Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna

Abstract

This paper is motivated by two common challenges in hedonic price modeling: nonlinear price functions, which require flexible modeling approaches, and the inherent spatial heterogeneity in real estate markets. We apply additive mixed regression models (AMM) to estimate hedonic price equations for rents in Vienna. Non-linear effects of continuous covariates as well as a smooth time trend are modeled non-parametrically through P-splines. Unobserved district-specific heterogeneity is modeled in two ways: First, by location specific intercepts with the postal code serving as a location variable. Second, in order to permit spatial variation in the nonlinear price gradients, we introduce multiplicative scaling factors for nonlinear covariates. This allows highly nonlinear implicit price functions to vary within a regularized framework, accounting for district-specific spatial heterogeneity, which leads to a considerable improvement of model quality and predictive power. Our findings provide insight into the spatially heterogeneous structure of price gradients in Vienna, showing substantial spatial variation. Accounting for spatial heterogeneity in a very general way, this approach permits higher accuracy in prediction and allows for location-specific nonlinear rent index construction.