% Author: Simon-Pierre Boucher — contact@spboucher.ai
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\section{Related literature}
\label{sec:lit}

\subsection{Measuring vertical inequity: from ratio studies to modern tests}

The empirical study of assessment equity is nearly as old as the modern
property tax. Its workhorse is the \emph{sales ratio study}: for each sale
$i$, compute the ratio $r_i = AV_i/SP_i$ of assessed value to sale price and
ask whether $r_i$ is uniform across the value distribution. The
practitioner's canon --- codified in the IAAO \textit{Standard on Ratio
Studies} \citep{iaao2013standard} and the mass-appraisal manuals of
\citet{eckert1990property} and \citet{gloudemans2011fundamentals} ---
summarizes a jurisdiction with the median ratio, the coefficient of
dispersion (COD) for horizontal uniformity, and the price-related
differential (PRD) or, since 2013, the coefficient of price-related bias
(PRB) for vertical equity. These diagnostics discipline assessment practice
across North America, and we report all of them, with bootstrap confidence
intervals, for every Quebec municipality with sufficient sales.

The academic literature grew out of dissatisfaction with those summary
measures. \citet{paglin1972equity} proposed regressing assessed value on
sale price in levels and reading regressivity off a positive intercept;
\citet{cheng1974property} moved the test to logarithms, where the slope
$\beta$ has the clean interpretation of an elasticity and $\beta<1$ signals
regressivity. Subsequent work refined the specification menu ---
\citet{bell1984administrative} and \citet{sunderman1990testing} allowed
splines and structural breaks, and \citet{sirmans1995vertical} surveyed the
proliferating test battery. A decisive critique came from
\citet{kochin1982vertical} and \citet{kennedy1984unfair}: because the sale
price is itself a noisy measure of market value, the log-log slope is
attenuated toward zero even under perfectly proportional assessment ---
ratio studies are biased \emph{toward} finding regressivity.
\citet{clapp1990new} answered with a rank-based instrumental-variables
estimator whose coarse instrument is nearly orthogonal to transitory price
noise; \citet{goolsby1997assessment} and \citet{mcmillen2020assessment}
document how severely the correction can matter, and
\citet{quintos2020prb} extends the toolkit with machine-learning
diagnostics. Our design follows this lesson to the letter: we report the
na\"ive estimates, the Clapp IV, and quantile profiles
\citep{mcmillen2020assessment} side by side, and treat the IV as the lower
bound on true regressivity.

\subsection{Evidence: pervasive regressivity, mostly documented in the U.S.}

Substantively, the modern consensus is that assessment regressivity is the
rule rather than the exception. \citet{berry2021reassessing} computes ratio
statistics for essentially every U.S. county and finds that the
lowest-decile home within a jurisdiction faces an effective tax rate roughly
double that of the top decile; \citet{avenancio2022assessment} show in the
\textit{QJE} that the same machinery generates a 10--13\% assessment gap
against Black and Hispanic homeowners, driven partly by unpriced
neighbourhood attributes and partly by differential appeals;
\citet{amornsiripanitch2022residential} attributes much of the gradient to
assessors' inability to capture unobserved quality that scales with price.
Earlier strands documented the same pattern city by city ---
\citet{engle1975deassessment} in Boston, \citet{baar1981property} across
low-income neighbourhoods, \citet{mcmillen2011assessment} and
\citet{mcmillen2008thin} in Illinois, where thin markets and infrequent
reassessment emerge as structural drivers, \citet{hodge2017assessment} in
collapsing Detroit, and \citet{plummer2014evidence} and
\citet{ihlanfeldt2023appraisal} on the role of appeals and exemptions.
\citet{ross2012assessor} shows regressivity responds to the institutional
incentives of assessors themselves. The mechanism menu that emerges ---
stale valuations, hard-to-value heterogeneous properties, thin markets,
asymmetric appeals --- guides our heterogeneity analysis directly.

\subsection{Canada: a conspicuous gap}

For Canada the cupboard is nearly bare. Ontario's assessment corporation
publishes an internal vertical-equity review of its own values
\citep{mpac2022vertical}, and \citet{found2017property} compare tax
\emph{rates} across cities, but neither measures sale-level equity.
For Quebec, \citet{carbonnier2024property} establishes with survey microdata
that property tax payments are steeply regressive relative to
\emph{income}; the assessment channel --- whether the tax base itself is
mismeasured against \emph{market value} --- has never been examined at
scale, for Quebec or for any Canadian province. This is the gap the present
paper fills. The Canadian case is of independent interest precisely because
its institutions differ from the fragmented U.S. county system on the
dimensions the U.S. literature blames: Quebec assessment is governed by a
uniform provincial statute and manual \citep{lfm2026, mamh2024manuel},
performed by certified professional evaluators, and synchronized to a
statutory market-condition date. Finding large regressivity \emph{despite}
this apparatus sharpens the interpretation considerably: the problem is not
lax governance but the intrinsic difficulty of mass appraisal, compounded by
triennial staleness.

\subsection{Hedonic foundations}

Finally, the paper connects to the hedonic tradition. Mass appraisal is
applied hedonics \citep{rosen1974hedonic, malpezzi2003hedonic}: the
assessor's model prices a bundle of structural and locational attributes,
and equity failures are hedonic specification failures --- unpriced
land-share gradients \citep{bostic2007land}, depreciation curvature, or
neighbourhood effects that Quebec practitioners have long modelled in the
Quebec City market \citep{desrosiers2000hedonic}. Reading our subgroup
estimates through this lens turns an audit into a diagnosis: the assessment
gap is largest exactly where the hedonic problem is hardest.