Endogenous spatial structure and delineation of submarkets: A new framework with application to housing markets

Definition of housing submarkets is important at both conceptual and empirical levels. In the housing studies literature, submarkets have been defined according to three different criteria: i) similarity in hedonic housing characters, ii) similarity in hedonic prices; iii) substitutability of housing units. We argue that the simultaneous fulfilment of criteria i) and ii) is a sufficient condition for criteria iii) to be fulfilled. Criterion i) is directly observable, while criterion ii) can be checked by a model able to detect and analyse spatial heterogeneity in the shadow prices. Here, we propose a new framework, based on a synthesis of spatial econometrics, functional data analysis (FDA) and geographically weighted regression (GWR). The framework is applied to a hedonic regression model where the dependent variable is logarithm of house prices per square meter and housing features are regressors. Thus, we delineate submarkets by clustering (jointly) on the surfaces of the estimated functional partial effects and housing features. The above model addresses two main limitations of previous approaches. First, endogeneity in spatial structure can be incorporated in the model. Second, the framework does not require delineation of housing submarkets a priori. Application to the housing market of the Aveiro-Ílhavo urban conglomeration in Portugal implies submarkets that emphasize the historical and endogenous evolution of the urban spatial structure.