spb/wp1_uqo

1% ============================================================================2\section{Introduction}3\label{sec:introduction}4% ============================================================================56The hedonic price function of \citet{rosen1974hedonic} remains the standard instrument for recovering the implicit prices of housing attributes. Regressing prices on structural characteristics, location and neighbourhood amenities decomposes market values into attribute-specific gradients that are used in appraisal, mass assessment, cost--benefit analysis and the evaluation of urban policy \citep{malpezzi2003hedonic, sirmans2005composition, bishop2020best}. Almost all of this work estimates the conditional mean. A least-squares hedonic regression therefore imposes a single implicit price for each attribute, whatever the position of the property in the price distribution: a buyer of a \$275,000 house is assumed to capitalise park or transit proximity in the same proportion as the buyer of a \$1.5 million house. Nothing in hedonic theory requires this. The hedonic price function is an envelope of bid functions of heterogeneous households, and the gradient of that envelope can legitimately differ across segments of the market when preferences, budget constraints and substitution possibilities differ \citep{rosen1974hedonic, epple1987hedonic, ekeland2004identification}. Empirically, quantile regression has repeatedly rejected coefficient constancy across the conditional price distribution \citep{zietz2008determinants, mcmillen2008quantile, mak2010quantile, liao2012hedonic}.78A second well-documented feature of housing data is spatial dependence. Neighbouring properties share unobserved locational attributes and are priced with reference to one another, so that regression residuals are spatially autocorrelated and the price of a property is correlated with the prices of its neighbours \citep{can1992specification, basu1998analysis, anselin1988spatial, lesage2009introduction}. Combining the two concerns leads to spatial quantile regression. The combination is not straightforward, because a spatial lag of the dependent variable is endogenous and must be instrumented inside a quantile objective; the available estimators are the two-stage ``fitted-value'' quantile regressions of \citet{amemiya1982two}, \citet{powell1983asymptotic}, \citet{chen1996twostage} and \citet{kim2004quantile}, the instrumental-variable quantile regression of \citet{chernozhukov2005iv, chernozhukov2006quantile, chernozhukov2008instrumental} adapted to spatial autoregressive models by \citet{su2011instrumental}, and the conditionally parametric approaches surveyed by \citet{mcmillen2013quantile}. Applications to housing remain few \citep{kostov2009spatial, liao2012hedonic, wen2017spatial, gu2023hospital, squires2025airport}.910This paper applies a two-stage spatial quantile regression to residential asking prices in the province of Quebec. The data are a snapshot of 42,481 Centris listings, the province-wide multiple listing service, covering four product types: single-family houses, condominiums, small multi-unit buildings (``plexes'') and vacant land. For each segment we estimate the conditional quantile function of the log asking price at $\tau \in \{0.10, 0.25, 0.50, 0.75, 0.90\}$, first without and then with a spatial lag of neighbouring log prices instrumented by the spatially lagged covariates, and we test whether the coefficients of six broker-reported amenity indicators (highway, hospital, park, school, public transit and golf course) differ between the tails of the distribution. The contribution is empirical and modest in scope. We know of no spatial quantile hedonic study of the Quebec market, where the hedonic tradition of \citet{desrosiers2000sorting}, \citet{theriault2003modelling}, \citet{kestens2006heterogeneity} and \citet{dube2011spatial, dube2013commuter, dube2014did} has concentrated on conditional-mean models of Qu\'ebec City and Montreal; and we know of no study that compares amenity capitalisation across quantiles for several product types drawn from the same listing platform.1112The results, all of which are obtained from asking prices in a single cross-section and must be read as conditional capitalisation differentials rather than as welfare measures \citep{kuminoff2014capitalization}, are as follows. For single-family houses, the implicit prices of highway, transit and park proximity decline monotonically along the conditional distribution: the highway coefficient falls from 0.205 at the 10th percentile to 0.034 at the 90th, transit from 0.178 to 0.053 and park from 0.122 to 0.014, and the equality of the coefficients at $\tau = 0.10$ and $\tau = 0.90$ is rejected at the 1 percent level for each of them. The hospital indicator changes sign, from $-$0.085 at the 10th percentile to $+$0.041 at the 90th, and the difference is again significant. School proximity carries a stable discount of about 11 log points at every quantile. For condominiums no amenity coefficient differs significantly between the tails; for multiplexes the highway and hospital coefficients do; for vacant land the school and golf coefficients do. Residual spatial autocorrelation is strong in every segment (Moran's $I$ between 0.51 and 0.58 on OLS residuals), and the instrumented spatial lag estimated at the median lies between 0.13 (multiplexes) and 0.32 (vacant land). Introducing the lag attenuates the median highway, transit and school coefficients for houses by roughly a third to a half, which indicates that part of what a non-spatial model attributes to an amenity indicator is the price level of the surrounding listings.1314Three qualifications shape the presentation. First, the amenity indicators are binary broker classifications without distance or quality information, and the asking price is not a transaction price. Second, the inference relies on a paired bootstrap that resamples listings independently; it ignores spatial dependence and the generated-regressor nature of the fitted spatial lag, and no standard errors are available for the spatial-lag coefficient itself. Third, the numerical record of the study consists of the console log of the original estimation run; the raw Centris snapshot is not redistributable and could not be re-run for this revision. Every number in the paper is taken from that log, the tables and figures are generated from it by a versioned script, and the limitations this imposes are stated explicitly in Section~\ref{sec:robustness} and Appendix~\ref{app:audit}.1516The remainder of the paper is organised as follows. Section~\ref{sec:literature} reviews the hedonic, spatial and quantile literatures and situates the Quebec evidence. Section~\ref{sec:data} describes the Centris data and the construction of the four estimation samples. Section~\ref{sec:methodology} sets out the estimators, the spatial weights, the inference procedures and the interpretation of the estimates. Section~\ref{sec:results} reports the results, Section~\ref{sec:robustness} discusses robustness and the limits of the available evidence, Section~\ref{sec:discussion} interprets the findings, and Section~\ref{sec:conclusion} concludes.17