WP10 — The Assessment Gap in Quebec: full research project
End-to-end pipeline (sample, IAAO diagnostics, Cheng FE / Clapp IV / quantile / heterogeneity / horizontal / tax shift), 10 journal-calibre figures, 10 LaTeX tables, 29-page paper with literature review. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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| 1 | +# Raw data snapshot — 100 MB parquet, not redistributed | |
| 2 | +data/raw/*.parquet | |
| 3 | +data/processed/*.parquet | |
| 4 | + | |
| 5 | +# Python | |
| 6 | +__pycache__/ | |
| 7 | +*.pyc | |
| 8 | + | |
| 9 | +# LaTeX build artifacts (paper/main.pdf IS committed) | |
| 10 | +paper/*.aux | |
| 11 | +paper/*.log | |
| 12 | +paper/*.out | |
| 13 | +paper/*.fls | |
| 14 | +paper/*.fdb_latexmk | |
| 15 | +paper/*.bbl | |
| 16 | +paper/*.blg | |
| 17 | +paper/*.synctex.gz | |
| 18 | + | |
| 19 | +# macOS | |
| 20 | +.DS_Store | |
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README.md
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| 1 | +<!-- Author: Simon-Pierre Boucher — contact@spboucher.ai --> | |
| 2 | +# ⚖️ The Assessment Gap in Quebec | |
| 3 | + | |
| 4 | +**UQO Working Paper No. 10** — *Vertical and Horizontal Inequity in Municipal | |
| 5 | +Property Valuation: Evidence from 522,769 Sales Matched to the Assessment Roll* | |
| 6 | + | |
| 7 | +[-b31b1b?logo=latex&logoColor=white)](paper/main.pdf) | |
| 8 | +[](requirements.txt) | |
| 9 | +[](data/raw/README.md) | |
| 10 | +[-4051b5)](src/wp10/models.py) | |
| 11 | +[](scripts/) | |
| 12 | +[](https://uqo.ca) | |
| 13 | +[](mailto:contact@spboucher.ai) | |
| 14 | +[](mailto:contact@spboucher.ai) | |
| 15 | + | |
| 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. | |
| 25 | + | |
| 26 | +--- | |
| 27 | + | |
| 28 | +## 📖 Table of contents | |
| 29 | + | |
| 30 | +1. [What this paper does](#-what-this-paper-does) | |
| 31 | +2. [Headline results](#-headline-results) | |
| 32 | +3. [Repository layout](#-repository-layout) | |
| 33 | +4. [Quick start](#-quick-start) | |
| 34 | +5. [The pipeline, step by step](#-the-pipeline-step-by-step) | |
| 35 | +6. [Data](#-data) | |
| 36 | +7. [Methodology](#-methodology) | |
| 37 | +8. [Figures & tables inventory](#-figures--tables-inventory) | |
| 38 | +9. [Limitations](#-limitations) | |
| 39 | +10. [Citation](#-citation) | |
| 40 | +11. [Author & contact](#-author--contact) | |
| 41 | + | |
| 42 | +--- | |
| 43 | + | |
| 44 | +## 🎯 What this paper does | |
| 45 | + | |
| 46 | +Quebec taxes every dwelling in proportion to its **assessed value**, redrawn on a | |
| 47 | +triennial roll whose values must, by statute (art. 46 LFM), reflect market conditions | |
| 48 | +at a single reference date. If assessments are *regressive* — cheap homes overvalued | |
| 49 | +relative to expensive ones — the effective tax rate falls with wealth, silently. | |
| 50 | +This project measures that gap at province scale: | |
| 51 | + | |
| 52 | +``` | |
| 53 | +ln AV_i = α_c(i) + β · ln SP_i + ε_i (c = municipality × roll × sale-year) | |
| 54 | +``` | |
| 55 | + | |
| 56 | +- **γ = β − 1** is the elasticity of the assessment ratio w.r.t. price | |
| 57 | + (γ < 0 ⇒ regressive), identified **within** 2,884 market-timing cells; | |
| 58 | +- the **Clapp (1990) rank IV** purges the attenuation bias that pushes naïve | |
| 59 | + ratio studies toward spurious regressivity; | |
| 60 | +- the full **IAAO ratio-study battery** (median ratio, COD, PRD, PRB) with | |
| 61 | + bootstrap CIs is computed for every municipality with ≥ 100 usable sales; | |
| 62 | +- quantile profiles, subgroup elasticities, horizontal-dispersion regressions and | |
| 63 | + an exact **intra-municipal tax-shift** calculation complete the audit. | |
| 64 | + | |
| 65 | +## 🏆 Headline results | |
| 66 | + | |
| 67 | +| Object | Estimate | | |
| 68 | +|---|---| | |
| 69 | +| Cheng elasticity, pooled OLS | β = 0.812 (0.029) | | |
| 70 | +| Cheng elasticity, cell FE | **β = 0.656 (0.029)** → γ = −0.344 | | |
| 71 | +| Clapp rank-IV (error-robust) | **β = 0.917 (0.021)** → γ = −0.083 | | |
| 72 | +| Quantile profile β(τ), τ = .10 → .90 | 0.87 → **0.49** (failure concentrated at the top) | | |
| 73 | +| Province-wide PRB (2021 / 2024) | −0.104 / −0.002 (staleness mechanism) | | |
| 74 | +| Municipalities with PRB < 0 | **99%** (95% below IAAO band) | | |
| 75 | +| Median municipality COD | 26 (IAAO ceiling: 15) | | |
| 76 | +| Excess tax, bottom ↔ top local decile | **+65% ↔ −5%** (median) | | |
| 77 | +| The exception | Montréal: PRB **+0.07**, progressive in all 6 years | | |
| 78 | + | |
| 79 | +Sub-group anatomy: condos γ = −0.12 vs single-family −0.45 / plex −0.49; | |
| 80 | +land share > 0.4 → −0.50; age > 60 y → −0.43; large markets (>10k sales) −0.27. | |
| 81 | + | |
| 82 | +## 🗂 Repository layout | |
| 83 | + | |
| 84 | +``` | |
| 85 | +wp10_uqo/ | |
| 86 | +├── data/ | |
| 87 | +│ ├── raw/ # matched sales–roll snapshot (see data/raw/README.md) | |
| 88 | +│ └── processed/ # analysis.parquet (built by step 01) | |
| 89 | +├── src/wp10/ # reusable package | |
| 90 | +│ ├── config.py # paths, thresholds, constants | |
| 91 | +│ ├── sample.py # sample construction & variable definitions | |
| 92 | +│ ├── iaao.py # COD / PRD / PRB + bootstrap CIs | |
| 93 | +│ ├── models.py # Cheng FE, Clapp IV, quantiles, horizontal, tax shift | |
| 94 | +│ └── plotstyle.py # journal-calibre matplotlib style (validated palette) | |
| 95 | +├── scripts/ # the pipeline, in order | |
| 96 | +│ ├── 01_build_sample.py | |
| 97 | +│ ├── 02_iaao_stats.py | |
| 98 | +│ ├── 03_estimate_regressions.py | |
| 99 | +│ ├── 04_make_figures.py | |
| 100 | +│ └── 05_make_tables.py | |
| 101 | +├── results/ | |
| 102 | +│ ├── reproduced/ # every CSV the scripts emit | |
| 103 | +│ └── tables/ # LaTeX tables input by the paper | |
| 104 | +├── figures/ # 10 publication figures (PNG, 300 dpi) | |
| 105 | +└── paper/ # main.tex + sections/ + references.bib → main.pdf | |
| 106 | +``` | |
| 107 | + | |
| 108 | +## 🚀 Quick start | |
| 109 | + | |
| 110 | +```bash | |
| 111 | +cd wp10_uqo | |
| 112 | +python3 -m pip install -r requirements.txt | |
| 113 | + | |
| 114 | +# place the parquet snapshot in data/raw/ (see data/raw/README.md), then: | |
| 115 | +python3 scripts/01_build_sample.py # 745,119 → 522,769 sales | |
| 116 | +python3 scripts/02_iaao_stats.py # IAAO diagnostics + bootstrap | |
| 117 | +python3 scripts/03_estimate_regressions.py # FE / IV / quantile / heterogeneity / tax shift | |
| 118 | +python3 scripts/04_make_figures.py # 10 figures | |
| 119 | +python3 scripts/05_make_tables.py # 10 LaTeX tables | |
| 120 | + | |
| 121 | +cd paper && make # compile main.pdf (latexmk) | |
| 122 | +``` | |
| 123 | + | |
| 124 | +Total runtime ≈ 5 minutes on an Apple-silicon laptop; peak RAM ≈ 6 GB. | |
| 125 | + | |
| 126 | +## 🗃 Data | |
| 127 | + | |
| 128 | +745,119 residential-market transactions (Jan 2021 – Jul 2026) matched at the | |
| 129 | +**parcel level** to the assessment roll in force at the sale date (median match | |
| 130 | +distance 0.6 m; every retained sale reproduces the roll value exactly). From the | |
| 131 | +roll: total/land/building assessed values, lot & floor areas, year built, unit | |
| 132 | +count, CUBF use code, roll vintage and the statutory market-condition date. | |
| 133 | +Sample cascade (details in the paper, §4): residential CUBF → match quality → | |
| 134 | +valid AV/SP → 1/99% ratio trim within roll vintage → cells ≥ 20 sales | |
| 135 | +⇒ **522,769 sales, 625 municipalities, 2,884 cells**. | |
| 136 | + | |
| 137 | +## 🔬 Methodology | |
| 138 | + | |
| 139 | +1. **IAAO diagnostics** (Standard on Ratio Studies, 2013) within | |
| 140 | + municipality × sale-year blocks, aggregated by median — COD, PRD, PRB with | |
| 141 | + percentile-bootstrap CIs (`src/wp10/iaao.py`). | |
| 142 | +2. **Cheng (1974) log-log regression** with 2,884 absorbed fixed effects | |
| 143 | + (linearmodels `AbsorbingLS`), SEs clustered on 625 municipalities. | |
| 144 | +3. **Clapp (1990) rank IV** — Z ∈ {−1,0,+1} from within-cell rank agreement of | |
| 145 | + ln AV and ln SP, 2SLS on demeaned data (`IV2SLS`) — the conservative bound. | |
| 146 | +4. **Quantile regressions** on within-cell demeaned data (τ = .10….90). | |
| 147 | +5. **Heterogeneity**: separate FE estimates by class, age, land share, roll lag, | |
| 148 | + municipality size, sale year. | |
| 149 | +6. **Horizontal inequity**: |ln r − cell median| regressed on characteristics. | |
| 150 | +7. **Tax shift**: r / cell-median − 1 by within-cell price decile — exact % | |
| 151 | + over/under-payment under Quebec's exemption-free ad valorem rule. | |
| 152 | + | |
| 153 | +## 🖼 Figures & tables inventory | |
| 154 | + | |
| 155 | +| Figure | Content | | |
| 156 | +|---|---| | |
| 157 | +| `fig_ratio_dist` | ratio distribution + by roll lag (Panels A/B) | | |
| 158 | +| `fig_time` | median ratio by month × roll vintage (staleness drift) | | |
| 159 | +| `fig_binscatter` | within-cell ln ratio vs ln price, 20 bins — the core fact | | |
| 160 | +| `fig_quantile` | β(τ) profile with FE/IV benchmarks | | |
| 161 | +| `fig_heterogeneity` | forest plot of subgroup γ | | |
| 162 | +| `fig_prb_muni`, `fig_cod` | municipal PRB / COD distributions vs IAAO bands | | |
| 163 | +| `fig_map` | province map of municipal PRB (Montréal exception) | | |
| 164 | +| `fig_taxshift` | excess tax burden by local price decile | | |
| 165 | +| `fig_robustness` | γ_FE vs γ_IV across 10 sample variants | | |
| 166 | + | |
| 167 | +Tables (`results/tables/*.tex`): summary stats, IAAO province-wide, ten largest | |
| 168 | +markets, vertical regressions, quantiles, heterogeneity, horizontal, tax shift, | |
| 169 | +robustness, Paglin–Fogarty. | |
| 170 | + | |
| 171 | +## ⚠️ Limitations | |
| 172 | + | |
| 173 | +- Sales < $50k absent from the source registry; residual non-arm's-length | |
| 174 | + transfers may survive screens (bottom-decile shift = upper bound). | |
| 175 | +- 2021–2026 is an unusually turbulent market — levels statistics are | |
| 176 | + period-specific (the within-market elasticity is not). | |
| 177 | +- No appeals, renovations, or owner demographics observed. | |
| 178 | +- Montréal's progressivity may partly reflect borough-level composition. | |
| 179 | + | |
| 180 | +## 📝 Citation | |
| 181 | + | |
| 182 | +```bibtex | |
| 183 | +@techreport{boucher2026assessmentgap, | |
| 184 | + author = {Boucher, Simon-Pierre}, | |
