Spatial regression-based model specifications for exogenous and endogenous spatial interaction

Spatial interaction models represent a class of models that are used for modelling origin-destination flow data. The focus of this paper is on the log-normal version of the model. In this context, we consider spatial econometric specifications that can be used to accommodate two types of dependence scenarios, one involving endogenous interaction and the other exogenous interaction. These model specifications replace the conventional assumption of independence between origin-destination flows with formal approaches that allow for two different types of spatial dependence in magnitudes. Endogenous interaction reflects situations where there is a reaction to feedback regarding flow magnitudes from regions neighbouring origin and destination regions. This type of interaction can be modelled using specifications proposed by LeSage and Pace (2008) who use spatial lags of the dependent variable to quantify the magnitude and extent of the feedback effects, hence the term endogenous interaction. Exogenous interaction represents a situation where spillovers arise from nearby (or perhaps even distant) regions, and these need to be taken into account when modelling observed variations in flows across the network of regions. In contrast to endogenous interaction, these contextual effects do not generate reactions to the spillovers, leading to a model specification that can be interpreted without considering changes in the long-run equilibrium state of the system of flows. As in the case of social networks, contextual effects are modelled using spatial lags of the explanatory variables that represent characteristics of neighbouring (or more generally connected) regions, but not spatial lags of the dependent variable, hence the term exogenous interaction. In addition to setting forth expressions for the true partial derivatives of non-spatial and endogenous spatial interaction models and associated scalar summary measures from Thomas-Agnan and LeSage (2014), we propose new scalar summary measures for the exogenous spatial interaction specification introduced here. An illustration applies the exogenous spatial interaction model to a flow matrix of teacher movements between 67 school districts in the state of Florida.