révision scientifique complète (editorial board, 2026-10-17)

- scoreboard uniforme (règle médiane pour tous les modèles ; Duan en robustesse) : le
  « renversement » forward-in-time de la v1.0 était un artefact de retransformation
- inférence : bootstrap par grappes (municipalités) + tests DM/GW groupés sur toutes
  les comparaisons ; décomposition niveau/compétence du generalization gap
- robustesse : splits groupés parcelle/bâtiment, FE spatiaux emboîtés, Box–Cox fin,
  sensibilité HGB ; nouvelle section 7, 9 tables et 1 figure
- méthodologie formalisée (13 équations) ; littérature 33 → 58 références vérifiées
- docs/REVIEW-REPORT.md, docs/CHANGELOG-REVISION.md ; version 1.1, October 2026

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed 22 days ago (Oct 18, 2026) parent 984118f Browse files

62 changed files +3,545 −758

modified README.md +76 −36

		`@@ -4,7 +4,7 @@`
4	4	UQO Working Paper No. 11 — *A Systematic Assessment of Hedonic Specifications
5	5	and Estimation Methods for the Quebec Housing Market, 2021–2026*
6	6
7		−[![Paper](https://img.shields.io/badge/paper-PDF%20(23%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
	7	+[![Paper](https://img.shields.io/badge/paper-PDF%20(40%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
8	8	[![Python](https://img.shields.io/badge/python-3.11%2B-3776AB?logo=python&logoColor=white)](requirements.txt)
9	9	[![Data](https://img.shields.io/badge/data-514%2C212%20sales%20·%20roll--matched%20parquet-4051b5)](data/raw/README.md)
10	10	[![Models](https://img.shields.io/badge/models-20%20·%204%20design%20axes-4051b5)](src/wp11/models.py)
		`@@ -15,13 +15,19 @@ and Estimation Methods for the Quebec Housing Market, 2021–2026*`
15	15	> TL;DR — A controlled horse race of 20 hedonic models on 514,212 Quebec sales
16	16	> (2021–2026) with assessor-grade structural attributes: 6 functional forms × a time-FE
17	17	> ladder × a spatial-FE ladder × 6 estimation methods, all scored on the **same
18		−> price-level scoreboard (Duan smearing / Box–Cox inversion) under two holdouts**
19		−> (random 80/20 and forward-in-time). Functional form is second-order (±2 pp of MdAPE);
20		−> spatial controls are first-order (~10 pp) but overfit at ~1 km granularity; **gradient
21		−> boosting wins under random validation** (MdAPE 14.4% vs 16.5% for the best linear
22		−> model) — but under the forward-in-time split every model degrades and the ML
23		−> advantage reverses (splines 19.1% vs boosting 21.2%, identical R²_ln): random
24		−> cross-validation is the wrong experiment for valuation models.
	18	+> price-level scoreboard (one retransformation rule for every model) under two
	19	+> holdouts** (random 80/20 and forward-in-time), with municipality-clustered bootstrap
	20	+> intervals and Diebold–Mariano-type tests on every comparison. Functional form is
	21	+> second-order (1.5 pp of MdAPE); spatial controls are first-order (~10 pp), and a ~1 km
	22	+> grid overfits when used alone but becomes the best linear specification once nested in
	23	+> municipalities; gradient boosting wins under random validation (14.4% vs 17.6% for
	24	+> the best linear model, −3.2 pp [−4.7, −1.9]), a gain that survives parcel- and
	25	+> building-grouped holdouts. Under the forward-in-time split (train < 2025, test 2025–26)
	26	+> every model degrades and the gap shrinks to 0.5 pp and to insignificance — but the
	27	+> decomposition shows this is a level (staleness) effect: re-levelled, boosting still
	28	+> leads by 2.9 pp. Random cross-validation hides the staleness cost; it does not reverse
	29	+> the ranking (the reversal reported in v1.0 was an artefact of an asymmetric
	30	+> retransformation, corrected in v1.1).
25	31
26	32	---
27	33
		`@@ -29,8 +35,8 @@ and Estimation Methods for the Quebec Housing Market, 2021–2026*`
29	35
30	36	\| Item \| Value \|
31	37	\|---\|---\|
32		−\| Version \| 1.0 (August 2026) \|
33		−\| SSRN \| [7626698](https://ssrn.com/abstract=7626698) — submitted 2026-10-17 (preliminary upload) \|
	38	+\| Version \| 1.1 (October 2026) — revised 2026-10-17 by the editorial-board review (see `docs/`); v1.0 = August 2026 \|
	39	+\| SSRN \| [7626698](https://ssrn.com/abstract=7626698) — v1.0 uploaded 2026-10-17; v1.1 PDF to be uploaded as a revision \|
34	40	\| Journal \| not yet submitted \|
35	41	\| Code & data \| reproducible from `scripts/` (see Quick start); raw parquet snapshot not redistributed \|
36	42
		`@@ -77,23 +83,35 @@ and accuracy by market segment.`
77	83
78	84	## 🏆 Headline results
79	85
	86	+All MdAPE in %, median retransformation rule for every model (v1.1 scoreboard).
	87	+
80	88	\| Object \| Random 80/20 holdout \| Forward-in-time holdout \|
81	89	\|---\|---\|---\|
82		−\| Functional-form range (A1–A6), MdAPE \| 16.5 % (splines) – 18.6 % (Box–Cox) \| 19.1 % – 21.0 % \|
83		−\| Data-driven Box–Cox exponent \| λ̂ = 0.25, buys nothing out of sample \| — \|
84		−\| Dropping spatial FE (C1 vs C2) \| 27.9 % vs 18.1 % (+10 pp) \| 26.5 % vs 20.5 % \|
85		−\| ~1.1 km grid FE (C4) \| 19.4 % — overfits vs 17.5 % at ~5.5 km \| 22.1 % \|
86		−\| Dropping time FE (B1 vs B3) \| 21.1 % vs 18.1 % \| 25.4 % vs 20.5 % \|
87		−\| Gradient boosting (D4) \| 14.4 % (−13 % vs best linear 16.5 %) \| 21.2 % \|
88		−\| Random forest (D3) \| 14.6 % \| 21.3 % \|
89		−\| Boosting without coordinates (D5) \| 23.2 % \| 26.2 % \|
90		−\| Semi-log + splines (A6) \| 16.5 % \| 19.1 % — beats boosting, same R²_ln (0.52) \|
91		−\| Implied monthly indices across forms \| agree within a few index points \| \|
92		−\| Boosted implicit age / area profiles \| track quadratic OLS closely \| \|
93		−
94		−Practical synthesis: a semi-log with splines, quarter effects and spatial FE matched to
95		−market thickness is within two points of the frontier in deployment conditions —
96		−transparent, auditable, fast. Validate against the future, not a shuffle of the past.
	90	+\| Functional-form range (A1–A6) \| 17.6 (splines) – 19.2 (quadratics) \| 20.4 (linear) – 23.3 \|
	91	+\| Splines vs. semi-log \| −1.4 pp [−1.8, −1.1] \| −1.4 pp [−2.3, −0.8] \|
	92	+\| Data-driven Box–Cox exponent \| λ̂ = 0.25 (0.35 on a fine grid), −0.5 pp vs. semi-log, worse on MAPE \| — \|
	93	+\| Dropping spatial FE (C1 vs C2) \| 28.8 vs 19.2 (+9.6 pp) \| 29.0 vs 23.3 \|
	94	+\| ~5.5 km grid vs. municipality FE (C3 vs C2) \| 18.7 vs 19.2 — not significant (−0.45 [−1.07, +0.37]) \| 24.3 vs 23.3 \|
	95	+\| ~1.1 km grid alone (C4) \| 21.0 — overfits (+1.8 pp [+1.2, +2.3]) \| 25.3 \|
	96	+\| ~1.1 km grid nested in municipalities (C4′) \| 17.3 — best linear specification \| 21.6 \|
	97	+\| Dropping time FE (B1 vs B3) \| 22.0 vs 19.2 \| 29.3 vs 23.3 \|
	98	+\| Gradient boosting (D4) vs. best linear (A6) \| 14.4 vs 17.6, −3.2 pp [−4.7, −1.9], DM t = −3.6 \| 21.2 vs 21.7, −0.5 pp [−1.7, +0.6], n.s. \|
	99	+\| Random forest (D3) \| 14.6 \| 21.3 \|
	100	+\| Boosting without coordinates (D5) \| 23.2 \| 26.2 \|
	101	+\| Parcel- / building-grouped holdout, D4 vs A6 \| 14.5 vs 17.6 / 14.6 vs 17.8 (gap unchanged) \| — \|
	102	+\| Staleness cost (forward − same-period random) \| — \| D4 +7.5 pp, A6 +4.7, A1 +3.3 \|
	103	+\| Median log level error, forward split \| — \| D4 +0.18, A6 +0.16, A1 +0.10 \|
	104	+\| Re-levelled forward MdAPE \| — \| D4 13.9 vs A6 16.8 (gap 2.9 ≈ random 3.5) \|
	105	+\| Boosting lead over splines by test quarter \| — \| 1.5 pp (2025Q1) → 0.0 (2026Q3) \|
	106	+\| Monthly indices, four linear forms \| agree within 2.5 index points \| \|
	107	+\| Boosted imputation index, July 2026 \| 160.5 vs 168.6–171.0 for the linear forms \| \|
	108	+\| Boosted age profile vs. quadratic OLS \| same shape, 0.10–0.13 log points flatter from age 20 \| \|
	109	+
	110	+Practical synthesis: a semi-log with splines, quarter effects and spatial fixed effects
	111	+nested from municipality down to a fine grid is within three points of the frontier under
	112	+random validation and indistinguishable from it in deployment. Supply the price level from
	113	+an index or a frequent refit, spend the flexibility budget on the spatial surface, and
	114	+validate against the future, not a shuffle of the past.
97	115
98	116	## 🗂 Repository layout
99	117
		`@@ -148,8 +166,9 @@ peak RAM ≈ 8 GB.`
148	166	\| 01 \| `01_build_sample.py` \| residential use codes, roll match ≤ 50 m / score ≥ 150, price ≥ $50k, floor area 20–2,000 m², known year built, 1/99 % trims within sale year; builds grid cells \| `data/processed/`, `results/reproduced/sample_counts.csv`, `summary_stats.csv` \|
149	167	\| 02 \| `02_horserace.py` \| fits the 20 models on each split, retransforms predictions to price levels, scores MdAPE/MAPE/RMSE_ln/R²_ln; Box–Cox profile likelihood \| `horserace_random.csv`, `horserace_temporal.csv`, `boxcox.csv` \|
150	168	\| 03 \| `03_extensions.py` \| constant-quality monthly indices by form, implicit ln-price profiles (quadratic OLS vs boosting), learning curves, accuracy by segment \| `index.csv`, `profiles.csv`, `learning.csv`, `segments.csv` \|
151		−\| 04 \| `04_make_figures.py` \| the 9 figures \| `figures/fig_*.png` \|
152		−\| 05 \| `05_make_tables.py` \| the 7 LaTeX tables \| `results/tables/*.tex` \|
	169	+\| 04 \| `04_make_figures.py` \| the 10 figures \| `figures/fig_*.png` \|
	170	+\| 05 \| `05_make_tables.py` \| the 16 LaTeX tables \| `results/tables/*.tex` \|
	171	+\| 06 \| `06_robustness.py` \| cluster-bootstrap CIs + clustered DM tests, same-period and by-quarter decomposition, level re-levelling, leakage decomposition, parcel- and building-grouped races, nested spatial FE, fine Box–Cox grid, boosting hyper-parameter sensitivity (run after 02; ≈ 20 min) \| `inference_.csv`, `pairs.csv`, `same_period.csv`, `by_quarter.csv`, `relevel.csv`, `leakage.csv`, `horserace_group_.csv`, `nested_fe.csv`, `boxcox_fine.csv`, `hgb_sensitivity.csv` \|
153	172
154	173	## 🗃 Data
155	174
		`@@ -161,23 +180,28 @@ physical configuration, use code. Sample cascade (paper §3): residential use co`
161	180	high-confidence match → price ≥ $50,000 → plausible floor area → known year built →
162	181	1/99 % trims ⇒ 514,212 sales (348,253 single-family, 75,734 condominiums, 74,909
163	182	plexes, 10,349 cottages, 4,881 mobile homes) over 1,115 municipalities, 5,255 cells of
164		−~5.5 km and 30,548 cells of ~1.1 km. Mean price $462,000 (median $399,000). The raw
	183	+~5.5 km and 30,548 cells of ~1.1 km. Mean price $440,207 (median $397,375); 86 further dwellings of undetermined class. One fifth of sales are repeat sales of the same parcel and 30% share exact coordinates with another sale (92% of condominiums). The raw
165	184	parquet (100 MB, transaction microdata) is not redistributed.
166	185
167	186	## 🔬 Methodology
168	187
169	188	1. One attribute set, one sample for every model (`src/wp11/sample.py`).
170	189	2. Axis A — six functional forms on a municipality + quarter FE backbone; Box–Cox λ by
171		− profile likelihood; log models retransformed with Duan smearing, Box–Cox inverted
172		− (`src/wp11/models.py`).
	190	+ profile likelihood. Every transformed-scale prediction is inverted with the same
	191	+ median rule (plain inversion); Duan smearing is computed for every model and
	192	+ reported as a robustness scoreboard (`src/wp11/models.py`).
173	193	3. Axis B / C — time-FE ladder (none → month) and spatial-FE ladder (none → ~1.1 km
174	194	grid) on the quadratic semi-log backbone.
175	195	4. Axis D — OLS, cross-validated ridge, random forest, gradient boosting with and
176	196	without coordinates, spatial k-NN comparables, all on the identical attribute set.
177	197	5. Two holdouts — random 80/20 and forward-in-time (train < 2025, test 2025–26, time
178		− effects carried forward); metrics on price levels, design clustered by municipality.
	198	+ effects carried forward), plus parcel- and building-grouped holdouts; metrics on price
	199	+ levels; municipality-clustered bootstrap intervals and clustered Diebold–Mariano tests
	200	+ (`src/wp11/inference.py`); level/skill decomposition of the forward error.
179	201	6. Extensions — implied monthly indices, implicit-price profiles, learning curves,
180	202	segment accuracy (`scripts/03_extensions.py`).
	203	+7. Robustness — retransformation rule, leakage-free holdouts, nested spatial FE, fine
	204	+ Box–Cox grid, boosting hyper-parameters (`scripts/06_robustness.py`).
181	205
182	206	## 🖼 Figures & tables inventory
183	207
		`@@ -192,10 +216,13 @@ parquet (100 MB, transaction microdata) is not redistributed.`
192	216	\| `fig_profiles` \| implicit ln-price profiles: quadratic OLS vs gradient boosting \|
193	217	\| `fig_learning` \| learning curves: MdAPE against training-set size \|
194	218	\| `fig_segments` \| MdAPE by market segment (random holdout) \|
	219	+\| `fig_horizon` \| forward-in-time MdAPE by test quarter (distance from the training window) \|
195	220
196	221	Tables (`results/tables/*.tex`): summary statistics, scoreboard random holdout,
197		−scoreboard forward-in-time holdout, Box–Cox profile, generalization gap, learning
198		−curves, segments.
	222	+scoreboard forward-in-time holdout, inference (bootstrap CIs + DM tests), targeted pairs,
	223	+Box–Cox profile, generalization gap, same-period / level decomposition, by-quarter
	224	+accuracy, learning curves, segments, median vs. Duan retransformation, grouped holdouts,
	225	+seen/unseen leakage decomposition, nested spatial FE, boosting hyper-parameters.
199	226
200	227	## ⚠️ Limitations
201	228
		`@@ -206,8 +233,13 @@ curves, segments.`
206	233	- Attributes are those of the assessment roll (no interior quality, renovations or
207	234	listing text); the ML advantage measured here is the value of flexible spatial
208	235	learning on that attribute set, not of richer data.
209		−- Tree ensembles are tuned lightly (fixed hyper-parameters); the ranking is robust to
210		− the choices tried but not exhaustively optimised.
	236	+- Tree ensembles use fixed, conventional hyper-parameters; four materially different
	237	+ configurations (including early stopping on a time-ordered validation set) leave the
	238	+ ranking unchanged (paper §7.5), but no linear model with a continuous spatial surface
	239	+ (kriging, bivariate splines) is estimated as a competitor.
	240	+- The forward-in-time test covers one regime (the 2025–26 recovery); the level
	241	+ re-levelling uses the test-set median ratio (an oracle upper bound for what a published
	242	+ index would deliver).
211	243
212	244	## 📝 Citation
213	245
		`@@ -222,7 +254,8 @@ curves, segments.`
222	254	type = {Working Paper},
223	255	number = {11},
224	256	year = {2026},
225		− month = {August}
	257	+ month = {October},
	258	+ note = {Version 1.1}
226	259	}
227	260	```
228	261
		`@@ -239,3 +272,10 @@ Université du Québec en Outaouais (UQO), Gatineau, QC.`
239	272	Language-Model and Vision Features* (now WP 14) and *Does the Sales Comparison
240	273	Approach Actually Work?* (now WP 16).
241	274	- Cover page, metadata and layout follow `Recherche-UQO/HARMONISATION.md` (2026-10-17).
	275	+- Revision 2026-10-17 (v1.1): full editorial-board review. Scientific report in
	276	+ `docs/REVIEW-REPORT.md`, audit trail (every changed number, old → new) in
	277	+ `docs/CHANGELOG-REVISION.md`; pre-revision PDF kept as `docs/main_pre-revision-20261017.pdf`
	278	+ (git tag `pre-revision-20261017`). Main correction: v1.0 applied Duan smearing to the
	279	+ linear log models but not to the tree ensembles; under a uniform rule the forward-in-time
	280	+ "reversal" disappears (the gap shrinks to 0.5 pp, n.s.) and the paper now decomposes the
	281	+ forward error into a common level (staleness) component and intact relative skill.

