révision scientifique complète (editorial board, 2026-10-17)

v1.0 -> v1.1 : conclusions reformulées en bornes (élagage 1/99 vs règle IAAO 1,5 x IQR),
exposition formelle du biais d'atténuation (bornes Kochin-Parks, 1re étape Clapp), spline par
quintile de prix, transfert fiscal sous 3 tris x 2 référentiels, PRB intra-municipale par
décalage/année, grandes villes, cadre LFM vérifié, 51 références toutes vérifiées (DOI),
script 06 + 8 tables, appendix A, docs/REVIEW-REPORT.md + docs/CHANGELOG-REVISION.md.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed 22 days ago (Oct 18, 2026) parent 22f67c2 Browse files

44 changed files +2,951 −900

modified README.md +84 −43

		`@@ -4,7 +4,7 @@`
4	4	UQO Working Paper No. 10 — *Vertical and Horizontal Inequity in Municipal
5	5	Property Valuation: Evidence from 522,769 Sales Matched to the Assessment Roll*
6	6
7		−[![Paper](https://img.shields.io/badge/paper-PDF%20(29%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
	7	+[![Paper](https://img.shields.io/badge/paper-PDF%20(45%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
8	8	[![Python](https://img.shields.io/badge/python-3.11%2B-3776AB?logo=python&logoColor=white)](requirements.txt)
9	9	[![Data](https://img.shields.io/badge/data-745%2C119%20matched%20sales%20·%20parquet-4051b5)](data/raw/README.md)
10	10	[![Estimation](https://img.shields.io/badge/estimation-statsmodels%20·%20linearmodels%20(AbsorbingLS%20%2B%20IV2SLS)-4051b5)](src/wp10/models.py)
		`@@ -14,14 +14,20 @@ Property Valuation: Evidence from 522,769 Sales Matched to the Assessment Roll*`
14	14	[![Contact](https://img.shields.io/badge/contact-simon--pierre.boucher%40uqo.ca-a02020?logo=maildotru&logoColor=white)](mailto:simon-pierre.boucher@uqo.ca)
15	15
16	16	> TL;DR — Matching 522,769 Quebec residential sales (2021–2026) to the triennial
17		−> assessment rolls that tax them, this paper delivers the **first province-wide audit
18		−> of property-assessment equity in Canada**. Within the same municipality × roll ×
19		−> year, the elasticity of the assessment ratio w.r.t. price is −0.34 (Cheng FE)
20		−> and still −0.08 under Clapp's measurement-error-robust IV. **99% of
21		−> municipalities fail the IAAO uniformity standard, 95%** fail its vertical-equity
22		−> standard — Montréal is the lone progressive large market. The median dwelling in the
23		−> bottom local price decile pays ~65% more property tax than uniform assessment
24		−> would imply; the top decile pays ~5% less.
	17	+> assessment rolls that tax them, this paper delivers the first province-wide ratio
	18	+> study of assessment equity for a Canadian province. Its central finding is that the
	19	+> measured regressivity hinges on the treatment of extreme assessment ratios. Under a
	20	+> lenient 1/99 trim the within-market elasticity of the assessment ratio w.r.t. price is
	21	+> −0.34 (Cheng FE) and −0.08 under Clapp's rank IV, and 95% of municipalities fail
	22	+> the IAAO vertical-equity band. Under the IAAO outlier rule (1.5 × IQR within cell,
	23	+> 9% of sales, 53% of the bottom price decile) the elasticity is −0.09 (IV: −0.01,
	24	+> n.s.), the province-wide PRB is +0.02, the COD is 17, the ten largest cities post CODs
	25	+> of 9–12 and three quarters of municipalities comply. Proportionality holds across the
	26	+> upper 80% of each market's price distribution under either treatment. Invariant to the
	27	+> rule: condos are assessed proportionally, single-family/plex/old/land-heavy/small-market
	28	+> dwellings are (mildly) regressive, and within-municipality PRB widened in 2021–2022.
	29	+> The bottom decile overpays 6–65% depending on the treatment; the top decile
	30	+> underpays 3–5%.
25	31
26	32	---
27	33
		`@@ -29,9 +35,9 @@ Property Valuation: Evidence from 522,769 Sales Matched to the Assessment Roll*`
29	35
30	36	\| Item \| Value \|
31	37	\|---\|---\|
32		−\| Version \| 1.0 (August 2026) \|
	38	+\| Version \| 1.1 (October 2026) — revised 2026-10-17 by the editorial-board review (see `docs/`) \|
33	39	\| SSRN \| not yet submitted \|
34		−\| Journal \| not yet submitted \|
	40	+\| Journal \| not yet submitted — target Regional Science and Urban Economics (fallback National Tax Journal); anonymous PDF in `Recherche-UQO/_soumissions/revues/assessment-gap-quebec/` \|
35	41	\| Code & data \| reproducible from `scripts/` (see Quick start); raw parquet snapshot not redistributed \|
36	42
37	43	## 📖 Table of contents
		`@@ -69,25 +75,36 @@ ln AV_i = α_c(i) + β · ln SP_i + ε_i (c = municipality × roll × sale-`
69	75	ratio studies toward spurious regressivity;
70	76	- the full IAAO ratio-study battery (median ratio, COD, PRD, PRB) with
71	77	bootstrap CIs is computed for every municipality with ≥ 100 usable sales;
72		−- quantile profiles, subgroup elasticities, horizontal-dispersion regressions and
73		− an exact intra-municipal tax-shift calculation complete the audit.
	78	+- the Kochin–Parks reverse-regression bound and the Clapp first stage make the
	79	+ measurement-error problem explicit (Appendix A);
	80	+- every statistic is re-computed under five outlier-trimming rules (baseline 1/99
	81	+ by vintage, 3 × IQR, 1.5 × IQR = IAAO Appendix B, 2.5/97.5 and 5/95 within cell);
	82	+- piecewise-linear and quantile profiles, subgroup elasticities (baseline and trimmed),
	83	+ horizontal-dispersion regressions and an intra-municipal tax-shift calculation
	84	+ under three sorting variables and two benchmarks complete the audit.
74	85
75	86	## 🏆 Headline results
76	87
77		−\| Object \| Estimate \|
78		−\|---\|---\|
79		−\| Cheng elasticity, pooled OLS \| β = 0.812 (0.029) \|
80		−\| Cheng elasticity, cell FE \| β = 0.656 (0.029) → γ = −0.344 \|
81		−\| Clapp rank-IV (error-robust) \| β = 0.917 (0.021) → γ = −0.083 \|
82		−\| Quantile profile β(τ), τ = .10 → .90 \| 0.87 → 0.49 (failure concentrated at the top) \|
83		−\| Province-wide PRB (2021 / 2024) \| −0.104 / −0.002 (staleness mechanism) \|
84		−\| Municipalities with PRB < 0 \| 99% (95% below IAAO band) \|
85		−\| Median municipality COD \| 26 (IAAO ceiling: 15) \|
86		−\| Excess tax, bottom ↔ top local decile \| +65% ↔ −5% (median) \|
87		−\| The exception \| Montréal: PRB +0.07, progressive in all 6 years \|
88		−
89		−Sub-group anatomy: condos γ = −0.12 vs single-family −0.45 / plex −0.49;
90		−land share > 0.4 → −0.50; age > 60 y → −0.43; large markets (>10k sales) −0.27.
	88	+\| Object \| Baseline (1/99 trim by vintage) \| IAAO-trimmed (1.5 × IQR within cell) \|
	89	+\|---\|---\|---\|
	90	+\| Sales \| 522,769 \| 471,148 (9.2% dropped; 53% of bottom price decile) \|
	91	+\| Cheng elasticity, cell FE: γ = β − 1 \| −0.344 (0.029) \| −0.088 (0.013) \|
	92	+\| Clapp rank-IV γ \| −0.083 (0.021) \| −0.013 (0.009), n.s. \|
	93	+\| Kochin–Parks bracket [β_F, 1/β_R] \| [0.656, 1.137] — contains 1 \| — \|
	94	+\| Province-wide COD / PRD / PRB \| 28.5 / 1.072 / −0.029 \| 17.0 / 1.004 / +0.025 \|
	95	+\| Municipalities (≥100 sales): COD > 15 \| 99% of 261 \| 30% of 241 \|
	96	+\| Municipalities: PRB < −0.05 / < −0.10 \| 95% / 84% \| 24% / 5% \|
	97	+\| Piecewise β by within-market price quintile (Q1 … Q5) \| 0.07, 0.89, 0.71, 1.00, 0.95 \| Q1 0.87, Q5 0.95 \|
	98	+\| Quantile β(τ), τ = .10 → .90 (conditional ln AV) \| 0.87 → 0.49 \| — \|
	99	+\| Ten largest cities: COD / PRB \| 16.9–30.5 / −0.39 to +0.07 \| 9.2–12.3 / −0.056 to +0.027 \|
	100	+\| Within-municipality median PRB, 2021–22 vs 2024–26 \| ≈ −0.2 every year (no gradient) \| −0.04 vs ≈ 0 \|
	101	+\| Excess tax, bottom ↔ top decile (sorted on price, median) \| +65% ↔ −5% \| +6.6% ↔ −3.2% \|
	102	+\| Excess tax, sorted on IAAO blended proxy \| +5.6% ↔ −0.2% \| — \|
	103	+
	104	+Sub-group anatomy (baseline → trimmed γ_FE): condos −0.12 → 0.00; single-family −0.45 →
	105	+−0.12; plex −0.49 → −0.12; land share > 0.4: −0.50 → −0.14; age > 60 y: −0.43 → −0.14;
	106	+munis > 10k sales (8 clusters): −0.27 → −0.05. Montréal is the least regressive large
	107	+city (γ_FE −0.18 → −0.03), not an exception.
91	108
92	109	## 🗂 Repository layout
93	110
		`@@ -107,12 +124,14 @@ wp10_uqo/`
107	124	│ ├── 02_iaao_stats.py
108	125	│ ├── 03_estimate_regressions.py
109	126	│ ├── 04_make_figures.py
110		−│ └── 05_make_tables.py
	127	+│ ├── 05_make_tables.py
	128	+│ └── 06_revision_analyses.py # bounds, trimming grid, spline, alt. tax shift (2026-10-17)
111	129	├── results/
112		−│ ├── reproduced/ # every CSV the scripts emit
113		−│ └── tables/ # LaTeX tables input by the paper
	130	+│ ├── reproduced/ # every CSV the scripts emit (rev_*.csv from step 06)
	131	+│ └── tables/ # 18 LaTeX tables input by the paper
114	132	├── figures/ # 10 publication figures (PNG, 300 dpi)
115		−└── paper/ # main.tex + sections/ + references.bib → main.pdf
	133	+├── docs/ # REVIEW-REPORT.md, CHANGELOG-REVISION.md, pre-revision PDF
	134	+└── paper/ # main.tex + sections/ + appendix/ + references.bib → main.pdf
116	135	```
117	136
118	137	## 🚀 Quick start
		`@@ -126,12 +145,13 @@ python3 scripts/01_build_sample.py # 745,119 → 522,769 sales`
126	145	python3 scripts/02_iaao_stats.py # IAAO diagnostics + bootstrap
127	146	python3 scripts/03_estimate_regressions.py # FE / IV / quantile / heterogeneity / tax shift
128	147	python3 scripts/04_make_figures.py # 10 figures
129		−python3 scripts/05_make_tables.py # 10 LaTeX tables
	148	+python3 scripts/06_revision_analyses.py # bounds, trimming grid, spline, tax-shift variants (~40 s)
	149	+python3 scripts/05_make_tables.py # 18 LaTeX tables
130	150
131	151	cd paper && make # compile main.pdf (latexmk)
132	152	```
133	153
134		−Total runtime ≈ 5 minutes on an Apple-silicon laptop; peak RAM ≈ 6 GB.
	154	+Total runtime ≈ 6 minutes on an Apple-silicon laptop; peak RAM ≈ 6 GB.
135	155
136	156	## 🗃 Data
137	157
		`@@ -157,8 +177,13 @@ valid AV/SP → 1/99% ratio trim within roll vintage → cells ≥ 20 sales`
157	177	5. Heterogeneity: separate FE estimates by class, age, land share, roll lag,
158	178	municipality size, sale year.
159	179	6. Horizontal inequity: \|ln r − cell median\| regressed on characteristics.
160		−7. Tax shift: r / cell-median − 1 by within-cell price decile — exact %
161		− over/under-payment under Quebec's exemption-free ad valorem rule.
	180	+7. Tax shift: r / benchmark − 1 by within-cell decile of a sorting variable
	181	+ (sale price, IAAO blended proxy, assessed value), cell-median or revenue-neutral
	182	+ aggregate benchmark — statutory incidence under the residual-category rate.
	183	+8. Revision analyses (`scripts/06_revision_analyses.py`): Kochin–Parks reverse
	184	+ bound and implied noise shares, Clapp first stage, piecewise-linear (Sunderman)
	185	+ profile, five outlier rules × full battery, trimmed heterogeneity and city
	186	+ diagnostics, PRB by lag band/year within municipalities, time-adjusted CODs.
162	187
163	188	## 🖼 Figures & tables inventory
164	189
		`@@ -176,16 +201,23 @@ valid AV/SP → 1/99% ratio trim within roll vintage → cells ≥ 20 sales`
176	201
177	202	Tables (`results/tables/*.tex`): summary stats, IAAO province-wide, ten largest
178	203	markets, vertical regressions, quantiles, heterogeneity, horizontal, tax shift,
179		−robustness, Paglin–Fogarty.
	204	+robustness, Paglin–Fogarty, plus the revision tables `rev_trim_grid`, `rev_spline`,
	205	+`rev_taxshift_alt`, `rev_het_trimmed`, `rev_cities`, `rev_cod`, `rev_prb_blocks`,
	206	+`rev_bounds` (Appendix A). Figures are drawn on the baseline sample; the trimmed
	207	+counterparts are tabulated.
180	208
181	209	## ⚠️ Limitations
182	210
183		−- Sales < $50k absent from the source registry; residual non-arm's-length
184		− transfers may survive screens (bottom-decile shift = upper bound).
185		−- 2021–2026 is an unusually turbulent market — levels statistics are
186		− period-specific (the within-market elasticity is not).
187		−- No appeals, renovations, or owner demographics observed.
188		−- Montréal's progressivity may partly reflect borough-level composition.
	211	+- No arm's-length flag in Quebec transaction records: 9% of sales have ratios the
	212	+ IAAO rule classifies as outliers, concentrated in the bottom price decile; whether
	213	+ they are over-assessed dwellings or nominal transfers cannot be settled, so results
	214	+ are reported as bounds (baseline = upper bound, IAAO-trimmed = lower bound).
	215	+- Sales < $50k absent from the source registry.
	216	+- 2021–2026 is an unusually turbulent market — level statistics are period-specific.
	217	+- No appeals, renovations, owner demographics or phase-in (étalement) resolutions
	218	+ observed; tax-shift figures are statutory, not economic, incidence.
	219	+- Cluster-robust SEs rest on 8 clusters for the >10k-sales band and on one
	220	+ municipality (HC-robust) for the city-level estimates.
189	221
190	222	## 📝 Citation
191	223
		`@@ -199,7 +231,8 @@ robustness, Paglin–Fogarty.`
199	231	type = {Working Paper},
200	232	number = {10},
201	233	year = {2026},
202		− month = {August}
	234	+ month = {October},
	235	+ note = {Version 1.1}
203	236	}
204	237	```
205	238
		`@@ -213,3 +246,11 @@ Université du Québec en Outaouais (UQO), Gatineau, QC.`
213	246
214	247	- Numbering: UQO Working Paper No. 10. (A June 2026 VQuant methodology paper also carried the label "WP 10"; it is now WP 13.)
215	248	- Cover page, metadata and layout follow `Recherche-UQO/HARMONISATION.md` (2026-10-17).
	249	+- Scientific revision 2026-10-17 (v1.0 → v1.1): editorial-board review report in
	250	+ `docs/REVIEW-REPORT.md`, audit trail in `docs/CHANGELOG-REVISION.md`; pre-revision
	251	+ PDF preserved as `docs/main_pre-revision-20261017.pdf` (git tag `pre-revision-20261017`).
	252	+ Headline conclusions changed: regressivity is now reported as bounds that depend on
	253	+ the outlier rule; the "Montréal exception" and the "staleness doubles inequity" claims
	254	+ of v1.0 were withdrawn after re-analysis.
	255	+- Figures are read by the paper from `figures/` (not `paper/figures/`), a deviation
	256	+ from the standard layout kept to avoid duplicating 10 PNG files.

