spb/wp11_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3% UQO Working Paper No. 114% Half a Million Prices, Twenty Models5%6% Build:  latexmk -pdf main.tex   (or `make` in this directory)7% Figures are read from ../figures/, tables from ../results/tables/.8% ============================================================================9\documentclass[12pt,letterpaper]{article}1011\usepackage[utf8]{inputenc}12\usepackage[T1]{fontenc}13\usepackage[english]{babel}1415\usepackage[letterpaper,margin=1in]{geometry}16\usepackage{setspace}17\onehalfspacing1819\usepackage{mathptmx}20\usepackage{microtype}2122\usepackage{amsmath,amssymb,amsthm}2324\usepackage{booktabs}25\usepackage{threeparttable}26\usepackage{makecell}2728\usepackage{graphicx}29\usepackage{subcaption}30\graphicspath{{../figures/}{./}}3132\usepackage[font=small,labelfont=bf,labelsep=period,justification=justified,singlelinecheck=false]{caption}3334\usepackage[dvipsnames]{xcolor}35\usepackage[colorlinks=true,linkcolor=NavyBlue,citecolor=NavyBlue,urlcolor=NavyBlue,breaklinks=true]{hyperref}3637\usepackage[authoryear,round,semicolon]{natbib}38\bibliographystyle{aer}3940\usepackage{titlesec}41\titleformat{\section}{\large\bfseries}{\thesection.}{0.5em}{}42\titleformat{\subsection}{\normalsize\bfseries}{\thesubsection.}{0.5em}{}43\titleformat{\subsubsection}{\normalsize\itshape}{\thesubsubsection.}{0.5em}{}44\usepackage{fancyhdr}45\pagestyle{fancy}\fancyhf{}46\renewcommand{\headrulewidth}{0pt}47\fancyfoot[C]{\thepage}48\usepackage{enumitem}49\setlist{nosep,leftmargin=*}5051% ============================================================================52% METADATA53% ============================================================================54\newcommand{\WPnumber}{11}55\newcommand{\WPtitle}{Half a Million Prices, Twenty Models}56\newcommand{\WPsubtitle}{A Systematic Assessment of Hedonic Specifications and57  Estimation Methods for the Quebec Housing Market, 2021--2026}58\newcommand{\WPdate}{August 2026}59\newcommand{\WPversion}{1.0}60\newcommand{\WPkeywords}{Hedonic pricing, Functional form, House price61  indexes, Machine learning, Automated valuation, Out-of-sample prediction}62\newcommand{\WPjel}{R31, C21, C52, C53}6364\newcommand{\WPauthor}{Simon-Pierre Boucher}65\newcommand{\WPaffiliation}{D\'epartement des sciences administratives\\66  Universit\'e du Qu\'ebec en Outaouais}67\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}68\newcommand{\WPaddress}{Gatineau -- Pavillon Alexandre-Tach\'e\\69  283, boulevard Alexandre-Tach\'e\\ Gatineau, Qu\'ebec, Canada J9A 1L8}7071\newcommand{\WPabstract}{%72Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still rests73on a series of specification choices --- functional form, temporal controls,74spatial controls, estimation method --- that are usually made by convention75and rarely stress-tested jointly. Using 514{,}212 Quebec residential sales76(2021--2026) whose structural descriptors come from the provincial77assessment roll, we run a controlled horse race of twenty hedonic models78organised along those four axes, scoring every model on identical holdouts79and on the same price-level scoreboard (log models are Duan-retransformed,80Box--Cox inverted). Four lessons emerge. (1)~Functional form is a81second-order choice: from linear to splines, the median absolute error82spans 16.5--18.6\%, and the data-driven Box--Cox exponent83($\hat\lambda=0.25$) buys nothing out of sample. (2)~Controls are84first-order: dropping spatial fixed effects costs ten error points ---85location granularity matters far more than curvature, but only up to the86point where cells thin out (a $\sim$1~km grid \emph{overfits}).87(3)~Under random validation, estimation method matters most: gradient88boosting reaches 14.4\% --- a 13\% improvement over the best linear model89--- with random forests close behind, and coordinates alone reproduce90what thousands of dummies buy. (4)~But the ranking is an artifact of the91split: under a forward-in-time holdout (train $<$~2025, test 2025--26)92every model degrades and the machine-learning advantage \emph{reverses}93--- the spline hedonic posts a lower median error than gradient boosting94and an identical log-scale $R^2$ --- a stark warning against evaluating95valuation models with random cross-validation alone. Constant-quality96monthly indices implied by the competing forms agree to within a few97index points, and the boosted model's implicit age and floor-area98profiles track the quadratic OLS closely --- interpretation and99prediction disagree less than the random-validation gap suggests.}100101\begin{document}102103\input{sections/titlepage}104105\setcounter{page}{1}106\input{sections/introduction}107\input{sections/literature}108\input{sections/data}109\input{sections/methodology}110\input{sections/results}111\input{sections/extensions}112\input{sections/discussion}113\input{sections/conclusion}114115\newpage116\bibliography{references}117118\end{document}119