Half a Million Prices, Twenty Models: A Systematic Assessment of Hedonic Specifications and Estimation Methods for the Quebec Housing Market, 2021–2026

Hedonic price models underpin mass appraisal, price indices, and housing research, yet specification choices — functional form, time effects, spatial controls, estimation method — are usually made ad hoc. This paper runs a controlled horse race of 20 models on 514,212 roll-matched Quebec residential sales (2021–2026) with assessor-grade structural attributes, scoring every model on the same price-level scoreboard via Duan smearing and Box–Cox inversion.

The design crosses four axes: six functional forms (linear to Box–Cox and cubic splines), a time-fixed-effects ladder (none to month), a spatial-fixed-effects ladder (none to a ~1.1 km grid), and six estimation methods (OLS, ridge, random forest, gradient boosting, spatial k-NN comparables). All models face two holdouts: a random 80/20 split and a forward-in-time split trained before 2025 and tested on 2025–2026.

Spatial controls are first-order, worth roughly 10 percentage points of median absolute percentage error, but overfit at ~1 km granularity; functional form is second-order, worth about ±2 points. Gradient boosting wins under random validation (MdAPE ≈ 14.4% vs 16.5% for the best linear model), but under the forward-in-time split every model degrades and the ranking reverses — splines reach 19.1% against 21.2% for boosting, at identical log R². Implied price indices and implicit-price profiles agree across forms far more than the accuracy gap suggests.