spb/wp10_uqo

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 and7is, by statute, an \emph{ad valorem} tax: every dwelling in a municipality8is meant to be taxed in proportion to its market value. That9proportionality rests entirely on the quality of the assessment roll. If10assessors systematically overvalue inexpensive homes relative to expensive11ones, the legal tax rate becomes a fiction---the effective rate falls with12value, and the resulting redistribution from modest toward affluent13neighbourhoods occurs without any legislative decision, embedded in a14technical document that few taxpayers contest. A large literature15documents this pattern in the United States, where assessment16regressivity has been measured at national scale17\citep{berry2021reassessing, avenancio2022assessment,18amornsiripanitch2022residential}. Whether the same pathology afflicts19Canadian assessment systems---centralised, professionally supervised, and20widely presumed to be of high quality---has not been examined with21sale-level data at the scale of a province.2223This paper provides a province-wide ratio study 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;28the median match distance is under one metre. The resulting file couples29every sale price with the taxable value that generated the owner's tax30bill, 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\'eal (79{,}58134usable sales) to towns with barely a hundred---and a housing cycle of35unusual amplitude: the post-pandemic boom, the 2022--2023 interest-rate36shock, and the subsequent recovery.3738Quebec's institutional design makes it a clean laboratory for equity39measurement. Every roll is redrawn on a three-year cycle, and article~4640of the \textit{Loi sur la fiscalit\'e municipale} requires that the values41entered on a roll reflect market conditions on July~1 of the second fiscal42year preceding the first year of the roll---a single reference date shared43by every property in the municipality \citep{lfm2026, mamh2024manuel}.44Within a municipality~$\times$~roll~$\times$~sale-year block, every45assessment therefore embodies the same market vintage, and any systematic46relationship between assessment ratios and prices inside such a block is47not a timing artefact. Our regression estimates absorb 2{,}884 such48fixed effects, so that vertical inequity is identified from comparisons49between cheap and expensive dwellings facing the same assessor, the same50roll and the same market moment.5152Three findings emerge, and the first qualifies the other two. First, the53measured degree of regressivity depends decisively on how extreme54assessment ratios are treated---a choice that ratio-study practice55regulates explicitly \citep{iaao2013standard} but that the academic56literature rarely reports. Under a lenient rule that trims only the 1st and5799th percentiles of the ratio within each roll vintage, the elasticity of58the assessment ratio with respect to the sale price---zero under59proportional assessment---is $-0.34$ (s.e.\ $0.03$) in the fixed-effects60log-log regression and $-0.08$ (s.e.\ $0.02$) under a rank-based61instrument in the spirit of \citet{clapp1990new}; 95\% of municipalities62then fall outside the IAAO band for price-related bias. Under the IAAO63outlier rule, which removes ratios beyond 1.5 interquartile ranges within64each market block---9\% of sales, more than half of them in the bottom65within-market price decile---the elasticity is $-0.09$ (s.e.\ $0.01$) and66the instrumental-variable estimate is $-0.01$ and statistically67indistinguishable from zero; the province-wide coefficient of68price-related bias is $+0.02$, inside the acceptable band, the coefficient69of dispersion falls from 28 to 17, and three quarters of municipalities70meet the vertical-equity standard. A piecewise-linear specification locates71the discrepancy precisely: assessments are proportional to price across72the upper 80\% of each market's price distribution ($\beta$ between 0.9573and 1.00) and lose contact with price only in the bottom quintile, where74the extreme ratios sit. Whether those sales are over-assessed homes or75non-market transfers recorded at prices below value cannot be settled with76the registry data available in Quebec, and we therefore report the two77treatments as bounds throughout.7879Second, the \emph{ordering} of difficulty is invariant to the trimming80rule. Condominiums---homogeneous units with abundant comparables---are81assessed proportionally under either treatment, while single-family homes82and plexes, buildings over sixty years old, properties whose assessed83value is mostly land, and municipalities with few sales remain regressive,84at roughly a quarter of the lenient-trim magnitude once outliers are85removed. This gradient tracks the difficulty of the mass-appraisal problem86\citep{bostic2007land, gloudemans2011fundamentals, mcmillen2008thin} and87is the part of the audit that survives every specification we tried.88Horizontal dispersion follows the same map: the ten largest cities post89trimmed CODs between 9 and 12, comfortably inside the IAAO ceiling, while9030\% of municipalities---almost all small---exceed it.9192Third, the statutory reference date lets us measure how far93\emph{staleness} contributes to the gap. The province-wide price-related94bias is three to four times larger in 2021--2022 than afterwards, but most95of that swing reflects composition across municipalities whose rolls were96referenced on different markets. Within municipalities, the median97price-related bias of the trimmed sample moves from $-0.04$ in 2021--2022,98when the boom pulled prices away from rolls anchored in 2018--202099conditions, to approximately zero from 2024 onward, and the within-market100elasticity is essentially flat across roll-lag bands. Staleness therefore101widens measured inequity at the margin but does not generate it.102103These findings bear on the tax burden in a specific way. Because the levy104is proportional to the rolled value within a municipality, a property whose105assessment ratio exceeds the local norm by $x$\% pays $x$\% more tax than106uniform assessment would imply. The median dwelling in the bottom107within-market price decile pays between 6\% and 65\% more than under108uniform assessment, depending on whether extreme-ratio sales are counted as109market transactions; the top decile pays 3--5\% less under any treatment,110and sorting on a value proxy that averages price and assessment, as the111IAAO recommends, yields an overpayment near 6\% for the bottom decile. The112redistribution is real but an order of magnitude smaller than the113lenient-trim figure suggests, and it is concentrated among the cheapest114tenth of the stock. These results complement \citet{carbonnier2024property},115who documents the regressivity of Quebec's property tax relative to income116with survey microdata but could not observe the assessment channel117isolated here.118119The paper makes two methodological contributions to the ratio-study120literature. It exploits a statutory single-date reference regime to121separate timing drift from vertical inequity by design, and it shows, on122more than half a million sales, that the classical attenuation critique of123\citet{kochin1982vertical} and the practitioners' outlier rules of the IAAO124interact: the lower tail of the ratio distribution is exactly where125transaction noise and non-market sales concentrate, so that the126measurement-error bias that \citet{clapp1990new} sought to correct127econometrically is largely a sample-screening problem. We make the128dependence explicit by reporting the Cheng, Clapp and reverse-regression129estimators \citep{kochin1982vertical, kennedy1984unfair}, quantile and130piecewise profiles, and the full IAAO battery under five trimming rules.131132The remainder of the paper proceeds as follows. Section~\ref{sec:lit}133positions the paper in the ratio-study and property-tax-equity134literatures. Section~\ref{sec:inst} describes Quebec's assessment135institutions. Section~\ref{sec:data} presents the data, the matched sample136and the two trimming rules. Section~\ref{sec:method} lays out the137diagnostics, the econometric specifications and the measurement-error138bounds. Section~\ref{sec:results} reports the results,139Section~\ref{sec:robust} the robustness battery, Section~\ref{sec:disc}140discusses mechanisms and policy implications, and Section~\ref{sec:concl}141concludes. Appendix~\ref{app:bounds} derives the bounds and collects142supplementary tables.143