added docs/CHANGELOG-REVISION.md +165 −0

		`@@ -0,0 +1,165 @@`
	1	+# Changelog — révision scientifique complète (editorial board, 2026-10-17)
	2	+
	3	+Papier : WP 11 — Half a Million Prices, Twenty Models (v1.0, August 2026 → v1.1, October 2026).
	4	+État de référence : tag git `pre-revision-20261017`, PDF `docs/main_pre-revision-20261017.pdf` (23 pages).
	5	+Rapport scientifique associé : `docs/REVIEW-REPORT.md`.
	6	+
	7	+## 1. Corrections majeures (où / avant / après / pourquoi / preuve)
	8	+
	9	+### 1.1 Règle de retransformation asymétrique → scoreboard uniforme (correction centrale)
	10	+- Où : `src/wp11/models.py` (`fit_predict`, `run_horserace`), §4.3 Methodology, §5, §7.1, abstract, intro, conclusion.
	11	+- Avant : les modèles linéaires en log (A2, A3, A5, A6, B, C, D1, D2) étaient multipliés par le facteur de
	12	+ smearing de Duan (ŝ ≈ 1.06–1.08) ; les ensembles d'arbres (D3, D4, D5) et le k-NN (D6) ne l'étaient pas
	13	+ (`np.exp(pred)` nu). Les métriques log (RMSE_ln, R²_ln) étaient calculées sur la prédiction smearée pour une
	14	+ famille et non pour l'autre.
	15	+- Après : règle « médiane » (inversion directe de la prédiction transformée, éq. 10) appliquée à tous les
	16	+ modèles pour le tableau principal ; règle « moyenne » (Duan, éq. 11, généralisée au Box–Cox par moyenne sur
	17	+ 1 000 résidus) calculée pour tous et rapportée en robustesse (Table 12).
	18	+- Pourquoi : la comparaison v1.0 opposait un A6 smearé (19.1 %) à un D4 non smearé (21.2 %) dans le split
	19	+ temporel — le « renversement » annoncé en titre de la v1.0 était un artefact : (i) résidus log asymétriques
	20	+ à gauche (skewness −1.4 à −1.8, médiane +0.06) donc le smearing abaisse par coïncidence la MdAPE de tout modèle
	21	+ log ; (ii) marché haussier en 2025-26 : tout facteur > 1 compense une partie de la staleness. Appliquée
	22	+ uniformément, aucune des deux règles ne renverse le classement (médiane : A6 21.7 vs D4 21.2 ; moyenne :
	23	+ 19.1 vs 18.4).
	24	+- Preuve : `results/reproduced/horserace_{random,temporal}.csv` (colonnes `mdape` vs `mdape_mean`, `smear`),
	25	+ `results/tables/retransformation.tex`, médianes de résidus vérifiées sur `data/processed/predictions_*.parquet`.
	26	+- Chiffres modifiés (ancien → nouveau, MdAPE %) — random : A1 18.2→18.2, A2 18.2→19.0, A3 17.0→18.0, A4 18.6→18.6,
	27	+ A5 18.1→19.2, A6 16.5→17.6, B1 21.1→22.0, B2 18.1→19.1, B4 18.3→19.3, C1 27.9→28.8, C3 17.5→18.7, C4 19.4→21.0,
	28	+ D2 16.7→17.7 ; D3/D4/D5/D6 inchangés (14.6/14.4/23.2/21.2). Forward : A1 20.4→20.4, A2 20.6→23.2, A3 19.2→21.8,
	29	+ A4 21.0→21.0, A5 20.5→23.3, A6 19.1→21.7, B1 25.4→29.3, B2 21.0→23.7, B4 20.3→22.9, C1 26.5→29.0, C3 21.3→24.3,
	30	+ C4 22.1→25.3, D2 19.5→22.3 ; D3/D4/D5/D6 inchangés (21.3/21.2/26.2/25.6). R²_ln des modèles log : +0.01 à +0.04
	31	+ (random), −0.03 à −0.04 (forward).
	32	+- Conséquence narrative : « the ranking reverses » (v1.0) → « the gap shrinks from 3.2 to 0.5 points and loses
	33	+ significance ; relative skill transfers intact, the level does not » (v1.1). Abstract, §1, §5.5, §8, §9 réécrits.
	34	+
	35	+### 1.2 Inférence statistique ajoutée (absente en v1.0)
	36	+- Avant : aucun intervalle, aucun test ; le README affirmait « design clustered by municipality » sans aucune
	37	+ implémentation.
	38	+- Après : `src/wp11/inference.py` — bootstrap par grappes (municipalités, B = 500) pour la MdAPE de chaque
	39	+ modèle et pour les différences ; test de type Diebold–Mariano / Giacomini–White à erreurs-types groupées sur les
	40	+ pertes APE et log² (éq. 13). Tables 4 (tous les modèles vs A6) et 5 (13 paires ciblées).
	41	+- Résultats clés : D4 vs A6 random −3.2 [−4.7, −1.9] (t = −3.6) ; forward −0.5 [−1.7, +0.6] (t = −1.6, p = 0.11) ;
	42	+ C3 vs C2 random −0.45 [−1.07, +0.37] (n.s.) ; C4 vs C2 +1.8 [+1.2, +2.3] ; B4 vs B3 +0.19 [+0.01, +0.37] ;
	43	+ D2 vs A6 +0.06 [−0.02, +0.16] (n.s.).
	44	+- Conséquence : la phrase « the 5.5 km grid beats municipality effects » est ramenée à « nominally better,
	45	+ within bootstrap noise » ; « month effects indistinguishable from quarter » précisé (légèrement pires, significatif).
	46	+
	47	+### 1.3 Décomposition du « generalization gap » (nouveau)
	48	+- Comparaison à période fixe (modèles random évalués sur les 31 465 ventes 2025-26 de leur test) : D4 13.7 → 21.2
	49	+ (coût de staleness 7.5), A6 17.0 → 21.7 (4.7), A1 17.1 → 20.4 (3.3). Biais de niveau médian forward : D4 +0.183,
	50	+ A6 +0.161, A1 +0.102. MdAPE re-nivelée forward : D4 13.9 vs A6 16.8 (écart 2.9 ≈ écart random 3.5).
	51	+ Par trimestre : avance D4 sur A6 de 1.5 pt (2025Q1) → 0 (2026Q3).
	52	+- Fichiers : `same_period.csv`, `relevel.csv`, `by_quarter.csv` ; Tables 8–9, Figure 6 (nouvelle).
	53	+
	54	+### 1.4 Fuite d'information dans le split aléatoire (nouveau)
	55	+- Faits : 20.6 % des ventes sont des reventes d'une même parcelle ; 30.3 % partagent des coordonnées exactes avec
	56	+ une autre vente (91.6 % des condos). Colonnes `parcel`, `coord` ajoutées à `sample.py` (reconstruction du
	57	+ parquet d'analyse, 514 212 ventes identiques).
	58	+- Splits groupés (`split("group_parcel")`, `split("group_coord")`) : course complète. Parcelle : D4 14.5 / A6 17.6
	59	+ (≈ inchangé). Bâtiment : D4 14.6 / A6 17.8 (écart 3.2 identique) ; seul D6 se dégrade (21.2 → 22.3).
	60	+ Décomposition vu/non vu : D4 12.0 vs 15.3 (coord.), A6 17.8 vs 17.6 ; condos D4 8.9 vs 10.2.
	61	+- Tables 13–14 ; §4.4, §7.2.
	62	+
	63	+### 1.5 Effets spatiaux fins : « seventeen K sales » et repli arbitraire
	64	+- Avant (§5.3) : « its cells average seventeen K sales each » — faux : 514 212 / 30 548 = 16.8 ventes par cellule
	65	+ (médiane 3). Corrigé. Cellules non vues (2.5 % des ventes test) tarifées au niveau de la cellule de référence :
	66	+ désormais explicité.
	67	+- Nouveau : C3′ (muni + grille 5.5 km) et C4′ (muni + grille 1.1 km) — solution de norme minimale (ridge α→0)
	68	+ ≈ pooling partiel vers la municipalité. Random : C4′ 17.3 % (meilleure spécification linéaire du papier),
	69	+ C3′ 17.7 % ; forward : 21.6 / 21.5 vs C2 23.3. Conclusion de l'axe C reformulée : « hierarchy, not coarseness ».
	70	+ Table 15 ; `nested_fe.csv`.
	71	+
	72	+### 1.6 Box–Cox : grille fine
	73	+- Grille 0.05 sur [−0.25, 0.75] : λ̂ = 0.35 (profil plat 0.25–0.55 à la tolérance du solveur itératif) ;
	74	+ MdAPE random 18.4 % (vs 18.6 % à 0.25). `boxcox_fine.csv`. Texte §5.1 et §7.4.
	75	+
	76	+### 1.7 Hyper-paramètres du boosting
	77	+- Quatre configurations alternatives (shallow, deep, régularisée, early stopping sur les 10 % derniers mois
	78	+ d'entraînement) sous les deux splits. `hgb_sensitivity.csv`, Table 16, §7.5. Random 14.3–14.7 % (baseline 14.4), forward 21.2–21.6 % (baseline 21.2) ; early stopping : 700 / 1 000 itérations, reproduit le baseline à 0.1 pt.
	79	+
	80	+### 1.8 Statistiques descriptives incohérentes
	81	+- Avant (§3.2, README) : « Prices average $462,000 (median $399,000) ». Table 1 : 440 207 / 397 375.
	82	+ Après : texte aligné sur la table ; ajout des 86 logements de classe indéterminée (la somme des classes v1.0
	83	+ faisait 514 126 ≠ 514 212) ; répartition par année ; nettoyage des lots > P99.5 explicité (était silencieux
	84	+ dans `sample.py`) ; bornes âge/étages/logements explicitées.
	85	+
	86	+### 1.9 Indices et profils : affirmations adoucies
	87	+- Avant : « all five [indices] agree to within a few index points » ; « curves sit within a tenth of a log
	88	+ point ». Après : les quatre formes linéaires s'accordent à ≤ 2.5 points ; l'indice boosting finit 9 points
	89	+ plus bas (160.5 vs 168.6–171.0 ; écart max 10.9) ; profil d'âge du boosting uniformément plus plat de 0.10–0.13
	90	+ log-point à partir de 20 ans (−0.20 vs −0.31 à 40 ans), surface : ≤ 0.05. Chiffres vérifiés dans
	91	+ `index.csv`, `profiles.csv`.
	92	+- Learning curves recalculées (règle médiane) : OLS 19.1 → 19.2 (v1.0 : 18.4 → 18.1) ; GB 17.6 → 14.5 ; écart
	93	+ 1.6 → 4.7 pts (v1.0 : < 1 → 3.6). Segments : condo 18.2 vs 9.1 (v1.0 OLS 20.4), grandes villes 17.7 vs 11.9,
	94	+ petites municipalités 24.8 vs 18.7 (v1.0 23.3), chalets 34.3 vs 32.1 (v1.0 33.9).
	95	+
	96	+### 1.10 Méthodologie formalisée
	97	+- §4 réécrit : équations (1)–(13) — fonction hédonique générale, six formes A1–A6, profil de vraisemblance Box–Cox
	98	+ (avec jacobien), ridge, règle k-NN, règles médiane/Duan, métriques, test DM groupé. Documentation du traitement
	99	+ des catégories non vues, du carry-forward et de son analogue pour les arbres (correction de la phrase « clamped
	100	+ month counter » : rien n'est écrêté dans le code ; les arbres sont constants par morceaux).
	101	+
	102	+### 1.11 Autres corrections éditoriales
	103	+- « 13 % improvement » → « 18 % » (14.4 vs 17.6) ; « 13–21 % » → « 18–25 % » ; intro « 27.9 % versus 17.5 % »
	104	+ vs README « vs 18.1 % » harmonisé (28.8 vs 19.2, référence = backbone C2).
	105	+- Hiérarchie de la discussion : liste à puces → prose (règle de style du protocole).
	106	+- Mots-clés harmonisés au vocabulaire commun (« hedonic price function », « forward-in-time holdout »,
	107	+ « automated valuation model »).
	108	+- `\WPversion` 1.0 → 1.1 ; `\WPdate` August 2026 → October 2026 ; page titre canonique intacte ; macro
	109	+ `\companionpaper` conservée (main.tex / main_anon.tex).
	110	+
	111	+## 2. Références
	112	+
	113	+### Vérifiées (Crossref `api.crossref.org/works?query.bibliographic=…`, 2026-10-17) et corrigées
	114	+Toutes les entrées conservées de la v1.0 (31) ont été retrouvées sur Crossref et dotées de leur DOI. Corrections :
	115	+- `box1964analysis` : pages 211–252 → 211–243 (244–252 = discussion).
	116	+- `bogin2020house` : number 1 → 1–2 ; DOI 10.1007/s11146-019-09712-0.
	117	+- `silver2018house` : l'article EURONA 2018 n'est pas indexé ; remplacé par la version vérifiée **IMF Working Paper
	118	+ 16/213 (2016)**, DOI 10.5089/9781475552249.001, même titre (ordre des mots corrigé).
	119	+- `ke2017lightgbm` : @article → @inproceedings (NIPS 2017, non indexé Crossref ; actes Curran Associates).
	120	+- `malpezzi2003hedonic` : DOI 10.1002/9780470690680.ch5 ; `anselin1988spatial` : DOI 10.1007/978-94-015-7799-1.
	121	+
	122	+### Retirées (non citées dans le texte et bibliographiquement défectueuses)
	123	+- `knight2003listing` (volume/pages vides ; en réalité chapitre Springer 2008, pp. 39–54).
	124	+- `diewert2004hedonic` (« Mimeo » en champ journal ; non indexé).
	125	+
	126	+### Ajoutées (27, toutes vérifiées sur Crossref, DOI dans le .bib)
	127	+hill2018geospatial (RIW 64(4) 737–756) · pace2020residuals (JREFE 60 170–180) · lorenz2023interpretable
	128	+(REE 51(5) 1178–1208) · diewert2016tokyo (RSUE 60 300–315) · diewert2015decomposition (Econometric Reviews 34
	129	+106–126) · diebold1995comparing (JBES 13(3) 253–263) · giacomini2006tests (Econometrica 74(6) 1545–1578) ·
	130	+bergmeir2012crossvalidation (Information Sciences 191 192–213) · roberts2017crossvalidation (Ecography 40(8)
	131	+913–929) · kuminoff2010which (JEEM 60(3) 145–160) · bishop2020best (REEP 14(2) 260–281) · bourassa2007spatial
	132	+(JREFE 35(2) 143–160) · bourassa2003submarkets (JHE 12(1) 12–28) · goodman2003segmentation (JHE 12(3) 181–201) ·
	133	+zurada2011comparison (JRER 33(3) 349–388) · antipov2012mass (ESWA 39(2) 1772–1778) · perezrave2019machine
	134	+(J. Property Research 36(1) 59–96) · mccluskey2013prediction (JPR 30(4) 239–265) · schulz2014automated (JPR 31(2)
	135	+131–153) · fik2003modeling (REE 31(4) 623–646) · clapp2003semiparametric (JREFE 27(3) 303–320) ·
	136	+pace1998spatiotemporal (JREFE 17(1) 15–33) · dube2013pooled (LSRS 6(1) 1–18) · hill2009boom (JHE 18(3) 193–205) ·
	137	+manning2001estimating (J. Health Econ. 20(4) 461–494) · thibodeau2003marking (REE 31(1) 1–22) ·
	138	+khoshnoud2023evolution (JREL 31(1) 1–47).
	139	+Total : 33 → 58 entrées (31 conservées + 27 ajoutées), toutes citées, toutes vérifiées.
	140	+
	141	+## 3. Réanalyses exécutées (laptop, Apple Silicon 18 cœurs, Python 3.14 / scikit-learn 1.6.1)
	142	+
	143	+\| Script \| Contenu \| Durée \| Sorties \|
	144	+\|---\|---\|---\|---\|
	145	+\| `01_build_sample.py` \| reconstruction de l'échantillon (+ clés `parcel`, `coord`) — 514 212 ventes identiques \| 2 s \| `data/processed/analysis.parquet` \|
	146	+\| `02_horserace.py` \| 20 modèles × 2 splits, règles médiane + Duan, prédictions sauvegardées \| 3 min 28 s \| `horserace_.csv`, `boxcox.csv`, `predictions_.parquet` (non commités) \|
	147	+\| `03_extensions.py` \| indices, profils, learning curves, segments (règle médiane) \| 4 min 18 s \| `index.csv`, `profiles.csv`, `learning.csv`, `segments.csv` \|
	148	+\| `06_robustness.py` (nouveau) \| bootstrap + DM, même période, par trimestre, fuite, re-nivellement, paires, splits groupés (2 courses complètes), FE emboîtés, Box–Cox fin, sensibilité HGB \| 16 min 16 s \| `inference_.csv`, `same_period.csv`, `by_quarter.csv`, `leakage.csv`, `relevel.csv`, `pairs.csv`, `horserace_group_.csv`, `nested_fe.csv`, `boxcox_fine.csv`, `hgb_sensitivity.csv` \|
	149	+\| `04_make_figures.py` \| 10 figures (+ `fig_horizon.png`) \| < 1 min \| `figures/` \|
	150	+\| `05_make_tables.py` \| 16 tables LaTeX (9 nouvelles) \| < 1 s \| `results/tables/` \|
	151	+
	152	+Tous les nombres du texte proviennent de ces sorties ; aucune table n'est tapée à la main.
	153	+
	154	+## 4. Éléments non modifiés / analyses recommandées non exécutées
	155	+- Modèle linéaire à surface spatiale (krigeage des résidus, splines bivariées en lat/lng, effets hiérarchiques
	156	+ bayésiens) : non estimé (hors cadre « 20 modèles ») — recommandé pour fermer l'écart linéaire/boosting par l'autre
	157	+ côté.
	158	+- Holdout spatialement bloqué (cellules entières en test) : non exécuté (change la question en extrapolation
	159	+ spatiale ; les FE spatiaux y sont par construction inopérants).
	160	+- Re-nivellement par un indice publié (hors échantillon, non oracle) : non exécuté (aucun indice externe
	161	+ chargé ; le re-nivellement présenté utilise le ratio médian du test, borne supérieure).
	162	+- Variante « médiane calibrée » (exp(ẑ + médiane des résidus d'entraînement)) : discutée, non tabulée.
	163	+- Fenêtres temporelles alternatives (p. ex. train < 2024, test 2024) : non exécutées — limite déclarée §8.4.
	164	+- Comparaison avec LightGBM / XGBoost natifs ou réseaux de neurones : hors périmètre.
	165	+- La règle de nettoyage des lots > P99.5 → 0 (héritée) est documentée mais conservée pour préserver l'échantillon.

