# 🏇 Half a Million Prices, Twenty Models

UQO Working Paper No. 11 — A Systematic Assessment of Hedonic Specifications and Estimation Methods for the Quebec Housing Market, 2021–2026

$Paper$

TL;DR — A controlled horse race of 20 hedonic models on 514,212 Quebec sales with assessor-grade structural attributes: 6 functional forms × time-FE ladder × spatial-FE ladder × 6 estimation methods, all scored on the same price-level scoreboard (Duan smearing / Box–Cox inversion) under two holdouts (random 80/20 and forward-in-time). Functional form is second-order (±2 pp of MdAPE); spatial controls are first-order (~10 pp) but overfit at ~1 km granularity; 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 ML advantage reverses (splines 19.1% vs boosting 21.2%, identical R²_ln): random cross-validation is the wrong experiment for valuation models. Implied price indices and implicit-price profiles agree across forms far more than the accuracy gap suggests.

# 🎯 The four design axes

Axis	Models	Question
A. Functional form	linear, semi-log, log-log, Box–Cox (λ̂ by profile likelihood), quadratics, cubic splines	does curvature matter?
B. Time effects	none / year / quarter / month FE	how fine must the time dummies be?
C. Spatial controls	none / municipality / ~5.5 km grid / ~1.1 km grid FE	how fine can location FE get before overfitting?
D. Estimation method	OLS, ridge (CV), random forest, gradient boosting (± coordinates), spatial k-NN comparables	what do the machines actually buy?

Every model: same sales, same attributes (floor area, lot, age, storeys, units, class, physical link), metrics on price levels (MdAPE, MAPE, RMSE_ln, R²_ln), municipality-clustered design, and two splits — random 80/20 and train < 2025 / test 2025–26 with carry-forward time effects.

# 🗂 Repository layout

text

wp11_uqo/
├── data/raw/                 # snapshot (NOT in git — see data/raw/README.md)
├── src/wp11/                 # config, sample, models (the harness), plotstyle
├── scripts/
│   ├── 01_build_sample.py    # 745,119 → 514,212 sales
│   ├── 02_horserace.py       # 20 models × 2 splits + Box–Cox profile
│   ├── 03_extensions.py      # indices, implicit-price profiles, learning curves, segments
│   ├── 04_make_figures.py    # 9 journal-calibre figures
│   └── 05_make_tables.py     # 7 LaTeX tables
├── results/{reproduced,tables}/
├── figures/
└── paper/                    # main.tex + sections/ + references.bib → main.pdf

# 🚀 Quick start

bash

cd wp11_uqo
python3 -m pip install -r requirements.txt
# place the parquet snapshot in data/raw/ (not distributed), then:
for s in scripts/0*.py; do python3 "$s"; done
cd paper && make

Runtime ≈ 10 minutes on an Apple-silicon laptop (the boosting and forest fits dominate); peak RAM ≈ 8 GB.

# 📝 Citation

bibtex

@techreport{boucher2026horserace,
  author      = {Boucher, Simon-Pierre},
  title       = {Half a Million Prices, Twenty Models: A Systematic Assessment
                 of Hedonic Specifications and Estimation Methods for the
                 Quebec Housing Market},
  institution = {Universit\'e du Qu\'ebec en Outaouais,
                 D\'epartement des sciences administratives},
  type        = {Working Paper},
  number      = {11},
  year        = {2026},
  month       = {August}
}

# 👤 Author & contact

Simon-Pierre Boucher — Département des sciences administratives, Université du Québec en Outaouais (UQO), Gatineau, QC. 📧 contact@spboucher.ai