices and their effects on estimation and testing in spatial regressions

This paper collects in one place some of the consequences of using two special spatial weight matrices in the spatial econometrics literature. The two weight matrices considered are the equal weight spatial matrix and the complete bipartite network. In particular, we summarize the effects of these special weight matrices on the statistical properties of commonly used spatial estimators as well as commonly used tests for spatial dependence. • This paper collects in one place some of the consequences of using two special spatial weight matrices in the spatial econometrics literature. • The two special weight matrices considered are the equal weight spatial matrix and the complete bipartite network. • The verdict on testing for zero spatial correlation under an equal weight matrix is not good, limiting power for the Cliff-Ord type test, and degenerate test statistics. • For the complete bipartite network spatial weight matrix in a SEM model, the Moran I test for zero spatial correlation is never rejected when the alternative is positive spatial correlation. • A summary Table is given for the consequence on estimation and testing using these two special weight matrices.