spb/wp1_uqo

1% ============================================================================2\section{Introduction}3\label{sec:introduction}4% ============================================================================56The hedonic pricing model, formalized by \citet{rosen1974hedonic}, remains the workhorse framework for estimating the implicit prices of housing attributes. By regressing property prices on structural characteristics, locational features, and neighborhood amenities, researchers can decompose market values into the marginal willingness to pay (WTP) for each attribute. This approach has generated an extensive empirical literature across international housing markets \citep{malpezzi2003hedonic, sirmans2005composition, chin2006influences}.78However, standard hedonic models estimated by ordinary least squares (OLS) impose a critical assumption: that implicit prices are constant across the conditional price distribution. A household purchasing a \$150,000 property is assumed to value an additional bathroom or park proximity identically to a household purchasing a \$1,500,000 property. This homogeneity assumption has been increasingly questioned on both theoretical and empirical grounds \citep{zietz2008determinants, liao2012hedonic, mak2010quantile}. From a theoretical perspective, \citet{rosen1974hedonic} himself acknowledged that the hedonic price function reflects a market equilibrium between heterogeneous buyers and sellers, and there is no reason to expect the marginal valuation of attributes to be invariant across market participants. From an empirical standpoint, housing markets are characterized by substantial preference heterogeneity: budget-constrained households prioritize functional accessibility (transit, highways), while luxury-market buyers emphasize prestige, privacy, and environmental quality \citep{waddell1993exogenous, bayer2007migration}.910Two methodological developments address this limitation. First, quantile regression \citep{koenker1978regression, koenker2005quantile} allows coefficients to vary across the conditional distribution, revealing how implicit prices differ between affordable and luxury properties. Unlike mean regression, quantile regression characterizes the entire conditional distribution of the response variable, providing a more complete picture of the relationship between housing prices and their determinants \citep{hao2007quantile}. Second, spatial econometric methods \citep{lesage2009introduction, anselin1988spatial} account for the well-documented spatial dependence in housing markets, where neighboring property prices and characteristics influence valuations through spillover effects. The combination of these two approaches---spatial quantile regression---remains relatively rare in the literature, despite its theoretical appeal \citep{liao2012hedonic, su2012profile}.1112The Canadian housing market presents a particularly interesting case for studying amenity capitalization heterogeneity. Canada experienced one of the most pronounced housing price escalations among OECD countries between 2000 and 2022, with the composite benchmark price rising over 300\% nationally \citep{cmhc2023housing}. Within Canada, the Quebec market exhibits distinctive characteristics: a bilingual regulatory environment, a unique civil law tradition affecting property transactions, and significant price variation between the Montreal metropolitan area and regional markets \citep{statisticscanada2023housing}. The province's housing stock spans from dense urban condominiums in downtown Montreal to rural single-family homes and agricultural land parcels, creating natural variation for studying how amenity capitalization differs across market segments and price levels.1314Despite these features, the Canadian housing literature---and the Quebec market in particular---remains largely confined to mean-based hedonic estimates. Recent Quebec-focused studies have examined social housing impacts \citep{dube2023yimby}, park premiums \citep{dube2025park}, supervised consumption site effects \citep{montreal2024consumption}, and rail transit capitalization \citep{dube2011spatial}, but none have investigated distributional heterogeneity in amenity capitalization using spatial quantile methods. The broader Canadian spatial hedonic literature includes studies of Toronto \citep{des2011spatial}, Vancouver \citep{pace2004spatial}, and pan-Canadian analyses \citep{bourassa2010spatial}, but quantile regression applications remain scarce.1516This paper makes four contributions to the literature. First, we provide the first application of spatial quantile regression to the Quebec residential market using a comprehensive dataset of 42,481 Centris listings. Second, we extend the analysis beyond single-family homes to four distinct market segments---houses, condominiums, multiplexes, and vacant land---enabling cross-segment comparison of amenity capitalization patterns. Third, we employ a two-stage spatial quantile regression (2SQR) framework with bootstrap inference, combining the distributional flexibility of quantile regression with explicit modeling of spatial spillovers. Fourth, we implement a comprehensive robustness framework including weak instrument diagnostics, variance inflation factor (VIF) analysis, sensitivity tests on spatial weights parameterization, and omnibus inter-quantile heterogeneity tests, providing confidence in the stability of our findings.1718Our results reveal substantial heterogeneity. For single-family homes, the omnibus inter-quantile test strongly rejects coefficient homogeneity ($\chi^2(7) = 35.74$, $p < 0.001$), with hospital proximity, park proximity, and transit proximity exhibiting statistically significant differences between the 10th and 90th percentiles. Notably, hospital proximity shifts from a significant discount of 8.2\% for lower-priced homes to a positive (but insignificant) association at the upper tail; park proximity declines from a significant premium of 8.7\% to an insignificant negative coefficient. The spatial lag parameter ranges from 0.04 to 0.23 across segments at the median, with first-stage $F$-statistics exceeding 100 in all segments, well above the \citet{stock2002survey} threshold for instrument relevance. The OLS model with corrected distance measures explains 68.5\% of house price variation (adjusted $R^2 = 0.685$). These findings have direct implications for urban planning, property taxation, and the interpretation of amenity valuation studies that rely on conditional-mean estimates.1920The remainder of this paper is organized as follows. Section~\ref{sec:literature} reviews the relevant literature on hedonic pricing, spatial econometrics, quantile regression, and housing market segmentation. Section~\ref{sec:methodology} presents the econometric framework, including the 2SQR estimator, bootstrap inference, and diagnostic tests. Section~\ref{sec:data} describes the data source, variable construction, and sample characteristics. Section~\ref{sec:results} reports the empirical results across all four market segments. Section~\ref{sec:robustness} presents the robustness checks. Section~\ref{sec:discussion} discusses theoretical and policy implications, and Section~\ref{sec:conclusion} concludes with directions for future research.21