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		`@@ -0,0 +1,118 @@`
	1	+# Rapport de l'editorial board — WP 11 « Half a Million Prices, Twenty Models » (2026-10-17)
	2	+
	3	+Révision v1.0 (August 2026, 23 p.) → v1.1 (October 2026). Journal d'audit détaillé : `docs/CHANGELOG-REVISION.md`.
	4	+Comité : économie immobilière, économétrie appliquée, économétrie spatiale, évaluation foncière, apprentissage
	5	+automatique, édition scientifique. Revue cible : Journal of Housing Economics (repli JRER / IJF).
	6	+
	7	+## 1. Diagnostic général
	8	+
	9	+Le papier pose une question nette et utile — quels choix de spécification hédonique comptent réellement pour la
	10	+précision hors échantillon — et y répond par un dispositif expérimental propre (un jeu d'attributs, quatre axes, un
	11	+seul scoreboard, deux holdouts) sur un échantillon rare par sa taille et la qualité des descripteurs (rôle
	12	+d'évaluation). La contribution est réelle et conservée. Trois faiblesses structurelles de la v1.0 ont été
	13	+identifiées et corrigées :
	14	+
	15	+1. Le résultat phare était un artefact. Les modèles linéaires en log étaient retransformés par smearing de Duan
	16	+ et les ensembles d'arbres non. Dans le split temporel, le smearing (facteur ≈ 1.06) compense une partie de la
	17	+ staleness du niveau dans un marché haussier ; c'est ce qui produisait « A6 19.1 % vs D4 21.2 % » et le
	18	+ « renversement » affiché en abstract. Sous une règle uniforme, le boosting reste devant (21.2 vs 21.7, écart non
	19	+ significatif). Correction intégrale (code, tables, texte) ; la v1.1 le dit explicitement.
	20	+2. Aucune inférence. Des différences de 0.2 à 0.6 point étaient interprétées comme des résultats. Ajout d'un
	21	+ bootstrap par grappes (municipalités) et de tests Diebold–Mariano/Giacomini–White groupés sur toutes les
	22	+ comparaisons. Plusieurs affirmations tombent (grille 5.5 km > municipalités ; mois ≈ trimestre) ou se précisent.
	23	+3. Mécanisme du « generalization gap » non identifié. La v1.0 confondait difficulté de la période test et
	24	+ staleness du modèle. Décomposition ajoutée (même période, biais de niveau, re-nivellement, horizon par
	25	+ trimestre) : la compétence relative des ensembles transfère intacte (écart re-nivelé 2.9 pts ≈ 3.5 en random),
	26	+ c'est le niveau qui ne transfère pas, un peu plus pour les arbres (feuille terminale en t). Ce résultat est plus
	27	+ faible que le « renversement » mais plus utile et défendable.
	28	+
	29	+## 2. Diagnostic par section
	30	+
	31	+\| Section \| Forces \| Faiblesses / erreurs trouvées \| Action \|
	32	+\|---\|---\|---\|---\|
	33	+\| Abstract \| clair, chiffré \| chiffres issus du scoreboard asymétrique ; « reverses », « identical R² » faux ; trop long pour la page 2 (débordait sur une page blanche) \| réécrit, 4 leçons reformulées, mention de la correction \|
	34	+\| 1 Introduction \| bonne mise en situation Rosen → ML \| « 13 % improvement » (vrai : 18 %) ; « 27.9 vs 17.5 » (comparait C1 à C3 au lieu du backbone) ; aucune mention de l'inférence ni des fuites \| réécrit ; renvoi à la nouvelle §7 \|
	35	+\| 2 Literature \| couvre les trois courants \| mince (33 réf., 29 citées) ; manquaient Hill–Scholz, Pace–Hayunga, Lorenz et al., Diewert–Shimizu, Kuminoff et al., DM/GW, Bergmeir–Benítez, Roberts et al., Dubé–Legros ; deux entrées non citées et défectueuses \| +27 réf. vérifiées, −2 retirées ; Mayer et al. 2019 identifié comme antécédent direct (updating) \|
	36	+\| 3 Data \| cascade d'échantillon transparente \| moyenne/médiane des prix fausses dans le texte (462k/399k vs 440k/397k) ; 86 ventes « other » omises ; nettoyage des lots > P99.5 non documenté ; bornes âge/étages non dites \| corrigé ; répartition annuelle ; repeat sales et coordonnées partagées quantifiés \|
	37	+\| 4 Methodology \| design clair \| aucune équation ; Duan non écrit ; inversion Box–Cox sans discussion du biais ; « clamped month counter » inexact (rien n'est écrêté ; arbres constants par morceaux) ; catégories non vues → référence arbitraire non dit ; hyper-paramètres « a priori » sans analyse \| 13 équations ; règles médiane/moyenne ; carry-forward ; holdouts groupés ; inférence ; décomposition niveau/skill \|
	38	+\| 5 Results \| lecture par axe efficace \| « seventeen K sales » (17) ; ordre A sous split temporel non discuté (A1 gagne par coïncidence de biais) ; différences non testées \| réécrit avec IC/tests ; §5.5 refondue (décomposition) \|
	39	+\| 6 Extensions \| objets économiques pertinents \| « all five agree within a few points » (indice GB −9 pts) ; « within a tenth of a log point » (0.10–0.13 systématique, profil plus plat) ; learning/segments chiffrés sous scoreboard asymétrique \| affirmations ramenées aux chiffres ; mécanismes de l'écart d'indice discutés \|
	40	+\| 7 Robustness \| — (n'existait pas) \| — \| nouvelle section : retransformation, fuites, FE emboîtés, Box–Cox fin, hyper-paramètres HGB \|
	41	+\| 8 Discussion \| hiérarchie utile \| liste à puces ; « the machines lose their edge » (faux) ; « 3–7 points » sans mécanisme \| prose ; hiérarchie révisée ; mécanisme niveau vs skill ; implications réécrites \|
	42	+\| 9 Conclusion \| synthèse pratique \| reprenait le renversement ; « within two points of the frontier in deployment » \| réécrite \|
	43	+
	44	+## 3. Méthodologie — verdict motivé (§3 du master prompt)
	45	+
	46	+- Spécification justifiée : oui, le design par axes est la force du papier ; la v1.1 le formalise (éq. 1–9).
	47	+- Hypothèses d'estimation explicites : désormais oui (OLS via ridge α = 10⁻⁶, solution de norme minimale ;
	48	+ encodage one-hot avec référence ; splines : 6 nœuds uniformes, 8 fonctions de base ; RF/HGB : paramètres listés).
	49	+- Variables définies : oui (notation unifiée §4.1 ; bornes et nettoyages §3.2).
	50	+- Effets fixes appropriés : oui, avec la nuance majeure trouvée en révision : les FE fins doivent être emboîtés
	51	+ (C4′ 17.3 % = meilleure spécification linéaire ; C4 seule 21.0 %). Le repli « cellule de référence » pour les
	52	+ cellules non vues est désormais documenté et corrigé par l'emboîtement.
	53	+- Dépendance spatiale/temporelle : traitée par l'inférence groupée (municipalités) et par les holdouts
	54	+ temporel, par parcelle et par bâtiment. Limite : pas de holdout bloqué spatialement (déclaré).
	55	+- Erreurs-types : absentes en v1.0 → bootstrap par grappes + DM groupé (éq. 13). Le DM sur la perte APE teste la
	56	+ MAPE, pas la MdAPE ; le bootstrap couvre la médiane — distinction explicitée.
	57	+- Construction de l'échantillon transparente : oui (cascade 745 119 → 514 212, reproduite à l'identique).
	58	+- Robustesse : cinq analyses ajoutées (§7) ; toutes exécutées, aucune revendiquée sans sortie.
	59	+- Interprétation : « 18 % improvement » = (17.6−14.4)/17.6 ; « ten points » = 28.8 − 19.2 ; profils en log-points.
	60	+- Significativité statistique vs économique : distinguée systématiquement (ex. C3 vs C2, D2 vs A6, D4 vs A6
	61	+ forward : non significatifs ; D4 vs A6 random : −3.2 [−4.7, −1.9]).
	62	+- Langage causal : aucun ; le papier est prédictif/descriptif.
	63	+
	64	+## 4. Résultats — incohérences trouvées et état des réanalyses
	65	+
	66	+- Toutes les incohérences texte/table de la v1.0 sont listées au CHANGELOG §1.1, 1.5, 1.8, 1.9, 1.11.
	67	+- Nouveaux résultats (tous issus de `results/reproduced/*.csv`) :
	68	+ - Scoreboard uniforme (Tables 2–3) ; IC et tests (Tables 4–5) ; décomposition (Tables 8–9, Fig. 6) ;
	69	+ retransformation (Table 12) ; splits groupés (Table 13) ; vu/non vu (Table 14) ; FE emboîtés (Table 15) ;
	70	+ sensibilité HGB (Table 16) ; Box–Cox fin (texte §7.4).
	71	+ - Sensibilité HGB : quatre configurations alternatives (shallow, deep, régularisée, early stopping sur les 10 % derniers mois) donnent 14.3–14.7 % (random) et 21.2–21.6 % (forward) contre 14.4 / 21.2 pour le baseline ; le classement et la décomposition ne dépendent pas des hyper-paramètres fixés a priori.
	72	+- Vérifications de cohérence finales : abstract ↔ §1 ↔ §5 ↔ §8–9 ↔ README ↔ tables (chiffres relus un à un après
	73	+ régénération des tables ; voir CHANGELOG §1.1 pour la liste ancien → nouveau).
	74	+
	75	+## 5. Littérature
	76	+
	77	+33 entrées en v1.0 → 58 en v1.1 ; 100 % vérifiées sur Crossref avec DOI (sauf LightGBM, actes NIPS non indexés,
	78	+référence standard). 2 entrées retirées (non citées, défectueuses), 5 corrigées, 27 ajoutées et intégrées à
	79	+l'argument (fonctionnelle : Kuminoff et al. 2010, Bishop et al. 2020, Khoshnoud et al. 2023 ; spatial : Pace et al.
	80	+1998, Clapp 2003, Fik et al. 2003, Bourassa et al. 2003/2007, Goodman–Thibodeau 2003, Pace–Hayunga 2020,
	81	+Dubé–Legros 2013 ; indices : Hill et al. 2009, Hill–Scholz 2018, Diewert et al. 2015, Diewert–Shimizu 2016 ;
	82	+ML/AVM : Zurada et al. 2011, Antipov–Pokryshevskaya 2012, McCluskey et al. 2013, Schulz et al. 2014, Pérez-Rave et al.
	83	+2019, Lorenz et al. 2023, Thibodeau 2003 ; validation : Diebold–Mariano 1995, Giacomini–White 2006,
	84	+Bergmeir–Benítez 2012, Roberts et al. 2017 ; retransformation : Manning–Mullahy 2001).
	85	+
	86	+## 6. Limites restantes
	87	+
	88	+1. Un seul régime temporel testé (reprise 2025-26, +15 % en 18 mois) ; l'ordre des coûts de staleness entre
	89	+ familles pourrait différer dans un marché plat ou baissier.
	90	+2. Le re-nivellement utilise le ratio médian du test (oracle) : borne supérieure de ce qu'un indice publié
	91	+ permettrait.
	92	+3. Pas de modèle linéaire à surface spatiale continue (krigeage, splines bivariées) ni d'effets hiérarchiques
	93	+ proprement estimés ; l'emboîtement C4′ est un pooling partiel implicite (norme minimale), pas un modèle
	94	+ hiérarchique explicite.
	95	+4. Les holdouts groupés neutralisent reventes et bâtiments partagés, pas le voisinage immédiat.
	96	+5. Attributs du rôle seulement (pas de qualité intérieure, texte d'annonce, photos) ; l'avantage ML mesuré est celui
	97	+ de la flexibilité spatiale sur cet ensemble d'attributs.
	98	+6. La règle « lots > P99.5 → 0 » héritée du pipeline est documentée mais discutable.
	99	+7. Longueur : 40 pages avec 16 tables et 10 figures ; pour la soumission, les Tables 4–5, 12–16 iraient en annexe.
	100	+
	101	+## 7. Analyses recommandées non exécutées
	102	+
	103	+Voir CHANGELOG §4 : surface spatiale linéaire (krigeage / splines lat-lng / hiérarchique bayésien) ; holdout bloqué
	104	+spatialement ; re-nivellement par indice externe ; fenêtres temporelles alternatives (rolling origin) ; variante
	105	+« médiane calibrée » ; LightGBM/XGBoost natifs et réseaux de neurones ; coût de retraining mensuel (course
	106	+glissante) — cette dernière est la plus importante pour la revue cible.
	107	+
	108	+## 8. Maturité pour publication
	109	+
	110	+- Verdict : manuscrit désormais défendable en revue (JHE) sous réserve d'une coupe (annexes) et, idéalement, d'une
	111	+ course glissante (retraining mensuel) qui transformerait la §5.5 en recommandation opérationnelle chiffrée.
	112	+- Risques de rejet : (i) « un seul marché, une seule période » — mitigé par l'échelle provinciale et la
	113	+ décomposition ; (ii) absence d'un modèle linéaire spatialement sophistiqué comme concurrent (un rapporteur
	114	+ spatial le demandera) ; (iii) la correction d'un résultat phare publié en v1.0 sur SSRN doit être assumée
	115	+ explicitement (fait dans l'abstract et §7.1) — c'est un point d'intégrité, pas une faiblesse.
	116	+- Points forts pour la revue : taille et qualité des données, design expérimental, inférence complète,
	117	+ décomposition niveau/compétence inédite dans la littérature AVM, résultat « hierarchy, not coarseness » sur les FE
	118	+ spatiaux.

