Q5/T1 pilot — Sherbrooke's land allocations pass the vacant-lot test
2026-07-19 · wave 33 · ACADEMIC lane · first execution of a Q5 test
(analysis/q5-allocation-note.md, T1): do Quebec assessors' land/building
splits track what vacant ground actually sells for? Pilot city: Sherbrooke
(smallest roll, re-parsed in full).
The test
If Quebec's ~⅓ residential land shares were an artifact of assessors under-allocating value to land on improved parcels (hypothesis H2), then the implied land value per m² of built parcels should sit below the assessed value per m² of vacant parcels — the one class where land value is observed nearly directly (vacant assessments were 97–99% land in every roll we parsed).
Sherbrooke's roll carries the assessor's own neighbourhood code per unit ("unité de voisinage," RL0107A) and lot area (RL0302A), so the comparison runs within the assessor's own micro-markets: 456 neighbourhood units; 233 with ≥3 vacant and ≥10 improved residential parcels.
Results
| Comparison (improved-implied ÷ vacant-benchmark land $/m², per-neighbourhood medians) | Median | IQR | Hoods |
|---|---|---|---|
| All qualifying neighbourhoods | 1.34 | [1.00, 3.08] | 233 |
| Size-matched (vacant lots within 0.5–2× the hood's median improved lot area) | 1.06 | [0.97, 1.51] | 170 |
Size matters because vacant lots skew large (median 1,256 m² vs 697 m² for improved) and per-m² values fall with lot size. Once size-matched, the typical neighbourhood's built parcels carry land allocations within ~6% of the vacant-lot benchmark, and 71% of neighbourhoods fall in [0.8, 1.5]. The remaining right tail (a tenth of hoods above ~3×) is consistent with the known selection problem — surviving vacant lots are disproportionately the unbuildable and unserviced ones, which biases the benchmark down and the ratio up. That bias direction means the headline 1.06 is, if anything, an overestimate of any over-allocation.
A second Q5 fact fell out of the parse: every one of Sherbrooke's 56,325 units carries market reference date 2023-07-01 (RL0401A) — the 2026 roll prices July 2023 conditions, a 2.5-year vintage lag, exactly the H3 mechanism and now measured rather than assumed.
What the pilot means
- No support for the suppression version of H2 in the pilot city. If anything, improved-parcel land is allocated at or slightly above observable vacant-land prices. Sherbrooke's 27% residential land share appears anchored to what its ground actually fetches — the ⅓-land Quebec world looks like an economic fact (H1) plus a stale-vintage discount (H3, now dated precisely), not bookkeeping.
- The incidence machinery's credibility improves. The scenario that most threatened our cross-province numbers — "Quebec households hold more land value than the rolls say" — finds no support where it was cheapest to check. The Q5 caveat stays (one city, one regime side), but it is now a caveat with adverse evidence, not an open flank.
- The method scales. The same computation runs on any Quebec roll from the committed parser's data, and on Vancouver/Surrey (both carry lot sizes) for the BC side — the natural next pilot, since H2's other direction (BC over-allocating to land) is untested. The full T1 design and the remaining tests (teardowns, Ottawa–Gatineau, ratio studies) stay specified in the Q5 note for academic hands.
Caveats
- One city; urban Quebec only; residential usage only.
- Vacant-lot selection (unbuildable/unserviced lots) biases the benchmark down; frontage/servicing differences are uncontrolled. Both push the ratio up — conservative for our conclusion.
- Neighbourhood medians weight small hoods equally; the value-weighted variant (1.59 unmatched) is reported in the wave log for transparency and carries the same size confound.
Sources
- MAMH open roll, Sherbrooke RL43027_2026.xml (68MB, 56,325 units), re-downloaded and parsed in full 2026-07-19; fields RL0105A (usage), RL0107A (neighbourhood unit), RL0302A (lot area m²), RL0401A (market reference date), RL0402A/RL0403A (land/building values). https://www.donneesquebec.ca/recherche/dataset/roles-d-evaluation-fonciere-du-quebec
- Test design and hypotheses:
analysis/q5-allocation-note.md(w32). - Aggregate land shares:
data/land-shares.csv(w20).