1\section{Dealer repricing, competition and inventory dynamics}\label{sec:dynamics}23\subsection{Markdown hazards and cut sizes (H2)}45Figure~\ref{fig:hazards}(a) shows the empirical daily hazard of a first sustained markdown by listing age. It is low in the first days (0.7~percent per day), doubles by the end of the first week (1.1~percent) and reaches a plateau of 1.4--1.5~percent per day between the second and fourth weeks, after which it declines slightly among the surviving listings. In the discrete-time model of Table~\ref{tab:hazards}, column~(1), estimated on the 1.37~million listing-days at risk of a first cut, the listing-age bins are jointly significant ($\chi^2(8) = 157$) and the coefficients rise monotonically from 0.91 (days 1--3, relative to the entry day) to 1.8 (beyond three weeks), so the first half of H2 is supported: the probability of a markdown increases with the time a vehicle has been on the lot and then plateaus. Relative price matters: a listing that enters 10~percent above its hedonic value has a 7.7~percent higher daily markdown hazard (coefficient 0.74 on the residual, $p < 0.001$), and a 10~percent higher price than its local competitor set adds 3.9~percent ($p < 0.001$); the listing-level Cox model with dealer-clustered sandwich errors (column~2) gives almost identical coefficients (0.72 and 0.36). Higher-mileage vehicles are cut more often (a 10~percent higher mileage raises the hazard by about 1~percent), while the price level itself and the vehicle's age are not related to the markdown hazard once the relative price is held fixed. The density of local competitors is the one preregistered covariate without a stable effect: its coefficient is positive and significant in the Cox model (0.11) but close to zero and insignificant in the discrete-time model with region and calendar-week effects (0.02, standard error 0.03), and the robustness suite shows that it changes sign across markdown definitions. The cut-size regression (column~5) is unambiguous: the first cut is 2.7~percent of the entry price at the median, it is larger for listings that entered above their hedonic value (a 10~percent overpricing raises the cut by 22~percent) and for expensive vehicles in absolute terms, and it declines with listing age at the time of the cut, that is, late cuts are smaller than early ones.67\begin{table}[tbp]\centering\caption{Markdown and listing-exit models (S2)}\label{tab:hazards}8\scriptsize\input{tables/tab05_hazards}9\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: cloglog = discrete-time complementary log-log hazard on listing-days with listing-age bins, powertrain, body, source class, region and calendar-week effects, standard errors clustered by dealer. Cox = proportional-hazards model at the listing level with entry covariates and dealer-clustered sandwich errors. Cut size = OLS on the log of the first cut (percent of entry price) with make--model, region and week fixed effects. The entry hedonic residual is from Model A2. $^{*}$, $^{**}$, $^{***}$: 10, 5, 1 percent.\end{minipage}10\end{table}1112\begin{figure}[tbp]\centering\includegraphics[width=\textwidth]{figures/fig05_hazard_curves.pdf}13\caption{Empirical daily hazards by listing age (S2) with 95\% Wilson intervals. (a) First sustained markdown. (b) Observed listing exit. (c) Implied survival by source class.}\label{fig:hazards}\end{figure}1415\subsection{Competitor price response (H3)}1617Figure~\ref{fig:es} and Table~\ref{tab:competition} report the event study of equation~\eqref{eq:es}. The daily probability that a dealer cuts the price of a listing is 1.44~percent on average. On the day a close competitor (same make and model, model year within one year, within 25~km) cuts its price, that probability is 0.89 percentage points higher (standard error 0.21), a 60~percent increase relative to the base rate. The association is, however, entirely contemporaneous: the coefficients for days $+1$ to $+6$ are zero or negative, and the only other positive coefficients appear at $k=+7$, $k=+14$ and $k=-7$, a weekly periodicity. The leads are jointly significant ($p < 10^{-4}$), so the pretrend test fails in the sense that a dealer's cut today also predicts a competitor's cut a week later; lagged and lead sums are of the same order. Adding dealer-by-weekday fixed effects, which absorb each dealer's repricing calendar, reduces the same-day coefficient to 0.55 points and the seven-day harmonics to 0.17 and 0.33 points, but does not change the picture. The placebo, in which competitor series are permuted across listings within make--model cells, yields coefficients indistinguishable from zero at every horizon (joint $p = 0.18$), which confirms that the same-day association is spatially structured and not an artefact of the fixed effects. Results are similar at 10~km (larger coefficients, fewer competitors) and 50~km (smaller), when errors are clustered by region, and with coarser fixed effects. For the first markdown only (panel~b), the same-day coefficient is 0.73 points against a base rate of 1.14~percent, again with no lagged response and the same weekly harmonics (0.49 points with dealer-by-weekday effects).1819We draw two conclusions. First, there is no evidence of a lagged strategic response: dealers do not follow a competitor's cut within the next one to six days. Second, the strong same-day co-movement, its weekly harmonics and its robustness to dealer-by-weekday effects point to common local shocks and synchronised repricing routines (dealers and dealer groups that update their inventory feeds on fixed days, manufacturer incentive calendars, local demand shocks) rather than to observation and reaction. Because the design has no exogenous source of variation in competitor cuts, the estimates are associations and we make no causal claim; the reflection problem of \citet{manski1993reflection} applies with full force.2021\begin{table}[tbp]\centering\caption{Competitor price-response event study (dependent variable: own sustained cut on day $t$, percentage points)}\label{tab:competition}22\resizebox{\textwidth}{!