Rental Price Dynamics in Germany: A Distributional Regression Model with Heterogenous Covariate Effects

Modeling real estate prices in the context of hedonic models typically involves fitting a Generalized Additive Model, where only the mean of a (lognormal) distribution is regressed on a set of variables, without taking into account other parameters of the distribution. Thus far, the application of regression models that model the full conditional distribution of the prices, has been infeasible for large data sets, even on powerful machines. Moreover, accounting for heterogeneity of effects regarding time and location, is often achieved by naive stratification of the data rather than on a model basis. We apply a novel batchwise backfitting algorithm in the context of a structured additive regression model that enables us to efficiently model all distributional parameters of an appropriate distribution. Using a large German dataset of rental prices comprising over a million observations, we choose variables relevant for modeling the location and scale parameters using a boosting variant of the algorithm. Moreover, we identify heterogeneity of covariates’ effects on the parameters with respect to both time and location on a model basis. In this way, we allow varying influence of variables on the prices’ distribution depending on the dwelling’s location and the date of sale. Modeling the full distribution of prices further enables us to investigate the influence of the variables not only on the median, but also on other quantiles of rental prices.