% Author: Simon-Pierre Boucher — contact@spboucher.ai
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% UQO Working Paper No. 11
% Half a Million Prices, Twenty Models
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\newcommand{\WPnumber}{11}
\newcommand{\WPtitle}{Half a Million Prices, Twenty Models}
\newcommand{\WPsubtitle}{A Systematic Assessment of Hedonic Specifications and
  Estimation Methods for the Quebec Housing Market, 2021--2026}
\newcommand{\WPdate}{August 2026}
\newcommand{\WPversion}{1.0}
\newcommand{\WPkeywords}{Hedonic pricing, Functional form, House price
  indexes, Machine learning, Automated valuation, Out-of-sample prediction}
\newcommand{\WPjel}{R31, C21, C52, C53}

\newcommand{\WPauthor}{Simon-Pierre Boucher}
\newcommand{\WPaffiliation}{D\'epartement des sciences administratives\\
  Universit\'e du Qu\'ebec en Outaouais}
\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}
\newcommand{\WPaddress}{Gatineau -- Pavillon Alexandre-Tach\'e\\
  283, boulevard Alexandre-Tach\'e\\ Gatineau, Qu\'ebec, Canada J9A 1L8}

\newcommand{\WPabstract}{%
Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still rests
on a series of specification choices --- functional form, temporal controls,
spatial controls, estimation method --- that are usually made by convention
and rarely stress-tested jointly. Using 514{,}212 Quebec residential sales
(2021--2026) whose structural descriptors come from the provincial
assessment roll, we run a controlled horse race of twenty hedonic models
organised along those four axes, scoring every model on identical holdouts
and on the same price-level scoreboard (log models are Duan-retransformed,
Box--Cox inverted). Four lessons emerge. (1)~Functional form is a
second-order choice: from linear to splines, the median absolute error
spans 16.5--18.6\%, and the data-driven Box--Cox exponent
($\hat\lambda=0.25$) buys nothing out of sample. (2)~Controls are
first-order: dropping spatial fixed effects costs ten error points ---
location granularity matters far more than curvature, but only up to the
point where cells thin out (a $\sim$1~km grid \emph{overfits}).
(3)~Under random validation, estimation method matters most: gradient
boosting reaches 14.4\% --- a 13\% improvement over the best linear model
--- with random forests close behind, and coordinates alone reproduce
what thousands of dummies buy. (4)~But the ranking is an artifact of the
split: under a forward-in-time holdout (train $<$~2025, test 2025--26)
every model degrades and the machine-learning advantage \emph{reverses}
--- the spline hedonic posts a lower median error than gradient boosting
and an identical log-scale $R^2$ --- a stark warning against evaluating
valuation models with random cross-validation alone. Constant-quality
monthly indices implied by the competing forms agree to within a few
index points, and the boosted model's implicit age and floor-area
profiles track the quadratic OLS closely --- interpretation and
prediction disagree less than the random-validation gap suggests.}

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