UQO Working Paper No. 3· v2.0· November 2026· 89 pages
Hedonic Housing Price Models for the United States: Validation Design, Market Price Levels and the Comparison of Parametric, Quantile and Machine-Learning Approaches
The lead of gradient-boosted trees over a hedonic regression shrinks with the spatial scale of the validation blocks: 18.7 points of out-of-sample R² under a random split, 13.2 under ZIP3 blocks, 4.8 under state blocks and 6.3 under leave-one-state-out.
Semi-log OLS, quantile regression and boosted ensembles are estimated on one corrected design matrix for 783,872 active Zillow listings and compared under seven validation designs with ZIP3-cluster bootstrap intervals. The advantage is real for interpolation, smaller for new states, and absent only in one ten-state partition; what does not transfer is the market price level, which twenty local listings largely restore. Prices are asking prices from a single snapshot, and no estimate is causal.
Simon-Pierre Boucher — contact@spboucher.ai
18.7 pts [17.6, 19.9]
XGBoost lead over OLS in out-of-sample R² under the random split (0.833 against 0.6456), with a 95% ZIP3-cluster bootstrap interval
16.8 → 13.2 → 4.8 → 6.3 pts
the same lead under ZIP5 blocks, ZIP3 blocks, state blocks (interval 3.5 to 6.2) and leave-one-state-out (interval 4.7 to 7.6), where XGBoost is ahead in 44 of 51 held-out states
+2.6 pts [−0.1, 7.4]
OLS minus XGBoost under the single ten-state holdout, which withholds 55.6% of the listings including the five largest states; the two are indistinguishable there, while LightGBM stays 2.4 points ahead of OLS
0.635 → 0.699
leave-one-state-out R² of XGBoost once each held-out state's mean log price is estimated from twenty randomly drawn local listings: 83% of the gain of an oracle level correction (0.712)
25.0% vs 8.5%
share of the test variance of log prices left as state-level error under the ten-state holdout by a 1,000-round XGBoost and by OLS; 17.6% with rounds selected inside the training states, 7.7% under leave-one-state-out
23 of 63
OLS slopes significant at 5% under a wild cluster bootstrap by state (9 after Holm's adjustment); state-clustered standard errors are on median 11.7 times the HC3 errors
8 of 14
differences between the 10th and 90th conditional percentiles that survive Romano–Wolf or Holm control (10 by the paired ZIP3-cluster bootstrap before adjustment)
Abstract
Whether gradient-boosted trees price homes better than a hedonic regression depends on how the comparison is validated. On 783,872 Zillow asking prices covering every U.S. state, semi-log OLS, quantile regression and boosted ensembles are estimated on one corrected design matrix and compared under seven validation designs with ZIP3-cluster bootstrap intervals. Under random and ZIP-blocked splits XGBoost leads OLS by 13.2–18.7 points of out-of-sample R²; under state blocks and leave-one-state-out the lead shrinks to 4.8–6.3 points; under a single ten-state holdout the two are indistinguishable. Out-of-state error is dominated by market price levels: twenty local listings raise leave-one-state-out R² from 0.635 to 0.699. State-level feature encodings inflate random-split accuracy and transfer only partly. Wild-cluster inference by state leaves 23 of 63 OLS slopes significant, 8 of 14 inter-quantile differences survive multiplicity control, and SHAP rankings are stable across ensembles. Estimates are listing-price associations, not willingness to pay.
JEL: R31, C21, C45, C52
Key Results
The OLS–ensemble gap as a function of validation scale
The hedonic regression and the ensembles are run through the same seven designs (random, size-matched random, ZIP5, ZIP3 and state blocks, leave-one-state-out, ten-state holdout), with boosting rounds selected inside the training groups, five seeds per fit and cluster-bootstrap intervals on every difference.
Out-of-state error is a level error, and it is cheaply correctable
Held-out squared error is decomposed into within-state and between-state parts; a feasible correction based on twenty local listings recovers 83% of the oracle level correction under leave-one-state-out, after which the ensembles' within-market advantage reasserts itself.
