Endogenous spatial regimes

The pioneering work of Getis and Ord on local spatial statistics has a counterpart in spatial econometrics in treating spatial heterogeneity. This can be approached from a continuous or a discrete perspective. In a discrete perspective, referred to as spatial regimes, the coefficients vary by discrete subregions of the data. Whereas the estimation of spatial regime regressions is well understood, the delineation of the regimes themselves remains a topic of active interest. Generally speaking, two broad classes of methods can be distinguished, one in which the delineation is carried out separately from the coefficient estimation and one where the two are tightly integrated. Tightly integrated approaches are referred to as endogenous spatial regimes. A number of different methods have been suggested in the literature, including finite mixture models, GWR-based methods, and penalized regression. One drawback of regime delineation is that the results do not necessarily satisfy a spatial contiguity constraint, i.e., observations are grouped despite not being spatially connected. In this paper, we outline a heuristic to determine the spatial regimes endogenously, as an extension of the well-known SKATER algorithm for spatially constrained clustering. This guarantees that the resulting regimes consist of contiguous observations. We outline the method and apply it in the context of the determination of housing submarkets, which is represented by rich literature in applied spatial econometrics. We use a well-known Kaggle data set as the empirical example, which contains observations on house sales in King County, Washington. We compare the estimation of a hedonic house price model using the endogenous spatial regimes approach to a range of more traditional methods, including pooled regression, the use of administrative districts, data-driven regimes based on a-spatial and spatial clustering of explanatory variables, and finite mixture regression. We evaluate the results in terms of fit and assess the trade-offs between the spatial and a-spatial approaches.