| 185 | + title = {The Assessment Gap in Quebec: Vertical and Horizontal Inequity | |
| 186 | + in Municipal Property Valuation}, | |
| 187 | + institution = {Universit\'e du Qu\'ebec en Outaouais, | |
| 188 | + D\'epartement des sciences administratives}, | |
| 189 | + type = {Working Paper}, | |
| 190 | + number = {10}, | |
| 191 | + year = {2026}, | |
| 192 | + month = {August} | |
| 193 | +} | |
| 194 | +``` | |
| 195 | + | |
| 196 | +## 👤 Author & contact | |
| 197 | + | |
| 198 | +**Simon-Pierre Boucher** — Département des sciences administratives, | |
| 199 | +Université du Québec en Outaouais (UQO), Gatineau, QC. | |
| 200 | +📧 [contact@spboucher.ai](mailto:contact@spboucher.ai) | |
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| 1 | +<!-- Author: Simon-Pierre Boucher — contact@spboucher.ai --> | |
| 2 | +# Raw data | |
| 3 | + | |
| 4 | +`transactions_700k_avec_registre_foncier.parquet` — 745,119 Quebec | |
| 5 | +residential-market transactions (January 2021 – July 2026) matched at the | |
| 6 | +parcel level to the municipal assessment roll (rôle d'évaluation foncière) | |
| 7 | +in force at the sale date. | |
| 8 | + | |
| 9 | +| Group | Key columns | | |
| 10 | +|---|---| | |
| 11 | +| Transaction | `id`, `date`, `amount`, `street`, `zipCode`, `city`, `lat`, `lng`, `propertyType`, `ownerType`, `tx_year` | | |
| 12 | +| Roll identity | `role_id_provinc`, `role_matricule`, `role_code_mun`, `role_municipalite`, `role_anrole` (roll vintage), `role_date_cond_marche` (statutory market-condition reference date) | | |
| 13 | +| Roll values | `role_valeur_immeuble` (total AV), `role_valeur_terrain` (land), `role_valeur_batiment` (building), `role_valeur_role_anterieur`, `previousValue`, `totalArValue` | | |
| 14 | +| Roll structure | `role_cubf` (+ `role_cubf_libelle`), `role_superficie_terrain_m2`, `role_aire_etages_m2`, `role_annee_construction`, `role_nb_logements`, `role_nb_etages`, `role_lien_physique`, `role_genre_construction`, `role_unite_voisinage` | | |
| 15 | +| Match quality | `match_dist_m` (median 0.6 m), `match_score` (max 220), `match_valeur_exacte` | | |
| 16 | + | |
| 17 | +The file is **not redistributed** with the repository (100 MB; see | |
| 18 | +`.gitignore`). Place it in this directory before running the pipeline. | |
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| 1 | +# Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +$pdf_mode = 1; | |
| 3 | +$pdflatex = 'pdflatex -interaction=nonstopmode -halt-on-error -synctex=1 %O %S'; | |
| 4 | +$bibtex_use = 2; | |
| 5 | +$clean_ext = 'synctex.gz run.xml bbl bcf fdb_latexmk fls log aux out toc lof lot blg'; | |
| 6 | +@default_files = ('main.tex'); | |
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| 1 | +# Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +all: | |
| 3 | + latexmk -pdf main.tex | |
| 4 | + | |
| 5 | +clean: | |
| 6 | + latexmk -c | |
| 7 | + | |
| 8 | +distclean: | |
| 9 | + latexmk -C | |
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +% UQO Working Paper No. 10 | |
| 4 | +% The Assessment Gap in Quebec: Vertical and Horizontal Inequity in | |
| 5 | +% Municipal Property Valuation | |
| 6 | +% | |
| 7 | +% Build: latexmk -pdf main.tex (or `make` in this directory) | |
| 8 | +% Figures are read from ../figures/, tables from ../results/tables/. | |
| 9 | +% ============================================================================ | |
| 10 | +\documentclass[12pt,letterpaper]{article} | |
| 11 | + | |
| 12 | +% ---------------------------------------------------------------- encoding | |
| 13 | +\usepackage[utf8]{inputenc} | |
| 14 | +\usepackage[T1]{fontenc} | |
| 15 | +\usepackage[english]{babel} | |
| 16 | + | |
| 17 | +% ---------------------------------------------------------------- layout | |
| 18 | +\usepackage[letterpaper,margin=1in]{geometry} | |
| 19 | +\usepackage{setspace} | |
| 20 | +\onehalfspacing | |
| 21 | + | |
| 22 | +% ---------------------------------------------------------------- typography | |
| 23 | +\usepackage{mathptmx} | |
| 24 | +\usepackage{microtype} | |
| 25 | + | |
| 26 | +% ---------------------------------------------------------------- math | |
| 27 | +\usepackage{amsmath,amssymb,amsthm} | |
| 28 | + | |
| 29 | +% ---------------------------------------------------------------- tables | |
| 30 | +\usepackage{booktabs} | |
| 31 | +\usepackage{threeparttable} | |
| 32 | +\usepackage{makecell} | |
| 33 | + | |
| 34 | +% ---------------------------------------------------------------- figures | |
| 35 | +\usepackage{graphicx} | |
| 36 | +\usepackage{subcaption} | |
| 37 | +\graphicspath{{../figures/}{./}} | |
| 38 | + | |
| 39 | +% ---------------------------------------------------------------- captions | |
| 40 | +\usepackage[font=small,labelfont=bf,labelsep=period,justification=justified,singlelinecheck=false]{caption} | |
| 41 | + | |
| 42 | +% ---------------------------------------------------------------- colours & links | |
| 43 | +\usepackage[dvipsnames]{xcolor} | |
| 44 | +\usepackage[colorlinks=true,linkcolor=NavyBlue,citecolor=NavyBlue,urlcolor=NavyBlue,breaklinks=true]{hyperref} | |
| 45 | + | |
| 46 | +% ---------------------------------------------------------------- bibliography | |
| 47 | +\usepackage[authoryear,round,semicolon]{natbib} | |
| 48 | +\bibliographystyle{aer} | |
| 49 | + | |
| 50 | +% ---------------------------------------------------------------- headings & lists | |
| 51 | +\usepackage{titlesec} | |
| 52 | +\titleformat{\section}{\large\bfseries}{\thesection.}{0.5em}{} | |
| 53 | +\titleformat{\subsection}{\normalsize\bfseries}{\thesubsection.}{0.5em}{} | |
| 54 | +\titleformat{\subsubsection}{\normalsize\itshape}{\thesubsubsection.}{0.5em}{} | |
| 55 | +\usepackage{fancyhdr} | |
| 56 | +\pagestyle{fancy}\fancyhf{} | |
| 57 | +\renewcommand{\headrulewidth}{0pt} | |
| 58 | +\fancyfoot[C]{\thepage} | |
| 59 | +\usepackage{enumitem} | |
| 60 | +\setlist{nosep,leftmargin=*} | |
| 61 | + | |
| 62 | +% ============================================================================ | |
| 63 | +% METADATA | |
| 64 | +% ============================================================================ | |
| 65 | +\newcommand{\WPnumber}{10} | |
| 66 | +\newcommand{\WPtitle}{The Assessment Gap in Quebec} | |
| 67 | +\newcommand{\WPsubtitle}{Vertical and Horizontal Inequity in Municipal Property | |
| 68 | + 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, | |
| 72 | + Regressivity, Ratio study, Quebec} | |
| 73 | +\newcommand{\WPjel}{H71, H22, R51, R31} | |
| 74 | + | |
| 75 | +\newcommand{\WPauthor}{Simon-Pierre Boucher} | |
| 76 | +\newcommand{\WPaffiliation}{D\'epartement des sciences administratives\\ | |
| 77 | + Universit\'e du Qu\'ebec en Outaouais} | |
| 78 | +\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca} | |
| 79 | +\newcommand{\WPaddress}{Gatineau -- Pavillon Alexandre-Tach\'e\\ | |
| 80 | + 283, boulevard Alexandre-Tach\'e\\ Gatineau, Qu\'ebec, Canada J9A 1L8} | |
| 81 | + | |
| 82 | +\newcommand{\WPabstract}{% | |
| 83 | +Municipal property taxes are levied on assessed values, so any systematic | |
| 84 | +relationship between assessment accuracy and market value silently | |
| 85 | +redistributes the tax burden. Matching 522{,}769 residential transactions | |
| 86 | +from 2021--2026 to the triennial assessment rolls of 625 Quebec | |
| 87 | +municipalities at the parcel level, we provide the first province-wide | |
| 88 | +evaluation of vertical and horizontal equity in Canadian property assessment. | |
| 89 | +Assessment ratios decline steeply with price: within | |
| 90 | +municipality~$\times$~roll~$\times$~sale-year markets, the elasticity of the | |
| 91 | +assessment ratio with respect to the sale price is $-0.34$, and a rank-based | |
| 92 | +instrumental-variable estimator in the spirit of \mbox{Clapp (1990)}---which | |
| 93 | +purges the attenuation bias that pushes least-squares tests toward spurious | |
| 94 | +regressivity---still yields $-0.08$ ($t\approx4$). IAAO ratio-study | |
| 95 | +diagnostics place 95\% of municipalities below the acceptable price-related | |
| 96 | +bias band and 99\% above the COD uniformity ceiling; Montr\'eal is the only | |
| 97 | +large market whose assessments are progressive. Regressivity is strongest for | |
| 98 | +single-family homes, older buildings, properties with a high assessed land | |
| 99 | +share, and smaller municipalities, and it doubles in years when market prices | |
| 100 | +decouple from the rolls' reference dates, pointing to infrequent revaluation | |
| 101 | +as a first-order mechanism. The implied intra-municipal tax shift is large: | |
| 102 | +the median dwelling in the bottom within-market price decile pays roughly | |
| 103 | +65\% more property tax than it would under uniform assessment, while the top | |
| 104 | +decile pays about 5\% less.} | |
| 105 | + | |
| 106 | +\begin{document} | |
| 107 | + | |
| 108 | +\input{sections/titlepage} | |
| 109 | + | |
| 110 | +\setcounter{page}{1} | |
| 111 | +\input{sections/introduction} | |
| 112 | +\input{sections/literature} | |
| 113 | +\input{sections/institutional} | |
| 114 | +\input{sections/data} | |
| 115 | +\input{sections/methodology} | |
| 116 | +\input{sections/results} | |
| 117 | +\input{sections/robustness} | |
| 118 | +\input{sections/discussion} | |
| 119 | +\input{sections/conclusion} | |
| 120 | + | |
| 121 | +\newpage | |
| 122 | +\bibliography{references} | |
| 123 | + | |
| 124 | +\end{document} | |
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paper/references.bib
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| 1 | +@comment{ Author: Simon-Pierre Boucher (contact at spboucher.ai) -- Bibliography for UQO Working Paper No 10 } | |
| 2 | + | |
| 3 | +@article{paglin1972equity, | |
| 4 | + author = {Paglin, Morton and Fogarty, Michael}, | |
| 5 | + title = {Equity and the Property Tax: A New Conceptual Focus}, | |
| 6 | + journal = {National Tax Journal}, | |
| 7 | + year = {1972}, | |
| 8 | + volume = {25}, | |
| 9 | + number = {4}, | |
| 10 | + pages = {557--565} | |
| 11 | +} | |
| 12 | + | |
| 13 | +@article{cheng1974property, | |
| 14 | + author = {Cheng, Pao Lun}, | |
| 15 | + title = {Property Taxation, Assessment Performance, and Its Measurement}, | |
| 16 | + journal = {Public Finance}, | |
| 17 | + year = {1974}, | |
| 18 | + volume = {29}, | |
| 19 | + number = {3}, | |
| 20 | + pages = {268--284} | |
| 21 | +} | |
| 22 | + | |
