Using Bayesian Posterior Model Probabilities to Identify Omitted Variables in Spatial Regression Models

LeSage and Pace (2009) consider the impact of omitted variables in the face of spatial dependence in the disturbance process of a linear regression relationship. Remarkably, they show that this can lead to a spatial regression model specification containing a spatial lag of the dependent and explanatory variables, providing an econometric as opposed to economic theory motivation for use of spatial regression models in applied work. Another implication of this econometric situation is the presence of global spatial spillovers. Global spillovers reflect a situation where changes in a characteristic of one observation/region (potentially) impacts outcomes in all other observations/regions. Specifically, global spillovers impact the neighbors, neighbors to the neighbors, neighbors to the neighbors to the neighbors, and so on, with decreasing influence as we move to higher-order/more distant neighbors.We explore the econometric role played by omitted variables under alternative scenarios that give rise to both spatial regression specifications involving either local or global spatial spillovers. Local spillovers are those that impact only immediately neighboring observations, but not higher-order neighbors (e.g., neighbors to neighbors and so on). In addition to theoretical consideration of the alternative scenarios that practitioners might use to identify an appropriate local versus global spatial spillover specification, we explore performance of Bayesian model comparison methods in distinguishing between local and global spillover specifications that arise with varying levels of correlation between included an omitted variables