Urban house price surfaces near a World Heritage Site: Modeling conditional price and spatial heterogeneity

• Bivariate smoothing splines allow modeling of horizontal, anisotropic spatial effects on rents.
• Semiparametric quantile regressions permit such effects to vary vertically over the conditional rent distribution.
• Within this modeling framework, we investigate the price effects of a World Heritage Site.
• Our results provide empirical evidence for horizontal and vertical effects in rents.
• Beside strong east-west patterns, there is a pronounced positive effect of the World Heritage Site on rent.

In housing price regression, a large bundle of non-separable structural and location characteristics, potentially affecting prices nonlinearly, constitute the relevant set of predictors. Spatial subcenters and complex spatial association structures may, therefore, exist or, stated differently, horizontal market segmentation might be prevalent. Moreover, it is not unlikely for the housing price generating market mechanisms to vary across different parts of the conditional price distribution. This can ultimately cause disparate price segments to exhibit varying functional relationships through different subsets of characteristics and lead to vertical market segmentation. In order to take nonlinearity, horizontal and vertical market segmentation into account within the scope of housing price regressions, we propose incorporating a semiparametric approach into the quantile regression framework. In our empirical application, we investigate rental data from the German city of Regensburg, which contains an Old Town on the World Heritage List. Focusing on location effects exerted by the World Heritage Site, we illustrate how statements about horizontal and vertical market segmentation can be derived from a semiparametric quantile regression model based on empirical evidence and economic reasoning.