added docs/CHANGELOG-REVISION.md +66 −0

		`@@ -0,0 +1,66 @@`
	1	+# WP 10 — Journal d'audit de la révision scientifique (2026-10-17)
	2	+
	3	+État de départ : tag `pre-revision-20261017`, `docs/main_pre-revision-20261017.pdf` (v1.0, 29 p.). État d'arrivée : v1.1, 45 p.
	4	+Aucun fichier original n'a été supprimé ; les anciens résultats (`results/reproduced/*.csv`, tables, figures) sont inchangés ; tous
	5	+les nouveaux chiffres proviennent de `scripts/06_revision_analyses.py` (38 s, laptop Apple silicon) et des tables générées par
	6	+`scripts/05_make_tables.py` (fonctions `t_rev_*`).
	7	+
	8	+## 1. Corrections majeures (où / avant / après / pourquoi / preuve)
	9	+
	10	+\| # \| Où \| Avant (v1.0) \| Après (v1.1) \| Pourquoi \| Preuve \|
	11	+\|---\|---\|---\|---\|---\|---\|
	12	+\| 1 \| Abstract, intro, résultats §6.3, conclusion \| régressivité « pervasive, large, unambiguous » : γ_FE −0,34, γ_IV −0,08 ; 95 % munis < −0,05 ; 99 % COD > 15 \| bornes : base (−0,34 / −0,08 ; 95 % ; 99 %) vs IAAO 1,5 × IQR (−0,088 (0,013) / −0,013 (0,009) n.s. ; 24 % ; 30 %) \| règle IAAO annexe B ; 53 % du décile 1 sont des outliers \| `rev_trim_grid.csv`, `rev_outlier_by_decile.csv`, Table 5 \|
	13	+\| 2 \| Intro, §6.4 (quantiles) \| « failure concentrated at the top… under-assessed at an accelerating rate » \| τ = quantile conditionnel de ln AV ; spline : β = 0,07 (Q1), 0,89, 0,71, 1,00, 0,95 → défaillance en bas \| erreur d'interprétation du quantile \| `rev_spline.csv`, Table 6, fig. 6 \|
	14	+\| 3 \| Intro, résultats, discussion, conclusion \| « PRB doubles in 2021-22 … direct evidence that infrequent revaluation is a first-order driver » \| PRB province = composition ; PRB médiane intra-muni base ≈ −0,2 toutes années ; élagué −0,044/−0,043 → ≈ 0 ; γ plat par bande \| décomposition between/within \| `rev_prb_blocks*.csv`, `rev_iaao_year_trimmed.csv`, Table 16 \|
	15	+\| 4 \| Intro, §6.1, §6.8, discussion, légendes fig. 4–5 \| « Montréal the only progressive large market, in all six years » \| γ_FE Montréal −0,18 (base) / −0,03 (élagué), γ_IV +0,03 ; 10 villes élaguées : COD 9,2–12,3, PRB −0,056 à +0,027 ; « least regressive, not an exception » \| PRB pondérée par niveaux + 49 % condos \| `rev_cities*.csv`, Table 12 \|
	16	+\| 5 \| Abstract, intro, §6.7, conclusion \| « bottom decile pays ~65 % more… top ~5 % less » \| 6–65 % selon le traitement ; +5,6 % (proxy IAAO) ; +6,6 % (élagué) ; −5,4 % si tri sur AV ; top −3 à −5 % \| tri sur prix charge le bruit u dans D1 \| `rev_taxshift_alt.csv`, `rev_trim_grid.csv`, Table 11 \|
	17	+\| 6 \| §5.3 Méthodologie, annexe A \| pas d'algèbre ; « IV = lower bound, truth lies between » \| plim β_F = β(1−λ) ; borne 1/β_R = 1,137 (contient 1) ; bruit requis 0,28 (β = 1) / 0,25 (IV) ; biais vers le haut de l'IV de Clapp (Z dépend de ε) ; Griliches–Hausman \| rigueur \| `rev_bounds.csv`, Table A.1 \|
	18	+\| 7 \| §5.2, §6.2 \| « absorbing the cell FE steepens it » (lu comme plus d'iniquité) \| ajout : amplification mécanique de l'atténuation par les EF \| Griliches & Hausman 1986 \| éq. 7 \|
	19	+\| 8 \| §3 Institutionnel \| « between 18 and 54 months elapse » ; « exact mapping… no caps » ; « appeal rates low » ; MAMH « audits rolls » \| 98,5 % ≤ 54 mois, max 102 (art. 14.2, 72) ; étalement 253.27 et 253.51 ; révision art. 124 sans statistiques ; art. 264 proportion médiane ; art. 5 MRC ; art. 244.29-30 catégorie résiduelle ; absence de déclaration de pleine concurrence \| texte de loi consolidé (LégisQuébec, 17 oct. 2026) \| `rev_misc.csv` (share_lag_gt_54 = 0,01454, max_lag = 102) \|
	20	+\| 9 \| §5.1 \| COD ≤ 15 pour tout ; PRB ±0,05 seul critère \| COD 5–15 (unifamilial ancien), 5–10 (récent), 5–20 (2–4 logements, saisonnier, mobile) ; PRB ±0,05 et IC hors ±0,10 = inacceptable (§9.2.7) ; part < −0,10 ajoutée (84 % → 5 %) \| texte IAAO 2013 \| PDF IAAO (audits2.ga.gov) \|
	21	+\| 10 \| §6.6 Horizontal \| « rises by 0.75 log points per decade » ; « land-heavy … noisy valuations » \| 0,75 point de pourcentage ; land share n.s. (+0,003, s.e. 0,030) ; R² = 0,045 \| lecture de la table \| `horizontal.csv` \|
	22	+\| 11 \| §7 Robustesse \| « t-statistics exceed 11 in every variant » ; « moves by less than 0.005 » ; « F far above thresholds » \| t > 6 (6,6 pour trim 5/95), 11 en base ; < 0,01 ; F = 2 418, coef 0,509, R² 0,59 \| calcul \| `robustness.csv`, `rev_bounds.csv` \|
	23	+\| 12 \| §4.2 Données \| classes sans les 574 « autres » ; cellules = muni × année implicite \| 574 ajoutés ; 85 muni-années à 2 rôles sur 2 798 \| vérification \| `rev_misc.csv` \|
	24	+\| 13 \| §5.2, tables 7–8 \| pas de nombre de clusters \| 625 ; 527/66/121/29 ; 540/77/8 ; villes = 1 (HC robuste) \| Cameron–Miller \| `rev_clusters.csv` \|
	25	+\| 14 \| Littérature \| voir §3 ci-dessous \| — \| — \| — \|
	26	+
	27	+## 2. Autres corrections éditoriales
	28	+
	29	+- « four times stronger » → gradient donné en chiffres ; « first province-wide evaluation… Canadian » → « first province-wide ratio study for a Canadian province » ; superlatifs retirés (« strikingly », « enormous », « almost embarrassing fidelity », « remarkably »).
	30	+- Listes à puces du §6.5 converties en prose (protocole).
	31	+- Légendes des fig. 1–10 : « baseline sample » précisé ; renvois aux tables élaguées ; fig. 6 : « decline concentrated in the four lowest vigintiles » ; fig. 7 : τ défini.
	32	+- Table 2 (IAAO) notes : normes COD par classe ; Table 4 : 1re étape ; Table 9 : trim 5/95 « pooled ».
	33	+- `\WPversion` 1.0 → 1.1 ; `\WPdate` August 2026 → October 2026 ; mots-clés + « assessment ratio », « measurement error ».
	34	+- Préambule : `url`, `pdflscape`, `placeins` (barrières de flottants) ; `\appendix` + `appendix/appendix.tex`.
	35	+- `main_anon.tex` régénéré à l'identique (titlepage_anon, pdfauthor vide) ; recherche plein texte : Boucher/UQO/Outaouais/spboucher/acknowledg = 0, « Gatineau » = 3 (nom de ville dans les tableaux, légitime).
	36	+
	37	+## 3. Références
	38	+
	39	+Retirées (6) : bell1984administrative (introuvable Crossref/Web), mpac2022vertical (introuvable), found2017property (hors sujet), baar1981property
	40	+(sans DOI ; une seule citation secondaire ; non nécessaire), clapp1990methods (non citée), quintos2020prb (titre inexistant).
	41	+Corrigées (5) : mcmillen2022allocative → `mcmillen2023measures` (JHE 61, 101950, DOI 10.1016/j.jhe.2023.101950) ; oates2016local pages 415–433 ;
	42	+cheng1974property numéro 3–4 + note RePEc ; avenancio2022assessment DOI 10.1093/qje/qjac009 ; ihlanfeldt2023appraisal → clé `ihlanfeldt2022homestead`.
	43	+DOI ajoutés à toutes les entrées existantes indexées (Crossref `api.crossref.org/works?query.bibliographic=…`, 2026-10-17).
	44	+Ajoutées (17, toutes vérifiées) :
	45	+cheng1970common 10.1086/ntj41791700 · kochin1984reply 10.1111/j.1465-7295.1984.tb00687.x · klepper1984consistent 10.2307/1911466 ·
	46	+griliches1986errors 10.1016/0304-4076(86)90058-8 · koenker1978regression 10.2307/1913643 · cameron2015practitioner 10.3368/jhr.50.2.317 ·
	47	+abadie2023clustering 10.1093/qje/qjac038 · birch2014regression 10.1080/10835547.2013.12092083 · birch2017reducing 10.63642/1357-1419.1197 ·
	48	+quintos2020gini 10.63642/1357-1419.1225 · cornia2005multifamily 10.1080/10835547.2005.12091152 · mcmillen2013appeals 10.1111/j.1540-6229.2011.00326.x ·
	49	+mcmillen2023measures 10.1016/j.jhe.2023.101950 · mcmillen2026homestead 10.1086/740783 · harris2001social 10.1068/a33128 ·
	50	+bird2012tale (Lincoln Institute, ISBN 978-1-55844-225-2, page éditeur) · gloudemans2011prb (Fair & Equitable 9(8):3-8, vérifiée par bibliographie secondaire).
	51	+Désormais citées : oates1969effects, oates2016local, slack2014political (déjà au .bib).
	52	+Sources de vérification non-Crossref : RePEc (Cheng 1974) ; lincolninst.edu (McMillen 2011, Bird et al. 2012) ; LégisQuébec (LFM) ; PDF IAAO 2013 (audits2.ga.gov).
	53	+
	54	+## 4. Réanalyses exécutées
	55	+
	56	+\| Script \| Durée \| Sorties \|
	57	+\|---\|---\|---\|
	58	+\| `scripts/06_revision_analyses.py` \| 38 s \| `rev_bounds.csv`, `rev_spline.csv`, `rev_taxshift_alt.csv`, `rev_cod.csv`, `rev_prb_blocks.csv`, `rev_prb_blocks_trimmed.csv`, `rev_iaao_year_trimmed.csv`, `rev_cities.csv`, `rev_cities_trimmed.csv`, `rev_trim.csv`, `rev_trim_taxshift.csv`, `rev_trim_grid.csv`, `rev_het_trimmed.csv`, `rev_clusters.csv`, `rev_outlier_by_decile.csv`, `rev_misc.csv` \|
	59	+\| `scripts/05_make_tables.py` (étendu) \| 2 s \| `rev_trim_grid.tex`, `rev_spline.tex`, `rev_taxshift_alt.tex`, `rev_prb_blocks.tex`, `rev_cities.tex`, `rev_het_trimmed.tex`, `rev_bounds.tex`, `rev_cod.tex` \|
	60	+
	61	+Pipeline 01–05 non relancé (résultats de base inchangés et vérifiés cohérents avec `data/processed/analysis.parquet`).
	62	+
	63	+## 5. Éléments non modifiés faute de données / hors périmètre
	64	+
	65	+Figures 1–10 (dessinées sur l'échantillon de base ; les contreparties élaguées sont tabulées) ; wild-cluster bootstrap ; validation des ventes ;
	66	+arrondissements ; recensement ; résolutions d'étalement ; dépendance spatiale.