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52	57	% METADATA
53	58	% ============================================================================
		`@@ -55,9 +60,9 @@`
55	60	\newcommand{\WPtitle}{Half a Million Prices, Twenty Models}
56	61	\newcommand{\WPsubtitle}{A Systematic Assessment of Hedonic Specifications and
57	62	Estimation Methods for the Quebec Housing Market, 2021--2026}
58		−\newcommand{\WPdate}{August 2026}
59		−\newcommand{\WPversion}{1.0}
60		−\newcommand{\WPkeywords}{hedonic pricing, functional form, house price indexes, machine learning, automated valuation, out-of-sample prediction}
	63	+\newcommand{\WPdate}{October 2026}
	64	+\newcommand{\WPversion}{1.1}
	65	+\newcommand{\WPkeywords}{hedonic price function, functional form, spatial fixed effects, machine learning, automated valuation model, forward-in-time holdout, house price index}
61	66	\newcommand{\WPjel}{R31, C21, C52, C53}
62	67
63	68	\newcommand{\WPauthor}{Simon-Pierre Boucher}
		`@@ -68,34 +73,39 @@`
68	73	283, boulevard Alexandre-Tach\'e\\ Gatineau, Qu\'ebec, Canada J9A 1L8}
69	74
70	75	\newcommand{\WPabstract}{%
71		−Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still rests
72		−on a series of specification choices --- functional form, temporal controls,
73		−spatial controls, estimation method --- that are usually made by convention
74		−and rarely stress-tested jointly. Using 514{,}212 Quebec residential sales
	76	+Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still
	77	+rests on specification choices---functional form, temporal controls,
	78	+spatial controls, estimation method---that are made by convention and
	79	+rarely stress-tested jointly. Using 514{,}212 Quebec residential sales
75	80	(2021--2026) whose structural descriptors come from the provincial
76	81	assessment roll, we run a controlled horse race of twenty hedonic models
77		−organised along those four axes, scoring every model on identical holdouts
78		−and on the same price-level scoreboard (log models are Duan-retransformed,
79		−Box--Cox inverted). Four lessons emerge. (1)~Functional form is a
80		−second-order choice: from linear to splines, the median absolute error
81		−spans 16.5--18.6\%, and the data-driven Box--Cox exponent
82		−($\hat\lambda=0.25$) buys nothing out of sample. (2)~Controls are
83		−first-order: dropping spatial fixed effects costs ten error points ---
84		−location granularity matters far more than curvature, but only up to the
85		−point where cells thin out (a $\sim$1~km grid \emph{overfits}).
86		−(3)~Under random validation, estimation method matters most: gradient
87		−boosting reaches 14.4\% --- a 13\% improvement over the best linear model
88		−--- with random forests close behind, and coordinates alone reproduce
89		−what thousands of dummies buy. (4)~But the ranking is an artifact of the
90		−split: under a forward-in-time holdout (train $<$~2025, test 2025--26)
91		−every model degrades and the machine-learning advantage \emph{reverses}
92		−--- the spline hedonic posts a lower median error than gradient boosting
93		−and an identical log-scale $R^2$ --- a stark warning against evaluating
94		−valuation models with random cross-validation alone. Constant-quality
95		−monthly indices implied by the competing forms agree to within a few
96		−index points, and the boosted model's implicit age and floor-area
97		−profiles track the quadratic OLS closely --- interpretation and
98		−prediction disagree less than the random-validation gap suggests.}
	82	+organised along those four axes, scoring every model on identical
	83	+holdouts and on the same price-level scoreboard with a single
	84	+retransformation rule, with a municipality-clustered bootstrap interval
	85	+and a Diebold--Mariano-type test on every comparison. Four lessons
	86	+emerge. (1)~Functional form is second-order: from linear to splines the
	87	+median absolute error spans 17.6--19.2\%, and the data-driven Box--Cox
	88	+exponent gains half a point. (2)~Controls are first-order: dropping
	89	+spatial fixed effects costs ten error points; a $\sim$1~km grid used
	90	+alone overfits, but nested within municipalities it becomes the most
	91	+accurate linear specification---the bias--variance trade-off in
	92	+absorbing location is resolved by hierarchy, not coarseness. (3)~Under
	93	+random validation the estimation method dominates: gradient boosting
	94	+reaches 14.4\%, an 18\% improvement over the best linear model
	95	+(95\% interval 1.9--4.7 points) that survives holdouts grouped by parcel
	96	+and by building and comes almost entirely from a flexible surface over
	97	+space. (4)~Under a forward-in-time holdout (train $<$~2025, test
	98	+2025--26) every model degrades and the gap shrinks to half a point and
	99	+to insignificance. Decomposing the error shows that relative pricing
	100	+skill transfers forward intact (re-levelled, boosting leads by 2.9
	101	+points) while every frozen model under-prices the typical future sale
	102	+by 10--20\%, the ensembles slightly more. Random cross-validation hides
	103	+this staleness cost; it does not, as a previous version of this paper
	104	+claimed on the basis of an asymmetric retransformation, reverse the
	105	+ranking. Constant-quality indices agree across functional forms to
	106	+within 2.5 points but a boosted imputation index rises nine points less,
	107	+and the boosted model's implicit age and area profiles share the shape
	108	+of the quadratic OLS gradients with a milder depreciation path.}
99	109
100	110	\hypersetup{pdftitle={Half a Million Prices, Twenty Models}, pdfauthor={Simon-Pierre Boucher}}
101	111
		`@@ -113,10 +123,11 @@ prediction disagree less than the random-validation gap suggests.}`
113	123	\input{sections/methodology}
114	124	\input{sections/results}
115	125	\input{sections/extensions}
	126	+\input{sections/robustness}
116	127	\input{sections/discussion}
117	128	\input{sections/conclusion}
118	129
119		−\newpage
	130	+\clearpage
120	131	\bibliography{references}
121	132
122	133	\end{document}

modified paper/main_anon.pdf +0 −0

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modified paper/main_anon.tex +41 −30

