spb/wp1_uqo

1% ============================================================================2% Figures3% ============================================================================45\clearpage6\section*{Figures}78\begin{figure}[!htbp]9\centering10\includegraphics[width=0.95\textwidth]{figures/fig1_coef_plots_amenities.png}11\caption{Amenity Coefficients by Quantile and Market Segment}12\label{fig:coef_plots}13\begin{minipage}{0.9\textwidth}14\footnotesize15\textit{Notes:} Each panel shows quantile regression coefficients with 95\% bootstrap confidence intervals (shaded). Dotted horizontal lines indicate OLS estimates. Declining curves (highway, transit, park) indicate stronger capitalization in affordable homes; the hospital panel shows a sign reversal from negative (affordable) to positive (luxury).16\end{minipage}17\end{figure}1819\begin{figure}[!htbp]20\centering21\includegraphics[width=0.95\textwidth]{figures/fig2_wtp_by_quantile.png}22\caption{Implicit Prices (Willingness to Pay) by Quantile and Market Segment}23\label{fig:wtp}24\begin{minipage}{0.9\textwidth}25\footnotesize26\textit{Notes:} WTP is computed as $P(\tau) \times [\exp(\hat\beta(\tau)) - 1]$, where $P(\tau)$ is the sample price at quantile $\tau$, in Canadian dollars. The divergence between quantile-specific WTP and the OLS-implied WTP (which would be a constant line) illustrates the policy-relevant heterogeneity documented in this paper.27\end{minipage}28\end{figure}2930\begin{figure}[!htbp]31\centering32\includegraphics[width=0.95\textwidth]{figures/fig3_ols_vs_qr_vs_sqr.png}33\caption{Comparison of Amenity Coefficients Across Estimation Methods}34\label{fig:ols_qr_sqr}35\begin{minipage}{0.9\textwidth}36\footnotesize37\textit{Notes:} Comparison of OLS, quantile regression at the median ($\tau = 0.50$), and two-stage spatial quantile regression (2SQR, $\tau = 0.50$). The spatial lag absorbs part of the amenity effect, reducing coefficient magnitudes in the 2SQR model. The attenuation is most pronounced for highway and transit proximity, suggesting that these amenity effects are substantially confounded by spatial spillovers in OLS specifications.38\end{minipage}39\end{figure}4041\begin{figure}[!htbp]42\centering43\includegraphics[width=0.85\textwidth]{figures/fig4_pseudo_r2.png}44\caption{Pseudo-$R^2$ by Quantile and Market Segment}45\label{fig:pseudo_r2}46\begin{minipage}{0.9\textwidth}47\footnotesize48\textit{Notes:} Model fit increases with the quantile for houses and condos, suggesting that structural and amenity variables explain more variance at the upper end of the price distribution. The land segment has the lowest pseudo-$R^2$ throughout, reflecting the absence of structural variables and the dominance of unobserved site-specific factors (zoning, development potential).49\end{minipage}50\end{figure}5152\begin{figure}[!htbp]53\centering54\includegraphics[width=0.85\textwidth]{figures/fig5_spatial_lag_rho.png}55\caption{Spatial Lag Parameter ($\rho$) by Quantile and Market Segment}56\label{fig:rho}57\begin{minipage}{0.9\textwidth}58\footnotesize59\textit{Notes:} Estimated via 2SQR. Condo $\rho$ declines sharply from 0.34 to zero as price increases, consistent with the thin-market hypothesis for luxury condos. Plex $\rho$ increases with price, reflecting stronger comparable-sales effects for higher-valued investment properties. House and land $\rho$ are relatively stable across quantiles.60\end{minipage}61\end{figure}6263\begin{figure}[!htbp]64\centering65\includegraphics[width=0.95\textwidth]{figures/fig6_price_distributions.png}66\caption{Price Distributions (Log Scale) by Market Segment}67\label{fig:distributions}68\begin{minipage}{0.9\textwidth}69\footnotesize70\textit{Notes:} Red dashed lines indicate the five quantiles $\tau \in \{0.10, 0.25, 0.50, 0.75, 0.90\}$. The right skewness of the raw price distribution (most visible for houses and plex) confirms the appropriateness of the log transformation.71\end{minipage}72\end{figure}7374\begin{figure}[!htbp]75\centering76\includegraphics[width=0.95\textwidth]{figures/fig7_wald_heatmap.png}77\caption{Inter-Quantile Heterogeneity of Amenity Coefficients (Wald Test Statistics)}78\label{fig:wald}79\begin{minipage}{0.9\textwidth}80\footnotesize81\textit{Notes:} Each cell shows the Wald statistic for testing $\beta(\tau_j) = \beta(\tau_{j+1})$ between adjacent quantiles. Warm colors indicate stronger heterogeneity. The house segment exhibits the most pervasive heterogeneity, with highway and transit showing significant shifts across multiple adjacent quantile pairs. $^{*}p<0.05$, $^{**}p<0.01$, $^{***}p<0.001$.82\end{minipage}83\end{figure}84