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1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3\section{Related literature}4\label{sec:lit}56\subsection{Measuring vertical inequity: from ratio studies to modern tests}78The empirical study of assessment equity is nearly as old as the modern9property tax. Its workhorse is the \emph{sales ratio study}: for each sale10$i$, compute the ratio $r_i = AV_i/SP_i$ of assessed value to sale price and11ask whether $r_i$ is uniform across the value distribution. The12practitioner's canon --- codified in the IAAO \textit{Standard on Ratio13Studies} \citep{iaao2013standard} and the mass-appraisal manuals of14\citet{eckert1990property} and \citet{gloudemans2011fundamentals} ---15summarizes a jurisdiction with the median ratio, the coefficient of16dispersion (COD) for horizontal uniformity, and the price-related17differential (PRD) or, since 2013, the coefficient of price-related bias18(PRB) for vertical equity. These diagnostics discipline assessment practice19across North America, and we report all of them, with bootstrap confidence20intervals, for every Quebec municipality with sufficient sales.2122The academic literature grew out of dissatisfaction with those summary23measures. \citet{paglin1972equity} proposed regressing assessed value on24sale price in levels and reading regressivity off a positive intercept;25\citet{cheng1974property} moved the test to logarithms, where the slope26$\beta$ has the clean interpretation of an elasticity and $\beta<1$ signals27regressivity. Subsequent work refined the specification menu ---28\citet{bell1984administrative} and \citet{sunderman1990testing} allowed29splines and structural breaks, and \citet{sirmans1995vertical} surveyed the30proliferating test battery. A decisive critique came from31\citet{kochin1982vertical} and \citet{kennedy1984unfair}: because the sale32price is itself a noisy measure of market value, the log-log slope is33attenuated toward zero even under perfectly proportional assessment ---34ratio studies are biased \emph{toward} finding regressivity.35\citet{clapp1990new} answered with a rank-based instrumental-variables36estimator whose coarse instrument is nearly orthogonal to transitory price37noise; \citet{goolsby1997assessment} and \citet{mcmillen2020assessment}38document how severely the correction can matter, and39\citet{quintos2020prb} extends the toolkit with machine-learning40diagnostics. Our design follows this lesson to the letter: we report the41na\"ive estimates, the Clapp IV, and quantile profiles42\citep{mcmillen2020assessment} side by side, and treat the IV as the lower43bound on true regressivity.4445\subsection{Evidence: pervasive regressivity, mostly documented in the U.S.}4647Substantively, the modern consensus is that assessment regressivity is the48rule rather than the exception. \citet{berry2021reassessing} computes ratio49statistics for essentially every U.S. county and finds that the50lowest-decile home within a jurisdiction faces an effective tax rate roughly51double that of the top decile; \citet{avenancio2022assessment} show in the52\textit{QJE} that the same machinery generates a 10--13\% assessment gap53against Black and Hispanic homeowners, driven partly by unpriced54neighbourhood attributes and partly by differential appeals;55\citet{amornsiripanitch2022residential} attributes much of the gradient to56assessors' inability to capture unobserved quality that scales with price.57Earlier strands documented the same pattern city by city ---58\citet{engle1975deassessment} in Boston, \citet{baar1981property} across59low-income neighbourhoods, \citet{mcmillen2011assessment} and60\citet{mcmillen2008thin} in Illinois, where thin markets and infrequent61reassessment emerge as structural drivers, \citet{hodge2017assessment} in62collapsing Detroit, and \citet{plummer2014evidence} and63\citet{ihlanfeldt2023appraisal} on the role of appeals and exemptions.64\citet{ross2012assessor} shows regressivity responds to the institutional65incentives of assessors themselves. The mechanism menu that emerges ---66stale valuations, hard-to-value heterogeneous properties, thin markets,67asymmetric appeals --- guides our heterogeneity analysis directly.6869\subsection{Canada: a conspicuous gap}7071For Canada the cupboard is nearly bare. Ontario's assessment corporation72publishes an internal vertical-equity review of its own values73\citep{mpac2022vertical}, and \citet{found2017property} compare tax74\emph{rates} across cities, but neither measures sale-level equity.75For Quebec, \citet{carbonnier2024property} establishes with survey microdata76that property tax payments are steeply regressive relative to77\emph{income}; the assessment channel --- whether the tax base itself is78mismeasured against \emph{market value} --- has never been examined at79scale, for Quebec or for any Canadian province. This is the gap the present80paper fills. The Canadian case is of independent interest precisely because81its institutions differ from the fragmented U.S. county system on the82dimensions the U.S. literature blames: Quebec assessment is governed by a83uniform provincial statute and manual \citep{lfm2026, mamh2024manuel},84performed by certified professional evaluators, and synchronized to a85statutory market-condition date. Finding large regressivity \emph{despite}86this apparatus sharpens the interpretation considerably: the problem is not87lax governance but the intrinsic difficulty of mass appraisal, compounded by88triennial staleness.8990\subsection{Hedonic foundations}9192Finally, the paper connects to the hedonic tradition. Mass appraisal is93applied hedonics \citep{rosen1974hedonic, malpezzi2003hedonic}: the94assessor's model prices a bundle of structural and locational attributes,95and equity failures are hedonic specification failures --- unpriced96land-share gradients \citep{bostic2007land}, depreciation curvature, or97neighbourhood effects that Quebec practitioners have long modelled in the98Quebec City market \citep{desrosiers2000hedonic}. Reading our subgroup99estimates through this lens turns an audit into a diagnosis: the assessment100gap is largest exactly where the hedonic problem is hardest.101