		`@@ -48,6 +48,11 @@`
48	48	\usepackage{enumitem}
49	49	\setlist{nosep,leftmargin=*}
50	50
	51	+% Float placement: let text and floats share pages
	52	+\setcounter{topnumber}{3}\setcounter{bottomnumber}{2}\setcounter{totalnumber}{4}
	53	+\renewcommand{\topfraction}{0.9}\renewcommand{\bottomfraction}{0.6}
	54	+\renewcommand{\textfraction}{0.08}\renewcommand{\floatpagefraction}{0.5}
	55	+
51	56	% ============================================================================
52	57	% METADATA
53	58	% ============================================================================
		`@@ -55,9 +60,9 @@`
55	60	\newcommand{\WPtitle}{Half a Million Prices, Twenty Models}
56	61	\newcommand{\WPsubtitle}{A Systematic Assessment of Hedonic Specifications and
57	62	Estimation Methods for the Quebec Housing Market, 2021--2026}
58		−\newcommand{\WPdate}{August 2026}
59		−\newcommand{\WPversion}{1.0}
60		−\newcommand{\WPkeywords}{hedonic pricing, functional form, house price indexes, machine learning, automated valuation, out-of-sample prediction}
	63	+\newcommand{\WPdate}{October 2026}
	64	+\newcommand{\WPversion}{1.1}
	65	+\newcommand{\WPkeywords}{hedonic price function, functional form, spatial fixed effects, machine learning, automated valuation model, forward-in-time holdout, house price index}
61	66	\newcommand{\WPjel}{R31, C21, C52, C53}
62	67
63	68	\newcommand{\WPauthor}{Simon-Pierre Boucher}
		`@@ -68,34 +73,39 @@`
68	73	283, boulevard Alexandre-Tach\'e\\ Gatineau, Qu\'ebec, Canada J9A 1L8}
69	74
70	75	\newcommand{\WPabstract}{%
71		−Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still rests
72		−on a series of specification choices --- functional form, temporal controls,
73		−spatial controls, estimation method --- that are usually made by convention
74		−and rarely stress-tested jointly. Using 514{,}212 Quebec residential sales
	76	+Fifty years after \mbox{Rosen (1974)}, applied hedonic practice still
	77	+rests on specification choices---functional form, temporal controls,
	78	+spatial controls, estimation method---that are made by convention and
	79	+rarely stress-tested jointly. Using 514{,}212 Quebec residential sales
75	80	(2021--2026) whose structural descriptors come from the provincial
76	81	assessment roll, we run a controlled horse race of twenty hedonic models
77		−organised along those four axes, scoring every model on identical holdouts
78		−and on the same price-level scoreboard (log models are Duan-retransformed,
79		−Box--Cox inverted). Four lessons emerge. (1)~Functional form is a
80		−second-order choice: from linear to splines, the median absolute error
81		−spans 16.5--18.6\%, and the data-driven Box--Cox exponent
82		−($\hat\lambda=0.25$) buys nothing out of sample. (2)~Controls are
83		−first-order: dropping spatial fixed effects costs ten error points ---
84		−location granularity matters far more than curvature, but only up to the
85		−point where cells thin out (a $\sim$1~km grid \emph{overfits}).
86		−(3)~Under random validation, estimation method matters most: gradient
87		−boosting reaches 14.4\% --- a 13\% improvement over the best linear model
88		−--- with random forests close behind, and coordinates alone reproduce
89		−what thousands of dummies buy. (4)~But the ranking is an artifact of the
90		−split: under a forward-in-time holdout (train $<$~2025, test 2025--26)
91		−every model degrades and the machine-learning advantage \emph{reverses}
92		−--- the spline hedonic posts a lower median error than gradient boosting
93		−and an identical log-scale $R^2$ --- a stark warning against evaluating
94		−valuation models with random cross-validation alone. Constant-quality
95		−monthly indices implied by the competing forms agree to within a few
96		−index points, and the boosted model's implicit age and floor-area
97		−profiles track the quadratic OLS closely --- interpretation and
98		−prediction disagree less than the random-validation gap suggests.}
	82	+organised along those four axes, scoring every model on identical
	83	+holdouts and on the same price-level scoreboard with a single
	84	+retransformation rule, with a municipality-clustered bootstrap interval
	85	+and a Diebold--Mariano-type test on every comparison. Four lessons
	86	+emerge. (1)~Functional form is second-order: from linear to splines the
	87	+median absolute error spans 17.6--19.2\%, and the data-driven Box--Cox
	88	+exponent gains half a point. (2)~Controls are first-order: dropping
	89	+spatial fixed effects costs ten error points; a $\sim$1~km grid used
	90	+alone overfits, but nested within municipalities it becomes the most
	91	+accurate linear specification---the bias--variance trade-off in
	92	+absorbing location is resolved by hierarchy, not coarseness. (3)~Under
	93	+random validation the estimation method dominates: gradient boosting
	94	+reaches 14.4\%, an 18\% improvement over the best linear model
	95	+(95\% interval 1.9--4.7 points) that survives holdouts grouped by parcel
	96	+and by building and comes almost entirely from a flexible surface over
	97	+space. (4)~Under a forward-in-time holdout (train $<$~2025, test
	98	+2025--26) every model degrades and the gap shrinks to half a point and
	99	+to insignificance. Decomposing the error shows that relative pricing
	100	+skill transfers forward intact (re-levelled, boosting leads by 2.9
	101	+points) while every frozen model under-prices the typical future sale
	102	+by 10--20\%, the ensembles slightly more. Random cross-validation hides
	103	+this staleness cost; it does not, as a previous version of this paper
	104	+claimed on the basis of an asymmetric retransformation, reverse the
	105	+ranking. Constant-quality indices agree across functional forms to
	106	+within 2.5 points but a boosted imputation index rises nine points less,
	107	+and the boosted model's implicit age and area profiles share the shape
	108	+of the quadratic OLS gradients with a milder depreciation path.}
99	109
100	110	\hypersetup{pdftitle={Half a Million Prices, Twenty Models}, pdfauthor={}}
101	111
		`@@ -113,10 +123,11 @@ prediction disagree less than the random-validation gap suggests.}`
113	123	\input{sections/methodology}
114	124	\input{sections/results}
115	125	\input{sections/extensions}
	126	+\input{sections/robustness}
116	127	\input{sections/discussion}
117	128	\input{sections/conclusion}
118	129
119		−\newpage
	130	+\clearpage
120	131	\bibliography{references}
121	132
122	133	\end{document}

