Abstract
Spatial interaction models represent a class of models that are used for modeling origin-destination flow data. The interest in such models is motivated by the need to understand and explain the flows of tangible entities such as persons or commodities or intangible ones such as capital, information or knowledge between regions. These models attempt to explain interaction between origin and destination regions using (i) origin-specific attributes characterizing the ability of the origins to generate flows, (ii) destination-specific characteristics representing the attractiveness of destinations, and (iii) variables that characterize the way spatial separation of origins from destinations constrains or impedes the interaction. They implicitly assume that using spatial separation variables such as distance between origin and destination regions will eradicate the spatial dependence among the sample of spatial flows.
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Notes
- 1.
Intraregional flows are recorded on the main diagonal of the flow matrix.
- 2.
The west most region at the beginning of the line of regions has a single neighbor to the right, and the east most region at the end of the line has a single neighbor to the left.
- 3.
Our expressions differ slightly from those of LeSage and Thomas-Agnan (2014) because of our modification of the model specification to incorporate X i variables to model intraregional variation in flows.
- 4.
This example is identical to Thomas-Agnan and LeSage (2014).
- 5.
Florida has county-level districts so that districts and counties coincide in our analysis.
- 6.
Santos Silva and Tenreyro (2006) note there is strong evidence that disturbances from log-linear gravity models are heteroscedastic.
- 7.
In the case of interregional commodity flows, the measure of regional size is typically gross regional product or regional income. The model predicts more interaction in the form of commodity flows between regions of similar (economic) size than regions dissimilar in size. For the case of migration flows, population would be a logical measure of regional size, and in other contexts such as ours involving teacher flows between school districts, use of the number of teachers in each district seems a reasonable measure of district size.
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LeSage, J.P., Fischer, M.M. (2016). Spatial Regression-Based Model Specifications for Exogenous and Endogenous Spatial Interaction. In: Patuelli, R., Arbia, G. (eds) Spatial Econometric Interaction Modelling. Advances in Spatial Science. Springer, Cham. https://doi.org/10.1007/978-3-319-30196-9_2
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