Two-stage least squares estimation in a spatial lag model under a complete bipartite network

This paper considers a spatial lag model with a complete bipartite network weighting matrix which is important in network theory. We show that two-stage least squares is equivalent to ordinary least squares and both estimators are inconsistent for the cross-section data case. This result has also been derived for the spatial lag model with an equal weight matrix by Kelejian and Prucha in 2002. We also show that the fixed effects two-stage least squares estimator is consistent in case we have panel data and the spatial lag model includes time fixed effects. This is different from the result for an equal weight matrix derived by Kelejian et al. in 2006.