Endogenous Spatial Regression and Delineation of Submarkets: A New Framework with Application to Housing Markets

Housing submarkets have been defined by different criteria: (i) similarity in house attributes; (ii) similarity in hedonic prices; and (iii) substitutability of houses. We show that spatial clustering on (i) and (ii) also satisfies criterion (iii) and develop inferences based on functional linear regression of a hedonic house price model. Then, we delineate submarkets by clustering (jointly) on the surfaces of the estimated functional partial effects and housing features. The above model incorporates both spatial heterogeneity and endogenous spatial dependence. Application to an urban conglomeration in Portugal implies submarkets that emphasize the historical and endogenous evolution of urban spatial structure.