% Author: Simon-Pierre Boucher — contact@spboucher.ai
% ============================================================================
\section{Introduction}
\label{sec:intro}

Every applied hedonic study begins with a series of quiet decisions. Log
the price or not? Dummies for years or for months? Neighbourhood fixed
effects, and how fine? Least squares or, increasingly, a gradient-boosted
ensemble? Fifty years after \citet{rosen1974hedonic} established that
theory places no restriction on the shape of the price surface, these
choices are still made largely by convention --- the semi-log survives as
the default \citep{sirmans2005composition}, the classic form
comparisons predate the out-of-sample era \citep{halvorsen1981choice,
cropper1988choice}, and the machine-learning comparisons that have
multiplied since \citet{mullainathan2017machine} typically change the
sample, the features and the validation scheme all at once, making it
impossible to say \emph{which} ingredient buys the reported gains.

This paper runs the comparison the way one would design an experiment.
From 514{,}212 Quebec residential sales (2021--2026) matched at the
parcel level to the provincial assessment roll --- so that every model
sees the same assessor-grade attribute set: floor area, lot area, age,
storeys, units, property class, physical configuration --- we estimate
\textbf{twenty models organised along four axes}, varying one design
choice at a time: six functional forms (linear to Box--Cox to splines),
a ladder of time controls (none to month fixed effects), a ladder of
spatial controls (none to a $\sim$1~km grid), and six estimation methods
(OLS to random forests, gradient boosting, and a $k$-nearest-neighbour
comparables rule). Every model is scored on the same price-level
scoreboard --- log models retransformed with Duan smearing, Box--Cox
inverted --- and, crucially, under \textbf{two holdouts}: the standard
random 80/20 split, and a forward-in-time split (train before 2025, test
2025--26) that mimics how a valuation model is actually deployed.

Four results organise the paper.

\textbf{First, functional form is a second-order choice.} Across linear,
semi-log, log-log, profile-likelihood Box--Cox
($\hat\lambda = 0.25$), quadratic and spline specifications --- holding
controls fixed --- the median absolute error spans 16.5\% to 18.6\%.
Splines beat the textbook semi-log by 1.6 points; the data-driven
Box--Cox transformation, the great hope of the 1980s debate, buys
nothing out of sample, vindicating \citet{cropper1988choice} and
\citet{cassel1985cost} on modern data at scale.

\textbf{Second, controls are first-order --- with a twist.} Removing all
spatial controls costs ten error points (27.9\% versus 17.5\%), an order
of magnitude more than any curvature decision; a $\sim$5.5~km grid beats
both municipality effects and, notably, a $\sim$1.1~km grid, whose
30{,}548 cells overfit --- the bias--variance trade-off in absorbing
location is real and non-monotonic. Time effects show the same shape in
miniature: anything beats nothing (three points), granularity beyond
quarters buys nothing.

\textbf{Third, under random validation the estimation method dominates.}
Gradient boosting reaches a median error of 14.4\% and random forests
14.6\%, against 16.5\% for the best linear model --- a 13\% improvement
--- and stripping the coordinates from the boosting model degrades it to
23.2\%, showing that what the machine mainly learns is a flexible price
surface over space \citep{bourassa2010predicting}. The na\"ive
$k$-NN comparables rule (21.2\%) confirms that neither raw proximity nor
raw flexibility suffices: the gains come from their combination.

\textbf{Fourth --- our headline --- the ranking is an artifact of the
validation scheme.} Under the forward-in-time split every model degrades,
but not equally: the machine-learning advantage \emph{reverses} on the
median error (gradient boosting 21.2\% versus 19.1\% for the spline
hedonic) and equalizes exactly on log-scale $R^2$ (0.52 for both).
Random cross-validation lets flexible models interpolate the price level
of their own test period; when the test period lies in the future --- the
only case that matters for deployment --- that advantage is leakage, not
skill. Comparisons of valuation models that report random cross-validation
alone, i.e.\ most of the applied ML literature, systematically overstate
the practical value of model flexibility \citep{clapp2002predicting,
steurer2021metrics}.

The paper then asks what the specification choices do to the objects
economists actually extract from hedonic models. Constant-quality monthly
indices implied by the month effects of four linear forms --- and by
repricing a fixed portfolio with the boosting model --- agree to within a
few index points across the largest housing cycle in recent Canadian
history. And the boosting model's partial-dependence profiles in age and
floor area track the quadratic OLS closely: the machine agrees with the
economist about the gradients and disagrees mainly about the residual
surface. Interpretation and prediction, in other words, conflict far less
than the accuracy scoreboard suggests.

Section~\ref{sec:lit} situates the exercise in the functional-form,
spatial-hedonic and ML-valuation literatures. Section~\ref{sec:data}
describes the data, Section~\ref{sec:method} the experimental design.
Section~\ref{sec:results} reports the horse race,
Section~\ref{sec:ext} the index, implicit-price, learning-curve and
segment extensions, Section~\ref{sec:disc} discusses implications, and
Section~\ref{sec:concl} concludes.