modified paper/references.bib +371 −60

		`@@ -7,7 +7,8 @@`
7	7	year = {1974},
8	8	volume = {82},
9	9	number = {1},
10		− pages = {34--55}
	10	+ pages = {34--55},
	11	+ doi = {10.1086/260169}
11	12	}
12	13
13	14	@article{halvorsen1981choice,
		`@@ -17,7 +18,8 @@`
17	18	year = {1981},
18	19	volume = {10},
19	20	number = {1},
20		− pages = {37--49}
	21	+ pages = {37--49},
	22	+ doi = {10.1016/0094-1190(81)90021-8}
21	23	}
22	24
23	25	@article{cassel1985cost,
		`@@ -27,7 +29,8 @@`
27	29	year = {1985},
28	30	volume = {18},
29	31	number = {2},
30		− pages = {135--142}
	32	+ pages = {135--142},
	33	+ doi = {10.1016/0094-1190(85)90012-9}
31	34	}
32	35
33	36	@article{cropper1988choice,
		`@@ -37,7 +40,8 @@`
37	40	year = {1988},
38	41	volume = {70},
39	42	number = {4},
40		− pages = {668--675}
	43	+ pages = {668--675},
	44	+ doi = {10.2307/1935831}
41	45	}
42	46
43	47	@article{box1964analysis,
		`@@ -47,7 +51,8 @@`
47	51	year = {1964},
48	52	volume = {26},
49	53	number = {2},
50		− pages = {211--252}
	54	+ pages = {211--243},
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51	56	}
52	57
53	58	@incollection{malpezzi2003hedonic,
		`@@ -58,7 +63,8 @@`
58	63	publisher = {Blackwell},
59	64	address = {Oxford},
60	65	year = {2003},
61		− pages = {67--89}
	66	+ pages = {67--89},
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62	68	}
63	69
64	70	@article{sirmans2005composition,
		`@@ -68,7 +74,8 @@`
68	74	year = {2005},
69	75	volume = {13},
70	76	number = {1},
71		− pages = {1--44}
	77	+ pages = {1--44},
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72	79	}
73	80
74	81	@article{duan1983smearing,
		`@@ -78,7 +85,8 @@`
78	85	year = {1983},
79	86	volume = {78},
80	87	number = {383},
81		− pages = {605--610}
	88	+ pages = {605--610},
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82	90	}
83	91
84	92	@article{goodman1998housing,
		`@@ -88,7 +96,8 @@`
88	96	year = {1998},
89	97	volume = {7},
90	98	number = {2},
91		− pages = {121--143}
	99	+ pages = {121--143},
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92	101	}
93	102
94	103	@article{dubin1998spatial,
		`@@ -98,7 +107,8 @@`
98	107	year = {1998},
99	108	volume = {7},
100	109	number = {4},
101		− pages = {304--327}
	110	+ pages = {304--327},
	111	+ doi = {10.1006/jhec.1998.0236}
102	112	}
103	113
104	114	@book{anselin1988spatial,
		`@@ -106,7 +116,8 @@`
106	116	title = {Spatial Econometrics: Methods and Models},
107	117	publisher = {Kluwer Academic},
108	118	address = {Dordrecht},
109		− year = {1988}
	119	+ year = {1988},
	120	+ doi = {10.1007/978-94-015-7799-1}
110	121	}
111	122
112	123	@article{hill2013hedonic,
		`@@ -116,25 +127,19 @@`
116	127	year = {2013},
117	128	volume = {27},
118	129	number = {5},
119		− pages = {879--914}
	130	+ pages = {879--914},
	131	+ doi = {10.1111/j.1467-6419.2012.00731.x}
120	132	}
121	133
122		−@article{silver2018house,
123		− author = {Silver, Mick},
124		− title = {How to Measure Hedonic Property Price Indexes Better},
125		− journal = {EURONA — Eurostat Review on National Accounts and Macroeconomic Indicators},
126		− year = {2018},
127		− volume = {1},
128		− pages = {35--66}
129		−}
130		−
131		−@article{diewert2004hedonic,
132		− author = {Diewert, W. Erwin},
133		− title = {Hedonic Regressions: A Review of Some Unresolved Issues},
134		− journal = {Mimeo, University of British Columbia},
135		− year = {2004},
136		− volume = {},
137		− pages = {}
	134	+@techreport{silver2018house,
	135	+ author = {Silver, Mick},
	136	+ title = {How to Better Measure Hedonic Residential Property Price Indexes},
	137	+ institution = {International Monetary Fund},
	138	+ type = {IMF Working Paper},
	139	+ number = {16/213},
	140	+ address = {Washington, DC},
	141	+ year = {2016},
	142	+ doi = {10.5089/9781475552249.001}
138	143	}
139	144
140	145	@article{mullainathan2017machine,
		`@@ -144,7 +149,8 @@`
144	149	year = {2017},
145	150	volume = {31},
146	151	number = {2},
147		− pages = {87--106}
	152	+ pages = {87--106},
	153	+ doi = {10.1257/jep.31.2.87}
148	154	}
149	155
150	156	@article{athey2019machine,
		`@@ -153,7 +159,8 @@`
153	159	journal = {Annual Review of Economics},
154	160	year = {2019},
155	161	volume = {11},
156		− pages = {685--725}
	162	+ pages = {685--725},
	163	+ doi = {10.1146/annurev-economics-080217-053433}
157	164	}
158	165
159	166	@article{breiman2001random,
		`@@ -163,7 +170,8 @@`
163	170	year = {2001},
164	171	volume = {45},
165	172	number = {1},
166		− pages = {5--32}
	173	+ pages = {5--32},
	174	+ doi = {10.1023/A:1010933404324}
167	175	}
168	176
169	177	@article{friedman2001greedy,
		`@@ -173,16 +181,18 @@`
173	181	year = {2001},
174	182	volume = {29},
175	183	number = {5},
176		− pages = {1189--1232}
	184	+ pages = {1189--1232},
	185	+ doi = {10.1214/aos/1013203451}
177	186	}
178	187
179		−@article{ke2017lightgbm,
180		− author = {Ke, Guolin and Meng, Qi and Finley, Thomas and Wang, Taifeng and Chen, Wei and Ma, Weidong and Ye, Qiwei and Liu, Tie-Yan},
181		− title = {{LightGBM}: A Highly Efficient Gradient Boosting Decision Tree},
182		− journal = {Advances in Neural Information Processing Systems},
183		− year = {2017},
184		− volume = {30},
185		− pages = {3146--3154}
	188	+@inproceedings{ke2017lightgbm,
	189	+ author = {Ke, Guolin and Meng, Qi and Finley, Thomas and Wang, Taifeng and Chen, Wei and Ma, Weidong and Ye, Qiwei and Liu, Tie-Yan},
	190	+ title = {{LightGBM}: A Highly Efficient Gradient Boosting Decision Tree},
	191	+ booktitle = {Advances in Neural Information Processing Systems 30 (NIPS 2017)},
	192	+ editor = {Guyon, I. and Von Luxburg, U. and Bengio, S. and Wallach, H. and Fergus, R. and Vishwanathan, S. and Garnett, R.},
	193	+ publisher = {Curran Associates},
	194	+ year = {2017},
	195	+ pages = {3146--3154}
186	196	}
187	197
188	198	@article{mayer2019estimation,
		`@@ -192,7 +202,8 @@`
192	202	year = {2019},
193	203	volume = {12},
194	204	number = {1},
195		− pages = {134--150}
	205	+ pages = {134--150},
	206	+ doi = {10.1108/JERER-08-2018-0035}
196	207	}
197	208
198	209	@article{bogin2020house,
		`@@ -201,8 +212,9 @@`
201	212	journal = {Journal of Real Estate Finance and Economics},
202	213	year = {2020},
203	214	volume = {60},
204		− number = {1},
205		− pages = {40--52}
	215	+ number = {1--2},
	216	+ pages = {40--52},
	217	+ doi = {10.1007/s11146-019-09712-0}
206	218	}
207	219
208	220	@article{steurer2021metrics,
		`@@ -212,7 +224,8 @@`
212	224	year = {2021},
213	225	volume = {38},
214	226	number = {2},
215		− pages = {99--129}
	227	+ pages = {99--129},
	228	+ doi = {10.1080/09599916.2020.1858937}
216	229	}
217	230
218	231	@article{pace1997spatial,
		`@@ -222,7 +235,8 @@`
222	235	year = {1997},
223	236	volume = {14},
224	237	number = {3},
225		− pages = {333--340}
	238	+ pages = {333--340},
	239	+ doi = {10.1023/A:1007762613901}
226	240	}
227	241
228	242	@article{case2004modeling,
		`@@ -232,7 +246,8 @@`
232	246	year = {2004},
233	247	volume = {29},
234	248	number = {2},
235		− pages = {167--191}
	249	+ pages = {167--191},
	250	+ doi = {10.1023/B:REAL.0000035309.60607.53}
236	251	}
237	252
238	253	@article{bourassa2010predicting,
		`@@ -242,7 +257,8 @@`
242	257	year = {2010},
243	258	volume = {32},
244	259	number = {2},
245		− pages = {139--159}
	260	+ pages = {139--159},
	261	+ doi = {10.1080/10835547.2010.12091276}
246	262	}
247	263
248	264	@article{desrosiers2000hedonic,
		`@@ -252,7 +268,8 @@`
252	268	year = {2000},
253	269	volume = {18},
254	270	number = {3},
255		− pages = {291--315}
	271	+ pages = {291--315},
	272	+ doi = {10.1108/14635780010338245}
256	273	}
257	274
258	275	@article{gencay1996nonlinear,
		`@@ -262,7 +279,8 @@`
262	279	year = {1996},
263	280	volume = {52},
264	281	number = {2},
265		− pages = {129--135}
	282	+ pages = {129--135},
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266	284	}
267	285
268	286	@article{kok2017big,
		`@@ -272,7 +290,8 @@`
272	290	year = {2017},
273	291	volume = {43},
274	292	number = {6},
275		− pages = {202--211}
	293	+ pages = {202--211},
	294	+ doi = {10.3905/jpm.2017.43.6.202}
276	295	}
277	296
278	297	@article{hong2020machine,
		`@@ -282,16 +301,8 @@`
282	301	year = {2020},
283	302	volume = {24},
284	303	number = {3},
285		− pages = {140--152}
286		−}
287		−
288		−@article{knight2003listing,
289		− author = {Knight, John R.},
290		− title = {Hedonic Modeling of the Home Selling Process},
291		− journal = {Journal of Real Estate Finance and Economics},
292		− year = {2003},
293		− volume = {},
294		− pages = {}
	304	+ pages = {140--152},
	305	+ doi = {10.3846/ijspm.2020.11544}
295	306	}
296	307
297	308	@book{iaao2013standard,
		`@@ -309,7 +320,8 @@`
309	320	year = {2002},
310	321	volume = {24},
311	322	number = {1},
312		− pages = {1--26}
	323	+ pages = {1--26},
	324	+ doi = {10.1080/10835547.2002.12091087}
313	325	}
314	326
315	327	@techreport{oecd2013handbook,
		`@@ -319,3 +331,302 @@`
319	331	address = {Luxembourg},
320	332	year = {2013}
321	333	}
	334	+
	335	+% ---------------------------------------------------------------------------
	336	+% References added in the 2026-10-17 revision (all verified on Crossref)
	337	+% ---------------------------------------------------------------------------
	338	+
	339	+@article{hill2018geospatial,
	340	+ author = {Hill, Robert J. and Scholz, Michael},
	341	+ title = {Can Geospatial Data Improve House Price Indexes? {A} Hedonic Imputation Approach with Splines},
	342	+ journal = {Review of Income and Wealth},
	343	+ year = {2018},
	344	+ volume = {64},
	345	+ number = {4},
	346	+ pages = {737--756},
	347	+ doi = {10.1111/roiw.12303}
	348	+}
	349	+
	350	+@article{pace2020residuals,
	351	+ author = {Pace, R. Kelley and Hayunga, Darren},
	352	+ title = {Examining the Information Content of Residuals from Hedonic and Spatial Models Using Trees and Forests},
	353	+ journal = {Journal of Real Estate Finance and Economics},
	354	+ year = {2020},
	355	+ volume = {60},
	356	+ number = {1--2},
	357	+ pages = {170--180},
	358	+ doi = {10.1007/s11146-019-09724-w}
	359	+}
	360	+
	361	+@article{lorenz2023interpretable,
	362	+ author = {Lorenz, Felix and Willwersch, Jonas and Cajias, Marcelo and Fuerst, Franz},
	363	+ title = {Interpretable Machine Learning for Real Estate Market Analysis},
	364	+ journal = {Real Estate Economics},
	365	+ year = {2023},
	366	+ volume = {51},
	367	+ number = {5},
	368	+ pages = {1178--1208},
	369	+ doi = {10.1111/1540-6229.12397}
	370	+}
	371	+
	372	+@article{diewert2016tokyo,
	373	+ author = {Diewert, W. Erwin and Shimizu, Chihiro},
	374	+ title = {Hedonic Regression Models for {Tokyo} Condominium Sales},
	375	+ journal = {Regional Science and Urban Economics},
	376	+ year = {2016},
	377	+ volume = {60},
	378	+ pages = {300--315},
	379	+ doi = {10.1016/j.regsciurbeco.2016.08.002}
	380	+}
	381	+
	382	+@article{diewert2015decomposition,
	383	+ author = {Diewert, W. Erwin and de Haan, Jan and Hendriks, Rens},
	384	+ title = {Hedonic Regressions and the Decomposition of a House Price Index into Land and Structure Components},
	385	+ journal = {Econometric Reviews},
	386	+ year = {2015},
	387	+ volume = {34},
	388	+ number = {1--2},
	389	+ pages = {106--126},
	390	+ doi = {10.1080/07474938.2014.944791}
	391	+}
	392	+
	393	+@article{diebold1995comparing,
	394	+ author = {Diebold, Francis X. and Mariano, Roberto S.},
	395	+ title = {Comparing Predictive Accuracy},
	396	+ journal = {Journal of Business \& Economic Statistics},
	397	+ year = {1995},
	398	+ volume = {13},
	399	+ number = {3},
	400	+ pages = {253--263},
	401	+ doi = {10.1080/07350015.1995.10524599}
	402	+}
	403	+
	404	+@article{giacomini2006tests,
	405	+ author = {Giacomini, Raffaella and White, Halbert},
	406	+ title = {Tests of Conditional Predictive Ability},
	407	+ journal = {Econometrica},
	408	+ year = {2006},
	409	+ volume = {74},
	410	+ number = {6},
	411	+ pages = {1545--1578},
	412	+ doi = {10.1111/j.1468-0262.2006.00718.x}
	413	+}
	414	+
	415	+@article{bergmeir2012crossvalidation,
	416	+ author = {Bergmeir, Christoph and Ben{\'i}tez, Jos{\'e} M.},
	417	+ title = {On the Use of Cross-Validation for Time Series Predictor Evaluation},
	418	+ journal = {Information Sciences},
	419	+ year = {2012},
	420	+ volume = {191},
	421	+ pages = {192--213},
	422	+ doi = {10.1016/j.ins.2011.12.028}
	423	+}
	424	+
	425	+@article{roberts2017crossvalidation,
	426	+ author = {Roberts, David R. and Bahn, Volker and Ciuti, Simone and Boyce, Mark S. and Elith, Jane and Guillera-Arroita, Gurutzeta and Hauenstein, Severin and Lahoz-Monfort, Jos{\'e} J. and Schr{\"o}der, Boris and Thuiller, Wilfried and Warton, David I. and Wintle, Brendan A. and Hartig, Florian and Dormann, Carsten F.},
	427	+ title = {Cross-Validation Strategies for Data with Temporal, Spatial, Hierarchical, or Phylogenetic Structure},
	428	+ journal = {Ecography},
	429	+ year = {2017},
	430	+ volume = {40},
	431	+ number = {8},
	432	+ pages = {913--929},
	433	+ doi = {10.1111/ecog.02881}
	434	+}
	435	+
	436	+@article{kuminoff2010which,
	437	+ author = {Kuminoff, Nicolai V. and Parmeter, Christopher F. and Pope, Jaren C.},
	438	+ title = {Which Hedonic Models Can We Trust to Recover the Marginal Willingness to Pay for Environmental Amenities?},
	439	+ journal = {Journal of Environmental Economics and Management},
	440	+ year = {2010},
	441	+ volume = {60},
	442	+ number = {3},
	443	+ pages = {145--160},
	444	+ doi = {10.1016/j.jeem.2010.06.001}
	445	+}
	446	+
	447	+@article{bishop2020best,
	448	+ author = {Bishop, Kelly C. and Kuminoff, Nicolai V. and Banzhaf, H. Spencer and Boyle, Kevin J. and von Gravenitz, Kathrine and Pope, Jaren C. and Smith, V. Kerry and Timmins, Christopher D.},
	449	+ title = {Best Practices for Using Hedonic Property Value Models to Measure Willingness to Pay for Environmental Quality},
	450	+ journal = {Review of Environmental Economics and Policy},
	451	+ year = {2020},
	452	+ volume = {14},
	453	+ number = {2},
	454	+ pages = {260--281},
	455	+ doi = {10.1093/reep/reaa001}
	456	+}
	457	+
	458	+@article{bourassa2007spatial,
	459	+ author = {Bourassa, Steven C. and Cantoni, Eva and Hoesli, Martin},
	460	+ title = {Spatial Dependence, Housing Submarkets, and House Price Prediction},
	461	+ journal = {Journal of Real Estate Finance and Economics},
	462	+ year = {2007},
	463	+ volume = {35},
	464	+ number = {2},
	465	+ pages = {143--160},
	466	+ doi = {10.1007/s11146-007-9036-8}
	467	+}
	468	+
	469	+@article{bourassa2003submarkets,
	470	+ author = {Bourassa, Steven C. and Hoesli, Martin and Peng, Vincent S.},
	471	+ title = {Do Housing Submarkets Really Matter?},
	472	+ journal = {Journal of Housing Economics},
	473	+ year = {2003},
	474	+ volume = {12},
	475	+ number = {1},
	476	+ pages = {12--28},
	477	+ doi = {10.1016/S1051-1377(03)00003-2}
	478	+}
	479	+
	480	+@article{goodman2003segmentation,
	481	+ author = {Goodman, Allen C. and Thibodeau, Thomas G.},
	482	+ title = {Housing Market Segmentation and Hedonic Prediction Accuracy},
	483	+ journal = {Journal of Housing Economics},
	484	+ year = {2003},
	485	+ volume = {12},
	486	+ number = {3},
	487	+ pages = {181--201},
	488	+ doi = {10.1016/S1051-1377(03)00031-7}
	489	+}
	490	+
	491	+@article{zurada2011comparison,
	492	+ author = {Zurada, Jozef and Levitan, Alan S. and Guan, Jian},
	493	+ title = {A Comparison of Regression and Artificial Intelligence Methods in a Mass Appraisal Context},
	494	+ journal = {Journal of Real Estate Research},
	495	+ year = {2011},
	496	+ volume = {33},
	497	+ number = {3},
	498	+ pages = {349--388},
	499	+ doi = {10.1080/10835547.2011.12091311}
	500	+}
	501	+
	502	+@article{antipov2012mass,
	503	+ author = {Antipov, Evgeny A. and Pokryshevskaya, Elena B.},
	504	+ title = {Mass Appraisal of Residential Apartments: An Application of Random Forest for Valuation and a {CART}-Based Approach for Model Diagnostics},
	505	+ journal = {Expert Systems with Applications},
	506	+ year = {2012},
	507	+ volume = {39},
	508	+ number = {2},
	509	+ pages = {1772--1778},
	510	+ doi = {10.1016/j.eswa.2011.08.077}
	511	+}
	512	+
	513	+@article{perezrave2019machine,
	514	+ author = {P{\'e}rez-Rave, Jorge Iv{\'a}n and Correa-Morales, Juan Carlos and Gonz{\'a}lez-Echavarr{\'i}a, Favi{\'a}n},
	515	+ title = {A Machine Learning Approach to Big Data Regression Analysis of Real Estate Prices for Inferential and Predictive Purposes},
	516	+ journal = {Journal of Property Research},
	517	+ year = {2019},
	518	+ volume = {36},
	519	+ number = {1},
	520	+ pages = {59--96},
	521	+ doi = {10.1080/09599916.2019.1587489}
	522	+}
	523	+
	524	+@article{mccluskey2013prediction,
	525	+ author = {McCluskey, William J. and McCord, Michael and Davis, Peadar T. and Haran, Martin and McIlhatton, David},
	526	+ title = {Prediction Accuracy in Mass Appraisal: A Comparison of Modern Approaches},
	527	+ journal = {Journal of Property Research},
	528	+ year = {2013},
	529	+ volume = {30},
	530	+ number = {4},
	531	+ pages = {239--265},
	532	+ doi = {10.1080/09599916.2013.781204}
	533	+}
	534	+
	535	+@article{schulz2014automated,
	536	+ author = {Schulz, Rainer and Wersing, Martin and Werwatz, Axel},
	537	+ title = {Automated Valuation Modelling: A Specification Exercise},
	538	+ journal = {Journal of Property Research},
	539	+ year = {2014},
	540	+ volume = {31},
	541	+ number = {2},
	542	+ pages = {131--153},
	543	+ doi = {10.1080/09599916.2013.846930}
	544	+}
	545	+
	546	+@article{fik2003modeling,
	547	+ author = {Fik, Timothy J. and Ling, David C. and Mulligan, Gordon F.},
	548	+ title = {Modeling Spatial Variation in Housing Prices: A Variable Interaction Approach},
	549	+ journal = {Real Estate Economics},
	550	+ year = {2003},
	551	+ volume = {31},
	552	+ number = {4},
	553	+ pages = {623--646},
	554	+ doi = {10.1046/j.1080-8620.2003.00079.x}
	555	+}
	556	+
	557	+@article{clapp2003semiparametric,
	558	+ author = {Clapp, John M.},
	559	+ title = {A Semiparametric Method for Valuing Residential Locations: Application to Automated Valuation},
	560	+ journal = {Journal of Real Estate Finance and Economics},
	561	+ year = {2003},
	562	+ volume = {27},
	563	+ number = {3},
	564	+ pages = {303--320},
	565	+ doi = {10.1023/A:1025838007297}
	566	+}
	567	+
	568	+@article{pace1998spatiotemporal,
	569	+ author = {Pace, R. Kelley and Barry, Ronald and Clapp, John M. and Rodriquez, Mauricio},
	570	+ title = {Spatiotemporal Autoregressive Models of Neighborhood Effects},
	571	+ journal = {Journal of Real Estate Finance and Economics},
	572	+ year = {1998},
	573	+ volume = {17},
	574	+ number = {1},
	575	+ pages = {15--33},
	576	+ doi = {10.1023/A:1007799028599}
	577	+}
	578	+
	579	+@article{dube2013pooled,
	580	+ author = {Dub{\'e}, Jean and Legros, Di{\`e}go},
	581	+ title = {Dealing with Spatial Data Pooled over Time in Statistical Models},
	582	+ journal = {Letters in Spatial and Resource Sciences},
	583	+ year = {2013},
	584	+ volume = {6},
	585	+ number = {1},
	586	+ pages = {1--18},
	587	+ doi = {10.1007/s12076-012-0082-3}
	588	+}
	589	+
	590	+@article{hill2009boom,
	591	+ author = {Hill, Robert J. and Melser, Daniel and Syed, Iqbal},
	592	+ title = {Measuring a Boom and Bust: The {Sydney} Housing Market 2001--2006},
	593	+ journal = {Journal of Housing Economics},
	594	+ year = {2009},
	595	+ volume = {18},
	596	+ number = {3},
	597	+ pages = {193--205},
	598	+ doi = {10.1016/j.jhe.2009.07.010}
	599	+}
	600	+
	601	+@article{manning2001estimating,
	602	+ author = {Manning, Willard G. and Mullahy, John},
	603	+ title = {Estimating Log Models: To Transform or Not to Transform?},
	604	+ journal = {Journal of Health Economics},
	605	+ year = {2001},
	606	+ volume = {20},
	607	+ number = {4},
	608	+ pages = {461--494},
	609	+ doi = {10.1016/S0167-6296(01)00086-8}
	610	+}
	611	+
	612	+@article{thibodeau2003marking,
	613	+ author = {Thibodeau, Thomas G.},
	614	+ title = {Marking Single-Family Property Values to Market},
	615	+ journal = {Real Estate Economics},
	616	+ year = {2003},
	617	+ volume = {31},
	618	+ number = {1},
	619	+ pages = {1--22},
	620	+ doi = {10.1111/j.1080-8620.2003.00055.x}
	621	+}
	622	+
	623	+@article{khoshnoud2023evolution,
	624	+ author = {Khoshnoud, Mahsa and Sirmans, G. Stacy and Zietz, Emily N.},
	625	+ title = {The Evolution of Hedonic Pricing Models},
	626	+ journal = {Journal of Real Estate Literature},
	627	+ year = {2023},
	628	+ volume = {31},
	629	+ number = {1},
	630	+ pages = {1--47},
	631	+ doi = {10.1080/09277544.2023.2201020}
	632	+}

