% ============================================================================
\section{Results}
\label{sec:results}
% ============================================================================

\subsection{Baseline Estimates}
\label{subsec:baseline}

Table~\ref{tab:regression} reports the two hedonic specifications estimated on the
full feature set (structural, amenity, room-detail, listing-signal, LLM text-derived,
and vision-derived attributes). Model~A, which includes living area and is estimated
on the 9{,}446 listings with a measured area, explains 75.5\% of the variation in log
prices ($R^2=0.755$, adjusted $0.748$). Model~B, the area-free specification estimated
on all 19{,}123 listings, explains 72.5\% ($R^2=0.725$, adjusted $0.721$). Adding the
machine-generated feature layers raises Model~A's $R^2$ from 0.717 (structural,
amenity, room, and listing attributes only) to 0.725 with the text layer and 0.755
with the vision layer---a cumulative gain of nearly four points from the two
AI-generated feature sets, over and above an already rich hedonic specification.

The estimated implicit prices are economically sensible and, with few exceptions,
statistically significant with standard errors clustered by municipality. In
Model~A, the living-area elasticity is 0.36 (a 10\% larger home commands roughly a
3.6\% higher price) and the lot-area elasticity is small but precisely estimated.
Each additional \textbf{bathroom} is associated with a 7.6\% premium and each parking
space with about 1\%. \textbf{Central air conditioning} carries a 5.5\% premium and
\textbf{public-transit} proximity 9.4\%, although the transit coefficient---like
other keyword amenities with a strong spatial component---is estimated much less
precisely once errors are allowed to correlate within municipalities.
\textbf{Waterfront} access is associated with a 6.0--6.4\% premium, significant at
conventional levels in the full-sample model. Age enters with a small negative linear
term and a positive quadratic, tracing the familiar depreciation-then-heritage
profile.

\input{tables/regression}

\subsection{Text- and Vision-Derived Attributes}
\label{subsec:ai_coeffs}

The two AI feature layers contribute distinct, largely orthogonal signal.

\paragraph{Text (LLM).} Beyond the keyword amenities, the structured specifications
carry independent information about finish and condition: a \textbf{renovated
kitchen} is associated with a 2.6\% premium, \textbf{hardwood flooring} with 2.4\%,
and the ordinal \textbf{condition} scale is positive and significant in both models
(1.6\% per step). Listings the model reads as \textbf{income properties} sell about
1.9\% below otherwise-comparable houses. The \textbf{new-construction} indicator,
by contrast, is indistinguishable from zero once age, the visual renovation level,
and the condition scales are controlled for---the premium a naive specification
would attribute to the label ``new'' is fully absorbed by the measured quality
attributes.

\paragraph{Vision (façade).} The image-derived attributes are jointly significant and
add the largest single increment to fit. Holding all structural, amenity, and text
attributes fixed, a one-point increase in \textbf{curb appeal} (1--10) is associated
with a 2.3\% higher price, and a one-step increase in the visual \textbf{renovation
level} with 2.4\%. A visible \textbf{luxury} cue adds 5.2\%, a \textbf{visible garage}
4.7\%, and each step of \textbf{landscaping} quality 1.5\%. Exterior materials price
as expected: \textbf{brick} ($+3.4$\%) and \textbf{stone} ($+3.7$\%) command premia,
while \textbf{vinyl} siding carries a 4.4\% discount. The visual \textbf{rural}
setting is associated with an 11.5\% discount relative to the omitted category. That
these visual measures remain significant after conditioning on the full text and
structural set---and with inference clustered at the municipality level---confirms
that the façade photograph carries price-relevant information available in no other
field.

\subsection{Validation of Machine-Generated Features}
\label{subsec:validation}

Before relying on the AI-generated attributes, we check that they order prices in the
expected direction. Figure~\ref{fig:validation} plots the median list price against the
vision model's curb-appeal and condition scores among listings with a detected
exterior shot. Both relationships are strongly monotone: median price rises steadily
from the lowest to the highest visual scores, with no reliance on the regression to
impose the pattern. Because these scores are produced by a model that never sees the
price, the monotonicity is independent evidence that the vision layer extracts a real,
price-relevant quality signal rather than noise. Table~\ref{tab:ai_summary} reports the
prevalence of the main text- and vision-derived attributes.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=\textwidth]{figures/fig_validation.pdf}
  \caption{Validation of the vision layer. Median list price rises monotonically with
  the model's curb-appeal (left) and condition (right) scores, among listings with a
  detected façade shot. The scores are generated without access to price.}
  \label{fig:validation}
\end{figure}

\subsection{Location Fixed Effects}
\label{subsec:location}

The 195 municipality fixed effects absorb the dominant locational component of price.
Relative to the reference city, the largest positive premia are estimated for
\textbf{Westmount} ($\approx+231$\%), \textbf{Hampstead} ($+173$\%), and
\textbf{Mont-Royal} ($+169$\%), followed by outlying municipalities at the low end
carrying discounts of 23--30\%. Figure~\ref{fig:premia} plots the extreme effects. The
magnitude and ordering align with well-known patterns in the Quebec housing market and
lend face validity to the specification.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=.74\textwidth]{figures/fig_premia.pdf}
  \caption{Estimated municipality fixed effects (Model~A), the twelve largest and eight
  smallest, expressed as percentage premia relative to the reference city.}
  \label{fig:premia}
\end{figure}