Cahiers de recherche UQO · WP10 · v1.1
The Assessment Gap in Quebec
Vertical and Horizontal Inequity in Municipal Property Valuation: Evidence from 522,769 Sales Matched to the Assessment Roll
- Année
- 2026
- Première parution
- octobre 2026
- Dernière révision
- octobre 2026
- Statut de publication
- Cahier de recherche
Whether Quebec assessments are regressive depends on how outliers are treated
Across 522,769 roll-matched sales, the within-market elasticity of the assessment ratio is −0.34 under a lenient 1/99 trim but −0.09 under the IAAO outlier rule, and proportionality holds across the upper 80% of every market.
Résumé
Municipal property taxes are levied on assessed values, so any systematic relationship between assessment ratios and market value redistributes the tax burden within a municipality. This paper matches 522,769 residential sales recorded in Quebec between 2021 and 2026 to the triennial assessment rolls of 625 municipalities at the parcel level and provides the first province-wide ratio study of vertical and horizontal assessment equity for a Canadian province. Because the Loi sur la fiscalité municipale pins every roll to a single statutory market-condition date, municipality × roll × sale-year fixed effects separate the mechanical drift of ratios between reference dates from within-market inequity by design.
The central finding is that the measured degree of regressivity hinges on the treatment of extreme assessment ratios. Under a lenient 1/99 trim, the within-market elasticity of the assessment ratio with respect to price is −0.34 (−0.08 under a rank instrument in the spirit of Clapp, 1990) and 95% of municipalities fall below the IAAO price-related-bias band. Under the IAAO outlier rule, which removes 9% of sales concentrated in the bottom price decile, the elasticity is −0.09 (−0.01 and insignificant under the instrument), the province-wide PRB is +0.02, the COD is 17, and three quarters of municipalities meet the vertical-equity standard. A piecewise specification shows that proportionality holds across the upper 80% of each market's price distribution and fails only in the bottom quintile.
Two patterns are invariant to the trimming rule: condominiums are assessed proportionally while single-family homes, plexes, older buildings, land-heavy properties and small municipalities remain mildly regressive, and within-municipality price-related bias widened in 2021–2022 when the post-pandemic boom pulled prices away from the rolls. The implied overpayment by the bottom within-market price decile ranges from about 6% to 65% depending on whether extreme-ratio sales are treated as market transactions, and the top decile underpays by 3–5%; narrowing that range requires sale-validation data that Quebec's registries do not currently provide.
Résultats clés
522,769
Quebec sales matched to assessment rolls, 2021–2026
625
municipalities with parcel-level roll matching
−0.34 / −0.09
assessment-ratio elasticity, lenient trim versus IAAO rule
17
province-wide COD under the IAAO outlier rule
upper 80%
share of each market's price distribution assessed proportionally
6–65%
overpayment by the bottom decile depending on outlier treatment
Contributions scientifiques
- First province-wide ratio study for a Canadian province
- 522,769 sales are matched at the parcel level to the rolls of 625 municipalities, with municipality × roll × sale-year cells (2,884) that separate statutory reference-date drift from within-market inequity by design.
- Regressivity is bounded, not pinned down
- The Cheng fixed-effects elasticity is −0.344 under a 1/99 trim and −0.088 under the IAAO 1.5 × IQR rule; the Clapp rank instrument gives −0.083 and −0.013 (insignificant); the Kochin–Parks bracket [0.656, 1.137] contains one.
- Failure is concentrated in the bottom quintile
- Piecewise slopes by within-market price quintile are 0.07, 0.89, 0.71, 1.00 and 0.95 on the baseline sample; 53% of bottom-decile sales are IAAO outliers, and the registry carries no arm's-length flag to settle their status.
- IAAO standards are met by most markets once outliers are removed
- Province-wide COD falls from 28.5 to 17.0 and PRB moves from −0.029 to +0.025; the ten largest cities post CODs of 9.2–12.3; municipalities with PRB below −0.05 drop from 95% to 24%.
- Robust anatomy of inequity
- Condominiums are assessed proportionally (trimmed elasticity 0.00) while single-family homes (−0.12), plexes (−0.12), land-heavy (−0.14) and old buildings (−0.14) stay mildly regressive; Montréal is the least regressive large city, not an exception.
- Staleness widens bias at the margin, not structurally
- The within-municipality PRB of the trimmed sample moves from −0.04 in 2021–2022 to zero from 2024; the province-wide swing is compositional; the modest redistribution implied is 5–7% overpayment by the cheapest decile and 3–5% underpayment by the most expensive.
Méthodologie
Méthodologie (5)
Cheng fixed-effects ratio regression
ln AV on ln SP within municipality × roll × sale-year cells by absorbing least squares; γ = β − 1 is the elasticity of the assessment ratio, with municipality-clustered standard errors (625 clusters).
Clapp rank instrument and measurement-error bounds
A rank instrument purges attenuation from transaction noise; the Kochin–Parks reverse-regression bracket and the implied noise shares make the errors-in-variables problem explicit (Appendix A).
IAAO ratio-study battery under five trimming rules
Median ratio, COD, PRD and PRB with bootstrap intervals for every municipality with at least 100 sales, recomputed under baseline 1/99, 3 × IQR, 1.5 × IQR (IAAO), 2.5/97.5 and 5/95 rules.
Piecewise, quantile and subgroup profiles
Piecewise-linear slopes by within-market price quintile, conditional quantiles of ln AV, subgroup elasticities by class, age, land share and market size, and horizontal-dispersion regressions.
Intra-municipal tax-shift calculation
Excess tax by within-market price decile under three sorting variables (price, assessed value, IAAO blended proxy) and two benchmarks, bracketing the redistribution at stake.
Données de recherche
- Matched sales and assessment rolls
- 745,119 Quebec residential transactions (2021–2026) matched to the triennial assessment rolls, filtered to 522,769 usable sales (471,148 under the IAAO rule) across 625 municipalities with roll vintage, land and building values, class, age and land share at the parcel level.
Reproductibilité
- Six numbered Python scripts (sample build, IAAO statistics, regressions, figures, tables, revision analyses); the revision script runs in 38 seconds on Apple silicon
- Every CSV in results/reproduced/, including 16 rev_*.csv files feeding the trimming grid, spline, tax-shift, city and bounds tables
- Ten figures and all LaTeX tables generated from results; anonymised PDF (main_anon.pdf) for journal submission
- Full LaTeX source of the 45-page paper; pre-revision PDF, review report and changelog archived in docs/
Artefacts de recherche
Historique des versions
| Version | Date | Description | Fichier |
|---|---|---|---|
| v1.1courante | octobre 2026 | Manuscrit courant tel que publié sur www.spboucher.ai (édition révisée après la révision scientifique du 2026-10-17 pour les cahiers 1–17). | PDF · 45 p. |