spb/wp1_uqo

1% ============================================================================2\section{Conclusion}3\label{sec:conclusion}4% ============================================================================56This paper combines three dimensions of housing market analysis that are usually studied separately: quantile-specific hedonic pricing, spatial dependence through an instrumented spatial lag, and cross-segment comparison across houses, condominiums, multiplexes, and vacant land in the Quebec residential market. Using 42,481 Centris listings, we document substantial heterogeneity in amenity capitalization that standard OLS hedonic models mask. The omnibus inter-quantile test decisively rejects coefficient homogeneity for the house segment. Highway, hospital, park, and transit proximity are each associated with significantly different capitalization gradients at the 10th versus 90th percentiles, with hospital proximity exhibiting a sign reversal from negative to positive. Spatial spillovers are significant across all segments, with approximate indirect effects accounting for 22--32\% of total capitalization.78These findings suggest that reporting a single mean implicit price for each housing attribute can mislead both researchers and policymakers. The OLS highway coefficient overstates the association for luxury homes by a factor of four while understating it for affordable homes by 35\%. For hospital proximity, the mean estimate ($-$4.9\%) averages a negative association for lower-priced homes with a positive association for higher-priced homes, and is therefore not representative of either tail. The policy implication is that mean-based hedonic estimates may misrepresent the distributional incidence of amenity investments, property tax assessments, and cost-benefit analyses.910We emphasize that the estimated coefficients are quantile-specific capitalization gradients---spatially adjusted conditional associations in listing prices---rather than causal effects of amenity access. The cross-sectional design, reliance on listing prices, use of broker-classified binary amenity indicators, and residual spatial autocorrelation in the 2SQR model all limit the causal interpretation. These caveats notwithstanding, the consistency of the heterogeneity patterns across multiple amenities and segments, and their alignment with theoretical predictions about preference heterogeneity, strengthens confidence in the core finding.1112Several avenues for future research would address the current limitations and deepen the analysis:1314\begin{enumerate}[nosep]15\item \textbf{Transaction-price replication.} Reproducing the analysis with sale prices from Quebec's \textit{Registre foncier} would validate the listing-price results and quantify any listing-premium bias.16\item \textbf{Continuous GIS distances.} Constructing distance measures to each amenity type would enable estimation of distance-decay functions and reduce the attenuation bias from binary indicators.17\item \textbf{Amenity quality measures.} Incorporating school quality scores, transit frequency data, hospital classification, and park size would separate amenity quality from mere proximity.18\item \textbf{Panel and quasi-experimental designs.} Difference-in-differences or event study designs around new transit openings, park constructions, or hospital relocations would strengthen causal identification \citep{kuminoff2010quasi}.19\item \textbf{Geographically weighted quantile regression.} GWQR models \citep{chen2012geographically} would reveal whether distributional heterogeneity itself varies across space---for example, whether the highway gradient differs between urban and rural Quebec.20\item \textbf{Machine learning benchmarks.} Quantile random forests \citep{meinshausen2006quantile} or gradient boosted quantile regression \citep{friedman2001greedy} could serve as flexible prediction benchmarks, though at the cost of coefficient interpretability.21\item \textbf{Spatial Durbin quantile models.} Including spatially lagged exogenous variables directly in the quantile regression would test whether neighbor characteristics have direct effects beyond the spatial lag.22\item \textbf{Temporal dynamics.} Multi-period analysis would reveal whether distributional heterogeneity fluctuates with housing market cycles or represents a structural feature of the Quebec market.23\end{enumerate}2425The central implication of this study is that amenity capitalization in housing markets is not a single average effect, but a spatially embedded and distributionally heterogeneous process. Hedonic analyses that ignore this heterogeneity risk producing estimates that are correct on average but wrong for every subpopulation they purport to describe.26