% Author: Simon-Pierre Boucher — contact@spboucher.ai
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\section{Introduction}
\label{sec:introduction}
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Housing is the largest asset class on household balance sheets and the collateral behind
most household debt, and its price is the single most consequential relative price most
families ever face. Yet a dwelling is the archetypal heterogeneous good: no two houses
are identical, and the most important attribute---\emph{where the dwelling stands}---is
not a scalar that can be read off a listing sheet. The hedonic approach pioneered by
\citet{lancaster1966new} and \citet{rosen1974hedonic} resolves this heterogeneity by
treating the dwelling as a bundle of attributes, each commanding an implicit price
determined in equilibrium by the interaction of buyers' marginal willingness to pay and
sellers' marginal cost of supply. Regressing the (log) price of a dwelling on its
measurable characteristics recovers these implicit prices, and the resulting estimates
provide the empirical backbone for constant-quality house-price indices
\citep{bailey1963regression,hill2013hedonic}, property assessment and mass appraisal
\citep{mccluskey2013prediction}, mortgage valuation, and the welfare analysis of local
amenities \citep{black1999better,chay2005does}.

How much of a home's value is the structure, and how much is the location? The question
is old---it is the empirical content of the realtor's adage ``location, location,
location'' \citep{kiel2008location}---but its answer matters far beyond folklore.
Assessment authorities must apportion value between land and improvements; property-tax
reform hinges on the incidence of the land component; the macro literature has shown
that land, not structure, drives both the level and the growth of aggregate housing
wealth \citep{davis2007price,knoll2017no}; and the dispersion of location values across
cities is the fingerprint of supply constraints and agglomeration
\citep{saiz2010geographic,gyourko2013superstar,combes2015empirics}. Credible answers
require holding the structural bundle fixed while letting location vary---precisely what
a hedonic model with fine geographic fixed effects delivers.

This paper estimates such a model for the Canadian residential market at national scale.
Using a cross-section of \textbf{140{,}931} active MLS listings spanning the nine
provinces present in the data---from British Columbia to Newfoundland and Labrador---we
decompose dwelling prices into structural attributes, dwelling type and ownership form,
and a rich set of \textbf{1{,}153 neighbourhood fixed effects} defined at the Forward
Sortation Area (FSA) level. To our knowledge this is among the most geographically
comprehensive single-equation hedonic exercises assembled for Canada, where the hedonic
tradition has remained largely metropolitan in scope
\citep{desrosiers1996shopping,haider2000effects}. It is made feasible by an absorbing
least-squares estimator in the lineage of \citet{abowd1999high} that sweeps out the
high-dimensional location effects without materialising thousands of dummy variables
\citep{guimaraes2010simple,correia2017reghdfe}.

Our main findings can be summarised as follows. The purely structural model explains 46\%
of the variation in log prices; adding province fixed effects raises this to 57\%, and
replacing them with FSA fixed effects lifts it to \textbf{77\%}. Neighbourhood location
\emph{alone} therefore accounts for roughly thirty percentage points of explanatory
power---more than all structural attributes combined, and a listing-level counterpart to
the large land shares found in aggregate data \citep{davis2007price,knoll2017no}.
Conditional on location, the living-area elasticity is estimated at 0.51--0.62: a 10\%
larger dwelling sells for about 5--6\% more. Each additional full bathroom commands a
premium of 11--15\%, whereas the number of bedrooms is economically negligible once floor
space is held fixed---a recurrent finding in the hedonic literature
\citep{sirmans2005composition}. The implicit prices are remarkably stable across
alternative samples, trimming rules and dwelling types, and the model attains an
out-of-sample $R^2$ of 0.76 with a median absolute valuation error of 16\%, a level of
accuracy competitive with the mass-appraisal benchmarks reported in the valuation
literature \citep{mccluskey2013prediction,mullainathan2017machine}. We map the estimated
neighbourhood premia and show that the highest-valued FSAs---concentrated in the City of
Vancouver and the Greater Toronto Area---trade at more than triple the national-median
level net of structure. A battery of additional analyses sharpens the picture: the
neighbourhood effects absorb 82\% of the spatial autocorrelation in raw residuals
(Moran's~$I$ falls from 0.46 to 0.08); floor space exhibits clear diminishing returns;
the location component of price decays with distance to the nearest major metropolis, as
the monocentric tradition predicts \citep{alonso1964location,muth1969cities,mills1967aggregative};
and the implicit prices vary sensibly across the price distribution and across provinces
while transferring well out-of-region.

The contribution is threefold. \emph{First}, we provide the first (to our knowledge)
listing-level structure-versus-location decomposition spanning the entire Canadian
market, quantifying the neighbourhood as its single largest priced component.
\emph{Second}, we bring the high-dimensional fixed-effects technology of modern applied
microeconomics \citep{abowd1999high,correia2017reghdfe} to a national housing
cross-section and validate the design directly, showing that more than a thousand
absorbed neighbourhood intercepts eliminate the bulk of spatial dependence that
parametric spatial models are built to address
\citep{dubin1988estimation,basu1998analysis,gibbons2012mostly}. \emph{Third}, we supply a
transparent accuracy benchmark for the automated-valuation debate: every coefficient of
the model is inspectable, yet its held-out performance is competitive with the
mass-appraisal standards reported in the literature
\citep{clapp2003semiparametric,mccluskey2013prediction}.

The remainder of the paper is organised as follows. Section~\ref{sec:literature}
positions the paper in six related literatures. Section~\ref{sec:data} describes the
data and variable construction. Section~\ref{sec:methodology} presents the empirical
strategy. Section~\ref{sec:results} reports the main results.
Section~\ref{sec:robustness} provides robustness checks, heterogeneity analyses, and
out-of-sample validation. Section~\ref{sec:discussion} interprets the findings against
the literature and discusses implications, limitations and future work.
Section~\ref{sec:conclusion} concludes.