modified paper/sections/conclusion.tex +34 −24

		`@@ -5,28 +5,38 @@`
5	5
6	6	We ran the hedonic specification debate as a controlled experiment:
7	7	twenty models, four design axes, one attribute set, one scoreboard, two
8		−holdouts, half a million sales. The verdict inverts the profession's
9		−implicit priorities. The choices that consume the most methodological
10		−attention --- functional form, transformation parameters --- move
11		−out-of-sample accuracy by at most two points of median error, while the
12		−choices often made by default --- whether and how finely to absorb space
13		−and time --- move it by three to ten. Machine-learning estimators
14		−dominate the standard scoreboard, but the standard scoreboard asks the
15		−wrong question: when the test set lies in the future, as it always does
16		−in deployment, the boosted ensemble's advantage reverses against a
17		−spline hedonic with good controls, because most of what it learned was a
18		−spatially fine price configuration that does not transfer across the
19		−market cycle.
	8	+holdouts, half a million sales, and a bootstrap interval on every
	9	+comparison. The verdict inverts the profession's implicit priorities.
	10	+The choices that consume the most methodological attention---functional
	11	+form, transformation parameters---move out-of-sample accuracy by at most
	12	+two points of median error, while the choices often made by
	13	+default---whether and how to absorb space and time---move it by three to
	14	+ten, and the way fine spatial effects are implemented matters more than
	15	+their resolution. Machine-learning estimators dominate the standard
	16	+scoreboard by three points, a gain that is real, grows with the sample
	17	+and comes almost entirely from a flexible surface over space. When the
	18	+test set lies in the future, as it always does in deployment, that gain
	19	+shrinks to half a point and loses significance, not because the learned
	20	+surface fails to transfer---re-levelled, it prices future sales as well
	21	+as it prices contemporaneous ones---but because every frozen model
	22	+carries a stale price level, and a boosted model carries a slightly
	23	+staler one than a linear model with carry-forward time effects.
20	24
21		−Meanwhile the objects economists actually harvest from hedonic models
22		−prove reassuringly stable: constant-quality indices agree across forms
23		−to within a few points over a full boom--bust--recovery cycle, and the
24		−machine's implicit age and area gradients replicate the quadratic OLS.
25		−The practical synthesis is almost embarrassingly simple: a semi-log with
26		−splines, quarter effects, and spatial fixed effects at a granularity
27		−matched to market thickness is within two points of the frontier in
28		−deployment conditions --- transparent, auditable, and fast. Where the
29		−extra accuracy of learning methods is worth its retraining cadence ---
30		−high-frequency AVMs, collateral monitoring --- our decomposition says to
31		−spend the flexibility budget on the spatial surface, and to validate,
32		−always, against the future rather than against a shuffle of the past.
	25	+The objects economists harvest from hedonic models prove stable along
	26	+the axis that generates the most debate and less so along the axis that
	27	+generates the least: constant-quality indices agree across functional
	28	+forms to within 2.5 points over a full boom--bust--recovery cycle but
	29	+differ by nine points between a time-dummy index and a boosted
	30	+imputation index, and the machine's implicit age and area gradients
	31	+share the shape of the quadratic OLS with a milder depreciation path.
	32	+The practical synthesis is simple. A semi-log with splines, quarter
	33	+effects and spatial fixed effects nested from municipality down to a
	34	+fine grid is within three points of the frontier under random
	35	+validation and indistinguishable from it in deployment---transparent,
	36	+auditable and fast. Where the extra within-period accuracy of learning
	37	+methods is worth a retraining cadence---high-frequency automated
	38	+valuation, collateral monitoring---our decomposition says to spend the
	39	+flexibility budget on the spatial surface, to supply the price level
	40	+from an index or a frequent refit rather than from the model, and to
	41	+validate, always, against the future rather than against a shuffle of
	42	+the past.

modified paper/sections/data.tex +43 −26

		`@@ -6,37 +6,53 @@`
6	6	\subsection{Sources}
7	7
8	8	We use a registry of 745{,}119 Quebec residential-market transactions
9		−recorded between January 2021 and July 2026 --- sale price, date, address
10		−and coordinates --- each matched at the parcel level to the municipal
	9	+recorded between January 2021 and July 2026---sale price, date, address
	10	+and coordinates---each matched at the parcel level to the municipal
11	11	assessment roll in force at the sale date (median match distance
12		−0.6~metres, validated against the roll's recorded value). The roll
13		−contributes the structural descriptors that are notoriously missing from
14		−transaction registries: total floor area, lot area, year of construction,
15		−number of dwelling units, number of storeys, physical configuration
16		−(detached, semi-detached, row, apartment-linked) and the standardized use
17		−code. This combination --- market prices with assessor-grade structure
18		−for half a million sales across an entire province --- is what makes a
19		−controlled specification race feasible: every model sees exactly the same
20		−attributes.
	12	+0.6~metres, validated against the roll's recorded value). The same
	13	+snapshot underlies \companionpaper{}. The roll contributes the
	14	+structural descriptors that are typically missing from transaction
	15	+registries: total floor area, lot area, year of construction, number of
	16	+dwelling units, number of storeys, physical configuration (detached,
	17	+semi-detached, row, apartment-linked) and the standardised use code.
	18	+This combination---market prices with assessor-grade structure for half a
	19	+million sales across an entire province---is what makes a controlled
	20	+specification race feasible: every model sees exactly the same
	21	+attributes, and the attribute set is the one a mass-appraisal office
	22	+actually holds.
21	23
22	24	\subsection{Sample}
23	25
24	26	We keep residential use codes (dwellings, cottages, mobile homes), require
25		−a high-confidence roll match (distance $\le 50$~m, score $\ge 150$), a
26		−price of at least \$50{,}000, a plausible floor area (20--2{,}000~m$^2$)
27		−and a known year of construction, and trim prices and floor areas at the
28		−1st and 99th percentiles within each sale year. The estimation sample
29		−contains \textbf{514{,}212 sales}: 348{,}253 single-family homes, 75{,}734
30		−condominiums, 74{,}909 plexes (2--5 units), 10{,}349 cottages and 4{,}881
31		−mobile homes, spread over 1{,}115 municipalities, 5{,}255 grid cells of
32		−$\sim$5.5~km and 30{,}548 cells of $\sim$1.1~km.
33		−Table~\ref{tab:sumstats} reports the descriptives. Prices average
34		−\$462{,}000 (median \$399{,}000); the window covers the tail of the
35		−post-pandemic boom, the 2022--2023 rate correction and the subsequent
36		−recovery --- a demanding environment for any static price model, which we
37		−exploit in the forward-in-time evaluation.
	27	+a high-confidence roll match (distance $\le 50$~m, match score
	28	+$\ge 150$), a price of at least \$50{,}000, a plausible floor area
	29	+(20--2{,}000~m$^2$) and a known year of construction, and trim prices and
	30	+floor areas at the 1st and 99th percentiles within each sale year.
	31	+Building age is the sale year minus the year of construction, bounded
	32	+between 0 and 150; storeys are bounded between 1 and 6 and dwelling units
	33	+between 1 and 12; lot areas above the 99.5th percentile, which are
	34	+implausible for residential parcels, are set to zero and treated as
	35	+units without an exclusive lot, together with condominiums. The
	36	+estimation sample contains \textbf{514{,}212 sales}: 348{,}253
	37	+single-family homes, 75{,}734 condominiums, 74{,}909 plexes (two to five
	38	+units), 10{,}349 cottages, 4{,}881 mobile homes and 86 dwellings of
	39	+undetermined class, spread over 1{,}115 municipalities, 5{,}255 grid
	40	+cells of $\sim$5.5~km and 30{,}548 cells of $\sim$1.1~km. Sales are
	41	+spread across the window (97{,}868 in 2021, 90{,}733 in 2022, 76{,}411 in
	42	+2023, 90{,}812 in 2024, 103{,}830 in 2025 and 54{,}558 in January--July
	43	+2026). Table~\ref{tab:sumstats} reports the descriptive statistics.
	44	+Prices average \$440{,}207 (median \$397{,}375), floor areas 132~m$^2$
	45	+and building ages 44 years; the window covers the tail of the
	46	+post-pandemic boom, the 2022--23 rate correction and the 2024--26
	47	+recovery, during which the constant-quality price level rose by roughly
	48	+70\% (Section~\ref{sec:ext}). This is a demanding environment for any
	49	+static price model, which the forward-in-time evaluation exploits.
	50	+One fifth of the sales (105{,}814) concern a parcel that sells more than
	51	+once in the window and 30\% share their exact coordinates with another
	52	+sale; Section~\ref{sec:holdouts} explains why these repeat and
	53	+co-located sales matter for validation.
38	54
39		−\begin{table}[t]
	55	+\begin{table}[tbp]
40	56	\centering
41	57	\begin{threeparttable}
42	58	\caption{Summary statistics, estimation sample}
		`@@ -47,7 +63,8 @@ exploit in the forward-in-time evaluation.`
47	63	\item \textit{Notes:} 514{,}212 residential sales, January 2021 -- July
48	64	2026. Structural descriptors from the assessment roll in force at the
49	65	sale date. Lot area is zero for condominiums and other units without an
50		−exclusive lot.
	66	+exclusive lot (and for the 0.5\% of lots above the 99.5th percentile,
	67	+see text).
51	68	\end{tablenotes}
52	69	\end{threeparttable}
53	70	\end{table}