Where the level information comes from
The neighbourhood block adds 16.0 points of random-split R² but only 3.8 out of state; the tax rate adds 8.6 in sample and subtracts 7.2 out of state, and raw coordinates add 20.0 and subtract 5.1. The school variables, state medians for 93.0% of listings, transfer partly: removing them lowers out-of-state R².
Boosting capacity acts through the region dummies
Held-out-state accuracy peaks after about 69 rounds and declines by 12.0 points by round 1,000; without the region dummies the curve is flat. Rounds selected inside the training states give 0.515 under the ten-state holdout, against 0.425 for the fully grown model.
Disciplined inference for the parametric and quantile models
Wild cluster bootstrap by state leaves 23 of 63 slopes significant; state-by-state estimation rejects slope homogeneity for every attribute (living-area elasticity with an inter-decile range of 0.32–0.72) and a fully interacted model gains 6.1 points of out-of-sample R² over state fixed effects.
A corrected design matrix and a stable SHAP ranking
A coding step that set ln(lot) to zero for 16.5% of listings is corrected throughout (lot elasticity 0.10 rather than 0.02). SHAP rankings have Spearman correlations of 0.905–0.987 across XGBoost, LightGBM and a random forest, and the third-ranked feature is a state identifier for 93.0% of listings.
Peer review
This paper went through a multi-referee review: 6 referee reports and 84 review items. The version presented on this page is the revised manuscript. Scores are on a 0–100 scale and are a diagnostic of the manuscript, not an acceptance probability.
Score after revision
71.9/100
57.9 before review · +14.0
Review dated November 4, 2026
- Review decision
- major revision
- Scientific integrity
- PASS
- Reproducibility
- R1reproduced from documented analysis data
- Maturity
- Asubmission-ready
- Referee reports
- 6
- Review items
- 84
Scores by dimension
Before reviewAfter revision
- Originality & contribution59.2 → 66.0
- Scientific rigor56.8 → 72.0
- Identification & methodology60.2 → 68.0
- Data & reproducibility50.0 → 80.0
- Robustness & validation59.2 → 75.0
- Writing65.5 → 70.0
- Figures & tables60.7 → 80.0
- Literature positioning58.5 → 78.0
Revised manuscript89 pages13 figures46 tables10 equations113 references35,659 words
What the review changed
Peer review replaced the earlier conclusion that OLS matches the best tree ensemble out of state with a comparison stated by validation design. Parity holds only for one ten-state partition and only against XGBoost; the paper now reports the gap at each spatial scale with intervals, corrects the design matrix for every model, and withdraws two mechanism claims. The title was changed accordingly.
- “OLS is as accurate out of state as the best tree ensemble” → ensembles lead by 18.7 points (random), 13.2 (ZIP3 blocks), 4.8 (state blocks) and 6.3 (leave-one-state-out); parity only under the ten-state holdout (+2.6 points [−0.1, 7.4]), where LightGBM remains ahead
- Held-out-state peak of 0.550 after 75 rounds (selected on the test set) → 0.515 with rounds selected inside the training states
- Explanation of the out-of-state loss by imputed school variables → withdrawn: removing the school variables lowers out-of-state R² (0.490 against 0.515); the capacity effect runs through the region dummies
- Inter-quantile differences: 10 of 13 significant → 8 of 14 after Holm or Romano–Wolf control, on the corrected design matrix
- OLS coefficients significant under state clustering: 33 of 63 → 23 of 63 slopes under a wild cluster bootstrap by state (9 after Holm)
- Estimation sample: 788,842 listings → 783,872 after screening implausible records, with the lot recoding applied to every model rather than to OLS only
Limitations stated in the paper
- The dependent variable is an asking price from a single snapshot of active listings; the extract contains no sale prices, so the model ranking could differ on transaction prices, and the sample is not reweighted to the housing stock.
