\section{Robustness, identification threats and limitations}\label{sec:robust}

\subsection{Sensitivity analyses}

Table~\ref{tab:robust} summarises the sensitivity of the headline estimates. Three results are not robust and are reported as such: the joint test of regional premia rejects with make--model controls or when the sampled portals are included, although every premium stays within a few percent; the exit-hazard coefficient on the entry residual changes sign when the left-censored stock is included (that stock has unknown listing age, so this variant is a lower bound on age and not a preferred specification); and the held-out validation of the liquidity index loses significance under rank standardisation and at two-week aggregation. The depreciation slopes, the listing-age profiles of both hazards, the relative-price effects on the markdown hazard and the cut size, the competitor event study and the leave-one-component-out checks are stable; the competitor-density coefficient in the markdown hazard is not (it changes sign across markdown definitions and is never significant with dealer clusters). An earlier version of the first-markdown model had conditioned on listings that eventually receive a cut because of a null-handling error in the risk set; it was discovered by the robustness audit, corrected, and the whole pipeline was rerun (experiment log E-016). The remainder of the table lists the sensitivity to the main measurement and sample choices, following the list fixed in the analysis plan: alternative markdown thresholds (0.5 and 2~percent), transient rules (24 and 72~hours), exit-confirmation windows (3 and 14~days), inclusion of the sampled portals and of private-seller listings in the hedonic sample, wider price filters, inclusion of the left-censored stock in the hazards, heterogeneity of the depreciation slopes by powertrain, model-year band, body class and source class, composition reweighting of the dealer-website sample to the portal's make--model--year distribution, alternative standardisation, aggregation and minimum-size rules for the liquidity index, and competitor radii of 10 and 50~km (Table~\ref{tab:competition}).

\IfFileExists{tables/tab09_robustness.tex}{%
\begin{table}[tbp]\centering\caption{Identification threats and sensitivity summary}\label{tab:robust}
\scriptsize\input{tables/tab09_robustness}
\begin{minipage}{\textwidth}\scriptsize\smallskip Notes: Each row re-estimates the baseline model under the alternative rule and reports the quantity in the second column. Details and all variants are in the replication package (\texttt{results/robustness/}).\end{minipage}
\end{table}}{\emph{[Table 9 is generated by \texttt{scripts/12\_robustness.py}.]}}

\subsection{Multiple testing}

The six primary preregistered tests are: H1 (joint nonlinearity, $p = 3\times10^{-134}$), H2 (listing-age profile of the markdown hazard, $p = 7\times10^{-30}$), H3 (joint test of the competitor-cut lags, $p = 1\times10^{-14}$, an association), H4 (joint region test in A4, $p = 0.53$), H5 (entry hedonic residual in the exit hazard, $p = 0.42$) and H6 (held-out validation slope, $p = 2\times10^{-13}$). Holm's step-down adjustment (\texttt{results/robustness/holm\_primary\_tests.csv}) leaves the conclusions unchanged: H1, H2, H3 and H6 remain significant at any conventional level (adjusted $p \le 6\times10^{-13}$) and H4 and H5 are not rejected (adjusted $p = 0.85$). The null results are therefore not artefacts of the number of tests, and the positive ones are not artefacts of selective reporting; every estimated specification, including failed and null ones, is retained in the experiment log.

\subsection{Identification threats}

\paragraph{Asking versus transaction prices.} Every price in this paper is a dealer's posted price. The hedonic coefficients measure how dealers \emph{price} quality, not what buyers pay; negotiated discounts, financing and trade-in terms are unobserved. Because Quebec law requires all-in advertised prices, posted prices are comparable across dealers, but the level of the asking--transaction gap and its variation with listing age are unknown here, as in the housing literature on list prices \citep{han2016askingprice,haurin2010listprices}.

\paragraph{Exit versus sale.} Listing disappearance is an event on a website. Cross-source matching shows that it is consistent (94~percent of matched exits coincide within a week) and that at least a tenth of exits are relistings; the true share of retail sales among exits is unknown and may vary by dealer and vehicle, which would bias the exit hazards if the variation is correlated with covariates. The exit results should be read as describing \emph{inventory turnover on dealer websites}.

\paragraph{Composition and selection.} The hedonic sample is the universe of listings on registry sources, not a random sample of Quebec dealers; the registry over-represents the Capitale-Nationale, Bas-Saint-Laurent, Chaudière-Appalaches and Côte-Nord regions relative to population, and under-represents Montréal. Region effects are identified from variation across dealers located in different regions and cannot be separated from dealer effects for single-location dealers; the reweighting exercise addresses composition but not unobserved dealer quality. Left-censored stock is excluded from durations, which removes the vehicles that had already been on the lot longest; the sensitivity analysis with the left-censored stock included (entry set at first observation, a lower bound on listing age) is reported in Table~\ref{tab:robust}.

\paragraph{Reflection and common shocks.} The competitor event study cannot distinguish a dealer's response to a neighbour's cut from a common shock that moves both; the same-day concentration, the weekly harmonics, the significant leads and the robustness to dealer-by-weekday effects all point to the latter. An exogenous shifter of competitor repricing (for example, a platform-specific feed outage or a manufacturer programme that affects one brand's dealers only) would be needed for a causal estimate, and we have not found one in this window.

\paragraph{Window length and seasonality.} Eleven weeks of late summer and autumn cannot identify seasonal patterns, the response to macroeconomic events (the Bank of Canada raised its policy rate on 28~October 2026, three days before the end of the panel), or the long-run dynamics of vehicle cohorts. Listing durations longer than about 70~days are right-censored by construction, and the plateau of the markdown hazard beyond three weeks is estimated on a shrinking risk set.

\paragraph{Measurement of the index.} The liquidity index is validated internally only; its components are mechanically related to one another through the stock of listings (exits and arrivals both enter per listing-day), and the held-out test uses next-week exits, which are themselves observed disappearances. The index should be read as a descriptive summary of turnover on dealer websites until external benchmarks become available.

\subsection{Economic and policy implications}

Three implications follow with appropriate caution. For dealers, the evidence that cuts are frequent, shallow and increasing in listing age, that overpriced vehicles are cut sooner and more deeply, and that deep cuts characterise slow markets, suggests that entry prices close to hedonic value shorten time on the lot without larger total concessions, a hypothesis that transaction data could test. For consumers and regulators, the regional null means that a Quebec buyer gains little, on average, from searching across regions for the same vehicle once quality is held fixed, although dispersion within remote regions is larger. For statistical agencies, the paper shows that listing panels can deliver a timely, reproducible turnover index at the regional level, provided that connector artefacts (sampled portals, start-up stock, oscillating feeds, flickering connectors) are diagnosed and excluded; the audit trail documented here is a template for that work.