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In spatial panel data modeling, researchers often need to choose a spatial weights matrix from a pool of candidates, and decide between static and dynamic specifications. We propose observed data deviance information criteria to resolve these specification problems in a Bayesian setting. The presence of high dimensional latent variables (i.e., the individual and time fixed effects) in spatial panel data models invalidates the use of a deviance information criterion (DIC) formulated with the conditional and the complete-data likelihood functions of spatial panel data models. We first show how to analytically integrate out these latent variables from the complete data likelihood functions to obtain integrated likelihood functions. We then use the integrated likelihood functions to formulate observed-data DIC measures for both static and dynamic spatial panel data models. Our simulation analysis indicates that the observed-data DIC measures perform satisfactorily to resolve specification problems in spatial panel data modeling. We also illustrate the usefulness of the proposed observed-data DIC measures using an application from the literature on spatial modeling of the house price changes in the US.


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