Functional regression over irregular domains: variation in the shadow price of living space

Abstract

ABSTRACTFunctional regression over irregular domains: variation in the shadow price of living space. Spatial Economic Analysis. Hedonic house price models need to account for spatial heterogeneity – the variation in the functional surface of shadow prices. In this context, the complexity of spatial domains raises issues for traditional spatial econometric methods. Specifically, discontinuities in the spatial surface need to be accounted for, including irregular boundaries, peninsulas and interior holes. Motivated by an application to housing markets, we develop a method for estimating the functional surface of a regression coefficient that varies over such an irregular spatial domain. Spatially varying coefficients for a specific regressor are estimated by a combination of three smoothing problems using splines based on finite element analysis. The effect of additional regressors is also allowed. We verify finite sample performance using a simulation study, and develop an application to the Aveiro–Ílhavo urban housing market in Portugal.