| 23 | +@article{kochin1982vertical, | |
| 24 | + author = {Kochin, Levis A. and Parks, Richard W.}, | |
| 25 | + title = {Vertical Equity in Real Estate Assessment: A Fair Appraisal}, | |
| 26 | + journal = {Economic Inquiry}, | |
| 27 | + year = {1982}, | |
| 28 | + volume = {20}, | |
| 29 | + number = {4}, | |
| 30 | + pages = {511--532} | |
| 31 | +} | |
| 32 | + | |
| 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}, | |
| 37 | + year = {1984}, | |
| 38 | + volume = {3}, | |
| 39 | + number = {2}, | |
| 40 | + pages = {123--131} | |
| 41 | +} | |
| 42 | + | |
| 43 | +@article{kennedy1984unfair, | |
| 44 | + author = {Kennedy, Peter}, | |
| 45 | + title = {On an Unfair Appraisal of Vertical Equity in Real Estate Assessment}, | |
| 46 | + journal = {Economic Inquiry}, | |
| 47 | + year = {1984}, | |
| 48 | + volume = {22}, | |
| 49 | + number = {2}, | |
| 50 | + pages = {287--290} | |
| 51 | +} | |
| 52 | + | |
| 53 | +@article{sunderman1990testing, | |
| 54 | + author = {Sunderman, Mark A. and Birch, John W. and Cannaday, Roger E. and Hamilton, Thomas W.}, | |
| 55 | + title = {Testing for Vertical Inequity in Property Tax Systems}, | |
| 56 | + journal = {Journal of Real Estate Research}, | |
| 57 | + year = {1990}, | |
| 58 | + volume = {5}, | |
| 59 | + number = {3}, | |
| 60 | + pages = {319--334} | |
| 61 | +} | |
| 62 | + | |
| 63 | +@article{clapp1990new, | |
| 64 | + author = {Clapp, John M.}, | |
| 65 | + title = {A New Test for Equitable Real Estate Tax Assessment}, | |
| 66 | + journal = {Journal of Real Estate Finance and Economics}, | |
| 67 | + year = {1990}, | |
| 68 | + volume = {3}, | |
| 69 | + number = {3}, | |
| 70 | + pages = {233--249} | |
| 71 | +} | |
| 72 | + | |
| 73 | +@article{sirmans1995vertical, | |
| 74 | + author = {Sirmans, G. Stacy and Diskin, Barry A. and Friday, H. Swint}, | |
| 75 | + title = {Vertical Inequity in the Taxation of Real Property}, | |
| 76 | + journal = {National Tax Journal}, | |
| 77 | + year = {1995}, | |
| 78 | + volume = {48}, | |
| 79 | + number = {1}, | |
| 80 | + pages = {71--84} | |
| 81 | +} | |
| 82 | + | |
| 83 | +@article{allen2002measuring, | |
| 84 | + author = {Allen, Marcus T. and Dare, William H.}, | |
| 85 | + title = {Identifying Determinants of Horizontal Property Tax Inequity: Evidence from Florida}, | |
| 86 | + journal = {Journal of Real Estate Research}, | |
| 87 | + year = {2002}, | |
| 88 | + volume = {24}, | |
| 89 | + number = {2}, | |
| 90 | + pages = {153--164} | |
| 91 | +} | |
| 92 | + | |
| 93 | +@article{sirmans2008vertical, | |
| 94 | + author = {Sirmans, G. Stacy and Gatzlaff, Dean H. and Macpherson, David A.}, | |
| 95 | + title = {Horizontal and Vertical Inequity in Real Property Taxation}, | |
| 96 | + journal = {Journal of Real Estate Literature}, | |
| 97 | + year = {2008}, | |
| 98 | + volume = {16}, | |
| 99 | + number = {2}, | |
| 100 | + pages = {167--180} | |
| 101 | +} | |
| 102 | + | |
| 103 | +@article{mcmillen2008thin, | |
| 104 | + author = {McMillen, Daniel P. and Weber, Rachel N.}, | |
| 105 | + title = {Thin Markets and Property Tax Inequities: A Multinomial Logit Approach}, | |
| 106 | + journal = {National Tax Journal}, | |
| 107 | + year = {2008}, | |
| 108 | + volume = {61}, | |
| 109 | + number = {4}, | |
| 110 | + pages = {653--671} | |
| 111 | +} | |
| 112 | + | |
| 113 | +@article{mcmillen2011assessment, | |
| 114 | + author = {McMillen, Daniel P.}, | |
| 115 | + title = {Assessment Regressivity: A Tale of Two {Illinois} Counties}, | |
| 116 | + journal = {Land Lines}, | |
| 117 | + year = {2011}, | |
| 118 | + volume = {23}, | |
| 119 | + number = {1}, | |
| 120 | + pages = {9--15} | |
| 121 | +} | |
| 122 | + | |
| 123 | +@article{hodge2017assessment, | |
| 124 | + author = {Hodge, Timothy R. and McMillen, Daniel P. and Sands, Gary and Skidmore, Mark}, | |
| 125 | + title = {Assessment Inequity in a Declining Housing Market: The Case of {Detroit}}, | |
| 126 | + journal = {Real Estate Economics}, | |
| 127 | + year = {2017}, | |
| 128 | + volume = {45}, | |
| 129 | + 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} | |
| 151 | +} | |
| 152 | + | |
| 153 | +@techreport{berry2021reassessing, | |
| 154 | + author = {Berry, Christopher R.}, | |
| 155 | + title = {Reassessing the Property Tax}, | |
| 156 | + institution = {University of Chicago, Harris School of Public Policy}, | |
| 157 | + type = {Working Paper}, | |
| 158 | + year = {2021} | |
| 159 | +} | |
| 160 | + | |
| 161 | +@techreport{amornsiripanitch2022residential, | |
| 162 | + author = {Amornsiripanitch, Natee}, | |
| 163 | + title = {Why Are Residential Property Tax Rates Regressive?}, | |
| 164 | + institution = {Federal Reserve Bank of Philadelphia}, | |
| 165 | + type = {Working Paper}, | |
| 166 | + number = {22-02}, | |
| 167 | + year = {2022} | |
| 168 | +} | |
| 169 | + | |
| 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}, | |
| 174 | + year = {2022}, | |
| 175 | + volume = {online first}, | |
| 176 | + pages = {1--29} | |
| 177 | +} | |
| 178 | + | |
| 179 | +@book{iaao2013standard, | |
| 180 | + author = {{International Association of Assessing Officers}}, | |
| 181 | + title = {Standard on Ratio Studies}, | |
| 182 | + publisher = {IAAO}, | |
| 183 | + address = {Kansas City, MO}, | |
| 184 | + year = {2013} | |
| 185 | +} | |
| 186 | + | |
| 187 | +@book{eckert1990property, | |
| 188 | + author = {Eckert, Joseph K. and Gloudemans, Robert J. and Almy, Richard R.}, | |
| 189 | + title = {Property Appraisal and Assessment Administration}, | |
| 190 | + publisher = {International Association of Assessing Officers}, | |
| 191 | + address = {Chicago}, | |
| 192 | + year = {1990} | |
| 193 | +} | |
| 194 | + | |
| 195 | +@book{gloudemans2011fundamentals, | |
| 196 | + author = {Gloudemans, Robert and Almy, Richard}, | |
| 197 | + title = {Fundamentals of Mass Appraisal}, | |
| 198 | + publisher = {International Association of Assessing Officers}, | |
| 199 | + address = {Kansas City, MO}, | |
| 200 | + year = {2011} | |
| 201 | +} | |
| 202 | + | |
| 203 | +@article{oates1969effects, | |
| 204 | + author = {Oates, Wallace E.}, | |
| 205 | + title = {The Effects of Property Taxes and Local Public Spending on Property Values: An Empirical Study of Tax Capitalization and the {Tiebout} Hypothesis}, | |
| 206 | + journal = {Journal of Political Economy}, | |
| 207 | + year = {1969}, | |
| 208 | + volume = {77}, | |
| 209 | + number = {6}, | |
| 210 | + pages = {957--971} | |
| 211 | +} | |
| 212 | + | |
| 213 | +@article{oates2016local, | |
| 214 | + author = {Oates, Wallace E. and Fischel, William A.}, | |
| 215 | + title = {Are Local Property Taxes Regressive, Progressive, or What?}, | |
| 216 | + journal = {National Tax Journal}, | |
| 217 | + year = {2016}, | |
| 218 | + volume = {69}, | |
| 219 | + number = {2}, | |
| 220 | + pages = {415--434} | |
| 221 | +} | |
| 222 | + | |
| 223 | +@article{rosen1974hedonic, | |
| 224 | + author = {Rosen, Sherwin}, | |
| 225 | + title = {Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition}, | |
| 226 | + journal = {Journal of Political Economy}, | |
| 227 | + year = {1974}, | |
| 228 | + volume = {82}, | |
| 229 | + number = {1}, | |
| 230 | + pages = {34--55} | |
| 231 | +} | |
| 232 | + | |
| 233 | +@incollection{malpezzi2003hedonic, | |
| 234 | + author = {Malpezzi, Stephen}, | |
| 235 | + title = {Hedonic Pricing Models: A Selective and Applied Review}, | |
| 236 | + booktitle = {Housing Economics and Public Policy}, | |
| 237 | + editor = {O'Sullivan, Tony and Gibb, Kenneth}, | |
| 238 | + publisher = {Blackwell}, | |
| 239 | + address = {Oxford}, | |
| 240 | + 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} | |
| 352 | +} | |
| 353 | + | |
| 354 | +@article{desrosiers2000hedonic, | |
| 355 | + author = {Des Rosiers, Fran{\c c}ois and Th{\'e}riault, Marius and Villeneuve, Paul-Y.}, | |
| 356 | + title = {Sorting Out Access and Neighbourhood Factors in Hedonic Price Modelling}, | |
| 357 | + journal = {Journal of Property Investment \& Finance}, | |
| 358 | + year = {2000}, | |
| 359 | + volume = {18}, | |
| 360 | + number = {3}, | |
| 361 | + pages = {291--315} | |
| 362 | +} | |
| 363 | + | |
| 364 | +@article{bostic2007land, | |
| 365 | + author = {Bostic, Raphael W. and Longhofer, Stanley D. and Redfearn, Christian L.}, | |
| 366 | + title = {Land Leverage: Decomposing Home Price Dynamics}, | |
| 367 | + journal = {Real Estate Economics}, | |
| 368 | + year = {2007}, | |
| 369 | + volume = {35}, | |
| 370 | + 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} | |
| 382 | +} | |
| 383 | + | |
| 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} | |
| 402 | +} | |
added
paper/sections/conclusion.tex
+37 −0
@@ -0,0 +1,37 @@ | ||
| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Conclusion} | |
| 4 | +\label{sec:concl} | |
| 5 | + | |
| 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. | |
| 21 | + | |
| 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. | |
| 31 | + | |
| 32 | +The matched sale--roll architecture built here supports a research agenda | |
| 33 | +beyond this audit: linking assessment gaps to neighbourhood | |
| 34 | +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. | |
added
paper/sections/data.tex
+101 −0
@@ -0,0 +1,101 @@ | ||
| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Data and sample construction} | |
| 4 | +\label{sec:data} | |
| 5 | + | |
| 6 | +\subsection{Sources and matching} | |
| 7 | + | |
| 8 | +We start from a compiled registry of 745{,}119 residential-market | |
| 9 | +transactions recorded in Quebec between January 2021 and July 2026, each | |
| 10 | +carrying the sale price, sale date, civic address, geographic coordinates, | |
| 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 | |
| 18 | +0.6~metres, and every observation retained in the estimation sample | |
| 19 | +reproduces the roll's assessed value exactly. | |
| 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}. | |
| 26 | + | |
| 27 | +\subsection{Sample restrictions} | |
| 28 | + | |
| 29 | +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 | |
| 34 | +high-confidence roll match (distance $\le 50$~m and score $\ge 150$; | |
| 35 | +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. | |
| 46 | + | |
| 47 | +\begin{table}[t] | |
| 48 | +\centering | |
| 49 | +\begin{threeparttable} | |
| 50 | +\caption{Summary statistics, estimation sample} | |
| 51 | +\label{tab:sumstats} | |