added docs/REVIEW-REPORT.md +128 −0

		`@@ -0,0 +1,128 @@`
	1	+# WP 10 — The Assessment Gap in Quebec : rapport de l'« editorial board » (révision scientifique du 2026-10-17)
	2	+
	3	+Version examinée : 1.0 (août 2026, 29 p., tag `pre-revision-20261017`). Version produite : 1.1 (octobre 2026, 45 p.).
	4	+Données brutes présentes localement (`data/raw/*.parquet`, 100 Mo) : toutes les réanalyses ci-dessous ont été exécutées
	5	+(`scripts/06_revision_analyses.py`, 38 s) ; aucune n'est hypothétique.
	6	+
	7	+## 1. Diagnostic général
	8	+
	9	+Le papier v1.0 repose sur une construction de données remarquable (522 769 ventes appariées à la parcelle aux rôles
	10	+triennaux de 625 municipalités, cellules municipalité × rôle × année) et sur un design propre (effets fixes de cellule
	11	+exploitant la date statutaire de l'art. 46 LFM). Sa conclusion centrale (« régressivité omniprésente, large et
	12	+statistiquement sans ambiguïté ; 95 % des municipalités échouent au test IAAO ; le décile inférieur paie 65 % de trop ;
	13	+Montréal seule exception ; la staleness double l'iniquité ») n'a pas résisté à l'examen :
	14	+
	15	+1. Traitement des ratios extrêmes. Le trim 1/99 par millésime de rôle laisse dans chaque marché 6,1 % de ratios > 1,5 et
	16	+ 3,2 % > 2 (prix déclaré inférieur à la moitié de la valeur au rôle). La règle de l'annexe B de l'IAAO (1,5 × IQR intra-strate,
	17	+ limite 5–10 % pour les grands échantillons non validés) retire 9,2 % des ventes, dont 53 % du décile de prix inférieur.
	18	+ Sous cette règle : γ_FE −0,344 → −0,088 ; γ_IV −0,083 → −0,013 (n.s.) ; COD 28,5 → 17,0 ; PRD 1,072 → 1,004 ; PRB −0,029 →
	19	+ +0,025 ; part des municipalités COD > 15 : 99 % → 30 % ; PRB < −0,05 : 95 % → 24 % ; PRB < −0,10 : 84 % → 5 % ; décile 1 :
	20	+ +64,9 % → +6,6 %. La grille de cinq règles (Table 5) est monotone. Le registre québécois ne portant aucun indicateur de
	21	+ pleine concurrence, la v1.1 présente les deux traitements comme bornes (supérieure/inférieure) et discute les deux lectures.
	22	+2. Localisation de la non-proportionnalité. La v1.0 affirmait, à partir du profil quantile, que « la défaillance est
	23	+ concentrée au sommet ». Erreur d'interprétation : τ indexe la distribution conditionnelle de ln AV sachant le prix, pas la
	24	+ distribution des prix. La spline (Sunderman et al. 1990) montre β = 0,07 dans le quintile inférieur de prix intra-marché et
	25	+ 0,89 / 0,71 / 1,00 / 0,95 au-dessus : la proportionnalité tient sur les 80 % supérieurs et casse en bas, exactement où
	26	+ siègent les ratios extrêmes. Le binscatter (fig. 6) le montrait déjà.
	27	+3. Biais d'atténuation. Exposition formelle ajoutée (éq. 6–8 et annexe A) : plim β_F = β(1−λ) ; borne inverse de
	28	+ Kochin–Parks/Kennedy 1/β_R = 1,137 → l'encadrement classique [0,656 ; 1,137] contient 1 ; l'IV de Clapp (β 0,917,
	29	+ F de 1re étape 2 418) implique un écart-type de bruit transactionnel de 0,25 log-point (0,28 pour rationaliser β = 1), invraisemblable
	30	+ pour des ventes de pleine concurrence (les AVM hédoniques sur données québécoises comparables, WP 11, atteignent 14–17 % de MdAPE
	31	+ erreur de modèle comprise) mais plausible pour un registre contenant des transferts à prix nominal. L'instrument de Clapp
	32	+ dépend du rang de AV donc de ε : biais vers le haut, d'où « encadrement descriptif » et non identification ponctuelle.
	33	+ L'amplification de l'atténuation par les effets fixes (Griliches–Hausman 1986) explique le « raidissement » pooled → FE.
	34	+4. Mécanisme « staleness ». La PRB province (−0,10 en 2021-22, −0,00 en 2024) est un effet de composition : la PRB
	35	+ médiane des blocs municipalité-année (échantillon de base) est −0,19 à −0,26 toutes les années et sans gradient par bande de
	36	+ décalage (−0,21/−0,22/−0,19) ; γ_FE est plat par bande (−0,34/−0,34/−0,36). Sur l'échantillon élagué, un effet intra-municipal
	37	+ existe mais modeste : PRB −0,044 (2021), −0,043 (2022), −0,016 (2023), ≈ 0 ensuite. Reformulé : « élargit à la marge, ne génère pas ».
	38	+5. « Exception montréalaise ». γ_FE intra-Montréal = −0,18 (base) / −0,03 (élagué) ; γ_IV +0,03. La PRB positive tient à la
	39	+ composition (49 % de condos) et au caractère pondéré par les niveaux de la PRB. Après élagage, les 10 grandes villes ont COD 9,2–12,3
	40	+ et PRB −0,056 à +0,027 ; Montréal est la moins régressive, pas une exception. Retiré du titre de section, des figures et de l'abstract.
	41	+6. Transfert fiscal. Dépend de la variable de tri : décile 1 = +64,9 % (prix, médiane), +59,2 % (prix, neutre en recettes),
	42	+ +5,6 % (proxy IAAO), −5,4 % (valeur au rôle, image miroir) ; échantillon élagué +6,6 %. Hypothèses explicitées (taux unique de la
	43	+ catégorie résiduelle, étalement art. 253.27 et 253.51, incidence statutaire vs capitalisation Oates 1969). Chiffre-phare remplacé
	44	+ par un intervalle 6–65 % et un « plus défendable » de 5–7 %.
	45	+7. Inférence. 625 clusters emboîtant les cellules : correct. Mais 8 clusters pour « > 10k ventes », 66 pour condos, 1 pour chaque
	46	+ ville (HC robuste) : signalé partout. t > 11 « dans toutes les variantes » était faux (6,6 pour le trim 5/95) ; corrigé.
	47	+8. Cadre institutionnel. Vérifié sur le texte consolidé de LégisQuébec (17 oct. 2026) : art. 5 (MRC = OMRE), 14 (triennal), 14.2
	48	+ (prolongation ministérielle → décalages jusqu'à 102 mois, 1,5 % des ventes ; la v1.0 disait « 18 à 54 mois »), 46 (texte exact),
	49	+ 72 (rôle non déposé reconduit), 124 (révision), 244.29–244.30 (taux variés, catégorie résiduelle), 253.27/253.51 (étalement —
	50	+ contredit l'« exactitude » de la v1.0), 264 (proportion médiane et facteur comparatif : le Québec fait déjà une étude de niveau
	51	+ annuelle). « Taux d'appel faibles » non sourcé → retiré. Absence de déclaration de pleine concurrence ajoutée.
	52	+
	53	+## 2. Diagnostic par section (v1.0 → v1.1)
	54	+
	55	+\| Section \| Forces \| Faiblesses / erreurs trouvées \| Traitement \|
	56	+\|---\|---\|---\|---\|
	57	+\| Abstract \| clair \| surclame (« first province-wide evaluation… Canadian » ; « doubles » ; « Montréal only progressive » ; 65 %) \| réécrit en bornes \|
	58	+\| Introduction \| motivation, design \| mêmes surclames ; « statistically unambiguous » ; quantile mal lu ; « four times stronger » \| réécrit ; 3 résultats dont le 1er qualifie les autres \|
	59	+\| Littérature \| bonne couverture US \| 2 réf. non vérifiables (Bell 1984, MPAC 2022), 1 titre inventé (Quintos « gradient boosting »), 1 réf. hors sujet (Found & Tomlinson), Baar 1981 sans DOI, mcmillen2022 « online first » (publié JHE 2023) ; pas de mention des règles d'élagage ni des bornes EIV \| 6 retirées/remplacées, 17 ajoutées (toutes DOI) ; §sur l'élagage et l'incidence \|
	60	+\| Institutionnel \| pertinent \| imprécisions légales (voir 1.8) ; « exact mapping » ; « appeal rates low » \| réécrit sur le texte de loi \|
	61	+\| Données \| cascade transparente \| 574 « autres » omis ; 85 muni-années à 2 rôles non dits ; rien sur la queue des ratios \| ajoutés ; §4.3 « deux traitements » \|
	62	+\| Méthodologie \| correcte \| pas d'algèbre de l'atténuation ; PRB sans le critère ±0,10 ; COD 15 appliqué aux plex/chalets (norme 20) ; quantile mal interprété ; tax shift sans hypothèses \| éq. 1–9 ; bornes ; spline ; §incidence \|
	63	+\| Résultats \| tables générées \| « 0.75 log points » (= points de %) ; « land-heavy noisy » contredit par coefficient n.s. ; « Montréal lone progressive » ; « accelerating rate at the top » \| corrigés ; 3 sous-sections nouvelles (sensibilité, spline, grandes villes) \|
	64	+\| Robustesse \| battery utile \| t > 11 faux ; « < 0.005 » faux (0,006) ; trim 5/95 pooled ≠ base ; F « enormous » non chiffré \| corrigés ; 2 tables (COD temps, PRB blocs) ; F = 2 418 \|
	65	+\| Discussion \| mécanismes \| « doubling » ; Montréal ; absence du mécanisme n° 1 (registre) \| réécrit (4 couches, 4 leviers dont validation des ventes) \|
	66	+\| Conclusion \| — \| reprend les surclames \| réécrite \|
	67	+
	68	+## 3. Méthodologie : verdict point par point (§3 du master prompt)
	69	+
	70	+- Spécification justifiée : oui (Cheng log-log, EF cellule). Hypothèses explicites : désormais oui (éq. 6).
	71	+- Variables définies : oui ; précision ajoutée sur les cellules à deux rôles.
	72	+- Effets fixes appropriés : oui ; mais ils amplifient l'atténuation — maintenant dit.
	73	+- Dépendance spatiale/temporelle : clustering municipal emboîtant les cellules, défendable ; dépendance spatiale inter-municipale non
	74	+ traitée (limite notée). Ajustement temporel intra-année : vérifié sans effet (Table 14).
	75	+- Erreurs-types : correctes au niveau agrégé ; peu de clusters dans trois sous-groupes → signalé ; wild bootstrap recommandé (non fait).
	76	+- Construction d'échantillon transparente : oui, et désormais la décision la plus lourde (élagage) est exhibée.
	77	+- Robustesse adressant les vraies menaces : la v1.0 testait tout sauf la menace décisive ; corrigé.
	78	+- Interprétation des coefficients : quantile corrigée ; « log points » corrigé.
	79	+- Significativité statistique vs économique : les γ_IV élagués (−0,01) sont distingués des γ_FE significatifs mais petits.
	80	+- Affirmations causales : « staleness is a first-order driver » retirée ; mécanismes présentés comme interprétations.
	81	+
	82	+## 4. Littérature
	83	+
	84	+Références v1.0 : 44 ; v1.1 : 51, toutes vérifiées (Crossref via API, DOI inscrit ; RePEc pour Cheng 1974 ; pages éditeur Lincoln
	85	+Institute pour McMillen 2011 et Bird–Slack–Tassonyi 2012 ; bibliographie secondaire pour Gloudemans 2011 F&E ; texte de loi pour LFM).
	86	+Retirées : Bell 1984 (introuvable), MPAC 2022 (introuvable), Found & Tomlinson 2017 (hors sujet), Baar 1981 (sans DOI, non nécessaire),
	87	+Clapp 1990 « vacant land » (non citée), Quintos « gradient boosting » (titre inexistant → remplacée par Quintos 2020 Gini, DOI 10.63642/1357-1419.1225).
	88	+Corrigées : mcmillen2022allocative → McMillen & Singh 2023 JHE 61:101950 ; Oates & Fischel pages 415–433 ; Cheng 1974 numéro 3–4 ;
	89	+Avenancio-León & Howard DOI 10.1093/qje/qjac009 ; hodge2017, mcmillen2020, ross2012, plummer2014, etc. : DOI ajoutés.
	90	+Ajoutées (DOI) : Cheng 1970 ; Kochin & Parks 1984 (réponse) ; Klepper & Leamer 1984 ; Griliches & Hausman 1986 ; Koenker & Bassett 1978 ;
	91	+Cameron & Miller 2015 ; Abadie et al. 2023 ; Birch & Sunderman 2014 ; Birch, Sunderman & Radetsky 2017 ; Cornia & Slade 2005 ; McMillen 2013 ;
	92	+McMillen & Singh 2023, 2026 ; Harris & Lehman 2001 ; Bird, Slack & Tassonyi 2012 ; Gloudemans 2011 (PRB) ; Oates 1969 et Oates & Fischel 2016
	93	+(déjà au .bib, désormais citées).
	94	+
	95	+## 5. Résultats : incohérences trouvées et corrigées
	96	+
	97	+Voir CHANGELOG §2. Principales : abstract/intro/conclusion vs tables (65 %, « 4×», « doubles »), t-stats, « < 0.005 », « 18–54 months »,
	98	+unités du tableau horizontal, classes manquantes (574), interprétation τ, « exact » du transfert fiscal, norme COD par classe.
	99	+
	100	+## 6. Réanalyses exécutées (script 06, sorties `results/reproduced/rev_.csv`, tables `results/tables/rev_.tex`)
	101	+
	102	+Bornes EIV + 1re étape ; spline 5 segments (EF cellule, SE clusterisées) ; transfert fiscal × 3 tris × 2 référentiels + part d'outliers
	103	+par décile ; COD municipal × 3 schémas temporels ; PRB par bande de décalage et par année sur blocs muni-année (base et élagé) ;
	104	+γ_FE/γ_IV des 10 grandes villes (base et élagé) ; grille de 5 règles d'élagage × batterie complète ; hétérogénéité élagée ; comptes de clusters.
	105	+
	106	+## 7. Analyses recommandées, non exécutées
	107	+
	108	+- Wild-cluster bootstrap (Cameron–Miller) pour les sous-groupes à 8 et 66 clusters.
	109	+- Validation des ventes : appariement au Registre foncier (acte, lien vendeur-acheteur, succession, prix « 1 $ et autres considérations »)
	110	+ pour trancher la nature des 9 % de ratios extrêmes — la extension décisive ; données non disponibles dans le dépôt.
	111	+- Analyse par arrondissement à Montréal et par unité de voisinage du rôle (`role_unite_voisinage`, présent dans les données brutes).
	112	+- Liaison aux caractéristiques de recensement (incidence par revenu).
	113	+- Prise en compte des résolutions d'étalement (art. 253.27) par municipalité pour un transfert fiscal exact.
	114	+- Dépendance spatiale des erreurs d'évaluation (Moran, SE Conley).
	115	+
	116	+## 8. Limites restantes
	117	+
	118	+Absence d'indicateur de pleine concurrence (borne irréductible) ; troncature < 50 k$ ; période 2021-26 atypique ; révisions/rénovations
	119	+non observées ; incidence statutaire ; peu de clusters dans trois sous-groupes.
	120	+
	121	+## 9. Maturité pour publication
	122	+
	123	+Cible : Regional Science and Urban Economics (repli National Tax Journal). La v1.1 est honnête et défendable ; sa contribution
	124	+est désormais double (première ratio study provinciale canadienne ; démonstration que l'« assessment gap » mesuré dépend de la règle
	125	+d'élagage — un point méthodologique transférable à la littérature US). Risques de rejet : (i) un rapporteur peut juger la conclusion
	126	+« entre les bornes » insuffisamment tranchée — la réponse est l'extension « validation des ventes » ; (ii) RSUE attendra davantage de
	127	+spatial (arrondissements, voisinages) ; (iii) NTJ demandera l'incidence par revenu. Recommandation : soumettre à NTJ ou au *Journal of
	128	+Housing Economics* en l'état ; pour RSUE, ajouter l'analyse par unité de voisinage avant soumission.

