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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 labeled MC 3 by Madigan and York 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 such 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 U.S. states and the District of Columbia during the 1990-2000 period. IntroductionThere is a great deal of literature on Bayesian model comparison for nonspatial regression models, where alternative models consist of those based on differing matrices of explanatory variables. For example, Zellner (1971) sets forth the basic Bayesian theory behind model comparison for the case where a discrete set of m alternative models are under consideration. The approach involves specifying prior probabilities for each model as well as prior distributions for the regression parameters. Posterior model probabilities are then calculated and used for inferences regarding the alternative models based on different sets of explanatory variables. More recent works such as that by Fernández, Ley, and Steel (2001a, b) consider cases where the number of possible models m is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. A Markov Chain Monte Carlo model composition methodology known as MC 3 proposed by Madigan and York (1995) has gained popularity in the mathematical statistics and econometrics literature (e.g., Denison, Mallick, and Smith 1998;Raftery, Madigan, and Hoeting 1997; Fernández, Ley, and Steel 2001a, b). The popularity of MC 3 arises in part from its ability to provide a theoretically justifiable approach to a question that often arises in regression modeling-which explanatory variables are most important in explaining variation in the dependent variable vector? This article develops the MC 3 methodology for two important spatial econometric regression models that have received widespread application (LeSage and Pace 2004). A host of additional complications arise when attempting to extend regression-based approaches to these spatial regression estimators. We provide theoretical details regarding these issues as well as computationally efficient solutions.The models for which we provide an MC 3 modeling approach are members of a class of spatial regression models introduced in Ord (1975) and elaborated in Ansel...

This study investigates the pattern of knowledge spillovers arising from patent activity between European regions. A Bayesian hierarchical model is developed that specifies region‐specific latent effects parameters modeled using a connectivity structure between regions that can reflect geographical proximity in conjunction with technological and other types of proximity. This approach exploits the fact that interregional relationships may exhibit industry‐specific technological linkages or transportation network linkages, which is in contrast to traditional studies relying exclusively on geographical proximity. We also allow for both symmetric and asymmetric knowledge spillovers between regions, and for heterogeneity across the regional sample. A series of formal Bayesian model comparisons provides support for a model based on technological proximity combined with spatial proximity, asymmetric knowledge spillovers, and heterogeneity in the disturbances. Estimates of region‐specific latent effects parameters structured in this fashion are produced by the model and used to draw inferences regarding the character of knowledge spillovers across the regions. The method is illustrated using sample data on patent activity covering 323 regions in nine European countries. Copyright © 2008 John Wiley & Sons, Ltd.

Abstract. We propose a spatial multinomial probit model to examine the determinants of land use change, at the parcel level, in the French Département du Rhones from 1992 to 2003. It is based on an economic model that assumes that landowners have a choice between four land use categories for a given parcel at a given date: (1) agricultural, (2) forest, (3) urban, and (4) no use. We estimate a model that allows for both covariates and spatial dependence, and we use these features to explore the relative importance of factors that drive landowners to choose a specific land use category.JEL classification: C11, C31, C35, R14

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