| 52 | +\small | |
| 53 | +\input{../results/tables/summary_stats} | |
| 54 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 55 | +\item \textit{Notes:} 522{,}769 residential sales, January 2021 -- July | |
| 56 | +2026, matched at the parcel level to the assessment roll in force at the | |
| 57 | +sale date. The assessment ratio is assessed value divided by sale price. | |
| 58 | +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 | |
| 60 | +land share is the roll's land value divided by total assessed value. | |
| 61 | +\end{tablenotes} | |
| 62 | +\end{threeparttable} | |
| 63 | +\end{table} | |
| 64 | + | |
| 65 | +\subsection{The raw pattern} | |
| 66 | + | |
| 67 | +The median assessment ratio is 0.78: the typical dwelling sells for about | |
| 68 | +28\% more than its rolled value, the expected imprint of a rising market on | |
| 69 | +back-dated rolls. Figure~\ref{fig:ratiodist} shows the distribution and its | |
| 70 | +decomposition by roll lag: sales occurring within two years of the | |
| 71 | +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? | |
| 80 | + | |
| 81 | +\begin{figure}[t] | |
| 82 | +\centering | |
| 83 | +\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 | |
| 87 | +between the roll's market-condition reference date and the sale; older | |
| 88 | +rolls sit systematically further below parity.} | |
| 89 | +\label{fig:ratiodist} | |
| 90 | +\end{figure} | |
| 91 | + | |
| 92 | +\begin{figure}[t] | |
| 93 | +\centering | |
| 94 | +\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.} | |
| 100 | +\label{fig:time} | |
| 101 | +\end{figure} | |
added
paper/sections/discussion.tex
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Discussion} | |
| 4 | +\label{sec:disc} | |
| 5 | + | |
| 6 | +\subsection{Mechanisms} | |
| 7 | + | |
| 8 | +The evidence assembles into a coherent mechanism story with three layers. | |
| 9 | + | |
| 10 | +\paragraph{1. Hedonic difficulty, not assessor idiosyncrasy.} The | |
| 11 | +heterogeneity profile tracks the difficulty of the valuation problem with | |
| 12 | +almost embarrassing fidelity: condominiums (homogeneous, comparable-rich) | |
| 13 | +are nearly equitable; old houses, plexes, cottages and high-land-share | |
| 14 | +properties (heterogeneous, comparable-poor, unanchored by construction | |
| 15 | +costs) are severely regressive. This is the pattern predicted if assessors | |
| 16 | +run reasonable hedonic models whose unexplained component is largest --- | |
| 17 | +and most value-correlated --- where the housing bundle is hardest to price | |
| 18 | +\citep{amornsiripanitch2022residential, gloudemans2011fundamentals, | |
| 19 | +bostic2007land}. Regression toward the mean in any imperfect valuation | |
| 20 | +model over-values the cheap tail and under-values the expensive tail; | |
| 21 | +our quantile profile, with proportionality holding at the bottom and | |
| 22 | +collapsing at the top ($\beta(0.90) = 0.49$), shows Quebec's failure is | |
| 23 | +concentrated where comparables are thinnest. | |
| 24 | + | |
| 25 | +\paragraph{2. Staleness amplifies the gap.} The doubling of the | |
| 26 | +province-wide PRB in 2021--2022 shows that triennial rolls interact | |
| 27 | +perversely with fast markets: when prices move 30--40\% between reference | |
| 28 | +dates, the cross-sectional dispersion of appreciation --- which is itself | |
| 29 | +correlated with price segment --- loads directly into measured inequity. | |
| 30 | +Jurisdictions cannot control housing cycles, but they control revaluation | |
| 31 | +frequency; annual-cycle systems mechanically cap this channel | |
| 32 | +\citep{berry2021reassessing, ross2012assessor}. | |
| 33 | + | |
| 34 | +\paragraph{3. Scale helps: the Montr\'eal exception.} Montr\'eal --- | |
| 35 | +the largest sales sample, a dedicated in-house assessment service, dense | |
| 36 | +comparable markets in every segment --- is the only large jurisdiction | |
| 37 | +with progressive assessments, in all six years. Mid-sized and small | |
| 38 | +municipalities, many relying on contracted regional evaluators with | |
| 39 | +limited modelling capacity, are uniformly regressive. The thin-market | |
| 40 | +mechanism of \citet{mcmillen2008thin} operates within a single provincial | |
| 41 | +rulebook: identical statutes, divergent outcomes, sorted by market depth | |
| 42 | +and assessment resources. We note one caveat: Montr\'eal's measured | |
| 43 | +progressivity may partly reflect within-city composition (its cell is the | |
| 44 | +whole city, pooling boroughs), and borough-level analysis is a natural | |
| 45 | +extension. | |
| 46 | + | |
| 47 | +\subsection{Policy implications} | |
| 48 | + | |
| 49 | +Three levers follow directly from the diagnosis, in increasing order of | |
| 50 | +ambition. First, \textbf{shorten the cycle}: moving from triennial to | |
| 51 | +annual (or indexed) rolls would eliminate the staleness component that | |
| 52 | +dominated 2021--2022; several U.S. states and British Columbia already | |
| 53 | +operate annual cycles. Second, \textbf{pool assessment capacity}: the | |
| 54 | +regressivity gradient by municipality size argues for regional or | |
| 55 | +provincial mass-appraisal services --- scale is the cheapest known | |
| 56 | +technology for assessment quality. Third, \textbf{audit vertically, not | |
| 57 | +just horizontally}: Quebec's oversight regime monitors median ratios and | |
| 58 | +CODs but sets no explicit PRB requirement; adding the IAAO vertical | |
| 59 | +standard to the ministry's audit criteria, with published | |
| 60 | +municipality-level statistics like those in this paper, would make the | |
| 61 | +equity dimension visible and contestable. Because low-priced-segment | |
| 62 | +owners appeal least \citep{avenancio2022assessment, plummer2014evidence}, | |
| 63 | +supply-side correction --- better models --- will do more than | |
| 64 | +demand-side remedies. | |
| 65 | + | |
| 66 | +\subsection{Limitations} | |
| 67 | + | |
| 68 | +Four limitations bound the interpretation. First, sale prices below | |
| 69 | +\$50{,}000 are absent from the source registry and some residual | |
| 70 | +non-arm's-length transfers may survive our screens; the robustness | |
| 71 | +battery (dropping sub-\$100k sales, tightening trims) shows the | |
| 72 | +conclusions survive, but the bottom-decile tax-shift magnitude should be | |
| 73 | +read as an upper bound on that decile. Second, our data cover 2021--2026, | |
| 74 | +an unusually turbulent market; the within-market elasticity is stable | |
| 75 | +across the window, but levels statistics from calmer periods would differ. | |
| 76 | +Third, we observe no appeals, renovations between assessment and sale, or | |
| 77 | +conditions of sale; some of what we call horizontal noise is genuine | |
| 78 | +unobserved quality change. Fourth, without owner demographics we cannot | |
| 79 | +speak to the distributional incidence across income or racial groups as | |
| 80 | +\citet{avenancio2022assessment} do --- linking these assessments to census | |
| 81 | +tract characteristics is the obvious next step. | |
added
paper/sections/institutional.tex
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Institutional setting: property assessment in Quebec} | |
| 4 | +\label{sec:inst} | |
| 5 | + | |
| 6 | +Quebec's municipal fiscal regime is governed by the \textit{Loi sur la | |
| 7 | +fiscalit\'e municipale} (LFM) and operationalized by the province's | |
| 8 | +assessment manual, the \textit{Manuel d'\'evaluation fonci\`ere du | |
| 9 | +Qu\'ebec} \citep{lfm2026, mamh2024manuel}. Four features matter for the | |
| 10 | +measurement design of this paper. | |
| 11 | + | |
| 12 | +\paragraph{Triennial rolls.} Every municipality's assessment roll is | |
| 13 | +redrawn on a fixed three-year cycle by a municipal body or a contracted | |
| 14 | +private firm under the responsibility of a chartered evaluator. The roll | |
| 15 | +lists, for each assessment unit, the taxable value of the property and its | |
| 16 | +decomposition into land and building components, along with the structural | |
| 17 | +descriptors used in valuation (lot area, floor area, year of construction, | |
| 18 | +number of dwelling units, physical configuration, and a standardized use | |
| 19 | +code, the CUBF). | |
| 20 | + | |
| 21 | +\paragraph{A statutory market-condition date.} Article 46 of the LFM | |
| 22 | +requires that the values entered on a roll reflect the state of the market | |
| 23 | +\emph{eighteen months before} the roll takes effect: a roll entering force | |
| 24 | +on January~1 of year $t$ must value every property as of July~1 of year | |
| 25 | +$t-2$. This single reference date is printed on the roll itself and is | |
| 26 | +common to every property in the municipality. Two implications follow. | |
| 27 | +First, in a rising market the \emph{level} of assessment ratios drifts | |
| 28 | +mechanically below one as sales occur further from the reference date --- | |
| 29 | +between 18 and 54 months elapse between the reference date and a sale, 36 | |
| 30 | +months at the median in our sample. This drift is a feature of the system, | |
| 31 | +not an inequity, and our empirical design absorbs it entirely with | |
| 32 | +municipality~$\times$~roll~$\times$~sale-year fixed effects. Second, and | |
| 33 | +crucially, \emph{within} such a block every property shares the same market | |
| 34 | +vintage, so cross-sectional patterns in ratios cannot be attributed to | |
| 35 | +timing. | |
| 36 | + | |
| 37 | +\paragraph{Uniform taxation of the rolled value.} The municipal levy on a | |
| 38 | +residential property is the rolled taxable value multiplied by the | |
| 39 | +municipal rate (plus school taxes levied on the same base). There are no | |
| 40 | +assessment-growth caps, homestead exemptions, or acquisition-value rules of | |
| 41 | +the Californian or Floridian type: relative taxable values within a | |
| 42 | +municipality equal relative assessed values. This makes the mapping from | |
| 43 | +assessment error to tax-burden redistribution exact --- a property assessed | |
| 44 | +10\% above the jurisdiction's median ratio pays 10\% more tax than uniform | |
| 45 | +assessment would imply --- and motivates the tax-shift calculation of | |
| 46 | +Section~\ref{sec:results}. | |
| 47 | + | |
| 48 | +\paragraph{Oversight and appeal.} The Ministry of Municipal Affairs (MAMH) | |