added paper/appendix/appendix.tex +57 −0

		`@@ -0,0 +1,57 @@`
	1	+% Author: Simon-Pierre Boucher — contact@spboucher.ai
	2	+% ============================================================================
	3	+\section{Measurement-error bounds and first stage}
	4	+\label{app:bounds}
	5	+
	6	+This appendix derives the bounds used in Section~\ref{sec:meas} and
	7	+reports the moments behind them. Write the within-cell demeaned variables
	8	+as in equation~\eqref{eq:me}, $\ln SP_i = \ln V_i + u_i$ and $\ln AV_i =
	9	+\beta \ln V_i + \varepsilon_i$, with $u_i$, $\varepsilon_i$ and $\ln V_i$
	10	+mutually uncorrelated and $\sigma^2_V$, $\sigma^2_u$, $\sigma^2_\varepsilon$
	11	+their variances. The observable within-cell moments are
	12	+\begin{equation}
	13	+\operatorname{Var}(\ln SP) = \sigma^2_V + \sigma^2_u, \qquad
	14	+\operatorname{Var}(\ln AV) = \beta^2\sigma^2_V + \sigma^2_\varepsilon, \qquad
	15	+\operatorname{Cov}(\ln AV, \ln SP) = \beta\,\sigma^2_V .
	16	+\label{eq:moments}
	17	+\end{equation}
	18	+The forward slope is $\hat\beta_F = \operatorname{Cov}/\operatorname{Var}(\ln
	19	+SP) \to \beta\sigma^2_V/(\sigma^2_V+\sigma^2_u) \le \beta$, and the inverse
	20	+of the reverse slope is $1/\hat\beta_R = \operatorname{Var}(\ln
	21	+AV)/\operatorname{Cov} \to \beta + \sigma^2_\varepsilon/(\beta\sigma^2_V)
	22	+\ge \beta$, which gives equation~\eqref{eq:bounds}. Given $\hat\beta_F$,
	23	+the noise share $\lambda = \sigma^2_u/\operatorname{Var}(\ln SP)$ that would
	24	+rationalise a true elasticity $\beta^\ast$ is $\lambda = 1 -
	25	+\hat\beta_F/\beta^\ast$, and the implied standard deviation of transaction
	26	+noise is $\sqrt{\lambda\operatorname{Var}(\ln SP)}$. Table~\ref{tab:bounds}
	27	+reports the moments, the bounds, the noise shares implied by $\beta^\ast =
	28	+1$ and by the Clapp estimate, and the first stage of the Clapp instrument.
	29	+Three features deserve comment. The bracket $[0.656, 1.137]$ contains one,
	30	+so the classical errors-in-variables model alone cannot establish
	31	+regressivity on the baseline sample; this is a property of the large
	32	+assessment-error variance (the within-cell correlation is 0.76), not of
	33	+the sample size. Rationalising proportionality requires a transaction-noise
	34	+standard deviation of 0.28 log points, and the Clapp estimate itself
	35	+implies 0.25; both exceed the out-of-sample dispersion of hedonic
	36	+predictions around prices on comparable Quebec data, which suggests that
	37	+part of the ``noise'' the instrument discounts is non-market sales rather
	38	+than bargaining dispersion. The first stage is strong by any standard, so
	39	+the instrument's limitation is the dependence of $Z$ on the assessment
	40	+rank discussed in Section~\ref{sec:meas}, not weak identification.
	41	+
	42	+\begin{table}[h]
	43	+\centering
	44	+\begin{threeparttable}
	45	+\caption{Within-cell moments, measurement-error bounds and Clapp first stage, baseline sample}
	46	+\label{tab:bounds}
	47	+\small
	48	+\input{../results/tables/rev_bounds}
	49	+\begin{tablenotes}[flushleft]\footnotesize
	50	+\item \textit{Notes:} All moments are computed on variables demeaned
	51	+within the 2{,}884 municipality~$\times$~roll~$\times$~sale-year cells.
	52	+The first-stage regression is of the demeaned $\ln SP$ on $Z \in
	53	+\{-1,0,+1\}$ with municipality-clustered standard errors; $F$ is the
	54	+square of the cluster-robust $t$-statistic.
	55	+\end{tablenotes}
	56	+\end{threeparttable}
	57	+\end{table}

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modified paper/main.tex +39 −24

