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

\subsection{A hierarchy of specification choices}

Read jointly, the four axes imply a clear hierarchy of returns to
specification effort, useful to anyone building a hedonic model:

\begin{enumerate}
\item \textbf{Get location right} ($\sim$10 points of median error):
any spatial absorption beats none by a margin that dwarfs every other
choice; the optimal granularity is interior --- around 5~km here ---
because finer cells trade bias for variance.
\item \textbf{Include some time control} ($\sim$3 points): in a moving
market, a model without time effects mistakes appreciation for
attributes; granularity beyond quarters is cosmetic.
\item \textbf{Choose the estimator for the job} ($\sim$2 points
deployed, $\sim$4 under random validation): boosting buys real accuracy
in interpolation-heavy uses (filling gaps within a period, mass
appraisal with contemporaneous comparables) and much less when the
target is the future.
\item \textbf{Stop worrying about functional form} ($\lesssim$2
points): splines are a cheap upgrade; the Box--Cox machinery is not
worth its complexity, exactly as \citet{cropper1988choice} concluded
from simulations four decades ago.
\end{enumerate}

\subsection{Why the machines lose their edge out of time}

The decomposition rows explain the generalization gap. The boosting
model's random-split advantage comes almost entirely from a flexible
spatial surface (removing coordinates costs it 8.8 points). That surface
is estimated \emph{jointly} with the time path, and trees clamp: beyond
the last training month the model prices 2025--26 sales at a frozen
level, exactly like the carry-forward linear models, while its
fine-grained spatial fit --- calibrated on the 2021--24 price
configuration --- partially decays as relative prices shift. The linear
models, coarser but more rigid, carry a structure that transfers better.
This is not an indictment of machine learning --- retrained monthly, the
boosting model would presumably keep its interpolation advantage --- but
it prices the \emph{retraining requirement} that random cross-validation
hides, and it matches the practitioner evidence that AVM accuracy decays
quickly out of sample period \citep{bogin2020house, kok2017big}.

\subsection{Implications}

\paragraph{For research.} Hedonic coefficients and indices are robust
objects: form and even estimator perturb them little
(Section~\ref{sec:ext}). Researchers using hedonics to \emph{measure}
--- indices, implicit prices, capitalization effects --- can keep simple
forms with good controls and report validation under a temporal split
when prediction claims are made.

\paragraph{For mass appraisal.} Quebec's assessors face exactly this
design problem every three years. Our results suggest the largest
accuracy gains lie not in exotic estimators but in spatial resolution
chosen by market thickness --- and that any model, linear or boosted,
frozen at a reference date degrades by 3--7 points of median error
within two years. This quantifies the staleness mechanism behind the
assessment inequities documented in our companion paper (UQO WP10): the
valuation technology's out-of-time decay is of the same magnitude as the
inequities measured there.

\paragraph{For the AVM literature.} Every comparison should report a
forward-in-time split alongside random cross-validation
\citep{steurer2021metrics}. On our data, the choice of split changes not
just magnitudes but the \emph{winner}.

\subsection{Limitations}

Our attribute set, though assessor-grade, omits listing-level quality
(renovations, finishes, views); richer features would likely raise the
machines' interpolation advantage. Hyper-parameters were deliberately
conventional --- a tuned boosted model would gain somewhat, as would a
spatially smarter linear model (e.g.\ kriging residuals,
\citealp{case2004modeling}). The forward split covers one specific
regime change (the 2025--26 recovery); other windows would shift
magnitudes. And Quebec's institutional homogeneity aids transferability
of results across municipalities but may limit it across countries.
