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\section{Introduction}
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A short-term rental listing is a bundle of characteristics priced by an
individual host rather than by a centralised market maker. The theory of
hedonic prices \citep{Rosen1974}, which builds on the characteristics view
of demand of \citet{Lancaster1966}, treats the observed price of such a
differentiated good as the sum of the implicit prices of its attributes,
and the hedonic price function has become the standard empirical tool for
housing and property markets \citep{Malpezzi2003, Sirmans2005}. Short-term
rental platforms offer an unusually complete view of this function: every
listing displays its capacity, its type, its amenities, its host's status
and its reputation, together with a price that the host chose. Since
\citet{WangNicolau2017} and \citet{Gibbs2018}, a sizeable literature has
estimated hedonic price equations for Airbnb listings in individual cities
and across cities \citep{ChenXie2017, Teubner2017, PerezSanchez2018,
Cai2019, Lorde2019, Gyodi2021, TongGunter2022}, with the recurrent finding
that capacity, room type, location and reputation signals explain most of
the cross-sectional variation in displayed prices, and with a secondary
literature on the value of trust signals such as Superhost status, review
scores and host photos \citep{Ert2016, Zervas2021}.

Quebec is an interesting and little-studied case. The province combines a
large metropolitan market (Montreal), a heritage tourism market (Quebec
City) and an extensive resort and cottage market in the Laurentians,
Charlevoix and the Eastern Townships, so that a provincial sample mixes
urban apartments with rural chalets in a way that single-city studies
cannot. Canadian evidence on short-term rentals has concentrated on their
housing-market consequences \citep{WachsmuthWeisler2018, Combs2020}; the
only hedonic study we are aware of, \citet{Deboosere2019}, estimates a
multilevel model of prices and revenue for Montreal and finds that
accessibility and professionalisation dominate. No provincial hedonic
analysis exists, and none uses the newer platform signals (the Guest
Favourite badge, introduced in 2023) or compares the hedonic model with
quantile, spatial and machine-learning estimators on the same data.

This paper estimates hedonic price functions for a province-wide
cross-section of Airbnb listings in Quebec scraped from the public search
pages of the platform in early 2026. The data are a snapshot of 5,000
listing cards, of which 3,456 display a price. They are not an Inside
Airbnb extract: the record is the listing card, which carries the title,
the displayed price, the star rating, the review count, capacity, bedroom
and bathroom counts, an amenity count, the Superhost and Guest Favourite
badges, the pet policy and the coordinates, but neither the room type, the
host identifier, the amenity list, the cleaning fee nor the minimum stay.
The limited field set is a constraint that shapes the paper, and we
describe exactly what each variable measures rather than relabelling it.

The first task of the paper is a measurement problem that any user of
scraped Airbnb prices must confront. The displayed price field is
bimodal on the logarithmic scale: one mode lies near \$150 and a second
near \$2,500, and 26.5\% of priced listings carry a ``nightly'' price
above \$1,000. The second mode is populated by ordinary one- and
two-bedroom rental units in Montreal, its listings have prices that are
about twenty times those of otherwise similar listings in the first mode,
and the pattern is best explained by the platform displaying the total
price of a multi-night stay for part of the search results. We document
this with a two-component mixture model and a regime regression, and we
estimate the hedonic models on the subsample priced at or below \$1,000,
with the threshold varied in robustness checks. The companion paper on
Airbnb and rents (UQO Working Paper No.~5) uses the same scrape and
reaches the same diagnosis; here we treat it as the point of departure.

The second task is the hedonic analysis itself. We estimate a sequence of
nested ordinary least squares specifications that add amenity, host and
reputation, location and finally city fixed effects to a structural
baseline, with heteroskedasticity-robust and city-clustered standard
errors; quantile regressions at five quantiles of the conditional
log-price distribution, with bootstrap tests of inter-quantile
differences; spatial lag, spatial error and spatial Durbin models
estimated by maximum likelihood on a nearest-neighbour weights matrix,
with direct and indirect impacts computed as in \citet{LeSagePace2009};
and five supervised learning models evaluated under both random and
spatially blocked cross-validation \citep{Roberts2017}, with the best
model interpreted through SHAP values \citep{Lundberg2017, Lundberg2020}.
Throughout, the estimates are read as conditional associations in a
cross-section of asking prices, not as structural marginal willingness to
pay \citep{Kuminoff2010, Bishop2020}.

Three results stand out. First, once the stay-price regime is removed,
the hedonic model behaves as the literature leads one to expect: capacity
variables, title category and location explain the bulk of price
variation, with an $R^2$ that rises from about one-third in the structural
baseline to about one-half with city fixed effects, compared with
$R^2$ values of 0.05 to 0.27 obtained on the contaminated full sample in
the first version of this paper. Second, reputation signals carry
precisely estimated but modest premia once capacity and location are
held fixed: Superhost status and the Guest Favourite badge are each worth
a few percent of the nightly price, the review score matters mainly at
the lower quantiles, and the number of reviews is negatively associated
with price, consistent with high-turnover listings being cheaper.
Third, flexible estimators improve on the fixed-effects hedonic model
by a meaningful but bounded margin: gradient-boosting models raise the
out-of-sample $R^2$ from 0.47 to 0.56 under random cross-validation and
from 0.41 to 0.48 when whole areas are held out, every model loses about
seven points of $R^2$ in the second design, and the SHAP decomposition of
the best model ranks capacity first and the badges last, as the hedonic
coefficients do, while exposing one sign-switching association (the
review count) that a constant coefficient averages away. The non-linearities that the learners capture
refine the hedonic surface rather than overturn it.

The contribution is therefore twofold. Substantively, the paper provides
the first province-wide hedonic estimates for Quebec's short-term rental
market and documents how implicit prices differ between the urban and the
resort segments and across the price distribution. Methodologically, it
shows how a measurement defect of scraped platform prices can be detected
and handled, and it benchmarks, on one data set, how much the choice of
estimator matters relative to the choice of sample.

The remainder of the paper is organised as follows.
Section~\ref{sec:data} describes the data, the price-field diagnosis and
the analysis sample. Section~\ref{sec:methodology} sets out the hedonic,
quantile, spatial and machine-learning specifications and the inference
used. Section~\ref{sec:results} reports the results,
Section~\ref{sec:robustness} the robustness checks, and
Section~\ref{sec:conclusion} concludes with limitations and directions
for future work.