Spatial interaction models of the gravity type are widely used to describe origin-destination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterize the origin region of interaction, variables that characterize the destination region of interaction, and variables that measure the separation between origin and destination regions. A violation of standard minimal assumptions for least squares estimation may be associated with two problems: spatial autocorrelation within the residuals, and spatial autocorrelation within explanatory variables. This paper compares a spatial econometric solution with the spatial statistical Moran eigenvector spatial filtering solution to accounting for spatial autocorrelation within model residuals. An example using patent citation data that capture knowledge flows across 257 European regions serves to illustrate the application of the two approaches.