Bayesian Model Averaging for Spatial Econometric Models

Abstract

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labelled MC to the third by Madigan and York (1995) is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin-destination population migration flows between the 48 US States and District of Columbia during the 1990 to 2000 period.

Keywords: spatial estimation of migration flows, posterior model probabilities, log-marginal likelihood, reversible jump MCMC

JEL Classification: C11, R11, R12