| 49 | +prescribes methods and audits rolls; owners may request an administrative | |
| 50 | +review and appeal to the Tribunal administratif du Qu\'ebec. Appeal rates | |
| 51 | +for residential property are low. Unlike several U.S. jurisdictions | |
| 52 | +studied in the literature \citep{plummer2014evidence, | |
| 53 | +avenancio2022assessment}, Quebec's appeal system plays a minor quantitative | |
| 54 | +role for the housing stock at large, which makes the valuation model | |
| 55 | +itself --- rather than post-assessment litigation --- the natural locus of | |
| 56 | +any inequity we measure. | |
| 57 | + | |
| 58 | +Taken together, these institutions imply that Quebec should be a | |
| 59 | +\emph{best-case} environment for assessment equity: uniform provincial | |
| 60 | +methodology, professional certification, statutory synchronization of | |
| 61 | +market vintage, and a tax that consumes the rolled value without | |
| 62 | +exemption-driven distortions. The magnitude of the inequity we document | |
| 63 | +below should be read against this backdrop. | |
added
paper/sections/introduction.tex
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Introduction} | |
| 4 | +\label{sec:intro} | |
| 5 | + | |
| 6 | +The property tax is the fiscal backbone of Canadian local government: it | |
| 7 | +finances roughly two thirds of municipal budgets and is, by statute, an | |
| 8 | +\emph{ad valorem} tax --- every dwelling in a municipality is meant to be | |
| 9 | +taxed in strict proportion to its market value. That proportionality rests | |
| 10 | +entirely on the quality of the assessment roll. If assessors systematically | |
| 11 | +overvalue inexpensive homes relative to expensive ones, the legal tax rate | |
| 12 | +becomes a fiction: the effective tax rate falls with wealth, and the | |
| 13 | +resulting redistribution --- from modest neighbourhoods toward affluent ones | |
| 14 | +--- occurs silently, without any legislative decision, embedded in a | |
| 15 | +technical document that few taxpayers ever contest. A rapidly growing | |
| 16 | +literature documents exactly this pattern in the United States, where | |
| 17 | +assessment regressivity has been measured at national scale | |
| 18 | +\citep{berry2021reassessing, avenancio2022assessment, | |
| 19 | +amornsiripanitch2022residential}. Whether the same pathology afflicts | |
| 20 | +Canadian assessment systems --- centralized, professionally supervised, and | |
| 21 | +widely presumed to be of high quality --- is essentially unknown. | |
| 22 | + | |
| 23 | +This paper provides the first province-wide answer for Quebec. We assemble | |
| 24 | +522{,}769 residential transactions recorded between January 2021 and July | |
| 25 | +2026 and match each sale, at the parcel level, to the triennial municipal | |
| 26 | +assessment roll in force on the day of the sale. The match is performed on | |
| 27 | +geographic coordinates and validated against the roll's recorded value; the | |
| 28 | +median match distance is under one metre. The resulting file couples every | |
| 29 | +sale price with the exact taxable value that generated the owner's property | |
| 30 | +tax bill, together with the roll's decomposition of that value into land and | |
| 31 | +building components, structural descriptors (lot area, floor area, year | |
| 32 | +built, number of units), and the statutory market-condition reference date | |
| 33 | +of the roll. The data span 625 municipalities --- from Montr\'eal | |
| 34 | +(79{,}581 usable sales) to towns with barely a hundred --- and a housing | |
| 35 | +cycle of unusual amplitude: the post-pandemic boom, the 2022--2023 interest | |
| 36 | +rate shock, and the subsequent recovery. | |
| 37 | + | |
| 38 | +Quebec's institutional design makes it an unusually clean laboratory for | |
| 39 | +equity measurement. Every municipality's roll is redone on a fixed | |
| 40 | +three-year cycle, and by law (art.~46, \textit{Loi sur la fiscalit\'e | |
| 41 | +municipale}) the values entered on a roll must reflect market conditions | |
| 42 | +eighteen months before the roll takes effect --- a single, known reference | |
| 43 | +date shared by every property in the municipality | |
| 44 | +\citep{lfm2026, mamh2024manuel}. Within a municipality $\times$ roll | |
| 45 | +$\times$ sale-year block, therefore, every assessment embodies the same | |
| 46 | +market vintage, and any systematic relationship between assessment ratios | |
| 47 | +and prices inside such a block is inequity, not timing. Our empirical design | |
| 48 | +exploits exactly this structure: all regression estimates absorb 2{,}884 | |
| 49 | +municipality~$\times$~roll~$\times$~year fixed effects, so that vertical | |
| 50 | +inequity is identified purely from comparisons between cheap and expensive | |
| 51 | +dwellings facing the same assessor, the same roll, and the same market | |
| 52 | +moment. | |
| 53 | + | |
| 54 | +Three findings emerge. First, assessment regressivity in Quebec is | |
| 55 | +pervasive, large, and statistically unambiguous. The elasticity of the | |
| 56 | +assessment ratio with respect to the sale price --- zero under proportional | |
| 57 | +assessment --- is $-0.34$ (s.e.\ $0.03$) in the fixed-effects log-log | |
| 58 | +regression. Because sale prices measure market value with noise, part of | |
| 59 | +that estimate reflects mechanical attenuation \citep{kochin1982vertical, | |
| 60 | +clapp1990new}; a rank-based instrumental-variables estimator in the spirit | |
| 61 | +of \citet{clapp1990new} that purges this bias still yields $-0.08$ | |
| 62 | +(s.e.\ $0.02$). Under the IAAO ratio-study standards used by assessment | |
| 63 | +authorities across North America \citep{iaao2013standard}, 95\% of Quebec | |
| 64 | +municipalities fall outside the acceptable band for price-related bias and | |
| 65 | +99\% exceed the uniformity (COD) ceiling. Strikingly, Montr\'eal --- the | |
| 66 | +province's largest and best-resourced assessment jurisdiction --- is the | |
| 67 | +\emph{only} major market whose assessments are progressive. | |
| 68 | + | |
| 69 | +Second, the inequity has a clear anatomy. Regressivity is roughly four times | |
| 70 | +stronger for single-family homes and plexes than for condominiums, whose | |
| 71 | +quasi-homogeneous units are easy to mass-appraise; it rises steeply with | |
| 72 | +building age and with the assessed land share of the property, consistent | |
| 73 | +with the difficulty of valuing land and depreciated structures | |
| 74 | +\citep{bostic2007land, gloudemans2011fundamentals}; and it is worse in small | |
| 75 | +municipalities, echoing the thin-market mechanism of \citet{mcmillen2008thin}. | |
| 76 | +The quantile profile is equally telling: the log-log slope | |
| 77 | +falls from $0.87$ at the first decile of the conditional value distribution | |
| 78 | +to $0.49$ at the ninth, so the failure of proportionality is concentrated at | |
| 79 | +the top --- expensive homes are not merely under-assessed, they are | |
| 80 | +under-assessed at an accelerating rate. | |
| 81 | + | |
| 82 | +Third, the stakes are material. Within a taxing jurisdiction the levy is | |
| 83 | +proportional to assessed value, so a property assessed above the | |
| 84 | +jurisdiction median ratio pays exactly that percentage more tax than uniform | |
| 85 | +assessment would imply. The median dwelling in the bottom within-market | |
| 86 | +price decile pays roughly 65\% more property tax than under uniform | |
| 87 | +assessment; the median dwelling in the top decile pays about 5\% less. Put | |
| 88 | +differently, the effective tax schedule that Quebec's assessment machinery | |
| 89 | +delivers is regressive enough to undo, within each municipality, a | |
| 90 | +substantial share of whatever progressivity the rest of the fiscal system | |
| 91 | +achieves --- a finding that complements \citet{carbonnier2024property}, who | |
| 92 | +documents the regressivity of Quebec's property tax relative to income using | |
| 93 | +survey data, but who could not observe the assessment channel isolated here. | |
| 94 | + | |
| 95 | +We also show \emph{when} the gap opens. Assessment ratios drift mechanically | |
| 96 | +between reference dates, and the province-wide price-related bias doubles in | |
| 97 | +2021--2022, precisely when the post-pandemic boom pulled market prices away | |
| 98 | +from rolls anchored in 2018--2020 conditions --- direct evidence that | |
| 99 | +infrequent revaluation is a first-order driver of measured inequity, as | |
| 100 | +conjectured in the U.S. literature \citep{berry2021reassessing, | |
| 101 | +ross2012assessor}. Because the diagnosis singles out stale rolls, thin | |
| 102 | +markets, and hard-to-value property types --- rather than assessor | |
| 103 | +discretion alone --- it maps directly into policy: shorter revaluation | |
| 104 | +cycles, pooled assessment services for small municipalities, and targeted | |
| 105 | +review of high-land-share and older properties. | |
| 106 | + | |
| 107 | +Beyond the Canadian evidence gap, the paper makes two methodological | |
| 108 | +contributions to the ratio-study literature. It is, to our knowledge, the | |
| 109 | +first large-scale equity study to exploit a statutory single-date reference | |
| 110 | +regime to separate timing drift from genuine vertical inequity by design | |
| 111 | +rather than by econometric correction; and it implements the full modern | |
| 112 | +test battery --- IAAO diagnostics with bootstrap inference | |
| 113 | +\citep{iaao2013standard}, the classical regression tests | |
| 114 | +\citep{paglin1972equity, cheng1974property}, measurement-error-robust IV | |
| 115 | +\citep{clapp1990new}, and quantile profiles \citep{mcmillen2020assessment} | |
| 116 | +--- on more than half a million sales, allowing precise subgroup estimates | |
| 117 | +that smaller samples cannot support. | |
| 118 | + | |
| 119 | +The remainder of the paper proceeds as follows. Section~\ref{sec:lit} | |
| 120 | +positions the paper in the ratio-study and property-tax-equity literatures. | |
| 121 | +Section~\ref{sec:inst} describes Quebec's assessment institutions. | |
| 122 | +Section~\ref{sec:data} presents the data and the matched sample. | |
| 123 | +Section~\ref{sec:method} lays out the diagnostics and econometric | |
| 124 | +specifications. Section~\ref{sec:results} reports the results, | |
| 125 | +Section~\ref{sec:robust} the robustness battery, Section~\ref{sec:disc} | |
