Spatial Durbin meets Tobler

An important practical use of coefficient estimates in a spatial regression model is to interpret the strength and range of implied spatial spillovers. In the classic spatial lag model, the structure of the reduced form ensures a smooth distance decay of neighboring multiplier effects. This can be viewed as following Tobler’s First Law of Geography. However, in the linear SLX and spatial Durbin models, this is no longer guaranteed. In this paper, we investigate the interplay between parameter space for the spatial coefficients and Tobler’s law, with a particular focus on the spatial Durbin model. We carry out a series of numerical illustrations and complement this with a small meta-analysis of empirical results reported in the literature. We provide a taxonomy of parameter values that yield different multiplier effects and the implied Tobler constraint. We close with some recommendations for practice.