Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes

Weighting matrices are typically assumed to be exogenous. However, in many cases this exogeneity assumption may not be reasonable. In these cases, typical model specifications and corresponding estimation procedures will no longer be valid. In this paper we specify a reasonably general spatial panel data model which contains a spatially lagged dependent variable in terms of an endogenous weighting matrix. We suggest an estimator for the regression parameters, and demonstrate its consistency and asymptotic normality. We also suggest an estimator for the large sample variance-covariance matrix of that distribution. We then apply our results to an interstate panel data cigarette demand model which contains an endogenous weighting matrix. Among other things, our results suggest that there is a bootlegging effect in which buyers, or, more generally "agents", cross state borders to purchase cigarette. Finally we provide the results of a Monte Carlo study that demonstrate that our procedure has very small bias and MSE even for small sample sizes.