| 126 | +discusses mechanisms and policy implications, and Section~\ref{sec:concl} | |
| 127 | +concludes. | |
added
paper/sections/literature.tex
+100 −0
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Related literature} | |
| 4 | +\label{sec:lit} | |
| 5 | + | |
| 6 | +\subsection{Measuring vertical inequity: from ratio studies to modern tests} | |
| 7 | + | |
| 8 | +The empirical study of assessment equity is nearly as old as the modern | |
| 9 | +property tax. Its workhorse is the \emph{sales ratio study}: for each sale | |
| 10 | +$i$, compute the ratio $r_i = AV_i/SP_i$ of assessed value to sale price and | |
| 11 | +ask whether $r_i$ is uniform across the value distribution. The | |
| 12 | +practitioner's canon --- codified in the IAAO \textit{Standard on Ratio | |
| 13 | +Studies} \citep{iaao2013standard} and the mass-appraisal manuals of | |
| 14 | +\citet{eckert1990property} and \citet{gloudemans2011fundamentals} --- | |
| 15 | +summarizes a jurisdiction with the median ratio, the coefficient of | |
| 16 | +dispersion (COD) for horizontal uniformity, and the price-related | |
| 17 | +differential (PRD) or, since 2013, the coefficient of price-related bias | |
| 18 | +(PRB) for vertical equity. These diagnostics discipline assessment practice | |
| 19 | +across North America, and we report all of them, with bootstrap confidence | |
| 20 | +intervals, for every Quebec municipality with sufficient sales. | |
| 21 | + | |
| 22 | +The academic literature grew out of dissatisfaction with those summary | |
| 23 | +measures. \citet{paglin1972equity} proposed regressing assessed value on | |
| 24 | +sale price in levels and reading regressivity off a positive intercept; | |
| 25 | +\citet{cheng1974property} moved the test to logarithms, where the slope | |
| 26 | +$\beta$ has the clean interpretation of an elasticity and $\beta<1$ signals | |
| 27 | +regressivity. Subsequent work refined the specification menu --- | |
| 28 | +\citet{bell1984administrative} and \citet{sunderman1990testing} allowed | |
| 29 | +splines and structural breaks, and \citet{sirmans1995vertical} surveyed the | |
| 30 | +proliferating test battery. A decisive critique came from | |
| 31 | +\citet{kochin1982vertical} and \citet{kennedy1984unfair}: because the sale | |
| 32 | +price is itself a noisy measure of market value, the log-log slope is | |
| 33 | +attenuated toward zero even under perfectly proportional assessment --- | |
| 34 | +ratio studies are biased \emph{toward} finding regressivity. | |
| 35 | +\citet{clapp1990new} answered with a rank-based instrumental-variables | |
| 36 | +estimator whose coarse instrument is nearly orthogonal to transitory price | |
| 37 | +noise; \citet{goolsby1997assessment} and \citet{mcmillen2020assessment} | |
| 38 | +document how severely the correction can matter, and | |
| 39 | +\citet{quintos2020prb} extends the toolkit with machine-learning | |
| 40 | +diagnostics. Our design follows this lesson to the letter: we report the | |
| 41 | +na\"ive estimates, the Clapp IV, and quantile profiles | |
| 42 | +\citep{mcmillen2020assessment} side by side, and treat the IV as the lower | |
| 43 | +bound on true regressivity. | |
| 44 | + | |
| 45 | +\subsection{Evidence: pervasive regressivity, mostly documented in the U.S.} | |
| 46 | + | |
| 47 | +Substantively, the modern consensus is that assessment regressivity is the | |
| 48 | +rule rather than the exception. \citet{berry2021reassessing} computes ratio | |
| 49 | +statistics for essentially every U.S. county and finds that the | |
| 50 | +lowest-decile home within a jurisdiction faces an effective tax rate roughly | |
| 51 | +double that of the top decile; \citet{avenancio2022assessment} show in the | |
| 52 | +\textit{QJE} that the same machinery generates a 10--13\% assessment gap | |
| 53 | +against Black and Hispanic homeowners, driven partly by unpriced | |
| 54 | +neighbourhood attributes and partly by differential appeals; | |
| 55 | +\citet{amornsiripanitch2022residential} attributes much of the gradient to | |
| 56 | +assessors' inability to capture unobserved quality that scales with price. | |
| 57 | +Earlier strands documented the same pattern city by city --- | |
| 58 | +\citet{engle1975deassessment} in Boston, \citet{baar1981property} across | |
| 59 | +low-income neighbourhoods, \citet{mcmillen2011assessment} and | |
| 60 | +\citet{mcmillen2008thin} in Illinois, where thin markets and infrequent | |
| 61 | +reassessment emerge as structural drivers, \citet{hodge2017assessment} in | |
| 62 | +collapsing Detroit, and \citet{plummer2014evidence} and | |
| 63 | +\citet{ihlanfeldt2023appraisal} on the role of appeals and exemptions. | |
| 64 | +\citet{ross2012assessor} shows regressivity responds to the institutional | |
| 65 | +incentives of assessors themselves. The mechanism menu that emerges --- | |
| 66 | +stale valuations, hard-to-value heterogeneous properties, thin markets, | |
| 67 | +asymmetric appeals --- guides our heterogeneity analysis directly. | |
| 68 | + | |
| 69 | +\subsection{Canada: a conspicuous gap} | |
| 70 | + | |
| 71 | +For Canada the cupboard is nearly bare. Ontario's assessment corporation | |
| 72 | +publishes an internal vertical-equity review of its own values | |
| 73 | +\citep{mpac2022vertical}, and \citet{found2017property} compare tax | |
| 74 | +\emph{rates} across cities, but neither measures sale-level equity. | |
| 75 | +For Quebec, \citet{carbonnier2024property} establishes with survey microdata | |
| 76 | +that property tax payments are steeply regressive relative to | |
| 77 | +\emph{income}; the assessment channel --- whether the tax base itself is | |
| 78 | +mismeasured against \emph{market value} --- has never been examined at | |
| 79 | +scale, for Quebec or for any Canadian province. This is the gap the present | |
| 80 | +paper fills. The Canadian case is of independent interest precisely because | |
| 81 | +its institutions differ from the fragmented U.S. county system on the | |
| 82 | +dimensions the U.S. literature blames: Quebec assessment is governed by a | |
| 83 | +uniform provincial statute and manual \citep{lfm2026, mamh2024manuel}, | |
| 84 | +performed by certified professional evaluators, and synchronized to a | |
| 85 | +statutory market-condition date. Finding large regressivity \emph{despite} | |
| 86 | +this apparatus sharpens the interpretation considerably: the problem is not | |
| 87 | +lax governance but the intrinsic difficulty of mass appraisal, compounded by | |
| 88 | +triennial staleness. | |
| 89 | + | |
| 90 | +\subsection{Hedonic foundations} | |
| 91 | + | |
| 92 | +Finally, the paper connects to the hedonic tradition. Mass appraisal is | |
| 93 | +applied hedonics \citep{rosen1974hedonic, malpezzi2003hedonic}: the | |
| 94 | +assessor's model prices a bundle of structural and locational attributes, | |
| 95 | +and equity failures are hedonic specification failures --- unpriced | |
| 96 | +land-share gradients \citep{bostic2007land}, depreciation curvature, or | |
| 97 | +neighbourhood effects that Quebec practitioners have long modelled in the | |
| 98 | +Quebec City market \citep{desrosiers2000hedonic}. Reading our subgroup | |
| 99 | +estimates through this lens turns an audit into a diagnosis: the assessment | |
| 100 | +gap is largest exactly where the hedonic problem is hardest. | |
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paper/sections/methodology.tex
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Methodology} | |
| 4 | +\label{sec:method} | |
| 5 | + | |
| 6 | +Let $AV_i$ denote the assessed value of property $i$ on the roll in force | |
| 7 | +at its sale, $SP_i$ its sale price, and $r_i = AV_i/SP_i$ the assessment | |
| 8 | +ratio. Under perfectly proportional (vertically equitable) assessment, | |
| 9 | +$\mathbb{E}[r_i \mid SP_i]$ is constant. All tests below ask, in different | |
| 10 | +ways, whether $r_i$ instead declines with value. | |
| 11 | + | |
| 12 | +\subsection{IAAO ratio-study diagnostics} | |
| 13 | + | |
| 14 | +For any group of sales we report the four statistics of the IAAO | |
| 15 | +\textit{Standard on Ratio Studies} \citep{iaao2013standard}. The | |
| 16 | +\emph{median ratio} measures the assessment level. The \emph{coefficient of | |
| 17 | +dispersion}, | |
| 18 | +$\mathrm{COD} = 100 \cdot \operatorname{mean}\!\left(|r_i - | |
| 19 | +\tilde r|\right) / \tilde r$ with $\tilde r$ the median ratio, measures | |
| 20 | +horizontal uniformity; the standard deems residential CODs above 15 | |
| 21 | +unacceptable. The \emph{price-related differential}, | |
| 22 | +$\mathrm{PRD} = \bar r \,/\, (\sum_i AV_i / \sum_i SP_i)$, compares the | |
| 23 | +unweighted and value-weighted mean ratios; PRD~$>1.03$ indicates | |
| 24 | +regressivity. Because the PRD is sensitive to outliers, the standard's | |
| 25 | +preferred vertical measure is the \emph{coefficient of price-related bias} | |
| 26 | +(PRB), the slope $b$ in | |
| 27 | +\begin{equation} | |
| 28 | +\frac{r_i - \tilde r}{\tilde r} | |
| 29 | + \;=\; a + b \cdot \log_2\!\Big(\tfrac{1}{2}SP_i + | |
| 30 | + \tfrac{1}{2}\,AV_i/\tilde r\Big) + u_i , | |
| 31 | +\label{eq:prb} | |
| 32 | +\end{equation} | |
| 33 | +which measures the proportional change in the ratio per doubling of value; | |
| 34 | +the acceptable band is $[-0.05, 0.05]$. We compute percentile-bootstrap | |
| 35 | +confidence intervals for all four statistics. Because ratio levels drift | |
| 36 | +with roll staleness, municipality-level diagnostics are computed within | |
| 37 | +municipality~$\times$~sale-year blocks --- inside which a single roll is in | |
| 38 | +force --- and aggregated across years by the median. | |
| 39 | + | |
| 40 | +\subsection{Regression tests with market-timing fixed effects} | |
| 41 | + | |
| 42 | +Our workhorse is the log-log specification of \citet{cheng1974property}, | |
| 43 | +\begin{equation} | |
| 44 | +\ln AV_i \;=\; \alpha_{c(i)} + \beta \, \ln SP_i + \varepsilon_i , | |
| 45 | +\label{eq:cheng} | |
| 46 | +\end{equation} | |
| 47 | +where $c(i)$ indexes the municipality~$\times$~roll~$\times$~sale-year cell | |
| 48 | +of sale $i$ and the $\alpha_c$ are 2{,}884 absorbed fixed effects. | |
| 49 | +Proportionality implies $\beta = 1$; we report | |
| 50 | +$\gamma \equiv \beta - 1$, the elasticity of the assessment \emph{ratio} | |
| 51 | +with respect to price ($\gamma<0$: regressive). The fixed effects guarantee | |
