Revisiting Estimation Methods for Spatial Econometric Interaction Models

Taking advantage of a generalization of the matrix formulation introduced by LeSage and Pace (2008), this article presents improvements in the computational performance and flexibility of three estimators of spatial econometric interaction models. By generalizing computational techniques for the evaluation of the likelihood function and also for the Hessian matrix the maximum likelihood estimator (MLE) achieves computation times that are not much longer than those of an ordinary least-squares (OLS) regression. The restructured likelihood also improves the performance of the Bayesian Markov chain Monte Carlo (MCMC) estimator considerably. Finally, the spatial two-stage least-squares (S2SLS) estimator presented in this article is the first one that exploits the efficiency gains of the matrix formulation. In addition to the computational improvements of the three estimation methods this article presents a new solution to the issue of defining the feasible parameter space that allows to verify the consistency of the spatial econometric interaction model with a minimal computational burden. All of these developments indicate that the spatial econometric alternative to the traditional gravity model has become an increasingly mature option and should eventually be considered a standard modeling approach for origin-destination flow problems.