Proposing a Global Model to Overcome the Bias-Variance Tradeoff in the Context of Hedonic House Price Models

The most widely used approaches in hedonic price modelling of real estate data and price index construction are Time Dummy and Imputation methods. Both methods, however, reveal extreme approaches regarding regression modeling of real estate data. In the time dummy approach, the data are pooled and the dependence on time is solely modelled via a (nonlinear) time effect through dummies. Possible heterogeneity of effects across time, i.e. interactions with time, are completely ignored. Hence, the approach is prone to biased estimates due to underfitting. The other extreme poses the imputation method where separate regression models are estimated for each time period. Whereas the approach naturally includes interactions with time, the method tends to overfit and therefore increased variability of estimates. In this paper, we therefore propose a generalized approach such that time dummy and imputation methods are special cases. This is achieved by reexpressing the separate regression models in the imputation method as an equivalent global regression model with interactions of all available regressors with time. Our approach is applied to a large dataseton offer prices for private single as well as semi-detached houses in Germany. More specifically, we a) compute a Time Dummy Method index based on a Generalized Additive Model allowing for smooth effects of the metric covariates on the price utilizing the pooled data set, b) construct an Imputation Approach model, where we fit a regression model separately for each time period, c) finally develop a global model that captures only relevant interactions of the covariates with time. An important methodolical aspect in developing the global model is the usage of model-based recursive partitioning trees to define data driven and parsimonious time intervals.