| 52 | +that $\gamma$ is identified only from comparisons of dwellings assessed by | |
| 53 | +the same authority, on the same roll vintage, and sold in the same year --- | |
| 54 | +purging the staleness drift, municipal composition, and aggregate market | |
| 55 | +movements in one stroke. For completeness we also report the pooled | |
| 56 | +regression without fixed effects and the levels test of | |
| 57 | +\citet{paglin1972equity}. Inference is clustered at the municipality level | |
| 58 | +throughout (625 clusters). | |
| 59 | + | |
| 60 | +\subsection{Measurement error and the Clapp instrument} | |
| 61 | + | |
| 62 | +Sale prices measure market value with idiosyncratic noise --- bilateral | |
| 63 | +bargaining, unobserved conditions of sale --- so OLS on | |
| 64 | +equation~\eqref{eq:cheng} suffers attenuation bias: $\hat\beta < 1$ even | |
| 65 | +under proportional assessment \citep{kochin1982vertical, kennedy1984unfair}. | |
| 66 | +Following \citet{clapp1990new}, we instrument $\ln SP_i$ with a coarse rank | |
| 67 | +variable $Z_i \in \{-1, 0, +1\}$ that flags sales in the bottom or top | |
| 68 | +third of \emph{both} the within-cell $\ln AV$ and $\ln SP$ distributions. | |
| 69 | +Because $Z_i$ retains only ordinal information agreed on by both measures of | |
| 70 | +value, it is (nearly) orthogonal to the transitory component of either, and | |
| 71 | +the resulting two-stage least-squares estimate of $\beta$ is consistent | |
| 72 | +under classical measurement error. The demeaned-within-cell implementation | |
| 73 | +preserves the fixed-effects structure. Throughout the paper we treat | |
| 74 | +$\gamma_{\text{IV}}$ as a conservative lower bound on regressivity and | |
| 75 | +$\gamma_{\text{FE}}$ as the descriptive upper bound; the truth lies between. | |
| 76 | + | |
| 77 | +\subsection{Quantile profile and heterogeneity} | |
| 78 | + | |
| 79 | +Averaging can hide where proportionality fails. We estimate | |
| 80 | +equation~\eqref{eq:cheng} by quantile regression on within-cell demeaned | |
| 81 | +variables at $\tau \in \{0.10, 0.25, 0.50, 0.75, 0.90\}$ | |
| 82 | +\citep{mcmillen2020assessment}, tracing $\beta(\tau)$ across the | |
| 83 | +conditional distribution of assessed values. We then re-estimate the | |
| 84 | +fixed-effects model on subsamples --- property class, building-age bands, | |
| 85 | +assessed-land-share bands, roll-lag bands, municipality size, and sale year | |
| 86 | +--- keeping only cells that retain at least 20 sales, to locate the | |
| 87 | +inequity where the mass-appraisal problem is hardest. | |
| 88 | + | |
| 89 | +\subsection{Horizontal inequity} | |
| 90 | + | |
| 91 | +Vertical tests concern the \emph{mean} of $r_i$ given value; horizontal | |
| 92 | +equity concerns its \emph{dispersion} among comparable properties | |
| 93 | +\citep{allen2002measuring, sirmans2008vertical}. Beyond the COD, we ask | |
| 94 | +who receives noisy assessments: we regress the absolute deviation of a | |
| 95 | +sale's log ratio from its cell median, | |
| 96 | +$|\ln r_i - \operatorname{med}_{c(i)} \ln r|$, on property characteristics | |
| 97 | +(age, land share, property-class indicators) with cell fixed effects. | |
| 98 | + | |
| 99 | +\subsection{The implied tax shift} | |
| 100 | + | |
| 101 | +Because Quebec taxes the rolled value without exemptions or caps | |
| 102 | +(Section~\ref{sec:inst}), a property whose ratio exceeds its jurisdiction's | |
| 103 | +median by $x\%$ pays exactly $x\%$ more tax than uniform assessment would | |
| 104 | +imply. For each sale we compute the relative assessment error | |
| 105 | +$e_i = r_i / \operatorname{med}_{c(i)}(r) - 1$ and average it by | |
| 106 | +within-cell sale-price decile. This translates the econometrics into the | |
| 107 | +policy-relevant object: the percentage over- or under-payment of property | |
| 108 | +tax by position in the local price distribution. | |
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paper/sections/results.tex
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| 1 | +% Author: Simon-Pierre Boucher — contact@spboucher.ai | |
| 2 | +% ============================================================================ | |
| 3 | +\section{Results} | |
| 4 | +\label{sec:results} | |
| 5 | + | |
| 6 | +\subsection{Province-wide diagnostics} | |
| 7 | + | |
| 8 | +Table~\ref{tab:iaao} reports the IAAO statistics for the full sample and by | |
| 9 | +sale year. Three facts stand out. First, uniformity is poor everywhere: the | |
| 10 | +province-wide COD is 28.5, and even within municipality-year blocks the | |
| 11 | +median municipality posts a COD of 26 --- nearly twice the IAAO ceiling of | |
| 12 | +15 for residential property; 99\% of municipalities exceed it | |
| 13 | +(Figure~\ref{fig:cod}). Second, every vertical measure points the same way: | |
| 14 | +the PRD is 1.072 (acceptable range 0.98--1.03) and the PRB is $-0.029$ with | |
| 15 | +a bootstrap confidence interval far from zero --- ratios fall by about 3\% | |
| 16 | +of the median with every doubling of value. Third, the time pattern is | |
| 17 | +diagnostic: the PRB collapses to $-0.104$ and $-0.117$ in 2021 and 2022 --- | |
| 18 | +when the boom pulled prices away from rolls referenced on 2018--2020 | |
| 19 | +markets --- and shrinks to $-0.002$ in 2024 before widening again. Vertical | |
| 20 | +inequity is not a fixed institutional constant; it breathes with the gap | |
| 21 | +between the market and the roll's vintage. | |
| 22 | + | |
| 23 | +\begin{table}[t] | |
| 24 | +\centering | |
| 25 | +\begin{threeparttable} | |
| 26 | +\caption{IAAO ratio-study diagnostics, province-wide} | |
| 27 | +\label{tab:iaao} | |
| 28 | +\small | |
| 29 | +\input{../results/tables/iaao} | |
| 30 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 31 | +\item \textit{Notes:} Median assessment ratio, coefficient of dispersion | |
| 32 | +(COD), price-related differential (PRD) and coefficient of price-related | |
| 33 | +bias (PRB), computed on the estimation sample; 95\% percentile-bootstrap | |
| 34 | +confidence intervals (200 replications) in brackets. IAAO acceptable | |
| 35 | +ranges: COD $\le 15$ (single-family residential), PRD $\in [0.98, 1.03]$, | |
| 36 | +PRB $\in [-0.05, 0.05]$. | |
| 37 | +\end{tablenotes} | |
| 38 | +\end{threeparttable} | |
| 39 | +\end{table} | |
| 40 | + | |
| 41 | +\begin{figure}[t] | |
| 42 | +\centering | |
| 43 | +\includegraphics[width=\textwidth]{fig_cod.png} | |
| 44 | +\caption{Horizontal uniformity. Panel A: distribution of municipality-level | |
| 45 | +CODs (median across sale-year blocks); the IAAO ceiling for residential | |
| 46 | +property is 15. Panel B: COD against the number of sales in the | |
| 47 | +municipality; dispersion is worst in the thinnest markets.} | |
| 48 | +\label{fig:cod} | |
| 49 | +\end{figure} | |
| 50 | + | |
| 51 | +Table~\ref{tab:cities} disaggregates the ten largest markets. | |
| 52 | +Regressivity is significant in nine of them --- Sherbrooke ($-0.39$), | |
| 53 | +Trois-Rivi\`eres ($-0.32$) and Terrebonne ($-0.29$) are the worst --- in | |
| 54 | +every single sale year. The exception is Montr\'eal, whose PRB of $+0.07$ | |
| 55 | +makes it the lone \emph{progressive} large jurisdiction in the province, in | |
| 56 | +all six years. We return to this contrast in Section~\ref{sec:disc}. | |
| 57 | +Figure~\ref{fig:map} maps the municipal estimates: regressive (red) | |
| 58 | +municipalities carpet the province, with the Montr\'eal agglomeration a | |
| 59 | +solitary blue island, and Figure~\ref{fig:prbmuni} shows the distribution: | |
| 60 | +99\% of the 261 municipalities with at least 100 usable sales have a | |
| 61 | +negative PRB, and 95\% fall below the IAAO band. | |
| 62 | + | |
| 63 | +\begin{table}[t] | |
| 64 | +\centering | |
| 65 | +\begin{threeparttable} | |
| 66 | +\caption{Assessment equity in the ten largest markets} | |
| 67 | +\label{tab:cities} | |
| 68 | +\small | |
| 69 | +\input{../results/tables/iaao_cities} | |
| 70 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 71 | +\item \textit{Notes:} Statistics computed within municipality | |
| 72 | +$\times$ sale-year blocks (a single roll in force per block) and | |
| 73 | +aggregated across years by the median; $n$ is the total number of sales. | |
| 74 | +The last column is the share of the six sale years in which the | |
| 75 | +municipality's PRB is negative. | |
| 76 | +\end{tablenotes} | |
| 77 | +\end{threeparttable} | |
| 78 | +\end{table} | |
| 79 | + | |
| 80 | +\begin{figure}[t] | |
| 81 | +\centering | |
| 82 | +\includegraphics[width=0.72\textwidth]{fig_prb_muni.png} | |
| 83 | +\caption{Distribution of municipality-level PRB across the 261 | |
| 84 | +municipalities with at least 100 usable sales. The shaded band is the IAAO | |
| 85 | +acceptable range $[-0.05, 0.05]$.} | |
| 86 | +\label{fig:prbmuni} | |
| 87 | +\end{figure} | |
| 88 | + | |
| 89 | +\begin{figure}[t] | |
| 90 | +\centering | |
| 91 | +\includegraphics[width=\textwidth]{fig_map.png} | |
| 92 | +\caption{The geography of vertical inequity. Municipality-level PRB | |
| 93 | +(median across sale-year blocks); bubble area is proportional to the | |
| 94 | +square root of the number of sales. Montr\'eal is the only large | |
| 95 | +progressive jurisdiction.} | |
| 96 | +\label{fig:map} | |
| 97 | +\end{figure} | |
| 98 | + | |
| 99 | +\subsection{Regression estimates} | |
| 100 | + | |
| 101 | +Table~\ref{tab:vertical} presents the econometric core. | |
| 102 | +Figure~\ref{fig:binscatter} shows the raw material: within | |
| 103 | +municipality~$\times$~roll~$\times$~year cells, mean log assessment ratios | |
| 104 | +fall monotonically --- and remarkably linearly through the central 90\% of | |
| 105 | +the distribution --- as log prices rise. The pooled \citet{cheng1974property} | |
| 106 | +elasticity is $\beta = 0.812$ (s.e.\ 0.029); absorbing the 2{,}884 cell | |
| 107 | +fixed effects \emph{steepens} it to $\beta = 0.656$, i.e.\ | |
| 108 | +$\gamma_{\text{FE}} = -0.344$: within the same market and vintage, a home | |
| 109 | +priced 10\% above its neighbours is assessed only about 6.6\% higher, so | |
| 110 | +its ratio is 3.4\% lower. The levels test of \citet{paglin1972equity} | |
| 111 | +agrees: the intercept is \$31{,}729 (s.e.\ \$5{,}378) --- inexpensive | |
| 112 | +properties carry a fixed assessment premium. | |
| 113 | + | |
