spb/wp11_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3\section{Introduction}4\label{sec:intro}56Every applied hedonic study begins with a series of quiet decisions. Log7the price or not? Dummies for years or for months? Neighbourhood fixed8effects, and how fine? Least squares or, increasingly, a gradient-boosted9ensemble? Fifty years after \citet{rosen1974hedonic} established that10theory places no restriction on the shape of the price surface, these11choices are still made largely by convention --- the semi-log survives as12the default \citep{sirmans2005composition}, the classic form13comparisons predate the out-of-sample era \citep{halvorsen1981choice,14cropper1988choice}, and the machine-learning comparisons that have15multiplied since \citet{mullainathan2017machine} typically change the16sample, the features and the validation scheme all at once, making it17impossible to say \emph{which} ingredient buys the reported gains.1819This paper runs the comparison the way one would design an experiment.20From 514{,}212 Quebec residential sales (2021--2026) matched at the21parcel level to the provincial assessment roll --- so that every model22sees the same assessor-grade attribute set: floor area, lot area, age,23storeys, units, property class, physical configuration --- we estimate24\textbf{twenty models organised along four axes}, varying one design25choice at a time: six functional forms (linear to Box--Cox to splines),26a ladder of time controls (none to month fixed effects), a ladder of27spatial controls (none to a $\sim$1~km grid), and six estimation methods28(OLS to random forests, gradient boosting, and a $k$-nearest-neighbour29comparables rule). Every model is scored on the same price-level30scoreboard --- log models retransformed with Duan smearing, Box--Cox31inverted --- and, crucially, under \textbf{two holdouts}: the standard32random 80/20 split, and a forward-in-time split (train before 2025, test332025--26) that mimics how a valuation model is actually deployed.3435Four results organise the paper.3637\textbf{First, functional form is a second-order choice.} Across linear,38semi-log, log-log, profile-likelihood Box--Cox39($\hat\lambda = 0.25$), quadratic and spline specifications --- holding40controls fixed --- the median absolute error spans 16.5\% to 18.6\%.41Splines beat the textbook semi-log by 1.6 points; the data-driven42Box--Cox transformation, the great hope of the 1980s debate, buys43nothing out of sample, vindicating \citet{cropper1988choice} and44\citet{cassel1985cost} on modern data at scale.4546\textbf{Second, controls are first-order --- with a twist.} Removing all47spatial controls costs ten error points (27.9\% versus 17.5\%), an order48of magnitude more than any curvature decision; a $\sim$5.5~km grid beats49both municipality effects and, notably, a $\sim$1.1~km grid, whose5030{,}548 cells overfit --- the bias--variance trade-off in absorbing51location is real and non-monotonic. Time effects show the same shape in52miniature: anything beats nothing (three points), granularity beyond53quarters buys nothing.5455\textbf{Third, under random validation the estimation method dominates.}56Gradient boosting reaches a median error of 14.4\% and random forests5714.6\%, against 16.5\% for the best linear model --- a 13\% improvement58--- and stripping the coordinates from the boosting model degrades it to5923.2\%, showing that what the machine mainly learns is a flexible price60surface over space \citep{bourassa2010predicting}. The na\"ive61$k$-NN comparables rule (21.2\%) confirms that neither raw proximity nor62raw flexibility suffices: the gains come from their combination.6364\textbf{Fourth --- our headline --- the ranking is an artifact of the65validation scheme.} Under the forward-in-time split every model degrades,66but not equally: the machine-learning advantage \emph{reverses} on the67median error (gradient boosting 21.2\% versus 19.1\% for the spline68hedonic) and equalizes exactly on log-scale $R^2$ (0.52 for both).69Random cross-validation lets flexible models interpolate the price level70of their own test period; when the test period lies in the future --- the71only case that matters for deployment --- that advantage is leakage, not72skill. Comparisons of valuation models that report random cross-validation73alone, i.e.\ most of the applied ML literature, systematically overstate74the practical value of model flexibility \citep{clapp2002predicting,75steurer2021metrics}.7677The paper then asks what the specification choices do to the objects78economists actually extract from hedonic models. Constant-quality monthly79indices implied by the month effects of four linear forms --- and by80repricing a fixed portfolio with the boosting model --- agree to within a81few index points across the largest housing cycle in recent Canadian82history. And the boosting model's partial-dependence profiles in age and83floor area track the quadratic OLS closely: the machine agrees with the84economist about the gradients and disagrees mainly about the residual85surface. Interpretation and prediction, in other words, conflict far less86than the accuracy scoreboard suggests.8788Section~\ref{sec:lit} situates the exercise in the functional-form,89spatial-hedonic and ML-valuation literatures. Section~\ref{sec:data}90describes the data, Section~\ref{sec:method} the experimental design.91Section~\ref{sec:results} reports the horse race,92Section~\ref{sec:ext} the index, implicit-price, learning-curve and93segment extensions, Section~\ref{sec:disc} discusses implications, and94Section~\ref{sec:concl} concludes.95