Revisiting estimation methods for spatial econometric interaction models

Abstract

This article develops improved calculation techniques for estimating the spatial econometric interaction model of LeSage and Pace (2008) by maximum likelihood (MLE), Bayesian Markov Chain Monte Carlo (MCMC) and spatial two-stage least-squares (S2SLS). The refined estimation methods derive the parameter estimates and their standard errors exclusively from moment matrices with low dimensions. For the computation of these moments, we exploit efficiency gains linked to a matrix formulation of the model, which we generalize to make more flexible use of the exogenous variables. To improve the MLE we restructure the Hessian matrix and the quadratic term in the likelihood function. We also derive a moment based formulation of the Bayesian MCMC estimator from the same likelihood restructuring. Finally, the S2SLS estimator presented in this article is the first one to exploit the efficiency gains of the matrix formulation and also solves the problem of collinearity among spatial instruments. Several benchmarks show that these moment based estimators scale very well to large samples and can be used to estimate models with 100 million flows in just a few minutes. In addition to the improved estimation methods, this article presents a new way to define a feasible parameter space for the spatial econometric interaction model, which allows to verify the models consistency with a minimal computational burden. All of these developments indicate that the spatial econometric extension of the traditional gravity model has become an increasingly mature alternative and should eventually be considered a standard modeling approach for origin-destination flows.