% Author: Simon-Pierre Boucher — contact@spboucher.ai
% ============================================================================
\section{Introduction}
\label{sec:intro}

The property tax is the fiscal backbone of Canadian local government: it
finances roughly two thirds of municipal budgets and is, by statute, an
\emph{ad valorem} tax --- every dwelling in a municipality is meant to be
taxed in strict proportion to its market value. That proportionality rests
entirely on the quality of the assessment roll. If assessors systematically
overvalue inexpensive homes relative to expensive ones, the legal tax rate
becomes a fiction: the effective tax rate falls with wealth, and the
resulting redistribution --- from modest neighbourhoods toward affluent ones
--- occurs silently, without any legislative decision, embedded in a
technical document that few taxpayers ever contest. A rapidly growing
literature documents exactly this pattern in the United States, where
assessment regressivity has been measured at national scale
\citep{berry2021reassessing, avenancio2022assessment,
amornsiripanitch2022residential}. Whether the same pathology afflicts
Canadian assessment systems --- centralized, professionally supervised, and
widely presumed to be of high quality --- is essentially unknown.

This paper provides the first province-wide answer for Quebec. We assemble
522{,}769 residential transactions recorded between January 2021 and July
2026 and match each sale, at the parcel level, to the triennial municipal
assessment roll in force on the day of the sale. The match is performed on
geographic coordinates and validated against the roll's recorded value; the
median match distance is under one metre. The resulting file couples every
sale price with the exact taxable value that generated the owner's property
tax bill, together with the roll's decomposition of that value into land and
building components, structural descriptors (lot area, floor area, year
built, number of units), and the statutory market-condition reference date
of the roll. The data span 625 municipalities --- from Montr\'eal
(79{,}581 usable sales) to towns with barely a hundred --- and a housing
cycle of unusual amplitude: the post-pandemic boom, the 2022--2023 interest
rate shock, and the subsequent recovery.

Quebec's institutional design makes it an unusually clean laboratory for
equity measurement. Every municipality's roll is redone on a fixed
three-year cycle, and by law (art.~46, \textit{Loi sur la fiscalit\'e
municipale}) the values entered on a roll must reflect market conditions
eighteen months before the roll takes effect --- a single, known reference
date shared by every property in the municipality
\citep{lfm2026, mamh2024manuel}. Within a municipality $\times$ roll
$\times$ sale-year block, therefore, every assessment embodies the same
market vintage, and any systematic relationship between assessment ratios
and prices inside such a block is inequity, not timing. Our empirical design
exploits exactly this structure: all regression estimates absorb 2{,}884
municipality~$\times$~roll~$\times$~year fixed effects, so that vertical
inequity is identified purely from comparisons between cheap and expensive
dwellings facing the same assessor, the same roll, and the same market
moment.

Three findings emerge. First, assessment regressivity in Quebec is
pervasive, large, and statistically unambiguous. The elasticity of the
assessment ratio with respect to the sale price --- zero under proportional
assessment --- is $-0.34$ (s.e.\ $0.03$) in the fixed-effects log-log
regression. Because sale prices measure market value with noise, part of
that estimate reflects mechanical attenuation \citep{kochin1982vertical,
clapp1990new}; a rank-based instrumental-variables estimator in the spirit
of \citet{clapp1990new} that purges this bias still yields $-0.08$
(s.e.\ $0.02$). Under the IAAO ratio-study standards used by assessment
authorities across North America \citep{iaao2013standard}, 95\% of Quebec
municipalities fall outside the acceptable band for price-related bias and
99\% exceed the uniformity (COD) ceiling. Strikingly, Montr\'eal --- the
province's largest and best-resourced assessment jurisdiction --- is the
\emph{only} major market whose assessments are progressive.

Second, the inequity has a clear anatomy. Regressivity is roughly four times
stronger for single-family homes and plexes than for condominiums, whose
quasi-homogeneous units are easy to mass-appraise; it rises steeply with
building age and with the assessed land share of the property, consistent
with the difficulty of valuing land and depreciated structures
\citep{bostic2007land, gloudemans2011fundamentals}; and it is worse in small
municipalities, echoing the thin-market mechanism of \citet{mcmillen2008thin}.
The quantile profile is equally telling: the log-log slope
falls from $0.87$ at the first decile of the conditional value distribution
to $0.49$ at the ninth, so the failure of proportionality is concentrated at
the top --- expensive homes are not merely under-assessed, they are
under-assessed at an accelerating rate.

Third, the stakes are material. Within a taxing jurisdiction the levy is
proportional to assessed value, so a property assessed above the
jurisdiction median ratio pays exactly that percentage more tax than uniform
assessment would imply. The median dwelling in the bottom within-market
price decile pays roughly 65\% more property tax than under uniform
assessment; the median dwelling in the top decile pays about 5\% less. Put
differently, the effective tax schedule that Quebec's assessment machinery
delivers is regressive enough to undo, within each municipality, a
substantial share of whatever progressivity the rest of the fiscal system
achieves --- a finding that complements \citet{carbonnier2024property}, who
documents the regressivity of Quebec's property tax relative to income using
survey data, but who could not observe the assessment channel isolated here.

We also show \emph{when} the gap opens. Assessment ratios drift mechanically
between reference dates, and the province-wide price-related bias doubles in
2021--2022, precisely when the post-pandemic boom pulled market prices away
from rolls anchored in 2018--2020 conditions --- direct evidence that
infrequent revaluation is a first-order driver of measured inequity, as
conjectured in the U.S. literature \citep{berry2021reassessing,
ross2012assessor}. Because the diagnosis singles out stale rolls, thin
markets, and hard-to-value property types --- rather than assessor
discretion alone --- it maps directly into policy: shorter revaluation
cycles, pooled assessment services for small municipalities, and targeted
review of high-land-share and older properties.

Beyond the Canadian evidence gap, the paper makes two methodological
contributions to the ratio-study literature. It is, to our knowledge, the
first large-scale equity study to exploit a statutory single-date reference
regime to separate timing drift from genuine vertical inequity by design
rather than by econometric correction; and it implements the full modern
test battery --- IAAO diagnostics with bootstrap inference
\citep{iaao2013standard}, the classical regression tests
\citep{paglin1972equity, cheng1974property}, measurement-error-robust IV
\citep{clapp1990new}, and quantile profiles \citep{mcmillen2020assessment}
--- on more than half a million sales, allowing precise subgroup estimates
that smaller samples cannot support.

The remainder of the paper proceeds as follows. Section~\ref{sec:lit}
positions the paper in the ratio-study and property-tax-equity literatures.
Section~\ref{sec:inst} describes Quebec's assessment institutions.
Section~\ref{sec:data} presents the data and the matched sample.
Section~\ref{sec:method} lays out the diagnostics and econometric
specifications. Section~\ref{sec:results} reports the results,
Section~\ref{sec:robust} the robustness battery, Section~\ref{sec:disc}
discusses mechanisms and policy implications, and Section~\ref{sec:concl}
concludes.
