1\section{Econometric framework and identification}\label{sec:method}23The hypotheses, estimands, samples and tests were written down before estimation and are reproduced in the replication package together with every amendment (three amendments were made after the data audit: quality fixed effects at the make--model level rather than make--model--year, because model-year effects absorb vehicle age in an 81-day window; a linear-probability specification for the competition event study; and a per-source definition of left-censoring after the portal start-ups were discovered). We summarise the six models here.45\subsection{Model A: hedonic asking prices (H1, H4)}67For listing $i$ with entry price $P_i$,8\begin{equation}\label{eq:hedonic}9\log P_i = f(\mathrm{Age}_i,\mathrm{KM}_i) + X_i'\beta + \mu_{m(i)} + \tau_{w(i)} + \theta_{s(i)} + \rho_{r(i)} + \varepsilon_i ,10\end{equation}11where $f$ is a sum of cubic B-splines in age and mileage (five degrees of freedom each, knots at quintiles), optionally augmented by their tensor product (A2t) or interacted with powertrain (A3); $X_i$ contains transmission, drivetrain, powertrain and body class; $\mu_{m}$ are make--model (A1--A3) or make--model--trim (A4) fixed effects; $\tau_w$ are entry-week effects; $\theta_s$ source-class effects; and $\rho_r$ region effects with Montréal as reference. A5 adds dealer fixed effects, which absorb region. Standard errors are clustered by dealer. The nonlinear components of the spline bases are orthogonalised on the linear term so that H1 is a cluster-robust Wald test that the nonlinear coefficients are zero; H4 is a Wald test that the sixteen region effects are jointly zero in A4. Out-of-sample performance is assessed by five-fold cross-validation grouped by dealer, against a linear benchmark and a gradient-boosting model (A6) with the same inputs.1213\subsection{Models B and C: markdown and exit hazards (H2, H5)}1415Listings in S2 are expanded to a listing-day risk set (1.66~million listing-days). For the first markdown, the risk set runs from entry to the day of the first sustained cut (318{,}323 listing-days, 15{,}692 events); for exit it runs to the confirmed exit or censoring day (43{,}311 events). We estimate discrete-time complementary log-log hazards16\begin{equation}\label{eq:hazard}17\operatorname{cloglog}\, h_{it} = g(a_{it}) + \gamma \log(1+N_{it}) + \delta\, r_i + \lambda\, \pi_{it} + Z_i'\beta + \rho_{r(i)} + \tau_{t} + \theta_{s(i)},18\end{equation}19with listing-age bins $g(\cdot)$, the number $N_{it}$ of competing listings (same make and model, model year within one year, different dealer, within 25~km) active on day $t$, the entry hedonic residual $r_i$ from A2 (the listing's price relative to its quality-adjusted value), the price position $\pi_{it}$ relative to the mean log price of its competitors (zero with an indicator when there is no competitor), vehicle characteristics $Z_i$, region, calendar-week and source-class effects; the exit model adds the number of prior cuts. Standard errors are clustered by dealer. Cox proportional-hazards models with dealer-clustered sandwich errors, Schoenfeld tests and a log-logistic accelerated-failure-time model are estimated at the listing level with entry covariates; the conditional size of the first cut is modelled by least squares on log cut size with make--model, region and week fixed effects.2021\subsection{Model D: competitor price response (H3)}2223For listing-day $(i,t)$ in S2, let $C_{i,t-k}$ indicate that at least one competitor in the 25-km set cut its price on day $t-k$. We estimate24\begin{equation}\label{eq:es}25\mathbb{1}[\text{cut}_{it}] = \sum_{k=-7}^{14}\beta_k\, C_{i,t-k} + \gamma\log(1+N_{it}) + g(a_{it}) + \alpha_{r(i),w(t)} + \alpha_{my(i),w(t)} + u_{it},26\end{equation}27with region-by-week and make--model--year-by-week fixed effects, by linear probability (the daily base rate is 1.4~percent, so the linear approximation is local), with errors clustered by dealer and, alternatively, by region. The leads $k<0$ test for pretrends and reverse timing; a placebo permutes competitor series across listings within make--model cells, breaking geography while preserving each series' own dynamics; a robustness specification adds dealer-by-weekday fixed effects to absorb repricing calendars. We interpret all estimates as conditional associations: there is no exogenous source of variation in competitor cuts, and common local demand shocks are the leading alternative explanation.2829\subsection{Model E: regional segmentation (H4)}3031Region effects from A4, within-specification dispersion (the interquartile range of A4 residuals by region), and a comparison of the Outaouais region, which borders Ontario, with the Montréal-area regions.3233\subsection{Model F: prediction}3435Log entry price, a first markdown within 30~days, and an exit within 30~days are predicted from entry information only, with a regularised linear or logistic baseline and gradient boosting, under chronological, dealer-holdout and region-holdout splits; we report root-mean-squared error, log loss, Brier score, calibration and bootstrap intervals.3637\subsection{The liquidity index (H6)}3839For market $m$ (region, or price tier, or body class) and panel week $w$, we compute exit intensity (confirmed exits per listing-day), markdown frequency (cuts per listing-day), markdown depth (median cut size), quality-adjusted dispersion (interquartile range of hedonic residuals among active listings, sign reversed) and arrival rate (entries per listing-day); higher values of the index mean a \emph{more liquid} market. Components are standardised across market-weeks, markets with fewer than 30 listing-days are set to missing, and three weighting schemes are compared: equal weights, the first principal component (signed so that exit intensity loads positively), and supervised weights from a ridge regression of next-week exit intensity on the non-exit components fitted on weeks 2--5. Internal validation regresses next-week exit intensity on an index built \emph{without} the exit component, with market fixed effects, on weeks 6--10. Uncertainty bands come from a block bootstrap over dealers (200 replications). Weeks 0--1 are excluded because of the portal start-ups. No external forecasting test is possible with 81 days of data, and none is claimed.4041\subsection{Inference and multiple testing}4243The six primary tests (H1 joint nonlinearity, H2 listing-age profile, H3 lag sum, H4 region joint test, H5 relative-price coefficient in the exit hazard, H6 held-out validation slope) are reported with Holm-adjusted $p$-values in Section~\ref{sec:robust}; secondary tests are unadjusted and labelled exploratory.44