		`@@ -30,6 +30,9 @@`
30	30	\usepackage{booktabs}
31	31	\usepackage{threeparttable}
32	32	\usepackage{makecell}
	33	+\usepackage{url}
	34	+\usepackage{pdflscape}
	35	+\usepackage{placeins}
33	36
34	37	% ---------------------------------------------------------------- figures
35	38	\usepackage{graphicx}
		`@@ -66,9 +69,9 @@`
66	69	\newcommand{\WPtitle}{The Assessment Gap in Quebec}
67	70	\newcommand{\WPsubtitle}{Vertical and Horizontal Inequity in Municipal Property
68	71	Valuation: Evidence from 522{,}769 Sales Matched to the Assessment Roll}
69		−\newcommand{\WPdate}{August 2026}
70		−\newcommand{\WPversion}{1.0}
71		−\newcommand{\WPkeywords}{property tax, assessment, vertical equity, regressivity, ratio study, Quebec}
	72	+\newcommand{\WPdate}{October 2026}
	73	+\newcommand{\WPversion}{1.1}
	74	+\newcommand{\WPkeywords}{property tax, assessment ratio, vertical equity, regressivity, ratio study, measurement error, Quebec}
72	75	\newcommand{\WPjel}{H71, H22, R51, R31}
73	76
74	77	\newcommand{\WPauthor}{Simon-Pierre Boucher}
		`@@ -80,27 +83,36 @@`
80	83
81	84	\newcommand{\WPabstract}{%
82	85	Municipal property taxes are levied on assessed values, so any systematic
83		−relationship between assessment accuracy and market value silently
84		−redistributes the tax burden. Matching 522{,}769 residential transactions
85		−from 2021--2026 to the triennial assessment rolls of 625 Quebec
86		−municipalities at the parcel level, we provide the first province-wide
87		−evaluation of vertical and horizontal equity in Canadian property assessment.
88		−Assessment ratios decline steeply with price: within
89		−municipality~$\times$~roll~$\times$~sale-year markets, the elasticity of the
90		−assessment ratio with respect to the sale price is $-0.34$, and a rank-based
91		−instrumental-variable estimator in the spirit of \mbox{Clapp (1990)}---which
92		−purges the attenuation bias that pushes least-squares tests toward spurious
93		−regressivity---still yields $-0.08$ ($t\approx4$). IAAO ratio-study
94		−diagnostics place 95\% of municipalities below the acceptable price-related
95		−bias band and 99\% above the COD uniformity ceiling; Montr\'eal is the only
96		−large market whose assessments are progressive. Regressivity is strongest for
97		−single-family homes, older buildings, properties with a high assessed land
98		−share, and smaller municipalities, and it doubles in years when market prices
99		−decouple from the rolls' reference dates, pointing to infrequent revaluation
100		−as a first-order mechanism. The implied intra-municipal tax shift is large:
101		−the median dwelling in the bottom within-market price decile pays roughly
102		−65\% more property tax than it would under uniform assessment, while the top
103		−decile pays about 5\% less.}
	86	+relationship between assessment ratios and market value redistributes the
	87	+tax burden within a municipality. We match 522{,}769 residential sales
	88	+recorded in Quebec between 2021 and 2026 to the triennial assessment rolls
	89	+of 625 municipalities at the parcel level and provide the first
	90	+province-wide ratio study of vertical and horizontal assessment equity for
	91	+a Canadian province. Because the \textit{Loi sur la fiscalit\'e
	92	+municipale} pins every roll to a single statutory market-condition date,
	93	+municipality~$\times$~roll~$\times$~sale-year fixed effects separate the
	94	+mechanical drift of ratios between reference dates from within-market
	95	+inequity by design. The central finding is that the measured degree of
	96	+regressivity hinges on the treatment of extreme assessment ratios. Under a
	97	+lenient 1/99 trim, the within-market elasticity of the assessment ratio
	98	+with respect to price is $-0.34$ ($-0.08$ under a rank instrument in the
	99	+spirit of Clapp, 1990) and 95\% of municipalities fall below the IAAO
	100	+price-related-bias band. Under the IAAO outlier rule, which removes 9\% of
	101	+sales concentrated in the bottom price decile, the elasticity is $-0.09$
	102	+($-0.01$ and insignificant under the instrument), the province-wide PRB is
	103	+$+0.02$, the COD is 17, and three quarters of municipalities meet the
	104	+vertical-equity standard. A piecewise specification shows that
	105	+proportionality holds across the upper 80\% of each market's price
	106	+distribution and fails only in the bottom quintile. Two patterns are
	107	+invariant to the trimming rule: condominiums are assessed proportionally
	108	+while single-family homes, plexes, older buildings, land-heavy properties
	109	+and small municipalities remain mildly regressive, and within-municipality
	110	+price-related bias widened in 2021--2022 when the post-pandemic boom pulled
	111	+prices away from the rolls. The implied overpayment by the bottom
	112	+within-market price decile ranges from about 6\% to 65\% depending on
	113	+whether extreme-ratio sales are treated as market transactions, and the top
	114	+decile underpays by 3--5\%; narrowing that range requires sale-validation
	115	+data that Quebec's registries do not currently provide.}
104	116
105	117	\hypersetup{pdftitle={The Assessment Gap in Quebec}, pdfauthor={Simon-Pierre Boucher}}
106	118
		`@@ -119,6 +131,9 @@ decile pays about 5\% less.}`
119	131	\input{sections/discussion}
120	132	\input{sections/conclusion}
121	133
	134	+\appendix
	135	+\input{appendix/appendix}
	136	+
122	137	\newpage
123	138	\bibliography{references}
124	139

modified paper/main_anon.pdf +0 −0

Binary file not shown.

modified paper/main_anon.tex +39 −24

		`@@ -30,6 +30,9 @@`
30	30	\usepackage{booktabs}
31	31	\usepackage{threeparttable}
32	32	\usepackage{makecell}
	33	+\usepackage{url}
	34	+\usepackage{pdflscape}
	35	+\usepackage{placeins}
33	36
34	37	% ---------------------------------------------------------------- figures
35	38	\usepackage{graphicx}
		`@@ -66,9 +69,9 @@`
66	69	\newcommand{\WPtitle}{The Assessment Gap in Quebec}
67	70	\newcommand{\WPsubtitle}{Vertical and Horizontal Inequity in Municipal Property
68	71	Valuation: Evidence from 522{,}769 Sales Matched to the Assessment Roll}
69		−\newcommand{\WPdate}{August 2026}
70		−\newcommand{\WPversion}{1.0}
71		−\newcommand{\WPkeywords}{property tax, assessment, vertical equity, regressivity, ratio study, Quebec}
	72	+\newcommand{\WPdate}{October 2026}
	73	+\newcommand{\WPversion}{1.1}
	74	+\newcommand{\WPkeywords}{property tax, assessment ratio, vertical equity, regressivity, ratio study, measurement error, Quebec}
72	75	\newcommand{\WPjel}{H71, H22, R51, R31}
73	76
74	77	\newcommand{\WPauthor}{Simon-Pierre Boucher}
		`@@ -80,27 +83,36 @@`
80	83
81	84	\newcommand{\WPabstract}{%
82	85	Municipal property taxes are levied on assessed values, so any systematic
83		−relationship between assessment accuracy and market value silently
84		−redistributes the tax burden. Matching 522{,}769 residential transactions
85		−from 2021--2026 to the triennial assessment rolls of 625 Quebec
86		−municipalities at the parcel level, we provide the first province-wide
87		−evaluation of vertical and horizontal equity in Canadian property assessment.
88		−Assessment ratios decline steeply with price: within
89		−municipality~$\times$~roll~$\times$~sale-year markets, the elasticity of the
90		−assessment ratio with respect to the sale price is $-0.34$, and a rank-based
91		−instrumental-variable estimator in the spirit of \mbox{Clapp (1990)}---which
92		−purges the attenuation bias that pushes least-squares tests toward spurious
93		−regressivity---still yields $-0.08$ ($t\approx4$). IAAO ratio-study
94		−diagnostics place 95\% of municipalities below the acceptable price-related
95		−bias band and 99\% above the COD uniformity ceiling; Montr\'eal is the only
96		−large market whose assessments are progressive. Regressivity is strongest for
97		−single-family homes, older buildings, properties with a high assessed land
98		−share, and smaller municipalities, and it doubles in years when market prices
99		−decouple from the rolls' reference dates, pointing to infrequent revaluation
100		−as a first-order mechanism. The implied intra-municipal tax shift is large:
101		−the median dwelling in the bottom within-market price decile pays roughly
102		−65\% more property tax than it would under uniform assessment, while the top
103		−decile pays about 5\% less.}
	86	+relationship between assessment ratios and market value redistributes the
	87	+tax burden within a municipality. We match 522{,}769 residential sales
	88	+recorded in Quebec between 2021 and 2026 to the triennial assessment rolls
	89	+of 625 municipalities at the parcel level and provide the first
	90	+province-wide ratio study of vertical and horizontal assessment equity for
	91	+a Canadian province. Because the \textit{Loi sur la fiscalit\'e
	92	+municipale} pins every roll to a single statutory market-condition date,
	93	+municipality~$\times$~roll~$\times$~sale-year fixed effects separate the
	94	+mechanical drift of ratios between reference dates from within-market
	95	+inequity by design. The central finding is that the measured degree of
	96	+regressivity hinges on the treatment of extreme assessment ratios. Under a
	97	+lenient 1/99 trim, the within-market elasticity of the assessment ratio
	98	+with respect to price is $-0.34$ ($-0.08$ under a rank instrument in the
	99	+spirit of Clapp, 1990) and 95\% of municipalities fall below the IAAO
	100	+price-related-bias band. Under the IAAO outlier rule, which removes 9\% of
	101	+sales concentrated in the bottom price decile, the elasticity is $-0.09$
	102	+($-0.01$ and insignificant under the instrument), the province-wide PRB is
	103	+$+0.02$, the COD is 17, and three quarters of municipalities meet the
	104	+vertical-equity standard. A piecewise specification shows that
	105	+proportionality holds across the upper 80\% of each market's price
	106	+distribution and fails only in the bottom quintile. Two patterns are
	107	+invariant to the trimming rule: condominiums are assessed proportionally
	108	+while single-family homes, plexes, older buildings, land-heavy properties
	109	+and small municipalities remain mildly regressive, and within-municipality
	110	+price-related bias widened in 2021--2022 when the post-pandemic boom pulled
	111	+prices away from the rolls. The implied overpayment by the bottom
	112	+within-market price decile ranges from about 6\% to 65\% depending on
	113	+whether extreme-ratio sales are treated as market transactions, and the top
	114	+decile underpays by 3--5\%; narrowing that range requires sale-validation
	115	+data that Quebec's registries do not currently provide.}
104	116
105	117	\hypersetup{pdftitle={The Assessment Gap in Quebec}, pdfauthor={}}
106	118
		`@@ -119,6 +131,9 @@ decile pays about 5\% less.}`
119	131	\input{sections/discussion}
120	132	\input{sections/conclusion}
121	133
	134	+\appendix
	135	+\input{appendix/appendix}
	136	+
122	137	\newpage
123	138	\bibliography{references}
124	139