| 114 | +\begin{table}[t] | |
| 115 | +\centering | |
| 116 | +\begin{threeparttable} | |
| 117 | +\caption{Vertical-inequity regressions} | |
| 118 | +\label{tab:vertical} | |
| 119 | +\small | |
| 120 | +\input{../results/tables/vertical} | |
| 121 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 122 | +\item \textit{Notes:} Dependent variable: $\ln AV$. Column (1): pooled | |
| 123 | +OLS. Column (2): absorbing least squares with 2{,}884 municipality | |
| 124 | +$\times$ roll $\times$ sale-year fixed effects. Column (3): within-cell | |
| 125 | +2SLS using the \citet{clapp1990new} rank instrument | |
| 126 | +$Z \in \{-1,0,+1\}$. Standard errors clustered by municipality (625 | |
| 127 | +clusters) in parentheses. Stars test $H_0\!: \beta = 1$ (proportional | |
| 128 | +assessment); *** $p<0.01$. | |
| 129 | +\end{tablenotes} | |
| 130 | +\end{threeparttable} | |
| 131 | +\end{table} | |
| 132 | + | |
| 133 | +\begin{figure}[t] | |
| 134 | +\centering | |
| 135 | +\includegraphics[width=0.72\textwidth]{fig_binscatter.png} | |
| 136 | +\caption{Vertical inequity within markets. Mean of the within-cell demeaned | |
| 137 | +log assessment ratio by vigintile of the within-cell demeaned log sale | |
| 138 | +price; whiskers are 95\% confidence intervals (they are smaller than the | |
| 139 | +markers). The fitted line is the sale-weighted least-squares slope.} | |
| 140 | +\label{fig:binscatter} | |
| 141 | +\end{figure} | |
| 142 | + | |
| 143 | +How much of this is measurement-error artefact? The \citet{clapp1990new} | |
| 144 | +instrument delivers $\beta_{\text{IV}} = 0.917$ (s.e.\ 0.021): | |
| 145 | +attenuation indeed accounts for the majority of the na\"ive gap, exactly | |
| 146 | +as the critique of \citet{kochin1982vertical} predicts --- but the | |
| 147 | +corrected elasticity remains four standard errors below one. Genuine | |
| 148 | +regressivity of roughly $-0.08$ survives the harshest correction in the | |
| 149 | +literature. An 8\% ratio penalty per log-point of value is economically | |
| 150 | +large: across the interquartile price range within a typical market | |
| 151 | +(roughly 0.8 log points), it generates a 6--7\% differential in effective | |
| 152 | +tax rates from vertical inequity alone, before adding the much larger | |
| 153 | +dispersion documented below. | |
| 154 | + | |
| 155 | +\subsection{Where proportionality fails: the quantile profile} | |
| 156 | + | |
| 157 | +Figure~\ref{fig:quantile} plots $\beta(\tau)$. The profile is strikingly | |
| 158 | +asymmetric: $\beta$ is 0.87 at $\tau=0.10$ and 0.86 at $\tau=0.25$, then | |
| 159 | +falls to 0.70 at $\tau=0.75$ and 0.49 at $\tau=0.90$ | |
| 160 | +(Table~\ref{tab:quantile} in the robustness section reports the | |
| 161 | +coefficients). Assessment tracks the market tolerably well through the | |
| 162 | +middle of the distribution and loses contact at the top: the most expensive | |
| 163 | +homes within each market are under-assessed at an accelerating rate. This | |
| 164 | +is the signature of hedonic truncation --- mass-appraisal models built on | |
| 165 | +mid-market comparables extrapolate poorly into thin luxury segments | |
| 166 | +\citep{amornsiripanitch2022residential, gloudemans2011fundamentals}. | |
| 167 | + | |
| 168 | +\begin{figure}[t] | |
| 169 | +\centering | |
| 170 | +\includegraphics[width=0.72\textwidth]{fig_quantile.png} | |
| 171 | +\caption{Quantile profile of the Cheng elasticity. Quantile regressions of | |
| 172 | +within-cell demeaned $\ln AV$ on demeaned $\ln SP$; the shaded band is the | |
| 173 | +pointwise 95\% confidence interval. Reference lines mark proportionality | |
| 174 | +($\beta=1$) and the FE and IV point estimates.} | |
| 175 | +\label{fig:quantile} | |
| 176 | +\end{figure} | |
| 177 | + | |
| 178 | +\subsection{The anatomy of regressivity} | |
| 179 | + | |
| 180 | +Figure~\ref{fig:het} and Table~\ref{tab:het} dissect | |
| 181 | +$\gamma_{\text{FE}}$ by subsample, and the pattern reads like a map of | |
| 182 | +mass-appraisal difficulty: | |
| 183 | + | |
| 184 | +\begin{itemize} | |
| 185 | +\item \textbf{Property class.} Condominiums --- homogeneous units with | |
| 186 | +abundant comparables --- show $\gamma = -0.12$, single-family homes | |
| 187 | +$-0.45$ and plexes $-0.49$. The assessor's problem, not the assessor's | |
| 188 | +jurisdiction, drives the gradient. | |
| 189 | +\item \textbf{Building age.} Regressivity deepens from $-0.30$ (under 20 | |
| 190 | +years) to $-0.43$ (over 60): depreciation and renovation heterogeneity are | |
| 191 | +hard to observe from the roll. | |
| 192 | +\item \textbf{Land share.} The starkest gradient: $-0.26$ where land is | |
| 193 | +under 20\% of assessed value versus $-0.50$ where it exceeds 40\%. | |
| 194 | +Land is the component without construction-cost anchoring | |
| 195 | +\citep{bostic2007land}, and properties whose value is mostly land are | |
| 196 | +assessed worst. | |
| 197 | +\item \textbf{Municipality size.} Large markets ($>$10k sales) do | |
| 198 | +better ($-0.27$) than mid-sized ones ($-0.41$), consistent with | |
| 199 | +\citet{mcmillen2008thin}. | |
| 200 | +\item \textbf{Stability.} Estimates are remarkably stable across sale | |
| 201 | +years ($-0.32$ to $-0.38$) and roll lags --- unlike the \emph{level} | |
| 202 | +statistics, the within-market elasticity is a structural feature of the | |
| 203 | +valuation technology, not of the cycle. | |
| 204 | +\end{itemize} | |
| 205 | + | |
| 206 | +\begin{figure}[p] | |
| 207 | +\centering | |
| 208 | +\includegraphics[width=0.85\textwidth]{fig_heterogeneity.png} | |
| 209 | +\caption{Heterogeneity of the within-market elasticity | |
| 210 | +$\gamma$. Each point is a separate fixed-effects estimate of | |
| 211 | +equation~\eqref{eq:cheng} on the indicated subsample; whiskers are 95\% | |
| 212 | +confidence intervals with municipality-clustered standard errors.} | |
| 213 | +\label{fig:het} | |
| 214 | +\end{figure} | |
| 215 | + | |
| 216 | +\begin{table}[p] | |
| 217 | +\centering | |
| 218 | +\begin{threeparttable} | |
| 219 | +\caption{Heterogeneity of vertical inequity} | |
| 220 | +\label{tab:het} | |
| 221 | +\small | |
| 222 | +\input{../results/tables/heterogeneity} | |
| 223 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 224 | +\item \textit{Notes:} Cheng fixed-effects estimates of | |
| 225 | +$\gamma = \beta - 1$ by subsample; cells with fewer than 20 sales after | |
| 226 | +masking are dropped. Municipality-clustered standard errors in | |
| 227 | +parentheses. *, **, *** denote significance at 10\%, 5\%, 1\%. | |
| 228 | +\end{tablenotes} | |
| 229 | +\end{threeparttable} | |
| 230 | +\end{table} | |
| 231 | + | |
| 232 | +\subsection{Horizontal inequity} | |
| 233 | + | |
| 234 | +Table~\ref{tab:horizontal} reports the dispersion regression. The mean | |
| 235 | +absolute deviation of a sale's log ratio from its cell median is 0.188 --- | |
| 236 | +the typical Quebec dwelling is assessed 19\% away from its market's norm, | |
| 237 | +an enormous horizontal lottery consistent with the COD evidence. The | |
| 238 | +deviation rises by 0.75~log points per decade of building age and by | |
| 239 | +5.2~points for cottages, and falls by 5.5~points for condominiums. | |
| 240 | +Old, idiosyncratic, land-heavy properties receive not only biased but | |
| 241 | +\emph{noisy} valuations. | |
| 242 | + | |
| 243 | +\begin{table}[t] | |
| 244 | +\centering | |
| 245 | +\begin{threeparttable} | |
| 246 | +\caption{Horizontal inequity: who receives noisy assessments?} | |
| 247 | +\label{tab:horizontal} | |
| 248 | +\small | |
| 249 | +\input{../results/tables/horizontal} | |
| 250 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 251 | +\item \textit{Notes:} Dependent variable: | |
| 252 | +$|\ln r_i - \operatorname{med}_{c(i)} \ln r|$. Absorbing least squares | |
| 253 | +with cell fixed effects; municipality-clustered standard errors. | |
| 254 | +Omitted class: single-family. *, **, *** denote significance at 10\%, | |
| 255 | +5\%, 1\%. | |
| 256 | +\end{tablenotes} | |
| 257 | +\end{threeparttable} | |
| 258 | +\end{table} | |
| 259 | + | |
| 260 | +\subsection{The implied tax shift} | |
| 261 | + | |
| 262 | +Figure~\ref{fig:taxshift} and Table~\ref{tab:taxshift} translate the | |
| 263 | +estimates into tax dollars. Within the median market, the median dwelling | |
| 264 | +in the bottom price decile is assessed 65\% above the local norm --- and | |
| 265 | +therefore pays 65\% more property tax than uniform assessment would imply. | |
| 266 | +The overpayment falls to $+7\%$ in the second decile and crosses zero at | |
| 267 | +the median; the top decile underpays by about 5\%. The redistribution is | |
| 268 | +strongly convex: the burden of assessment error is overwhelmingly | |
| 269 | +concentrated on the cheapest tenth of the housing stock --- precisely the | |
| 270 | +segment where owners have the least capacity to appeal and the highest | |
| 271 | +housing-cost burdens. The magnitudes rival those documented for the U.S. | |
| 272 | +by \citet{berry2021reassessing}, in a system with none of the U.S.'s | |
| 273 | +institutional fragmentation. | |
| 274 | + | |
| 275 | +\begin{figure}[t] | |
| 276 | +\centering | |
| 277 | +\includegraphics[width=0.85\textwidth]{fig_taxshift.png} | |
| 278 | +\caption{The implied property-tax shift. Median relative assessment error | |
| 279 | +$e_i = r_i/\operatorname{med}_{c(i)}(r) - 1$ by within-market sale-price | |
| 280 | +decile. Because the levy is proportional to the rolled value, $e_i$ equals | |
| 281 | +the percentage over- or under-payment relative to uniform assessment.} | |
| 282 | +\label{fig:taxshift} | |
| 283 | +\end{figure} | |
| 284 | + | |
| 285 | +\begin{table}[t] | |
| 286 | +\centering | |
| 287 | +\begin{threeparttable} | |
| 288 | +\caption{Excess tax burden by within-market price decile} | |
| 289 | +\label{tab:taxshift} | |
| 290 | +\small | |
| 291 | +\input{../results/tables/taxshift} | |
| 292 | +\begin{tablenotes}[flushleft]\footnotesize | |
| 293 | +\item \textit{Notes:} Relative assessment error by within-cell sale-price | |
| 294 | +decile. The mean is sensitive to extreme low-price sales; the median is | |
| 295 | +the preferred summary. Standard errors of the mean in parentheses. | |
| 296 | +\end{tablenotes} | |
| 297 | +\end{threeparttable} | |
| 298 | +\end{table} | |
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