No data. All results are model-generated under an illustrative parameterisation (config/baseline.yaml). No moment is
estimated; no Québec representativeness is claimed. The Canadian/Québec case study was not pursued.
Stationary local market with exogenous listing inflow. Listing decisions, construction, buyer heterogeneity in valuations
beyond the match draw, and spatial/segment spillovers (piazzesi2020segmented) are absent. One-sided entry means the Hosios
condition is the relevant efficiency benchmark only in the homogeneous case (gabrovski2025note).
Carrying cost is a permanent nonnegative type. Sellers whose reservation price rises with constraints (high LTV, loss aversion:
genesove1997equity, genesove2001lossaversion) are outside the model; so are learning and list-price revisions
(anenberg2016information) and stigma (taylor1999time), which can generate positive duration dependence.
Complete information within a match; no asymmetric information (kurlat2015asymmetries, garmaise2004asymmetries).
Buyers never exit. In the financing extension the buyer value can turn negative for low approval probabilities, a region we
exclude rather than model (an exit option would truncate it).
Welfare criterion. Steady-state flow surplus (no discounting across cohorts, no transition costs); the Hosios theorem concerns
the discounted problem, so the numerical optimum at $\beta=0.55$ is a flow-criterion result.
Dynamics. Unanticipated, perfectly understood shocks with free entry at every instant; prices jump immediately. Anticipation,
learning, or sticky buyer entry would slow price adjustment.
Quality. Lemma 1 makes quality a scale factor; correlated quality and urgency (e.g. distressed owners of poorly maintained
houses, clauretie2009foreclosure) is not modelled, although it is the main confounder of forced-sale discounts.
Numerical. Nine-type discretisation of $F$ (converged to 2e-4 % in the mean price); the match-value distribution is bounded in
the baseline, which matters for the frictionless limit (Prop. 2(iv)).
Liquidity versus quality: the urgency discount $D(c)$ is defined among identical houses; in data it requires conditioning on quality
and on the unobserved carrying cost (proxies: planned move dates, vacancy, double housing, estate sales).
Selection into sale: the observed index mixes within-type price changes and composition; the model's prediction is that the
composition term is small and of a sign governed by the shape of the match-value distribution, which is not directly observable.
Cash discount: measured gaps are conditional on sale and mix three terms whose signs differ; only the delay-bargaining term rises
monotonically with seller urgency.
Duration dependence: mixture (negative) versus learning/stigma (positive) require competing-risks models with unobserved
heterogeneity and withdrawal as a separate exit.
# Falsifiable predictions (stated in the conclusion)
Among observationally identical houses, the price concession of urgent sellers is larger, and their sale hazard higher, in
markets with fewer buyers per listing (Prop. 2(iii), Fig. 2–4).
The cross-sectional dispersion of prices among identical houses rises when matching efficiency or qualification falls
(Prop. 5(iii), Table 5).
After a liquidity shock, within-type prices move immediately whereas inventories and volumes adjust with a half-life of about
two months in the baseline; a temporary shock is followed by a sales rebound (Fig. 10).
The cash–mortgage gap rises with seller urgency and with approval delay, and its selection component can be negative for patient
sellers (Prop. 7, Fig. 5).
The withdrawal share of listings rises when liquidity falls, and the steady-state sales/listing ratio falls only in markets with
non-trivial withdrawal (Prop. 4(iv)).
In markets with heavy-tailed buyer valuations (e.g. unique or luxury properties), a more liquid market can lengthen time on market
for urgent sellers (Prop. 2(ii) Pareto case).