UQO Working Papers · WP01 · v1.1
Heterogeneous Amenity Capitalization in the Quebec Residential Market: A Spatial Quantile Regression Approach
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
Amenity capitalisation is not one number: it declines along the price distribution
For Quebec single-family houses the highway, transit and park differentials fall monotonically from the 10th to the 90th conditional percentile, the hospital indicator changes sign, and residual spatial autocorrelation (Moran's I 0.51–0.58) is strong in every segment.
Abstract
Hedonic regressions estimated at the conditional mean impose a single implicit price for each housing attribute across the price distribution. This paper asks whether the capitalisation of neighbourhood amenities into Quebec residential asking prices varies along the conditional price distribution, and whether it survives an adjustment for spatial dependence. Using a January 2026 snapshot of 42,481 Centris listings in four segments (single-family houses, condominiums, multiplexes and vacant land; estimation samples of 6,250, 1,031, 3,755 and 9,239), it estimates quantile regressions at τ ∈ {0.10, 0.25, 0.50, 0.75, 0.90} and a two-stage spatial quantile regression in which a k-nearest-neighbour spatial lag of neighbouring log prices is instrumented by spatially lagged covariates.
For houses, the coefficients of the highway, transit and park indicators decline monotonically along the distribution (highway from 0.205 at τ = 0.10 to 0.034 at τ = 0.90; transit from 0.178 to 0.053; park from 0.122 to 0.014) and the hospital indicator changes sign (from −0.085 to +0.041); the equality of the tail coefficients is rejected for all four, while the school discount of about 11 log points is constant. Condominiums show no detectable heterogeneity; multiplexes and vacant land show it for two amenities each. Moran's I on OLS residuals lies between 0.51 and 0.58 in every segment; the median spatial-lag coefficient ranges from 0.13 (multiplexes) to 0.32 (land), and its introduction attenuates the median highway, transit and school differentials for houses by a third to a half.
The estimates are quantile-specific capitalisation gradients in asking prices, not willingness-to-pay measures; inference relies on a paired bootstrap that ignores spatial dependence, and the spatial-lag coefficients carry no standard errors. All reported figures are drawn from the preserved log of the original estimation run, and the robustness analyses that a re-estimation should provide are stated explicitly.
Key findings
42,481
Centris listings, Quebec, 8 January 2026 snapshot
0.205 → 0.034
house highway coefficient from τ = 0.10 to 0.90
−0.085 → +0.041
hospital coefficient changes sign across quantiles
≈ −11 log pts
school discount, constant at every quantile
0.51–0.58
Moran's I on OLS residuals, all four segments
0.13–0.32
median spatial-lag coefficient across segments
Scientific contributions
- Capitalisation gradients instead of one implicit price
- For single-family houses the highway, transit and park differentials fall monotonically from the 10th to the 90th conditional percentile (highway 0.205 → 0.034, transit 0.178 → 0.053, park 0.122 → 0.014); tail equality is rejected for all three.
- A sign-changing hospital differential
- The hospital indicator moves from −0.085 at τ = 0.10 to +0.041 at τ = 0.90 for houses (Wald 12.1), whereas the school discount of 0.10–0.14 log points is the same at every quantile (Wald 0.05).
- Heterogeneity is segment-specific
- Significant tail heterogeneity appears for 4 of 6 amenities among houses, none among condominiums, and 2 of 6 each for multiplexes (highway, hospital) and vacant land (school, golf).
- Spatial dependence is strong and attenuates the gradients
- Moran's I on OLS residuals is 0.506–0.580; the median spatial lag (0.291 for houses) reduces the median highway, transit and school differentials by a third to a half (highway 0.113 → 0.057).
- An explicit audit trail
- Every figure in version 1.1 is parsed from the preserved console log of the original run; the v1.0 tables that could not be traced to that log, and the robustness checks without surviving output, were withdrawn and listed as analyses to execute.
Methodology
Methodology (4)
OLS hedonic benchmark and Moran's I
Semi-log hedonic regression with HC3 standard errors per segment, with Moran's I computed on OLS, quantile and second-stage residuals using a row-standardised inverse-distance 10-nearest-neighbour weight matrix.
Quantile regression with paired bootstrap
Koenker–Bassett quantile regressions at five quantiles with paired-bootstrap standard errors (B = 200) and Koenker–Machado pseudo-R²; inter-quantile Wald tests compare τ = 0.10 and τ = 0.90 (and adjacent pairs) using bootstrap variances.
Two-stage spatial quantile regression
A least-squares first stage regresses the spatial lag of log price on the covariates and their spatial lags (Kelejian–Prucha instruments); the quantile second stage uses the fitted lag, recorded at the median only and without bootstrap standard errors.
Dollar-equivalent implicit prices and impacts
Implicit prices P(τ)[exp(β̂(τ)) − 1] at reconstructed quantile price levels, and a scalar LeSage–Pace direct/indirect/total decomposition at the median spatial-lag estimate.
Research data
- Centris active-listing snapshot
- 42,481 active listings for the province of Quebec on 8 January 2026 in four product types, with asking price, structural attributes, coordinates, municipality, parking type and a broker text field from which six binary amenity indicators (highway, hospital, park, school, transit, golf) are derived; after filtering and trimming, estimation samples of 6,250 houses, 1,031 condominiums, 3,755 multiplexes and 9,239 parcels (20,275 listings). The snapshot is not redistributed.
Reproducibility
- Six numbered Python scripts from the OLS baseline to the multi-segment 2SQR with bootstrap; the preserved console log results/sqr_multi_segment_output.txt is the single source of every reported number
- scripts/06_tables_figures_from_log.py parses the log in about 5 seconds into 17 LaTeX tables, 5 figures and results/log_parsed.json, with completeness assertions
- Full LaTeX source of the 58-page paper with 125 Crossref-verified BibTeX entries; the pre-revision v1.0 PDF and the review report are kept in docs/
- Re-estimation on the raw Centris snapshot (about 15 minutes) is documented but was not re-run; the analyses it should add are listed explicitly in the paper
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.1current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 58 p. |