A1292
Title: Schools and house prices: Spatiotemporal regression of quantile functions on categorical covariates
Authors: Luke Barratt - Humboldt-Universität zu Berlin (Germany) [presenting]
John Aston - University of Cambridge (United Kingdom)
Abstract: A functional regression framework is developed for modelling how distributions of house prices vary over space, time, and local school quality. House prices near each school are treated as draws from a distribution characterised by its quantile function, which is estimated via monotone I-spline smoothing and represented in a log-quantile function space. A functional generalised additive model decomposes these distributional responses into spatial, temporal, and covariate effects, where the covariates are compositional indicators of Ofsted school inspection categories at various leads and lags. Working with quantile functions connects least-squares estimation to Frechet regression under the Wasserstein-2 geometry, aiding interpretability through optimal transport. Separable spatiotemporal covariance modelling of residuals enables efficient generalised least squares refitting via Kronecker structure. Applied to English house prices from 2005 to 2024, the method reveals that the impact of changing the Ofsted inspection category of the local school varies across the price distribution: lower-priced properties show stronger sensitivity to inspection outcomes, while at the upper end the effect is attenuated, consistent with wealthier households substituting towards private schooling. The framework thus offers a richer picture than conditional-mean regression alone, capturing how school quality reshapes entire local price distributions rather than merely shifting their average.
