1\section{Price formation and depreciation}\label{sec:prices}23\subsection{Hedonic asking prices}45Table~\ref{tab:hedonic} reports six specifications of equation~\eqref{eq:hedonic} on the 136{,}393 listings of S1. The linear benchmark (column~1) implies that asking prices fall by 8.5~percent per year of age and 3.2~percent per 10{,}000~km, conditional on make--model, entry week, source class and region; make--model effects alone explain most of the cross-sectional variance ($R^2 = 0.92$). Adding spline terms (column~2) raises the within-$R^2$ from 0.836 to 0.846 and lowers the in-sample root-mean-squared error from 0.167 to 0.162 log points; the tensor interaction (column~3) and the powertrain interactions (column~4) add little in sample. Trim fixed effects (column~5) reduce the error to 0.107 and dealer fixed effects (column~6) to 0.091, which shows that a substantial share of residual price variation is dealer-specific pricing rather than vehicle heterogeneity.67\begin{table}[tbp]\centering\caption{Hedonic asking-price models (S1, dependent variable: log entry price)}\label{tab:hedonic}8\resizebox{\textwidth}{!}{\input{tables/tab04_hedonic}}9\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: Standard errors clustered by dealer in parentheses; $^{*}$, $^{**}$, $^{***}$: 10, 5, 1 percent. Columns (2)--(6) add orthogonalised cubic B-spline terms in age and mileage (not shown); in column (3) the linear age and mileage coefficients are not separately interpretable because of the tensor terms. Reference categories: combustion engine, automatic transmission, all-wheel drive, dealer website, Montréal. Grouped-dealer CV = root-mean-squared error in five-fold cross-validation with dealers held out; a gradient-boosting model with the same inputs attains 0.159.\end{minipage}10\end{table}1112\begin{table}[tbp]\centering\caption{Hypothesis tests on the hedonic models (cluster-robust Wald tests)}\label{tab:hedtests}13\tabsize\input{tables/tab04b_hedonic_tests}14\end{table}1516\subsection{Nonlinear depreciation (H1)}1718The preregistered test of H1 is decisive (Table~\ref{tab:hedtests}): the nonlinear age and mileage terms are jointly significant ($\chi^2(12) = 664$), as are the tensor interaction ($\chi^2(49) = 667$) and the interaction of the age profile with powertrain ($\chi^2(35) = 312$). The out-of-sample criterion is met as well: with dealers held out, the spline specification lowers the root-mean-squared error from 0.176 to 0.171 log points (2.8~percent), beyond the 0.5~percent threshold set in the analysis plan; the tensor model does not improve on the additive splines out of sample (0.172), and gradient boosting, which can exploit make, model and trim interactions freely, reaches 0.159. Figure~\ref{fig:surface} shows the estimated surface. Relative to a one-year-old vehicle with 10{,}000~km of the same make and model, the quality-adjusted asking price is 14~percent lower at one year and 50{,}000~km, 27~percent lower at three years, 37~percent lower at five years and 57~percent lower at ten years (all at 50{,}000~km); at five years, moving from 10{,}000 to 200{,}000~km lowers the price from 28 to 59~percent below the reference. Age profiles are concave early and close to linear in logs afterwards, and the mileage gradient is steeper for younger vehicles, which is the signature of a market that prices expected remaining service rather than the odometer alone \citep{engers2009annualmiles}.1920\begin{figure}[tbp]\centering\includegraphics[width=\textwidth]{figures/fig02_depreciation_surface.pdf}21\caption{Quality-adjusted depreciation surface (Model A2t). (a) Predicted log asking price relative to a one-year-old vehicle with 10{,}000~km of the same make and model, over age and mileage; cells without data support are blank. (b) Age profiles at fixed mileage.}\label{fig:surface}\end{figure}2223\subsection{Regional segmentation (H4)}2425Table~\ref{tab:regions} and Figure~\ref{fig:map} report the region effects. With make--model--trim fixed effects, mileage, age, powertrain, body, transmission, drivetrain, entry week and source class held fixed, the sixteen regional premia relative to Montréal range from $-1.0$~percent (Lanaudière) to $+3.7$~percent (Bas-Saint-Laurent); none is individually significant at the 5~percent level with dealer-clustered standard errors, and the joint test does not reject equality ($\chi^2(16) = 14.9$, $p = 0.53$). The point estimates have a mild geographic pattern, with the remote regions (Bas-Saint-Laurent, Abitibi-Témiscamingue, Gaspésie, Saguenay) 2--4~percent above Montréal, consistent with transport costs and thinner local supply, but the data cannot distinguish these from zero. The Outaouais, which borders Ontario, asks 2.1~percent more than Montréal ($p = 0.14$), so there is no evidence of a cross-border discount. Within-specification dispersion, measured by the interquartile range of A2 residuals, is larger in the remote regions, that is, prices for the same vehicle are more dispersed where there are fewer competing listings. The conclusion is, however, sensitive to the quality controls: with make--model fixed effects only (Model A2, Table~\ref{tab:regions}, fourth column) the region effects are jointly significant ($p = 0.004$) even though every premium remains within $\pm 3$~percent, and adding the sampled portals to the sample also produces a rejection with trim fixed effects ($p = 0.014$; Section~\ref{sec:robust}). We therefore read H4 not as a strict null but as a bound: regional differences in quality-adjusted asking prices exist at most at the level of a few percent, smaller than the within-region dispersion for the same vehicle, and they are not statistically detectable once trim-level quality is held fixed.2627\begin{table}[tbp]\centering\caption{Quality-adjusted regional premia and dispersion}\label{tab:regions}28\tabsize\input{tables/tab06b_region_premia}29\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: A4 = Model A4 (make--model--trim FE); A2 = Model A2 (make--model FE); 95\% confidence intervals from dealer-clustered standard errors. Residual IQR = interquartile range of A2 residuals among S1 listings in the region.\end{minipage}30\end{table}3132\begin{figure}[tbp]\centering\includegraphics[width=\textwidth]{figures/fig07_regional_premia_map.pdf}33\caption{Regional premia. (a) Listing locations (hexagonal bins, log scale) and region effects (marker size proportional to the number of listings, colour = premium versus Montréal). (b) Region effects from Model A4 with 95\% confidence intervals.}\label{fig:map}\end{figure}34