UQO Working Paper No. 10· v2.0· November 2026· 92 pages
The Assessment Gap in Quebec
Bounds on Vertical Inequity in Municipal Property Valuation from 522,769 Sales Matched to the Assessment Roll
The price elasticity of assessment in Quebec is bounded to [0.900, 1.05], an identified set that includes proportionality: vertical inequity is bounded but not identified.
522,769 sales are matched at the parcel level to the triennial roll in force at the sale and compared within 2,884 municipality × roll × sale-year cells. The naïve estimates read as regressive, but a placebo of the paper's own measurement-error model at exact proportionality reproduces 14 of 17 headline statistics, and the rank instrument is itself biased toward regressivity. Because the transaction records carry no arm's-length indicator, the question cannot be settled without sale validation.
Simon-Pierre Boucher — contact@spboucher.ai
[0.900, 1.05]
Identified set for the price elasticity of assessment β from indirect inference on 9 observed moments (point estimate 0.947, flat criterion between 0.925 and 1.05). It includes proportionality (β = 1) and is conditional on the parametric measurement model.
14 of 17
Headline statistics reproduced by a placebo at exact proportionality with the measured price noise and an under-recorded-price tail; on the other three the placebo is more regressive than the data.
0.656 / 0.917
Naïve within-cell estimates of β (Cheng slope, s.e. 0.029; Clapp rank instrument, s.e. 0.021) on the baseline sample; they move to 0.912 and 0.987 under the IAAO outlier rule, which removes 9.2% of sales and 53% of the bottom within-cell price decile.
0.865
Probability limit of the rank instrument under proportionality at the paper's calibration, whatever the true β: the instrument is biased toward regressivity whenever price noise exceeds assessment noise.
+0.4% [−1.3, +2.4]
Tax paid by the median dwelling of the bottom within-market decile relative to uniform assessment under the pre-specified convention (null-expected value +0.5%); the top decile is at +0.4% [−0.1, +1.0].
46%
Share of the 48,348 flagged sales tagged by rule-based non-market markers; 98% lie on the high-ratio side, 45.6% are also below two thirds of the prior roll value, and 59.7% of resales within two years fall inside the fence. The remainder cannot be classified without deed data.
12.5
Trimmed coefficient of dispersion of the median municipality; the ten largest cities post 9.2–12.3 and 30% of municipalities exceed the IAAO ceiling after trimming. Horizontal dispersion is the finding that survives the identification problem.
Abstract
Property taxes are levied on assessed values, so any relation between assessment ratios and value redistributes the burden. We match 522,769 Quebec residential sales (2021–2026) to the triennial roll in force at the sale and estimate the price elasticity of assessment, β, within municipality × roll × sale-year cells. Naïve estimates (β̂F = 0.656; Clapp rank instrument 0.917) read as regressivity, but a committed placebo of the paper's own measurement-error model with an under-recorded-price tail reproduces 14 of 17 headline statistics at β = 1 and is more regressive than the data on the other three, and the instrument is biased toward regressivity. Indirect inference bounds β to [0.900, 1.05], an identified set that includes proportionality. The flagged low-price tail carries non-market markers, and a pre-specified tax-shift convention gives +0.4% [−1.3, +2.4] for the bottom decile. Vertical inequity in Quebec assessments is bounded but not identified without sale validation.
JEL: H71, H22, R51, R31, C26
Key Results
A parcel-matched, province-wide ratio study for Quebec
The first academic province-wide ratio study for a Canadian province to combine market-timing fixed effects, measurement-error bounds and an explicit outlier-treatment grid, on 522,769 sales in 625 municipalities.
A committed placebo of the measurement model
Exact proportionality is simulated on the real cell structure with Gaussian, mixture and resampled price-noise processes, and the full battery of the paper's statistics is recomputed with the same code as the observed values.
The sign of the rank instrument's bias
Because the instrument conditions on the rank of the mismeasured price, it is biased toward regressivity at the paper's calibration; instruments built on the assessment rank alone and the price rank alone return 1.133 and 0.717.
Partial identification by indirect inference
The measurement model is fitted to within-cell moments, the flagged share and trimmed slopes; identification comes from the shape of the flagged tail alone, and the result is reported as a set rather than a point.
Validation of the flagged tail and of the trimming rule
Prior roll values, fractional ratios, repeat sales and ownership markers are used to characterise the low-price tail, and trimming on the ratio is shown to be selection on the outcome, so the trimmed slope is a censored estimate rather than a bound.
Subgroup ordering reread as price noise
The ordering of subgroups (condominiums closest to proportional; plexes, old buildings, land-heavy properties and small municipalities furthest) is reproduced by the β = 1 placebo with each subgroup's own noise share, so it measures where sale prices are noisiest, not where assessors fail.
Peer review
This paper went through a multi-referee review: 6 referee reports and 70 review items. The version presented on this page is the revised manuscript. Scores are on a 0–100 scale and are a diagnostic of the manuscript, not an acceptance probability.