modified paper/references.bib +344 −198

		`@@ -1,5 +1,8 @@`
1		−@comment{ Author: Simon-Pierre Boucher (contact at spboucher.ai) -- Bibliography for UQO Working Paper No 10 }
	1	+@comment{ Author: Simon-Pierre Boucher (contact at spboucher.ai) -- Bibliography for UQO Working Paper No 10.
	2	+ Revised 2026-10-17: every entry verified against Crossref (DOI recorded) or the publisher's page;
	3	+ see docs/CHANGELOG-REVISION.md for the verification log. }
2	4
	5	+% ------------------------------------------------------------------ ratio-study tests
3	6	@article{paglin1972equity,
4	7	author = {Paglin, Morton and Fogarty, Michael},
5	8	title = {Equity and the Property Tax: A New Conceptual Focus},
		`@@ -7,17 +10,30 @@`
7	10	year = {1972},
8	11	volume = {25},
9	12	number = {4},
10		− pages = {557--565}
	13	+ pages = {557--565},
	14	+ doi = {10.1086/ntj41791839}
	15	+}
	16	+
	17	+@article{cheng1970common,
	18	+ author = {Cheng, Pao Lun},
	19	+ title = {The Common Level of Assessment in Property Taxation},
	20	+ journal = {National Tax Journal},
	21	+ year = {1970},
	22	+ volume = {23},
	23	+ number = {1},
	24	+ pages = {50--65},
	25	+ doi = {10.1086/ntj41791700}
11	26	}
12	27
13	28	@article{cheng1974property,
14	29	author = {Cheng, Pao Lun},
15	30	title = {Property Taxation, Assessment Performance, and Its Measurement},
16		− journal = {Public Finance},
	31	+ journal = {Public Finance / Finances Publiques},
17	32	year = {1974},
18	33	volume = {29},
19		− number = {3},
20		− pages = {268--284}
	34	+ number = {3--4},
	35	+ pages = {268--284},
	36	+ note = {RePEc: pfi:pubfin:v:29:y:1974:i:3-4:p:268-84}
21	37	}
22	38
23	39	@article{kochin1982vertical,
		`@@ -27,27 +43,30 @@`
27	43	year = {1982},
28	44	volume = {20},
29	45	number = {4},
30		− pages = {511--532}
	46	+ pages = {511--532},
	47	+ doi = {10.1111/j.1465-7295.1982.tb00364.x}
31	48	}
32	49
33		−@article{bell1984administrative,
34		− author = {Bell, Earl J.},
35		− title = {Administrative Inequity and Property Assessment: The Case for the Traditional Approach},
36		− journal = {Property Tax Journal},
	50	+@article{kennedy1984unfair,
	51	+ author = {Kennedy, Peter},
	52	+ title = {On an Unfair Appraisal of Vertical Equity in Real Estate Assessment},
	53	+ journal = {Economic Inquiry},
37	54	year = {1984},
38		− volume = {3},
	55	+ volume = {22},
39	56	number = {2},
40		− pages = {123--131}
	57	+ pages = {287--290},
	58	+ doi = {10.1111/j.1465-7295.1984.tb00686.x}
41	59	}
42	60
43		−@article{kennedy1984unfair,
44		− author = {Kennedy, Peter},
45		− title = {On an Unfair Appraisal of Vertical Equity in Real Estate Assessment},
	61	+@article{kochin1984reply,
	62	+ author = {Kochin, Levis A. and Parks, Richard W.},
	63	+ title = {Vertical Equity in Real Estate Assessment: Reply to {Kennedy}},
46	64	journal = {Economic Inquiry},
47	65	year = {1984},
48	66	volume = {22},
49	67	number = {2},
50		− pages = {287--290}
	68	+ pages = {291--296},
	69	+ doi = {10.1111/j.1465-7295.1984.tb00687.x}
51	70	}
52	71
53	72	@article{sunderman1990testing,
		`@@ -57,7 +76,8 @@`
57	76	year = {1990},
58	77	volume = {5},
59	78	number = {3},
60		− pages = {319--334}
	79	+ pages = {319--334},
	80	+ doi = {10.1080/10835547.1990.12090625}
61	81	}
62	82
63	83	@article{clapp1990new,
		`@@ -67,7 +87,8 @@`
67	87	year = {1990},
68	88	volume = {3},
69	89	number = {3},
70		− pages = {233--249}
	90	+ pages = {233--249},
	91	+ doi = {10.1007/BF00216188}
71	92	}
72	93
73	94	@article{sirmans1995vertical,
		`@@ -77,17 +98,41 @@`
77	98	year = {1995},
78	99	volume = {48},
79	100	number = {1},
80		− pages = {71--84}
	101	+ pages = {71--84},
	102	+ doi = {10.1086/ntj41789124}
	103	+}
	104	+
	105	+@article{goolsby1997assessment,
	106	+ author = {Goolsby, William C.},
	107	+ title = {Assessment Error in the Valuation of Owner-Occupied Housing},
	108	+ journal = {Journal of Real Estate Research},
	109	+ year = {1997},
	110	+ volume = {13},
	111	+ number = {1},
	112	+ pages = {33--45},
	113	+ doi = {10.1080/10835547.1997.12090863}
81	114	}
82	115
83	116	@article{allen2002measuring,
84	117	author = {Allen, Marcus T. and Dare, William H.},
85		− title = {Identifying Determinants of Horizontal Property Tax Inequity: Evidence from Florida},
	118	+ title = {Identifying Determinants of Horizontal Property Tax Inequity: Evidence from {Florida}},
86	119	journal = {Journal of Real Estate Research},
87	120	year = {2002},
88	121	volume = {24},
89	122	number = {2},
90		− pages = {153--164}
	123	+ pages = {153--164},
	124	+ doi = {10.1080/10835547.2002.12091091}
	125	+}
	126	+
	127	+@article{cornia2005multifamily,
	128	+ author = {Cornia, Gary C. and Slade, Barrett A.},
	129	+ title = {Property Taxation of Multifamily Housing: An Empirical Analysis of Vertical and Horizontal Equity},
	130	+ journal = {Journal of Real Estate Research},
	131	+ year = {2005},
	132	+ volume = {27},
	133	+ number = {1},
	134	+ pages = {17--46},
	135	+ doi = {10.1080/10835547.2005.12091152}
91	136	}
92	137
93	138	@article{sirmans2008vertical,
		`@@ -97,7 +142,84 @@`
97	142	year = {2008},
98	143	volume = {16},
99	144	number = {2},
100		− pages = {167--180}
	145	+ pages = {167--180},
	146	+ doi = {10.1080/10835547.2008.12090225}
	147	+}
	148	+
	149	+@article{birch2014regression,
	150	+ author = {Birch, John W. and Sunderman, Mark A.},
	151	+ title = {Regression Modeling for Vertical and Horizontal Property Tax Inequity},
	152	+ journal = {Journal of Housing Research},
	153	+ year = {2014},
	154	+ volume = {23},
	155	+ number = {1},
	156	+ pages = {89--104},
	157	+ doi = {10.1080/10835547.2013.12092083}
	158	+}
	159	+
	160	+@article{birch2017reducing,
	161	+ author = {Birch, John W. and Sunderman, Mark A. and Radetsky, Victor},
	162	+ title = {Reducing Vertical and Horizontal Inequity in Property Tax Assessments},
	163	+ journal = {Journal of Property Tax Assessment \& Administration},
	164	+ year = {2017},
	165	+ volume = {14},
	166	+ number = {2},
	167	+ pages = {71--81},
	168	+ doi = {10.63642/1357-1419.1197}
	169	+}
	170	+
	171	+@article{quintos2020gini,
	172	+ author = {Quintos, Carmela},
	173	+ title = {A {Gini} Measure for Vertical Equity in Property Assessments},
	174	+ journal = {Journal of Property Tax Assessment \& Administration},
	175	+ year = {2020},
	176	+ volume = {17},
	177	+ number = {2},
	178	+ doi = {10.63642/1357-1419.1225}
	179	+}
	180	+
	181	+@article{mcmillen2020assessment,
	182	+ author = {McMillen, Daniel and Singh, Ruchi},
	183	+ title = {Assessment Regressivity and Property Taxation},
	184	+ journal = {Journal of Real Estate Finance and Economics},
	185	+ year = {2020},
	186	+ volume = {60},
	187	+ number = {1--2},
	188	+ pages = {155--169},
	189	+ doi = {10.1007/s11146-019-09715-x}
	190	+}
	191	+
	192	+@article{mcmillen2023measures,
	193	+ author = {McMillen, Daniel and Singh, Ruchi},
	194	+ title = {Measures of Vertical Inequality in Assessments},
	195	+ journal = {Journal of Housing Economics},
	196	+ year = {2023},
	197	+ volume = {61},
	198	+ pages = {101950},
	199	+ doi = {10.1016/j.jhe.2023.101950}
	200	+}
	201	+
	202	+@article{mcmillen2026homestead,
	203	+ author = {McMillen, Daniel and Singh, Ruchi},
	204	+ title = {Assessment Regressivity and the Homestead Exemption},
	205	+ journal = {National Tax Journal},
	206	+ year = {2026},
	207	+ volume = {79},
	208	+ number = {2},
	209	+ pages = {393--407},
	210	+ doi = {10.1086/740783}
	211	+}
	212	+
	213	+% ------------------------------------------------------------------ evidence on regressivity
	214	+@article{engle1975deassessment,
	215	+ author = {Engle, Robert F.},
	216	+ title = {De Facto Discrimination in Residential Assessments: {Boston}},
	217	+ journal = {National Tax Journal},
	218	+ year = {1975},
	219	+ volume = {28},
	220	+ number = {4},
	221	+ pages = {445--451},
	222	+ doi = {10.1086/ntj41863140}
101	223	}
102	224
103	225	@article{mcmillen2008thin,
		`@@ -107,7 +229,8 @@`
107	229	year = {2008},
108	230	volume = {61},
109	231	number = {4},
110		− pages = {653--671}
	232	+ pages = {653--671},
	233	+ doi = {10.17310/ntj.2008.4.05}
111	234	}
112	235
113	236	@article{mcmillen2011assessment,
		`@@ -117,7 +240,41 @@`
117	240	year = {2011},
118	241	volume = {23},
119	242	number = {1},
120		− pages = {9--15}
	243	+ pages = {9--15},
	244	+ note = {Lincoln Institute of Land Policy}
	245	+}
	246	+
	247	+@article{mcmillen2013appeals,
	248	+ author = {McMillen, Daniel P.},
	249	+ title = {The Effect of Appeals on Assessment Ratio Distributions: Some Nonparametric Approaches},
	250	+ journal = {Real Estate Economics},
	251	+ year = {2013},
	252	+ volume = {41},
	253	+ number = {1},
	254	+ pages = {165--191},
	255	+ doi = {10.1111/j.1540-6229.2011.00326.x}
	256	+}
	257	+
	258	+@article{ross2012assessor,
	259	+ author = {Ross, Justin M.},
	260	+ title = {Interjurisdictional Determinants of Property Assessment Regressivity},
	261	+ journal = {Land Economics},
	262	+ year = {2012},
	263	+ volume = {88},
	264	+ number = {1},
	265	+ pages = {28--42},
	266	+ doi = {10.3368/le.88.1.28}
	267	+}
	268	+
	269	+@article{plummer2014evidence,
	270	+ author = {Plummer, Elizabeth},
	271	+ title = {The Effects of Property Tax Protests on the Assessment Uniformity of Residential Properties},
	272	+ journal = {Real Estate Economics},
	273	+ year = {2014},
	274	+ volume = {42},
	275	+ number = {4},
	276	+ pages = {900--937},
	277	+ doi = {10.1111/1540-6229.12080}
121	278	}
122	279
123	280	@article{hodge2017assessment,
		`@@ -127,27 +284,8 @@`
127	284	year = {2017},
128	285	volume = {45},
129	286	number = {2},
130		− pages = {237--258}
131		−}
132		−
133		−@article{mcmillen2020assessment,
134		− author = {McMillen, Daniel and Singh, Ruchi},
135		− title = {Assessment Regressivity and Property Taxation},
136		− journal = {Journal of Real Estate Finance and Economics},
137		− year = {2020},
138		− volume = {60},
139		− number = {1},
140		− pages = {155--169}
141		−}
142		−
143		−@article{avenancio2022assessment,
144		− author = {Avenancio-Le{\'o}n, Carlos F. and Howard, Troup},
145		− title = {The Assessment Gap: Racial Inequalities in Property Taxation},
146		− journal = {Quarterly Journal of Economics},
147		− year = {2022},
148		− volume = {137},
149		− number = {3},
150		− pages = {1383--1434}
	287	+ pages = {237--258},
	288	+ doi = {10.1111/1540-6229.12126}
151	289	}
152	290
153	291	@techreport{berry2021reassessing,
		`@@ -155,7 +293,8 @@`
155	293	title = {Reassessing the Property Tax},
156	294	institution = {University of Chicago, Harris School of Public Policy},
157	295	type = {Working Paper},
158		− year = {2021}
	296	+ year = {2021},
	297	+ doi = {10.2139/ssrn.3800536}
159	298	}
160	299
161	300	@techreport{amornsiripanitch2022residential,
		`@@ -164,24 +303,98 @@`
164	303	institution = {Federal Reserve Bank of Philadelphia},
165	304	type = {Working Paper},
166	305	number = {22-02},
167		− year = {2022}
	306	+ year = {2022},
	307	+ doi = {10.21799/frbp.wp.2022.02}
168	308	}
169	309
170		−@article{mcmillen2022allocative,
171		− author = {McMillen, Daniel and Singh, Ruchi},
172		− title = {Measures of Vertical Inequality in Assessments},
173		− journal = {Journal of Real Estate Finance and Economics},
	310	+@article{avenancio2022assessment,
	311	+ author = {Avenancio-Le{\'o}n, Carlos F. and Howard, Troup},
	312	+ title = {The Assessment Gap: Racial Inequalities in Property Taxation},
	313	+ journal = {Quarterly Journal of Economics},
174	314	year = {2022},
175		− volume = {online first},
176		− pages = {1--29}
	315	+ volume = {137},
	316	+ number = {3},
	317	+ pages = {1383--1434},
	318	+ doi = {10.1093/qje/qjac009}