- Many regressors are state-level or reporting-level encodings (school variables are state medians for 93.0% of listings; several fields are heavily imputed).
- State-cluster inference rests on 51 clusters with an effective number of 14.2 at the median, so p-values for state-level regressors remain approximate; spatial econometric models are not estimated.
- Hyperparameters other than the number of boosting rounds were not tuned, and the feasible level correction assumes randomly drawn local listings, which may overstate what non-random coverage achieves.
Data
Zillow active listings, one snapshot
A research extract of 839,313 active for-sale listing pages with 116 variables, completed on 8 January 2026. Five sequential filters leave 788,842 listings in the fifty states and the District of Columbia, 26,477 five-digit ZIP codes and 886 ZIP3 groups; prices are asking prices.
Trimmed estimation sample
Four screens (parking spaces above 20, stories above 10, lots above 640 acres, age at the 200-year cap) remove 4,970 listings (0.63%); the remaining 783,872 listings are the estimation sample for every model, with parking and stories winsorised.
Regressors and their limits
62 regressors covering structure, lot size, amenities, neighbourhood measures, market status and six interactions. School variables are state medians for 93.0% of listings, and several fields are imputed for 18.9–70.2% of listings; the South holds 56.6% of the sample, and the paper does not claim national representativeness.
Methodology
Semi-log OLS with geographic fixed effects and cluster inference
Progressively finer fixed effects, cluster-robust standard errors, a wild cluster bootstrap by state (51 clusters of very unequal size) and state-by-state estimation with ZIP3-cluster standard errors.
Quantile regression with multiplicity control
Five quantiles estimated on a 150,000-listing subsample of the corrected matrix, with paired ZIP3-cluster bootstrap tests of inter-quantile differences adjusted by Holm and Romano–Wolf.
Gradient-boosted ensembles under seven validation designs
XGBoost and LightGBM compared with OLS under random, size-matched random, ZIP5-, ZIP3- and state-blocked cross-validation, leave-one-state-out over 51 jurisdictions and a ten-state holdout, with rounds nested in the training groups and five seeds per fit.
Error decomposition, level correction and ablation
Held-out error split into level and within-state components, oracle and feasible level corrections, and block-by-block ablations of the feature set and of boosting capacity.
SHAP interpretation and spatial diagnostics
SHAP rankings compared across three ensembles and Moran's I computed on test-set residuals (0.471 for OLS against 0.236 for XGBoost).
Reproducibility
- The repository contains the sample-construction script that rebuilds the analytical sample from the raw table bit for bit, one design-matrix script holding both the original and the corrected codings, the estimation scripts for every model and validation design, and a generator that writes every exhibit and inline number from stored outputs.
- A single entry point chains the stages and a test suite asserts the rebuild against the stored artefacts; package versions are pinned and seeds are fixed throughout.
- Zillow's terms of use do not permit redistribution: the raw database and the derived analysis files are not distributed, are available from the author for verification, and have their sizes and SHA-256 checksums recorded in the repository.
- An appendix lists, statement by statement, the corrections relative to version 1.2; the random forest, Ridge, Lasso and Elastic Net benchmarks of an earlier version could not be reproduced because their code was lost, and are re-specified and labelled as such.
Cite this paper
Boucher, S.-P. (2026). Hedonic Housing Price Models for the United States: Validation Design, Market Price Levels and the Comparison of Parametric, Quantile and Machine-Learning Approaches. UQO Working Paper No. 3, Université du Québec en Outaouais.
@techreport{boucher2026wp3,
author = {Simon-Pierre Boucher},
title = {Hedonic Housing Price Models for the United States: Validation Design, Market Price Levels and the Comparison of Parametric, Quantile and Machine-Learning Approaches},
institution = {Université du Québec en Outaouais, Département des sciences administratives},
number = {3},
type = {UQO Working Paper},
year = {2026},
month = {nov},
url = {https://www.spboucher.ai/research/wp3},
}More in Real Estate & Urban Economics