}{\input{tables/tab06_competition}}23\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: Linear probability models on S2 listing-days with region-by-week and make--model--year-by-week fixed effects, log competitor density and listing-age effects; coefficients are percentage points, standard errors clustered by dealer (by region in column 2) in parentheses. Placebo: competitor-cut series permuted across listings within make--model cells. ``+ dealer $\times$ weekday FE'' adds dealer-by-weekday effects.\end{minipage}24\end{table}2526\begin{figure}[tbp]\centering\includegraphics[width=\textwidth]{figures/fig06_competitor_event_study.pdf}27\caption{Own repricing around a competitor's price cut (S2). (a) Any sustained own cut: main specification, placebo with permuted competitors, and the specification with dealer-by-weekday fixed effects. (b) First sustained markdown. Bars are 95\% confidence intervals (dealer-clustered).}\label{fig:es}\end{figure}2829\subsection{Listing exit and its validation (H5)}3031Figure~\ref{fig:hazards}(b) shows the exit hazard. It is very high on the first day after entry (13~percent), which reflects listings that are posted and withdrawn within a day (dealer-to-dealer transfers, duplicate postings, feed corrections), then falls to 2~percent, rises to about 3~percent per day in the second and third weeks, and declines thereafter to under 1~percent per day beyond two months; the implied survival curves by source class in panel~(c) are similar. The discrete-time exit model (Table~\ref{tab:hazards}, column~3) confirms strong negative duration dependence after the first days and shows that cheaper and, above all, higher-mileage vehicles disappear faster (a 10~percent higher mileage lowers the exit hazard by 5~percent; a 10~percent higher price by 3~percent), and that older vehicles exit faster. The preregistered relative-price test of H5 is not supported: the coefficient on the entry hedonic residual is positive (0.18 in the cloglog, 0.13 in the Cox model) but imprecise once errors are clustered by dealer ($p = 0.42$ and $0.54$), and the current price position relative to competitors has a negative but insignificant coefficient. Overpriced listings are cut sooner and more deeply (previous subsection), but they do not leave the market faster or more slowly within the horizon of the data. Competitor density raises the exit hazard mildly (Cox coefficient 0.05, $p = 0.09$). The Schoenfeld tests reject proportional hazards for most covariates in both models, which is expected given the shape of the first-day hazard; the discrete-time models with listing-age bins do not impose proportionality and the log-logistic accelerated-failure-time estimates (replication package) agree in sign.3233Because exit is not a sale, we validate it in three ways. First, for the 17{,}898 vehicles observed simultaneously on a dealer's own website and on the Otogo portal (matched by VIN, overlapping spells), exits coincide closely: among the 8{,}541 pairs where both listings exited, 80~percent exited within one day of each other and 94~percent within a week (median gap 0.4~days). Second, the exceptions are informative about feed failures: in 11~percent of the dealer-site exits the portal copy was still listed seven days later, against 3~percent in the other direction, so dealer websites generate more spurious exits than the portal. Third, relistings bound the share of non-sale exits from below: of the 47{,}398 confirmed exits observable for 30~days, 10.2~percent were followed by a new listing of the same VIN within 30~days on a reliable source and 5.8~percent by a listing at a location more than 5~km away; the median gap for these dealer-to-dealer transfers is 1.1~days (upper quartile 8.7~days). Over the whole window, 10{,}139 of 95{,}968 VINs (10.6~percent) were listed at two or more locations at least 5~km apart. Listing exit is therefore a consistent, cross-source event that overstates retail sales by at least one tenth, and we label it ``observed disappearance'' throughout.3435\subsection{Prediction (Model F)}3637Table~\ref{tab:prediction} and Figure~\ref{fig:pred} report the out-of-sample prediction of a first markdown and of an exit within 30~days of entry, from entry information only. On the chronological split (entries before 15~September used to predict entries from 15 to 25~September, the latest cohort whose 30-day outcomes are fully observable), gradient boosting attains a log loss of 0.405 for markdowns (area under the curve 0.785; base rate 0.19) and 0.585 for exits (0.727; base rate 0.59), both well calibrated (expected calibration error below 0.02), and improves on the logistic baseline. The gains disappear when dealers or regions are held out: areas under the curve fall to 0.58--0.61 and the logistic model does as well or better, because the single most informative feature is the dealer's own markdown or exit rate in the training data (a third of the gradient-boosting gain). Thirty-day repricing and exit are, to a first approximation, dealer practices rather than vehicle attributes, and they do not transfer to unseen dealers. A Cox model for time to exit with entry covariates attains a concordance of 0.66 on the later cohort.3839\begin{table}[tbp]\centering\caption{Out-of-sample prediction of 30-day markdown and exit (S2, entry information only)}\label{tab:prediction}40\resizebox{\textwidth}{!}{\input{tables/tab08_prediction}}41\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: Chronological = train on entries before 2026-09-15, test on 2026-09-15 to 2026-09-25 (latest entries with fully observable 30-day outcomes); dealer holdout = five-fold grouped cross-validation by dealer (pooled out-of-fold); region LORO = leave-one-region-out over the six largest regions (mean). 95\% intervals from 200 bootstrap resamples of test rows. Exit = observed disappearance, not a sale.\end{minipage}42\end{table}4344\begin{figure}[tbp]\centering\includegraphics[width=\textwidth]{figures/fig10_prediction.pdf}45\caption{Prediction performance. (a) Reliability diagrams on the chronological split. (b) Log loss by split and model with bootstrap intervals.}\label{fig:pred}\end{figure}46