177	319	}
178	320
	321	+@article{ihlanfeldt2022homestead,
	322	+ author = {Ihlanfeldt, Keith and Rodgers, Luke P.},
	323	+ title = {Homestead Exemptions, Heterogeneous Assessment, and Property Tax Progressivity},
	324	+ journal = {National Tax Journal},
	325	+ year = {2022},
	326	+ volume = {75},
	327	+ number = {1},
	328	+ pages = {7--31},
	329	+ doi = {10.1086/717587}
	330	+}
	331	+
	332	+% ------------------------------------------------------------------ Canada
	333	+@article{harris2001social,
	334	+ author = {Harris, Richard and Lehman, Michael},
	335	+ title = {Social and Geographic Inequities in the Residential Property Tax: A Review and Case Study},
	336	+ journal = {Environment and Planning A},
	337	+ year = {2001},
	338	+ volume = {33},
	339	+ number = {5},
	340	+ pages = {881--900},
	341	+ doi = {10.1068/a33128}
	342	+}
	343	+
	344	+@book{bird2012tale,
	345	+ author = {Bird, Richard M. and Slack, Enid and Tassonyi, Almos},
	346	+ title = {A Tale of Two Taxes: Property Tax Reform in {Ontario}},
	347	+ publisher = {Lincoln Institute of Land Policy},
	348	+ address = {Cambridge, MA},
	349	+ year = {2012},
	350	+ isbn = {978-1-55844-225-2}
	351	+}
	352	+
	353	+@article{carbonnier2024property,
	354	+ author = {Carbonnier, Cl{\'e}ment},
	355	+ title = {Property Tax Regressivity, the Case of {Qu{\'e}bec}},
	356	+ journal = {Public Finance Review},
	357	+ year = {2024},
	358	+ volume = {52},
	359	+ number = {2},
	360	+ pages = {155--181},
	361	+ doi = {10.1177/10911421231212354}
	362	+}
	363	+
	364	+@misc{lfm2026,
	365	+ author = {{Gouvernement du Qu\'ebec}},
	366	+ title = {Loi sur la fiscalit\'e municipale, {RLRQ}, c.\ {F-2.1}},
	367	+ howpublished = {L\'egisQu\'ebec, consolidated text consulted 17 October 2026, \url{https://www.legisquebec.gouv.qc.ca/fr/document/lc/F-2.1}},
	368	+ year = {2026},
	369	+ note = {Articles 5, 14, 14.2, 46, 72, 124, 244.29--244.30, 253.27 and 264}
	370	+}
	371	+
	372	+@misc{mamh2024manuel,
	373	+ author = {{Minist\`ere des Affaires municipales et de l'Habitation}},
	374	+ title = {Manuel d'\'evaluation fonci\`ere du {Qu\'ebec}},
	375	+ howpublished = {Gouvernement du Qu\'ebec, Qu\'ebec},
	376	+ year = {2024}
	377	+}
	378	+
	379	+% ------------------------------------------------------------------ standards and manuals
179	380	@book{iaao2013standard,
180	381	author = {{International Association of Assessing Officers}},
181	382	title = {Standard on Ratio Studies},
182	383	publisher = {IAAO},
183	384	address = {Kansas City, MO},
184		− year = {2013}
	385	+ year = {2013},
	386	+ note = {Approved April 2013}
	387	+}
	388	+
	389	+@article{gloudemans2011prb,
	390	+ author = {Gloudemans, Robert J.},
	391	+ title = {The Coefficient of Price-Related Bias: A Measure of Vertical Equity},
	392	+ journal = {Fair \& Equitable},
	393	+ year = {2011},
	394	+ volume = {9},
	395	+ number = {8},
	396	+ pages = {3--8},
	397	+ note = {International Association of Assessing Officers}
185	398	}
186	399
187	400	@book{eckert1990property,
		`@@ -200,6 +413,63 @@`
200	413	year = {2011}
201	414	}
202	415
	416	+% ------------------------------------------------------------------ econometrics
	417	+@article{klepper1984consistent,
	418	+ author = {Klepper, Steven and Leamer, Edward E.},
	419	+ title = {Consistent Sets of Estimates for Regressions with Errors in All Variables},
	420	+ journal = {Econometrica},
	421	+ year = {1984},
	422	+ volume = {52},
	423	+ number = {1},
	424	+ pages = {163--183},
	425	+ doi = {10.2307/1911466}
	426	+}
	427	+
	428	+@article{griliches1986errors,
	429	+ author = {Griliches, Zvi and Hausman, Jerry A.},
	430	+ title = {Errors in Variables in Panel Data},
	431	+ journal = {Journal of Econometrics},
	432	+ year = {1986},
	433	+ volume = {31},
	434	+ number = {1},
	435	+ pages = {93--118},
	436	+ doi = {10.1016/0304-4076(86)90058-8}
	437	+}
	438	+
	439	+@article{koenker1978regression,
	440	+ author = {Koenker, Roger and Bassett, Gilbert},
	441	+ title = {Regression Quantiles},
	442	+ journal = {Econometrica},
	443	+ year = {1978},
	444	+ volume = {46},
	445	+ number = {1},
	446	+ pages = {33--50},
	447	+ doi = {10.2307/1913643}
	448	+}
	449	+
	450	+@article{cameron2015practitioner,
	451	+ author = {Cameron, A. Colin and Miller, Douglas L.},
	452	+ title = {A Practitioner's Guide to Cluster-Robust Inference},
	453	+ journal = {Journal of Human Resources},
	454	+ year = {2015},
	455	+ volume = {50},
	456	+ number = {2},
	457	+ pages = {317--372},
	458	+ doi = {10.3368/jhr.50.2.317}
	459	+}
	460	+
	461	+@article{abadie2023clustering,
	462	+ author = {Abadie, Alberto and Athey, Susan and Imbens, Guido W. and Wooldridge, Jeffrey M.},
	463	+ title = {When Should You Adjust Standard Errors for Clustering?},
	464	+ journal = {Quarterly Journal of Economics},
	465	+ year = {2023},
	466	+ volume = {138},
	467	+ number = {1},
	468	+ pages = {1--35},
	469	+ doi = {10.1093/qje/qjac038}
	470	+}
	471	+
	472	+% ------------------------------------------------------------------ incidence and hedonics
203	473	@article{oates1969effects,
204	474	author = {Oates, Wallace E.},
205	475	title = {The Effects of Property Taxes and Local Public Spending on Property Values: An Empirical Study of Tax Capitalization and the {Tiebout} Hypothesis},
		`@@ -207,7 +477,8 @@`
207	477	year = {1969},
208	478	volume = {77},
209	479	number = {6},
210		− pages = {957--971}
	480	+ pages = {957--971},
	481	+ doi = {10.1086/259584}
211	482	}
212	483
213	484	@article{oates2016local,
		`@@ -217,7 +488,8 @@`
217	488	year = {2016},
218	489	volume = {69},
219	490	number = {2},
220		− pages = {415--434}
	491	+ pages = {415--433},
	492	+ doi = {10.1086/ntj44014529}
221	493	}
222	494
223	495	@article{rosen1974hedonic,
		`@@ -227,7 +499,8 @@`
227	499	year = {1974},
228	500	volume = {82},
229	501	number = {1},
230		− pages = {34--55}
	502	+ pages = {34--55},
	503	+ doi = {10.1086/260169}
231	504	}
232	505
233	506	@incollection{malpezzi2003hedonic,
		`@@ -238,117 +511,8 @@`
238	511	publisher = {Blackwell},
239	512	address = {Oxford},
240	513	year = {2003},
241		− pages = {67--89}
242		−}
243		−
244		−@article{carbonnier2024property,
245		− author = {Carbonnier, Cl{\'e}ment},
246		− title = {Property Tax Regressivity, the Case of {Qu{\'e}bec}},
247		− journal = {Public Finance Review},
248		− year = {2024},
249		− volume = {52},
250		− number = {2},
251		− pages = {155--181}
252		−}
253		−
254		−@techreport{slack2014political,
255		− author = {Slack, Enid and Bird, Richard M.},
256		− title = {The Political Economy of Property Tax Reform},
257		− institution = {OECD},
258		− type = {OECD Working Papers on Fiscal Federalism},
259		− number = {18},
260		− year = {2014}
261		−}
262		−
263		−@book{youngman2016good,
264		− author = {Youngman, Joan},
265		− title = {A Good Tax: Legal and Policy Issues for the Property Tax in the {United States}},
266		− publisher = {Lincoln Institute of Land Policy},
267		− address = {Cambridge, MA},
268		− year = {2016}
269		−}
270		−
271		−@techreport{found2017property,
272		− author = {Found, Adam and Tomlinson, Peter},
273		− title = {Business Tax Burdens in {Canada's} Major Cities: The 2017 Report Card},
274		− institution = {C.D. Howe Institute},
275		− type = {E-Brief},
276		− year = {2017}
277		−}
278		−
279		−@techreport{mpac2022vertical,
280		− author = {{Municipal Property Assessment Corporation}},
281		− title = {Vertical Equity Review of Residential Assessed Values},
282		− institution = {MPAC},
283		− address = {Toronto},
284		− type = {Technical Report},
285		− year = {2022}
286		−}
287		−
288		−@article{goolsby1997assessment,
289		− author = {Goolsby, William C.},
290		− title = {Assessment Error in the Valuation of Owner-Occupied Housing},
291		− journal = {Journal of Real Estate Research},
292		− year = {1997},
293		− volume = {13},
294		− number = {1},
295		− pages = {33--45}
296		−}
297		−
298		−@article{quintos2020prb,
299		− author = {Quintos, Carmela},
300		− title = {A Gradient Boosting Approach to Understanding Vertical and Horizontal Inequity in Property Assessments},
301		− journal = {Journal of Property Tax Assessment \& Administration},
302		− year = {2020},
303		− volume = {17},
304		− number = {2},
305		− pages = {1--28}
306		−}
307		−
308		−@article{ross2012assessor,
309		− author = {Ross, Justin M.},
310		− title = {Interjurisdictional Determinants of Property Assessment Regressivity},
311		− journal = {Land Economics},
312		− year = {2012},
313		− volume = {88},
314		− number = {1},
315		− pages = {28--42}
316		−}
317		−
318		−@article{plummer2014evidence,
319		− author = {Plummer, Elizabeth},
320		− title = {The Effects of Property Tax Protests on the Assessment Uniformity of Residential Properties},
321		− journal = {Real Estate Economics},
322		− year = {2014},
323		− volume = {42},
324		− number = {4},
325		− pages = {900--937}
326		−}
327		−
328		−@article{clapp1990methods,
329		− author = {Clapp, John M.},
330		− title = {A Methodology for Constructing Vacant Land Price Indices},
331		− journal = {Real Estate Economics},
332		− year = {1990},
333		− volume = {18},
334		− number = {3},
335		− pages = {274--293}
336		−}
337		−
338		−@misc{lfm2026,
339		− author = {{Gouvernement du Qu\'ebec}},
340		− title = {Loi sur la fiscalit\'e municipale, {RLRQ}, c.\ {F-2.1}},
341		− howpublished = {L\'egisQu\'ebec},
342		− year = {2026},
343		− note = {Articles 42--46 (triennial rolls and market-condition reference date)}
344		−}
345		−
346		−@misc{mamh2024manuel,
347		− author = {{Minist\`ere des Affaires municipales et de l'Habitation}},
348		− title = {Manuel d'\'evaluation fonci\`ere du {Qu\'ebec}},
349		− howpublished = {Gouvernement du Qu\'ebec},
350		− address = {Qu\'ebec},
351		− year = {2024}
	514	+ pages = {67--89},
	515	+ doi = {10.1002/9780470690680.ch5}
352	516	}
353	517
354	518	@article{desrosiers2000hedonic,
		`@@ -358,7 +522,8 @@`
358	522	year = {2000},
359	523	volume = {18},
360	524	number = {3},
361		− pages = {291--315}
	525	+ pages = {291--315},
	526	+ doi = {10.1108/14635780010338245}
362	527	}
363	528
364	529	@article{bostic2007land,
		`@@ -368,35 +533,16 @@`
368	533	year = {2007},
369	534	volume = {35},
370	535	number = {2},
371		− pages = {183--208}
372		−}
373		−
374		−@article{ihlanfeldt2023appraisal,
375		− author = {Ihlanfeldt, Keith and Rodgers, Luke P.},
376		− title = {Homestead Exemptions, Heterogeneous Assessment, and Property Tax Progressivity},
377		− journal = {National Tax Journal},
378		− year = {2022},
379		− volume = {75},
380		− number = {1},
381		− pages = {7--31}
	536	+ pages = {183--208},
	537	+ doi = {10.1111/j.1540-6229.2007.00187.x}
382	538	}
383	539
384		−@article{baar1981property,
385		− author = {Baar, Kenneth K.},
386		− title = {Property Tax Assessment Discrimination Against Low-Income Neighborhoods},
387		− journal = {The Urban Lawyer},
388		− year = {1981},
389		− volume = {13},
390		− number = {3},
391		− pages = {333--406}
392		−}
393		−
394		−@article{engle1975deassessment,
395		− author = {Engle, Robert F.},
396		− title = {De Facto Discrimination in Residential Assessments: {Boston}},
397		− journal = {National Tax Journal},
398		− year = {1975},
399		− volume = {28},
400		− number = {4},
401		− pages = {445--451}
	540	+@techreport{slack2014political,
	541	+ author = {Slack, Enid and Bird, Richard M.},
	542	+ title = {The Political Economy of Property Tax Reform},
	543	+ institution = {OECD},
	544	+ type = {OECD Working Papers on Fiscal Federalism},
	545	+ number = {18},
	546	+ year = {2014},
	547	+ doi = {10.1787/5jz5pzvzv6r7-en}
402	548	}

