Spatial interaction or gravity models have been used in regional science to model flows that take many forms, for example, population migration, commodity flows, traffic flows, and knowledge flows, all of which reflect movements between origin and destination regions. This chapter focuses on spatial autoregressive extensions to the conventional least-squares gravity models that relax the assumption of independence between flows. These models, proposed by LeSage and Pace (2008, Spatial econometric modeling of origin-destination flows. J Reg Sci 48(5):941–967, 2009), define spatial dependence in this type of setting to mean that larger observed flows from an origin region A to a destination region Z are accompanied by (i) larger flows from regions nearby the origin A to the destination Z, say regions B and C that are neighbors to region A, which they label origin dependence; (ii) larger flows from the origin region A to regions neighboring the destination region Z, say regions X and Y, which they label destination dependence; and (iii) larger flows from regions that are neighbors to the origin (B and C) to regions that are neighbors to the destination (X and Y), which they label origin-destination dependence. Spatial spillovers in these models can take the form of spillovers to both regions/observations neighboring the origin or destination in the dyadic relationships that characterize origin-destination flows as well as network effects that impact all other regions in the network. We set forth a simulation approach for these models that can be used to produce scalar expressions for the various types of spillover impacts that arise from changes in the explanatory variables of the model.
Spatial Dependence Gravity Model Network Effect Spatial Weight Matrix Destination Region
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