Managing the Bias-Variance Tradeoff in the Context of House Price Prediction and Hedonic Indices - An Application for German Housing Data

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. We b) construct an Imputation Approach model, where we fit a regression model separately for each year. Our work aims at constructing a global model that captures relevant interactions of the covariates with time, where time intervals are selected on a model basis. We therefore c) fit a model-based recursive partitioning tree to partition the time span and to account for parameter instability. We d) fit a global model, in which we interact the covariates with the time periods obtained from the recursive partitioning tree. We analyze the respective performance and choose the optimal model with respect to out-of-sample prediction accuracy. We find that parameter instability over time plays a role as the Imputation Approach outperforms the Time Dummy Model. However by choosing model-based interactions with time, we are able to reduce both model complexity and out-of-sample prediction error. We find the interaction between location and time appears to be the most important. Our work provides a model-based approach to account for parameter instability over time in the context of hedonic price models and index construction. We are able to reduce bias compared with standard Time Dummy Method indices, and receive less volatile results compared with the typical Imputation Approach. Further, our assessment no longer naively selects time periods that are interacted with the other explaining variables. We expect these improvements to be useful especially for smaller, e. g. regional data sets.