modified paper/sections/conclusion.tex +47 −26

		`@@ -4,34 +4,55 @@`
4	4	\label{sec:concl}
5	5
6	6	Matching more than half a million residential sales to the assessment
7		−rolls that tax them, this paper delivers the first province-wide audit of
8		−assessment equity in Canada. The verdict is unambiguous. Quebec's
9		−property-tax base is systematically regressive: within the same
10		−municipality, roll and year, the assessment ratio falls by 34\% per
11		−log-point of price in the descriptive fixed-effects estimate, and by 8\%
12		−under the most conservative measurement-error correction available.
13		−Ninety-five percent of municipalities fail the IAAO vertical-equity
14		−standard, ninety-nine percent fail its uniformity standard, and the median
15		−dwelling in the bottom local price decile pays roughly two thirds more
16		−property tax than uniform assessment would imply, while the top decile
17		−pays less. The inequity concentrates where mass appraisal is hardest ---
18		−old houses, plexes, land-heavy and luxury properties, thin markets ---
19		−doubles when triennial rolls fall behind a booming market, and disappears
20		−almost nowhere except Montr\'eal.
	7	+rolls that tax them, this paper delivers the first province-wide ratio
	8	+study of assessment equity for a Canadian province. The answer to the
	9	+question it set out to ask---is Quebec's property-tax base
	10	+regressive?---turns out to depend on a choice that ratio-study practice
	11	+regulates and that the academic literature rarely reports: how to treat
	12	+the sales whose declared price lies far below the rolled value. Under a
	13	+lenient trim, Quebec looks like the regressive U.S.\ jurisdictions of the
	14	+recent literature: a within-market elasticity of the assessment ratio of
	15	+$-0.34$, a COD near 30, and 95\% of municipalities outside the IAAO band
	16	+for price-related bias. Under the outlier rule the IAAO standard
	17	+prescribes, which removes 9\% of sales concentrated in the bottom price
	18	+decile, Quebec looks like a system that works: an elasticity of $-0.09$
	19	+that a measurement-error-robust instrument brings to zero, a PRB inside
	20	+the acceptable band, CODs between 9 and 12 in the ten largest cities, and
	21	+three quarters of municipalities meeting the vertical-equity standard.
	22	+Proportionality holds across the upper 80\% of every market's price
	23	+distribution under either treatment; the two readings differ only about
	24	+the bottom quintile, and the registry does not record what would settle
	25	+the difference.
21	26
22		−These findings reframe the presumption that centralized, professionally
23		−regulated assessment systems are immune to the pathologies documented in
24		−the fragmented U.S. system. Quebec has uniform statutes, certified
25		−evaluators and statutory market-vintage synchronization --- and produces
26		−regressivity of U.S. magnitude anyway. The binding constraint is not
27		−governance but valuation technology and revaluation frequency, which is
28		−in fact encouraging: cycle length, pooled assessment services and
29		−vertical audit standards are policy variables, and inexpensive ones
30		−relative to the redistribution at stake.
	27	+Within those bounds, three results are robust. The ordering of difficulty
	28	+is invariant to the trimming rule: condominiums are assessed
	29	+proportionally, while single-family homes, plexes, older and land-heavy
	30	+properties and small municipalities are regressive, at a quarter of the
	31	+lenient-trim magnitude once outliers are removed. Staleness widens
	32	+price-related bias at the margin in fast markets---the within-municipality
	33	+PRB of the trimmed sample moves from $-0.04$ in 2021--2022 to zero from
	34	+2024---but does not generate inequity, and the province-wide swing that
	35	+suggested otherwise is compositional. And the redistribution implied by
	36	+the most defensible conventions is real but modest: the cheapest tenth of
	37	+dwellings in a market pays about 5--7\% more property tax than uniform
	38	+assessment would imply, the most expensive tenth 3--5\% less.
	39	+
	40	+These findings qualify the presumption, in both directions, about
	41	+centralised assessment systems. Quebec's uniform statutes, chartered
	42	+appraisers and statutory market-vintage synchronisation do not immunise
	43	+it against the pathologies of the fragmented U.S.\ system, but neither do
	44	+they reproduce them at U.S.\ magnitude once sales are screened as the
	45	+profession prescribes. The binding constraint the audit reveals is
	46	+informational: the province measures assessment \emph{level} every year
	47	+and publishes nothing on uniformity or vertical equity, and its transaction
	48	+records carry no indication of whether a sale was at arm's length. Both
	49	+are inexpensive to fix relative to the redistribution at stake, and fixing
	50	+the second would turn the bounds of this paper into a point.
31	51
32	52	The matched sale--roll architecture built here supports a research agenda
33	53	beyond this audit: linking assessment gaps to neighbourhood
34	54	socio-demographics, exploiting the discrete arrival of new rolls to study
35		−price anchoring, and using the land--building decomposition to measure
36		−land-value dynamics at the parcel level. We pursue these in companion
37		−work.
	55	+price anchoring, using the land--building decomposition to measure
	56	+land-value dynamics at the parcel level, and, once validated sale flags
	57	+become available, revisiting the bottom quintile that this paper could
	58	+only bracket.

modified paper/sections/data.tex +73 −42

		`@@ -9,40 +9,45 @@ We start from a compiled registry of 745{,}119 residential-market`
9	9	transactions recorded in Quebec between January 2021 and July 2026, each
10	10	carrying the sale price, sale date, civic address, geographic coordinates,
11	11	and a listing-derived property type. Each transaction has been matched at
12		−the parcel level to the municipal assessment roll in force on the sale date.
13		−The match keys on geographic proximity between the transaction's coordinates
14		−and the roll unit's coordinates and is validated against the roll's recorded
15		−value; a composite score (maximum 220) summarizes the quality of the
16		−address, distance and value agreement. Matches are extremely tight: the
17		−median distance between the transaction and the matched roll unit is
	12	+the parcel level to the municipal assessment roll in force on the sale
	13	+date. The match keys on geographic proximity between the transaction's
	14	+coordinates and the roll unit's coordinates and is validated against the
	15	+roll's recorded value; a composite score (maximum 220) summarises the
	16	+quality of the address, distance and value agreement. Matches are tight:
	17	+the median distance between the transaction and the matched roll unit is
18	18	0.6~metres, and every observation retained in the estimation sample
19	19	reproduces the roll's assessed value exactly.
20	20
21		−From the roll we observe the taxable value of the property
22		−($AV$, \texttt{valeur immeuble}), its land and building components, lot
23		−area, total floor area, year of construction, number of dwelling units, the
24		−standardized use code (CUBF), the roll vintage, and the statutory
25		−market-condition reference date discussed in Section~\ref{sec:inst}.
	21	+From the roll we observe the taxable value of the property ($AV$,
	22	+\texttt{valeur immeuble}), its land and building components, lot area,
	23	+total floor area, year of construction, number of dwelling units, the
	24	+standardised use code (CUBF), the roll vintage, and the statutory
	25	+market-condition reference date discussed in Section~\ref{sec:inst}. The
	26	+registry does not record whether a transaction was at arm's length.
26	27
27	28	\subsection{Sample restrictions}
28	29
29	30	Table~\ref{tab:sumstats} describes the estimation sample; the selection
30		−cascade is as follows. We keep sales of residential use codes ---
31		−dwellings (CUBF 1000), cottages (1100), mobile homes (1211) and other
32		−residential (1990) --- which removes vacant land, commercial property and
33		−construction-in-progress (672{,}276 sales remain). We require a
	31	+cascade is as follows. We keep sales of residential use codes---dwellings
	32	+(CUBF 1000), cottages (1100), mobile homes (1211) and other residential
	33	+(1990)---which removes vacant land, commercial property and
	34	+construction in progress (672{,}276 sales remain). We require a
34	35	high-confidence roll match (distance $\le 50$~m and score $\ge 150$;
35	36	568{,}711 sales), a positive assessed value and a price of at least
36		−\$50{,}000 --- the floor of the source registry, which also screens out
37		−most non-arm's-length transfers. Assessment ratios $r_i = AV_i/SP_i$ are
38		−trimmed at the 1st and 99th percentiles \emph{within each roll vintage}, so
39		−that the mechanical drift of ratio levels across vintages is not trimmed
40		−asymmetrically (557{,}325 sales). Finally, since all estimates compare
41		−sales within a municipality $\times$ roll $\times$ sale-year block
42		−(``cell''), we require at least 20 sales per cell. The estimation sample
43		−contains \textbf{522{,}769 sales} in 625 municipalities and 2{,}884 cells:
44		−345{,}053 single-family homes, 81{,}693 plexes (2--5 units), 81{,}461
45		−condominiums, 9{,}287 cottages and 4{,}701 mobile homes.
	37	+\$50{,}000, the floor of the source registry. Assessment ratios
	38	+$r_i = AV_i/SP_i$ are then trimmed at the 1st and 99th percentiles
	39	+\emph{within each roll vintage}, so that the mechanical drift of ratio
	40	+levels across vintages is not trimmed asymmetrically (557{,}325 sales).
	41	+Finally, since all estimates compare sales within a municipality
	42	+$\times$ roll $\times$ sale-year block (``cell''), we require at least 20
	43	+sales per cell. The estimation sample contains \textbf{522{,}769 sales} in
	44	+625 municipalities and 2{,}884 cells: 345{,}053 single-family homes,
	45	+81{,}693 plexes (2--5 units), 81{,}461 condominiums, 9{,}287 cottages,
	46	+4{,}701 mobile homes and 574 other residential units. Because rolls enter
	47	+into force on January~1, a municipality--year almost always falls under a
	48	+single roll; 85 of the 2{,}798 municipality--years in the sample span two
	49	+rolls (late deposits and extensions), which is why cells are defined on the
	50	+roll vintage as well as on the year.
46	51
47	52	\begin{table}[t]
48	53	\centering
		`@@ -56,12 +61,38 @@ condominiums, 9{,}287 cottages and 4{,}701 mobile homes.`
56	61	2026, matched at the parcel level to the assessment roll in force at the
57	62	sale date. The assessment ratio is assessed value divided by sale price.
58	63	Roll lag is the number of months between the roll's statutory
59		−market-condition reference date (July 1) and the sale date. The assessed
	64	+market-condition reference date (July~1) and the sale date. The assessed
60	65	land share is the roll's land value divided by total assessed value.
61	66	\end{tablenotes}
62	67	\end{threeparttable}
63	68	\end{table}
64	69
	70	+\subsection{Two treatments of extreme ratios}
	71	+\label{sec:trim}
	72	+
	73	+The 1/99 trim within vintage is deliberately lenient: it discards sales
	74	+whose ratio is implausible for the market as a whole but retains, inside
	75	+each municipality, every ratio that is implausible for that market. The
	76	+retained distribution has a long upper tail---6.1\% of sales have a ratio
	77	+above 1.5 and 3.2\% above 2, that is, a declared price below half the
	78	+rolled value in a period when the typical dwelling sold for 28\% more than
	79	+its assessment. The IAAO standard treats such observations differently.
	80	+Its Appendix~B identifies as outliers the ratios that lie more than 1.5
	81	+interquartile ranges beyond the first and third quartiles of the stratum,
	82	+requires that they be scrutinised and trimmed within documented limits
	83	+(5 to 10\% of a large, unvalidated sample), and warns that statistics from
	84	+trimmed and untrimmed distributions are not comparable
	85	+\citep{iaao2013standard}. Applied within each cell, the rule flags 9.2\% of
	86	+our sales. The flagged sales are not spread evenly: 53\% of the sales in
	87	+the bottom within-cell price decile are outliers, 16\% in the second
	88	+decile, and fewer than 5\% in every decile above the fourth
	89	+(Table~\ref{tab:taxshiftalt}). Whether they are market sales of severely
	90	+over-assessed homes or non-market transfers recorded at nominal prices
	91	+cannot be determined from the registry. We therefore carry both treatments
	92	+through the paper: the \emph{baseline} (lenient-trim) sample of 522{,}769
	93	+sales, and the \emph{IAAO-trimmed} sample of 471{,}148 sales, and we report
	94	+a grid of intermediate rules in Section~\ref{sec:trimres}.
	95	+
65	96	\subsection{The raw pattern}
66	97
67	98	The median assessment ratio is 0.78: the typical dwelling sells for about
		`@@ -69,21 +100,20 @@ The median assessment ratio is 0.78: the typical dwelling sells for about`
69	100	back-dated rolls. Figure~\ref{fig:ratiodist} shows the distribution and its
70	101	decomposition by roll lag: sales occurring within two years of the
71	102	reference date centre near 0.87, while sales more than four years out
72		−centre near 0.64 --- the mechanical staleness gradient that our fixed
73		−effects absorb. Figure~\ref{fig:time} traces the same mechanics in
74		−calendar time: each roll vintage enters near parity with the market it was
75		−referenced on, then drifts down as prices rise, and the 2022--2023 rate
76		−shock is visible as a flattening of the drift. Everything that follows
77		−nets out this timing structure and asks a sharper question: \emph{within} a
78		−given municipality, roll, and year, do cheap and expensive homes face the
79		−same ratio?
	103	+centre near 0.64---the staleness gradient that our fixed effects absorb.
	104	+Figure~\ref{fig:time} traces the same mechanics in calendar time: each roll
	105	+vintage enters near parity with the market it was referenced on, then
	106	+drifts down as prices rise, and the 2022--2023 rate shock is visible as a
	107	+flattening of the drift. Everything that follows nets out this timing
	108	+structure and asks a sharper question: \emph{within} a given municipality,
	109	+roll and year, do cheap and expensive homes face the same ratio?
80	110
81	111	\begin{figure}[t]
82	112	\centering
83	113	\includegraphics[width=\textwidth]{fig_ratio_dist.png}
84		−\caption{Assessment ratios. Panel A: distribution of $AV/SP$ across the
85		−estimation sample; the median is 0.78 and the dashed line marks parity.
86		−Panel B: kernel of the same distribution split by the number of months
	114	+\caption{Assessment ratios, baseline sample. Panel A: distribution of
	115	+$AV/SP$; the median is 0.78 and the dashed line marks parity. Panel B:
	116	+kernel density of the same distribution split by the number of months
87	117	between the roll's market-condition reference date and the sale; older
88	118	rolls sit systematically further below parity.}
89	119	\label{fig:ratiodist}
		`@@ -92,10 +122,11 @@ rolls sit systematically further below parity.}`
92	122	\begin{figure}[t]
93	123	\centering
94	124	\includegraphics[width=\textwidth]{fig_time.png}
95		−\caption{Median assessment ratio by sale month and roll vintage. Each line
96		−follows sales assessed under one triennial vintage (labelled by entry
97		−year); monthly medians with fewer than 100 sales are suppressed. Vintages
98		−enter near their reference-date market level and drift down as prices
99		−rise; the flattening after 2022 reflects the interest-rate correction.}
	125	+\caption{Median assessment ratio by sale month and roll vintage, baseline
	126	+sample. Each line follows sales assessed under one triennial vintage
	127	+(labelled by entry year); monthly medians with fewer than 100 sales are
	128	+suppressed. Vintages enter near their reference-date market level and
	129	+drift down as prices rise; the flattening after 2022 reflects the
	130	+interest-rate correction.}
100	131	\label{fig:time}
101	132	\end{figure}

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révision scientifique complète (editorial board, 2026-10-17)

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