Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers

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.