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1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3\section{Introduction}4\label{sec:intro}56The property tax is the fiscal backbone of Canadian local government: it7finances roughly two thirds of municipal budgets and is, by statute, an8\emph{ad valorem} tax --- every dwelling in a municipality is meant to be9taxed in strict proportion to its market value. That proportionality rests10entirely on the quality of the assessment roll. If assessors systematically11overvalue inexpensive homes relative to expensive ones, the legal tax rate12becomes a fiction: the effective tax rate falls with wealth, and the13resulting redistribution --- from modest neighbourhoods toward affluent ones14--- occurs silently, without any legislative decision, embedded in a15technical document that few taxpayers ever contest. A rapidly growing16literature documents exactly this pattern in the United States, where17assessment regressivity has been measured at national scale18\citep{berry2021reassessing, avenancio2022assessment,19amornsiripanitch2022residential}. Whether the same pathology afflicts20Canadian assessment systems --- centralized, professionally supervised, and21widely presumed to be of high quality --- is essentially unknown.2223This paper provides the first province-wide answer for Quebec. We assemble24522{,}769 residential transactions recorded between January 2021 and July252026 and match each sale, at the parcel level, to the triennial municipal26assessment roll in force on the day of the sale. The match is performed on27geographic coordinates and validated against the roll's recorded value; the28median match distance is under one metre. The resulting file couples every29sale price with the exact taxable value that generated the owner's property30tax bill, together with the roll's decomposition of that value into land and31building components, structural descriptors (lot area, floor area, year32built, number of units), and the statutory market-condition reference date33of the roll. The data span 625 municipalities --- from Montr\'eal34(79{,}581 usable sales) to towns with barely a hundred --- and a housing35cycle of unusual amplitude: the post-pandemic boom, the 2022--2023 interest36rate shock, and the subsequent recovery.3738Quebec's institutional design makes it an unusually clean laboratory for39equity measurement. Every municipality's roll is redone on a fixed40three-year cycle, and by law (art.~46, \textit{Loi sur la fiscalit\'e41municipale}) the values entered on a roll must reflect market conditions42eighteen months before the roll takes effect --- a single, known reference43date shared by every property in the municipality44\citep{lfm2026, mamh2024manuel}. Within a municipality $\times$ roll45$\times$ sale-year block, therefore, every assessment embodies the same46market vintage, and any systematic relationship between assessment ratios47and prices inside such a block is inequity, not timing. Our empirical design48exploits exactly this structure: all regression estimates absorb 2{,}88449municipality~$\times$~roll~$\times$~year fixed effects, so that vertical50inequity is identified purely from comparisons between cheap and expensive51dwellings facing the same assessor, the same roll, and the same market52moment.5354Three findings emerge. First, assessment regressivity in Quebec is55pervasive, large, and statistically unambiguous. The elasticity of the56assessment ratio with respect to the sale price --- zero under proportional57assessment --- is $-0.34$ (s.e.\ $0.03$) in the fixed-effects log-log58regression. Because sale prices measure market value with noise, part of59that estimate reflects mechanical attenuation \citep{kochin1982vertical,60clapp1990new}; a rank-based instrumental-variables estimator in the spirit61of \citet{clapp1990new} that purges this bias still yields $-0.08$62(s.e.\ $0.02$). Under the IAAO ratio-study standards used by assessment63authorities across North America \citep{iaao2013standard}, 95\% of Quebec64municipalities fall outside the acceptable band for price-related bias and6599\% exceed the uniformity (COD) ceiling. Strikingly, Montr\'eal --- the66province's largest and best-resourced assessment jurisdiction --- is the67\emph{only} major market whose assessments are progressive.6869Second, the inequity has a clear anatomy. Regressivity is roughly four times70stronger for single-family homes and plexes than for condominiums, whose71quasi-homogeneous units are easy to mass-appraise; it rises steeply with72building age and with the assessed land share of the property, consistent73with the difficulty of valuing land and depreciated structures74\citep{bostic2007land, gloudemans2011fundamentals}; and it is worse in small75municipalities, echoing the thin-market mechanism of \citet{mcmillen2008thin}.76The quantile profile is equally telling: the log-log slope77falls from $0.87$ at the first decile of the conditional value distribution78to $0.49$ at the ninth, so the failure of proportionality is concentrated at79the top --- expensive homes are not merely under-assessed, they are80under-assessed at an accelerating rate.8182Third, the stakes are material. Within a taxing jurisdiction the levy is83proportional to assessed value, so a property assessed above the84jurisdiction median ratio pays exactly that percentage more tax than uniform85assessment would imply. The median dwelling in the bottom within-market86price decile pays roughly 65\% more property tax than under uniform87assessment; the median dwelling in the top decile pays about 5\% less. Put88differently, the effective tax schedule that Quebec's assessment machinery89delivers is regressive enough to undo, within each municipality, a90substantial share of whatever progressivity the rest of the fiscal system91achieves --- a finding that complements \citet{carbonnier2024property}, who92documents the regressivity of Quebec's property tax relative to income using93survey data, but who could not observe the assessment channel isolated here.9495We also show \emph{when} the gap opens. Assessment ratios drift mechanically96between reference dates, and the province-wide price-related bias doubles in972021--2022, precisely when the post-pandemic boom pulled market prices away98from rolls anchored in 2018--2020 conditions --- direct evidence that99infrequent revaluation is a first-order driver of measured inequity, as100conjectured in the U.S. literature \citep{berry2021reassessing,101ross2012assessor}. Because the diagnosis singles out stale rolls, thin102markets, and hard-to-value property types --- rather than assessor103discretion alone --- it maps directly into policy: shorter revaluation104cycles, pooled assessment services for small municipalities, and targeted105review of high-land-share and older properties.106107Beyond the Canadian evidence gap, the paper makes two methodological108contributions to the ratio-study literature. It is, to our knowledge, the109first large-scale equity study to exploit a statutory single-date reference110regime to separate timing drift from genuine vertical inequity by design111rather than by econometric correction; and it implements the full modern112test battery --- IAAO diagnostics with bootstrap inference113\citep{iaao2013standard}, the classical regression tests114\citep{paglin1972equity, cheng1974property}, measurement-error-robust IV115\citep{clapp1990new}, and quantile profiles \citep{mcmillen2020assessment}116--- on more than half a million sales, allowing precise subgroup estimates117that smaller samples cannot support.118119The remainder of the paper proceeds as follows. Section~\ref{sec:lit}120positions the paper in the ratio-study and property-tax-equity literatures.121Section~\ref{sec:inst} describes Quebec's assessment institutions.122Section~\ref{sec:data} presents the data and the matched sample.123Section~\ref{sec:method} lays out the diagnostics and econometric124specifications. Section~\ref{sec:results} reports the results,125Section~\ref{sec:robust} the robustness battery, Section~\ref{sec:disc}126discusses mechanisms and policy implications, and Section~\ref{sec:concl}127concludes.128