Stabilizing Geo-Spatial Splines with Helperpoints – How to Estimate Smooth Price Surfaces when there are Data Gaps

Abstract

This paper examines how to overcome an essential disadvantage of polynomial spline behavior: over-shooting of estimated spline functions in areas with poor data support. We introduce a new method that avoids the spline overshooting problem by placing helper points in data-gap areas before estimating the spline surface. We estimate helper point values via the Random Forest algorithm. Helper points force the algorithm to put a cost on deviating from reasonable local values in these areas. We show that our method can prevent spline overshooting where data are missing, can improve predictions in areas where data are scarce, but does not distort the spline surface in areas where data are plentiful. Our method also has a positive knock-on e ff ect in that it reduces the need for high (global) penalisation values and thus improves the spline’s response to changes in actual prices in regions with more data. Our method is particularly suited to the estimation of property price gradients, as property data are inherently unevenly distributed in space. We illustrate that our method can significantly improve the estimation of regional house price gradients using data for new apartment transactions in Vienna, Austria. To the best of our knowledge, our method is new - not only to the field of Real Estate Economics - but also to the spline literature.