Score after revision
70.2/100
58.6 before review · +11.6
Review dated November 4, 2026
- Review decision
- claims not supported as written → reframed and revised
- Scientific integrity
- PASS
- Reproducibility
- R1reproduced from documented analysis data
- Maturity
- Bone revision cycle from submission
- Referee reports
- 6
- Review items
- 70
Scores by dimension
Before reviewAfter revision
- Originality & contribution61.8 → 66.0
- Scientific rigor56.3 → 69.0
- Identification & methodology53.2 → 68.0
- Data & reproducibility52.8 → 70.0
- Robustness & validation64.2 → 76.0
- Writing71.8 → 72.0
- Figures & tables66.2 → 80.0
- Literature positioning61.2 → 78.0
Revised manuscript92 pages14 figures42 tables11 equations69 references36,981 words
What the review changed
Peer review changed the paper's thesis. The earlier version read its estimates as bounds on a real but modest regressivity; referees showed that exact proportionality with the paper's own measured price noise reproduces the headline numbers. The revised paper concludes that vertical inequity in Quebec assessments is bounded but not identified without sale validation.
- Thesis: modest regressivity concentrated at the bottom of each market → an identified set of [0.900, 1.05] for the price elasticity of assessment, which includes proportionality.
- Rank instrument: treated as a correction for measurement error → shown to be biased toward regressivity (probability limit 0.865 under proportionality at the paper's calibration).
- Tax shift for the bottom decile: an overpayment of about 5–7% → +0.4% [−1.3, +2.4] under a pre-specified convention, with a null-expected value of +0.5%.
- Subgroup ordering: read as a map of valuation difficulty → reproduced by proportionality with each subgroup's own price noise.
- Flagged low-price tail: status left open → 46% tagged by non-market markers, with prior-roll and repeat-sales evidence consistent with under-recorded prices; the remainder is unclassified.
- Added a committed placebo at exact proportionality that reproduces 14 of 17 headline statistics.
Limitations stated in the paper
- The identified set is conditional on a parametric measurement model: identification comes from the shape of the flagged tail, the mixture tail is a modelling choice, and a different tail family could move the lower edge.
- No usable bootstrap interval exists for the indirect-inference point estimate; the criterion profile is the only precision statement.
- The nature of the transaction feed is not documented in the paper, no deed was read and no validated sample exists; rule-based markers tag 46% of the flagged tail and the remainder is unclassified.
- Match attrition is price-dependent (83% matched in the bottom raw price decile against 90% in the top) and prices below $50,000 are absent, so selection is strongest in the segment the paper cannot classify.
Data
Transactions matched to the roll in force
A compiled file of 745,119 residential-market transactions recorded in Quebec between January 2021 and July 2026, matched at the parcel level on coordinates and validated on the recorded roll value; in the estimation sample the median match distance is 0.4 metres and every sale reproduces the roll's assessed value exactly. The records do not state whether a sale was at arm's length.
Estimation sample and cells
522,769 sales in 625 municipalities and 2,884 municipality × roll × sale-year cells of at least 20 sales: 345,053 single-family homes, 81,693 plexes, 81,461 condominiums, 9,287 cottages, 4,701 mobile homes and 574 other residential units. Ratios are trimmed at the 1st and 99th percentiles within roll vintage.
IAAO-trimmed sample
The 1.5 interquartile-range rule applied within each cell flags 48,348 sales (9.2%); the retained sample has 471,148 sales and is used wherever trimmed statistics are reported, alongside a grid of intermediate rules and screens that do not use the assessed value.
Assessment rolls
Georeferenced municipal assessment rolls published under the Québec open-data licence (vintages 2021–2026), giving taxable value, land and building components, lot and floor area, year built, units, the statutory market-condition reference date and the value on the previous roll.
Methodology
Within-market regression tests
Cheng log-log slope, Clapp rank instrument and reverse regression within municipality × roll × sale-year cells, which hold the roll's statutory market vintage fixed, with municipality block-bootstrap and wild-cluster-bootstrap inference.
IAAO ratio-study diagnostics
Median ratio, coefficient of dispersion, price-related differential and price-related bias for the province and for municipalities with sufficient sales, under the lenient trim and under the IAAO outlier rule.
Committed placebo
Simulation under β = 1 and four lower values, twenty seeds per process, with a mixture tail of under-recorded prices calibrated to the observed share of flagged sales and its bottom-decile concentration.
Indirect inference
A diagonally weighted criterion over 9 moments is profiled over β on a grid with nuisance parameters re-optimised at each point; the identified set is the grid values whose criterion lies within 3.84 of the grid minimum.
Pre-specified tax-shift convention
IAAO outlier rule, sorting on a blended value proxy and a cell-median benchmark, fixed before the numbers were read and reported next to 30 alternative conventions with their β = 1 null values.
Reproducibility
- The matching code, the sample construction and every estimation script are provided with the paper.
- A single entry point rebuilds every table, figure and in-text number from the raw file, and a test suite checks the sample schema, the chronology, the selection cascade and the headline estimates.
- The assessment rolls are public under the Québec open-data licence; the transaction records cannot be redistributed.
- Cell-level aggregates sufficient to reproduce the province-wide diagnostics, the trimming grid and the municipal compliance tables are released with the code.
Cite this paper
Boucher, S.-P. (2026). The Assessment Gap in Quebec. UQO Working Paper No. 10, Université du Québec en Outaouais.
@techreport{boucher2026wp10,
author = {Simon-Pierre Boucher},
title = {The Assessment Gap in Quebec},
institution = {Université du Québec en Outaouais, Département des sciences administratives},
number = {10},
type = {UQO Working Paper},
year = {2026},
month = {nov},
url = {https://www.spboucher.ai/research/wp10},
}More in Real Estate & Urban Economics