These essays present a comprehensive framework for modelling house prices, emphasising the heterogeneity of covariate effects with respect to location, time and other variables.
The work addresses the bias-variance trade-off associated with the constant parameter assumption in both Time Dummy and Imputation methods. A novel, generalised approach is proposed that unifies these techniques by transforming separate regression models into a global regression model with time interactions. This methodology is applied to a large dataset of asking prices for detached and semi-detached houses in Germany.
Furthermore, a Gaussian structured additive regression framework is introduced for estimating complex multiplicative interaction effects, with a particular focus on the relationship between price and time. A novel scaling approach is used to avoid the occurrence of negative scaling terms, thereby improving economic interpretability. Bayesian inference techniques using efficient Markov Chain Monte Carlo (MCMC) algorithms are applied along with extensive simulation experiments. The approach is then demonstrated using an analysis of dwelling prices in Germany, exploring the influence of time heterogeneity across multiple explanatory variables.
Finally, this work extends its focus to the effect of location heterogeneity and the modelling of housing prices beyond the mean. A batchwise backfitting algorithm is used within a structured additive regression model, which allows for efficient modelling of all distributional parameters of the price distribution. Using a large dataset of apartment prices in Germany, a model-based clustering algorithm identifies clusters with homogeneous location-specific effects on price. Relevant variables for modelling location and scale parameters in each regional cluster are selected in an automated procedure, allowing for different influences on the price distribution depending on location and price segment.
This integrated research contributes a versatile framework for analysing property prices.