UQO Working Papers · WP22 · v1.0
SHARP-HPI: A Spatially Hierarchical, Adaptive and Robust Framework for Quality-Adjusted Housing Price Indices
Monthly municipal indices for Quebec from 770,000 registered sales, 2021–2026
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
An empirical-Bayes hierarchy halves municipal index error in thin markets
On synthetic Quebec-like markets with known latent paths, SHARP-HPI brings the RMSE of municipal monthly changes to 1.58 log points, against 2.91 for per-cell state space and 24.28 for the median, with 98% coverage of 95% intervals.
Abstract
This paper develops and evaluates SHARP-HPI, a framework for monthly quality-adjusted housing price indices at the municipal level in thin markets. Stage one is a robust pooled hedonic regression with fine-scale location fixed effects, smoothly time-varying quality prices and provincial month effects; stage two models each geography's deviation from its parent (province, administrative region, regional county municipality, municipality) with heteroskedastic local-level state-space models whose innovation variances are calibrated by empirical Bayes across cells, so that the weight given to local sales adapts to their reliability.
The framework is applied to 769,995 registered sales in Quebec from January 2021 to October 2026 matched to the assessment roll, with an audited population definition (632,006 sales), a measured publication lag and real-time vintages. Against eleven benchmark estimators (median, stratified median, pooled and rolling time dummies, hedonic imputation, GEKS, HMTS, repeat sales, gradient boosting and a production hierarchical index), Monte Carlo experiments on synthetic Quebec-like markets show that the adaptive hierarchy halves the error of municipal monthly changes relative to per-cell state-space estimation and keeps interval coverage near nominal. Two deliberate counter-examples show where it does not: heavy-tailed contamination favours a coarser location partition, and at the regional level region-specific hedonic coefficients beat pooled coefficients plus a smoothed deviation.
The empirical panel covers 2,654 geography–class cells with reliability grades, effective sample sizes and local-data weights; aggregates agree closely with Teranet and CREA indices in Québec City and diverge by an explainable margin in Montréal. Every ingredient of the estimator exists in the literature; the contribution is their integration, the explicit reliability accounting and the documented performance.
Key findings
769,995
registered Quebec sales, January 2021 – October 2026
632,006
sales in the audited headline population
2,654
geography–class cells with reliability grades
1.58 vs 2.91
Monte Carlo RMSE of municipal monthly changes, log points
154.9
provincial house index, September 2026 (2021 = 100)
0.16 / 1.72
first-release revisions, province / municipalities, log points
Scientific contributions
- An audited population with real-time vintages
- 769,995 registered sales matched to the provincial assessment roll, an exclusion ledger leading to 632,006 headline sales, a measured publication lag of 10–13 days and monthly vintages that make revisions a measured quantity.
- Integration of known components, tested as a whole
- A single-sale hedonic observation equation, a four-level administrative hierarchy, empirical-Bayes calibration of pooling strength and reliability accounting for every cell-month, explicitly presented as an integration rather than a new class of model.
- Half the error of per-cell estimation in simulation
- Across nine Monte Carlo scenarios the municipal RMSE of monthly changes is 1.58 log points against 2.91 for per-cell state space, 12.52 for a cell-level time dummy and 24.28 for the median; empirical-Bayes calibration matters for coverage rather than point accuracy.
- Two counter-examples that the method loses
- With heavy-tailed contamination a coarser location partition wins (2.84 vs 4.62), and at the regional level direct region-specific hedonic coefficients beat pooled coefficients plus a smoothed deviation (1.17 vs 1.40).
- Robust to composition, consistent with external indices
- Dropping the smallest 40% of houses from 2024 in the Montréal region shifts the median by +23.4 log points but SHARP by +0.3; Québec City house prices rise 47.9 log points over 2021–2026 against 45.5 for CREA and 43.7 for Teranet.
- Reliability grades for every cell-month
- The panel of 2,654 geography–class cells over 69 months reports sale counts, effective sample sizes, local-data weights, 95% intervals and A–E grades; municipal house indices in grades A–C range from 133 (P10) to 174 (P90) in September 2026.
Methodology
Methodology (5)
Stage one: robust pooled hedonic regression
Huber-IRLS fixed-effects regression with a nested-grid location partition, smoothly drifting quality prices and provincial month effects, estimated on the full sample.
Stage two: nested state-space deviations
Each geography's mean residual is a noisy observation of a latent deviation from its parent, filtered and smoothed with a robust heteroskedastic local-level model whose innovation variance follows a grid-EM empirical-Bayes prior on log τ² across cells.
Eleven benchmarks on the same data
Median, stratified median, pooled and rolling time dummies, hedonic imputation (Laspeyres, Paasche, Fisher), GEKS, HMTS, repeat sales (BMN and Case–Shiller), static empirical Bayes, out-of-time gradient boosting and a production hierarchical index.
Monte Carlo with known latent paths
80 replications of nine synthetic Quebec-like scenarios, including quality drift with flat prices, heavy-tailed noise and two counter-examples, scoring RMSE, bias, lag and interval coverage at every level of the hierarchy.
Real-time and validation checks
Monthly vintages with revision statistics and publication policies; placebo, composition-shock, cluster bootstrap, Moran, ablation, aggregation and trimming checks; external comparison with Teranet and CREA.
Research data
- Quebec land-registry sales snapshot
- 769,995 registered sales from 2021-01-04 to 2026-10-07 (Quebec land registry feed, Vrai Prix production database backed up 2026-10-21), geocoded and matched to the MAMH assessment roll (3.75 million units); four earlier extractions measure the publication lag; MRNF SDA V2026-07 boundaries.
- External indices
- Teranet–National Bank, CREA MLS HPI and Statistics Canada NHPI/RPPI series downloaded 2026-10-21 for metropolitan-community comparisons in Québec City and Montréal.
Reproducibility
- Numbered pipeline scripts/01–62 (data, benchmarks, Monte Carlo, panel, vintages, validation, figures, tables) driven by a Makefile; pytest suite for state space, EB prior, estimators and panel invariance
- Every number in the manuscript is a generated macro (paper/tables/numbers.tex); index panel, reliability grades, revision and simulation summaries released as CSV/parquet
- Pre-specified research protocol with decision log, data dictionary, provenance report and limitations in docs/
- Full LaTeX source of the 49-page paper with 115 verified bibliography entries; raw microdata not redistributed
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.0current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 49 p. |