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\section{Robustness and Limitations}
\label{sec:robustness}
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\subsection{Robustness}
\label{subsec:robust}

Several features of the design guard against spurious results. The dual
specification (Section~\ref{subsec:econometrics}) ensures that estimates are not
driven by the non-random availability of living area: coefficients on attributes
common to both models retain their sign and rough magnitude whether or not area is
conditioned on. The ``\texttt{has\_}'' indicators accompanying each imputed field let
the regression separate observed from imputed information, so median imputation does
not silently attenuate the size coefficients. The price-per-square-foot trim removes
the residual parsing errors that would otherwise dominate the tails, and the
municipality fixed effects absorb the first-order spatial confound emphasized by
\citet{can1992spatial} and \citet{anselin1988spatial}.

\paragraph{Inference.} Because listings within a municipality share unobserved
local shocks, our preferred standard errors are clustered at the municipality level
(195 clusters; \citealp{cameron2015cluster}), the same level as the fixed effects.
Clustering matters exactly where theory predicts: the text- and vision-derived
quality attributes---which vary house by house within a municipality---are
essentially unaffected (curb appeal, renovation level, luxury, garage, materials,
landscaping, and the rural-setting discount all remain significant at the 5\% level
or better in Model~A, as do the LLM condition scale, renovated kitchen, and hardwood
indicators), whereas keyword amenities with a strong spatial component lose
precision (public-transit proximity falls to the 5\% boundary in Model~A and is
insignificant in Model~B; central air conditioning is insignificant in Model~B; the
curb-appeal score, precisely estimated in Model~A, loses significance in the broader
Model~B).
Heteroskedasticity-robust (HC3) standard errors
\citep{white1980heteroskedasticity,mackinnon1985some} yield the same qualitative
pattern with uniformly smaller intervals. This asymmetry is reassuring for our main
claim: the AI-generated attributes capture within-market, property-level quality
variation rather than repackaged location effects.

Table~\ref{tab:robustness} probes the stability of the predictive blend across
subsamples. Three patterns stand out. First, accuracy is comparable whether living
area is observed (median error 13.5\%) or imputed (14.4\%), confirming that the
area-free model prices the incomplete listings almost as well as the rich model.
Second, the model fits the broker-listed Realtor.ca inventory better
($R^2_{\text{OOS}}=0.80$) than the smaller, noisier for-sale-by-owner DuProprio
segment (0.58), though median errors are identical at 14.0\%; the gap is consistent
with the compositional and marketing differences between brokered and FSBO
platforms documented by \citet{hendel2009mls}. Third, the median error is stable
across price terciles (11--16\%), lowest in the mid-market and modestly higher in
the tails, where idiosyncratic and luxury attributes are harder to capture. (Within
a single tercile $R^2$ is uninformative because the price range is restricted; the
median error is the comparable metric.)

\input{tables/robustness}

\subsection{Limitations}
\label{subsec:limits}

Five limitations qualify the interpretation of our estimates.

\emph{Asking prices.} The dependent variable is the asking price of properties
listed for sale, not the transaction price. The list price is a strategic choice
that anchors buyer search and bargaining
\citep{horowitz1992list,knight2002listing,han2015microstructure}: it is set with
sale in mind and is highly correlated with the eventual transaction price, but
list-to-sale ratios vary systematically with market conditions and overpricing is
more common in thin segments. Two implications follow. First, our implicit prices
measure how sellers and their agents \emph{price} attributes into the ask, which
converges to buyers' valuation only insofar as the market disciplines the ask; the
economically sensible magnitudes and the monotone validation of
Section~\ref{subsec:validation} suggest the discipline is substantial. Second, any
attribute that shifts the list-to-sale ratio itself (e.g., attributes of hard-to-sell
properties) will carry a coefficient that mixes valuation and listing strategy.
Replicating the analysis on registry transaction prices is the natural next step.

\emph{Non-causality and content endogeneity.} Descriptions and photographs are
marketing instruments chosen by sellers and agents. Richer descriptions, more
photographs, and higher visual quality correlate with higher-end listing agents and
more valuable properties \citep{nowak2017textual}. The coefficients are therefore
\emph{predictive} associations, not causal effects; they should not be read as the
price change from physically adding a given attribute. We control for two observable
dimensions of marketing effort (photo count and virtual tours), but cannot rule out
that residual marketing quality loads on the AI-derived attributes.

\emph{Machine-generated features.} LLM and vision outputs can contain errors.
Zero-temperature decoding, strict schemas, and closed enumerations bound this risk
and make it reproducible, and classical measurement error in the extracted scores
would bias their coefficients toward zero---making our estimates conservative---but
we do not perform systematic human validation, and the visual layer judges each
property from a single façade photograph, ignoring interiors.

\emph{Selection.} Listed properties are not a random sample of the housing stock,
and listings with missing area or room detail are not missing at random (they tend
to be less complete listings). The ``\texttt{has\_}'' indicators and the two-part
design mitigate, but do not eliminate, the second concern.

\emph{Cross-section.} The data are a single-date snapshot, so the model captures no
market dynamics and the location premia are fixed as of 3~July~2026. Municipalities
with fewer than 20 listings are pooled, reducing spatial resolution where data are
sparse.