Stabilizing Geo-Spatial Surfaces in Data-Sparse Regions - An Application to Residential Property Prices

Penalized regression splines provide a flexible way to model spatial variation in real estate prices. However, when extrapolating to areas without data support, splines tend to "overshoot" and produce highly implausible estimates. Such data-poor locations are often of particular interest in urban economics (e.g., parks or beaches), as they can be used to infer the value of amenities. We introduce a spline construction method that addresses this overshooting problem by introducing helper point values in data gap areas prior to estimating the penalized regression spline surface. We estimate these helper point values using a decision-tree-based algorithm (XGBoost) that can effectively cluster and average local price levels. We find that the introduction of helper points eliminates the overshooting behavior in data gap areas, while preserving the flexibility of the spline surface elsewhere. We illustrate our approach using data for new apartment transactions in Vienna, Austria in 2020.