modified paper/sections/discussion.tex +94 −61

		`@@ -5,77 +5,110 @@`
5	5
6	6	\subsection{A hierarchy of specification choices}
7	7
8		−Read jointly, the four axes imply a clear hierarchy of returns to
9		−specification effort, useful to anyone building a hedonic model:
	8	+Read jointly, the four axes imply a hierarchy of returns to
	9	+specification effort. The first and largest return is to location:
	10	+any spatial absorption beats none by about ten points of median error, a
	11	+margin that dwarfs every other choice, and the granularity question is
	12	+one of implementation rather than of resolution. A fine grid used alone
	13	+overfits because thin cells are estimated from a handful of sales and
	14	+unseen cells are priced arbitrarily; the same grid nested within
	15	+municipalities, which pools thin cells toward their municipality, is the
	16	+most accurate linear specification we estimate. The second return is to
	17	+time controls: in a moving market a model without time effects mistakes
	18	+appreciation for attributes, at a cost of three points under random
	19	+validation and six when the level must be carried forward, while
	20	+granularity beyond quarters is cosmetic. The third return is to the
	21	+estimator, and its size depends on the question asked. Under random
	22	+validation gradient boosting buys three points over the best linear
	23	+model, a gain that is statistically unambiguous and that grows with the
	24	+training sample; in deployment the gain on the median error shrinks to
	25	+half a point and loses significance, because the ensembles carry a
	26	+slightly staler price level, while their relative pricing skill is
	27	+intact. The fourth and smallest return is to functional form: splines
	28	+are a cheap and reliable upgrade over the semi-log, and the Box--Cox
	29	+machinery is not worth its complexity, exactly as
	30	+\citet{cropper1988choice} concluded from simulations four decades ago.
10	31
11		−\begin{enumerate}
12		−\item \textbf{Get location right} ($\sim$10 points of median error):
13		−any spatial absorption beats none by a margin that dwarfs every other
14		−choice; the optimal granularity is interior --- around 5~km here ---
15		−because finer cells trade bias for variance.
16		−\item \textbf{Include some time control} ($\sim$3 points): in a moving
17		−market, a model without time effects mistakes appreciation for
18		−attributes; granularity beyond quarters is cosmetic.
19		−\item \textbf{Choose the estimator for the job} ($\sim$2 points
20		−deployed, $\sim$4 under random validation): boosting buys real accuracy
21		−in interpolation-heavy uses (filling gaps within a period, mass
22		−appraisal with contemporaneous comparables) and much less when the
23		−target is the future.
24		−\item \textbf{Stop worrying about functional form} ($\lesssim$2
25		−points): splines are a cheap upgrade; the Box--Cox machinery is not
26		−worth its complexity, exactly as \citet{cropper1988choice} concluded
27		−from simulations four decades ago.
28		−\end{enumerate}
	32	+\subsection{Why the forward-in-time split compresses the ranking}
29	33
30		−\subsection{Why the machines lose their edge out of time}
31		−
32		−The decomposition rows explain the generalization gap. The boosting
33		−model's random-split advantage comes almost entirely from a flexible
34		−spatial surface (removing coordinates costs it 8.8 points). That surface
35		−is estimated \emph{jointly} with the time path, and trees clamp: beyond
36		−the last training month the model prices 2025--26 sales at a frozen
37		−level, exactly like the carry-forward linear models, while its
38		−fine-grained spatial fit --- calibrated on the 2021--24 price
39		−configuration --- partially decays as relative prices shift. The linear
40		−models, coarser but more rigid, carry a structure that transfers better.
41		−This is not an indictment of machine learning --- retrained monthly, the
42		−boosting model would presumably keep its interpolation advantage --- but
43		−it prices the \emph{retraining requirement} that random cross-validation
44		−hides, and it matches the practitioner evidence that AVM accuracy decays
45		−quickly out of sample period \citep{bogin2020house, kok2017big}.
	34	+The decomposition of Section~\ref{sec:gap} clarifies what the
	35	+forward-in-time holdout measures. The boosting model's random-split
	36	+advantage comes almost entirely from a flexible spatial surface
	37	+(removing the coordinates costs it 8.8 points), and that surface
	38	+transfers to 2025--26 sales: re-levelled, the model prices them with a
	39	+13.9\% median error, against 16.8\% for the spline hedonic. What does
	40	+not transfer is the aggregate level. Trees are piecewise constant in the
	41	+month counter and the terminal leaf in time averages the last training
	42	+months rather than the last one, so a frozen boosted model enters the
	43	+test period with a slightly staler level than a linear model whose last
	44	+month effect is carried forward; by mid-2026 both are about 25\% below
	45	+the market and indistinguishable. The lesson is not that machine
	46	+learning fails out of sample. It is that the forward-in-time holdout
	47	+conflates two things---the common level error that any static model
	48	+incurs, and the relative accuracy the estimator contributes---and that
	49	+the first dominates the second within a few quarters. Retrained monthly,
	50	+or re-levelled with a published index as practitioners do
	51	+\citep{thibodeau2003marking, mayer2019estimation}, the boosted model
	52	+would presumably keep its interpolation advantage; the forward split
	53	+prices the \emph{retraining or re-levelling requirement} that random
	54	+cross-validation hides, and it matches the practitioner evidence that
	55	+automated-valuation accuracy decays quickly outside the sample period
	56	+\citep{bogin2020house, kok2017big}. It also explains why our first
	57	+version, which smeared the linear models but not the ensembles, found a
	58	+reversal: in a rising market an upward retransformation factor applied
	59	+to one family only offsets part of that family's staleness.
46	60
47	61	\subsection{Implications}
48	62
49		−\paragraph{For research.} Hedonic coefficients and indices are robust
50		−objects: form and even estimator perturb them little
51		−(Section~\ref{sec:ext}). Researchers using hedonics to \emph{measure}
52		−--- indices, implicit prices, capitalization effects --- can keep simple
53		−forms with good controls and report validation under a temporal split
54		−when prediction claims are made.
	63	+\paragraph{For research.} Hedonic indices are robust to functional form
	64	+and implicit-price gradients are robust to the estimator in shape, if
	65	+not in slope (Section~\ref{sec:ext}). Researchers using hedonic models to
	66	+\emph{measure}---indices, implicit prices, capitalization effects---can
	67	+keep simple forms with good, preferably hierarchical, spatial controls.
	68	+When prediction claims are made, they should report a forward-in-time
	69	+split alongside random cross-validation, and they should report
	70	+intervals: several of the differences that organise the applied
	71	+debate---a 5.5~km grid against municipality effects, month against
	72	+quarter effects, boosting against splines in deployment---are not
	73	+distinguishable from zero on half a million sales.
55	74
56	75	\paragraph{For mass appraisal.} Quebec's assessors face exactly this
57		−design problem every three years. Our results suggest the largest
58		−accuracy gains lie not in exotic estimators but in spatial resolution
59		−chosen by market thickness --- and that any model, linear or boosted,
60		−frozen at a reference date degrades by 3--7 points of median error
61		−within two years. This quantifies the staleness mechanism behind the
62		−assessment inequities documented in \companionpaper{}: the
63		−valuation technology's out-of-time decay is of the same magnitude as the
64		−inequities measured there.
	76	+design problem every three years. Our results suggest that the largest
	77	+accuracy gains lie in spatial resolution implemented hierarchically, that
	78	+flexible learners add a further three points within the period they are
	79	+estimated on, and that any model, linear or boosted, frozen at a
	80	+reference date under-prices the typical sale by 10--20\% within eighteen
	81	+months in a market like 2025--26. This quantifies the staleness
	82	+mechanism behind the assessment inequities documented in
	83	+\companionpaper{}: the valuation technology's out-of-time decay is of the
	84	+same order as the inequities measured there, and it is a level problem
	85	+that an index adjustment addresses before any change of estimator.
65	86
66		−\paragraph{For the AVM literature.} Every comparison should report a
67		−forward-in-time split alongside random cross-validation
68		−\citep{steurer2021metrics}. On our data, the choice of split changes not
69		−just magnitudes but the \emph{winner}.
	87	+\paragraph{For the automated-valuation literature.} Every comparison
	88	+should report a forward-in-time split, a leakage-free grouped split when
	89	+properties sell repeatedly or share coordinates, and a single
	90	+retransformation rule applied to all models
	91	+\citep{steurer2021metrics}. On our data the first changes the size and
	92	+significance of the headline gap, the second changes nothing, and the
	93	+third, applied asymmetrically, is enough to manufacture a reversal.
70	94
71	95	\subsection{Limitations}
72	96
73	97	Our attribute set, though assessor-grade, omits listing-level quality
74	98	(renovations, finishes, views); richer features would likely raise the
75		−machines' interpolation advantage. Hyper-parameters were deliberately
76		−conventional --- a tuned boosted model would gain somewhat, as would a
77		−spatially smarter linear model (e.g.\ kriging residuals,
78		−\citealp{case2004modeling}). The forward split covers one specific
79		−regime change (the 2025--26 recovery); other windows would shift
80		−magnitudes. And Quebec's institutional homogeneity aids transferability
81		−of results across municipalities but may limit it across countries.
	99	+learners' within-period advantage. Hyper-parameters were deliberately
	100	+conventional, and Section~\ref{sec:robust} shows that materially
	101	+different boosting configurations, including one tuned on a time-ordered
	102	+validation set, leave the ranking unchanged; a spatially smarter linear
	103	+model (kriged residuals, \citealp{case2004modeling}; semiparametric
	104	+location surfaces, \citealp{clapp2003semiparametric}) would narrow the
	105	+gap from the other side and is not estimated here. The forward split
	106	+covers one specific regime (the 2025--26 recovery), in which prices rose
	107	+by about 15\% in eighteen months; a flat or falling period would produce
	108	+a smaller level error and possibly a different ordering of staleness
	109	+across model families. The grouped holdouts remove leakage through
	110	+repeat sales and shared coordinates but not through neighbouring parcels
	111	+in the same street, which a spatially blocked holdout would address at
	112	+the cost of changing the question to spatial extrapolation. Finally,
	113	+Quebec's institutional homogeneity aids transferability of results
	114	+across municipalities but may limit it across countries.

modified paper/sections/extensions.tex +90 −61

		`@@ -3,26 +3,41 @@`
3	3	\section{Beyond the scoreboard: what the models imply}
4	4	\label{sec:ext}
5	5
6		−Accuracy is not the only output economists take from a hedonic model. This
7		−section asks whether the specification choices that move the scoreboard
8		−also move the two objects hedonic models are most often built to deliver:
9		−constant-quality price indices and implicit attribute prices.
	6	+Accuracy is not the only output economists take from a hedonic model.
	7	+This section asks whether the specification choices that move the
	8	+scoreboard also move the two objects hedonic models are most often built
	9	+to deliver, constant-quality price indices and implicit attribute prices,
	10	+and then characterises where and when the learners' advantage
	11	+materialises.
10	12
11		−\subsection{Price indices are form-robust}
	13	+\subsection{Price indices: form-robust, estimator-sensitive}
12	14
13		−Figure~\ref{fig:index} plots the constant-quality monthly index implied by
14		−the month fixed effects of four linear forms --- semi-log, log-log,
15		−quadratic and spline --- together with a gradient-boosting index obtained
16		−by repricing a fixed 20{,}000-sale reference portfolio at each month
17		−(an imputation \emph{\`a la} \citealp{hill2013hedonic}). All five track
18		−the same cycle --- the 2021--22 boom, the 2022--23 correction, the
19		−2024--26 recovery --- and the four linear forms agree to within a few
20		−index points throughout. The choice that dominates the accuracy
21		−scoreboard barely perturbs the index: reassuring news for statistical
22		−agencies, and consistent with the RPPI handbook's pragmatism about form
23		−\citep{oecd2013handbook, silver2018house}.
	15	+Figure~\ref{fig:index} plots the constant-quality monthly index implied
	16	+by the month fixed effects of four linear forms---semi-log, log-log,
	17	+quadratic and spline---together with a gradient-boosting index obtained
	18	+by repricing a fixed 20{,}000-sale reference portfolio at each month, a
	19	+hedonic imputation index in the sense of \citet{hill2013hedonic} and
	20	+\citet{hill2018geospatial}. All five track the same cycle: the 2021--22
	21	+boom, the 2022--23 correction and the 2024--26 recovery, over which the
	22	+constant-quality level rises by about 70\%. The four linear forms agree
	23	+to within 2.5 index points at every month, so the choice that generates
	24	+the most methodological discussion barely perturbs the index, consistent
	25	+with the RPPI handbook's pragmatism about form \citep{oecd2013handbook,
	26	+silver2018house}. The estimator is a different matter: the boosting
	27	+index rises less, ending in July 2026 at 160.5 against 168.6--171.0 for
	28	+the linear forms, a gap that opens gradually from 2024 and reaches nine
	29	+to eleven points. Two mechanisms contribute. The imputation index
	30	+reprices a fixed portfolio, so its weights differ from the time-dummy
	31	+index's implicit weights when appreciation is heterogeneous across
	32	+segments; and the boosting model's month counter enters through tree
	33	+splits that interact with location and attributes, so its ``time
	34	+effect'' is an average of locally varying paths rather than a single
	35	+common shift. Statistical agencies choosing between a time-dummy and an
	36	+imputation index should expect this order of disagreement when the
	37	+imputation model is a flexible learner; the agreement across linear
	38	+forms is reassuring, the agreement across estimators is not automatic.
24	39
25		−\begin{figure}[t]
	40	+\begin{figure}[tbp]
26	41	\centering
27	42	\includegraphics[width=\textwidth]{fig_index.png}
28	43	\caption{Constant-quality monthly price indices implied by competing
		`@@ -32,28 +47,36 @@ fixed effects. Gradient boosting: mean repriced value of a fixed`
32	47	\label{fig:index}
33	48	\end{figure}
34	49
35		−\subsection{Implicit prices: the machine agrees with the quadratic}
	50	+\subsection{Implicit prices: the machine broadly agrees with the quadratic}
36	51
37		−Figure~\ref{fig:profiles} compares the ln-price profiles in building age
38		−and floor area implied by the quadratic OLS coefficients with the partial-%
39		−dependence profiles of the boosting model \citep{friedman2001greedy}.
40		−The two agree over the bulk of the data: steep initial depreciation that
41		−flattens with age, and strongly concave returns to floor space. The
42		−visible divergences are where the quadratic \emph{cannot} bend --- the
43		−machine sees a milder gradient for very old stock (a vintage effect) and
44		−a small new-construction premium spike --- but through the ages and areas
45		−where 90\% of sales live, the curves sit within a tenth of a log point. The boosting model's advantage evidently comes from
46		−higher-order interactions and spatial flexibility, \emph{not} from a
47		−different view of the main attribute gradients --- so the interpretable
48		−quadratic form remains a faithful summary of the price surface even where
49		−it loses the prediction race \citep{mullainathan2017machine,
50		−athey2019machine}.
	52	+Figure~\ref{fig:profiles} compares the log-price profiles in building age
	53	+and floor area implied by the quadratic OLS coefficients with the
	54	+partial-dependence profiles of the boosting model
	55	+\citep{friedman2001greedy, lorenz2023interpretable}, each normalised to
	56	+its leftmost point. The two agree on the shape: steep initial
	57	+depreciation that flattens with age, and strongly concave returns to
	58	+floor space. On floor area the curves sit within 0.05 log points of each
	59	+other over the whole 50--400~m$^2$ range. On age the boosting profile is
	60	+uniformly flatter: it shows a small new-construction premium (the
	61	+profile peaks at five years, $+0.06$ log points above a new building,
	62	+where the quadratic can only decline), and from twenty years onward its
	63	+cumulative depreciation is 0.10--0.13 log points smaller than the
	64	+quadratic's ($-0.20$ against $-0.31$ at forty years, $-0.28$ against
	65	+$-0.41$ at sixty), with a milder gradient for very old stock, a vintage
	66	+effect the quadratic cannot bend to accommodate. These are differences
	67	+of degree in a shared shape, not of sign or ordering. The boosting
	68	+model's accuracy advantage therefore does not come from a different view
	69	+of the main attribute gradients; it comes from higher-order interactions
	70	+and, above all, from the spatial surface (Section~\ref{sec:results}).
	71	+The interpretable quadratic remains a faithful, if slightly steeper,
	72	+summary of the age--price relation even where it loses the prediction
	73	+race \citep{mullainathan2017machine, athey2019machine}.
51	74
52		−\begin{figure}[t]
	75	+\begin{figure}[tbp]
53	76	\centering
54	77	\includegraphics[width=\textwidth]{fig_profiles.png}
55		−\caption{Implicit ln-price profiles: quadratic OLS coefficients versus
56		−gradient-boosting partial dependence, each normalized to its leftmost
	78	+\caption{Implicit log-price profiles: quadratic OLS coefficients versus
	79	+gradient-boosting partial dependence, each normalised to its leftmost
57	80	point. Panel A: building age. Panel B: floor area.}
58	81	\label{fig:profiles}
59	82	\end{figure}
		`@@ -61,18 +84,19 @@ point. Panel A: building age. Panel B: floor area.}`
61	84	\subsection{Learning curves: data beat flexibility only at scale}
62	85
63	86	Figure~\ref{fig:learning} and Table~\ref{tab:learning} trace accuracy
64		−against training size from 10{,}000 to 400{,}000 sales. The OLS quadratic
65		−is essentially flat from the very first step (18.4\% at $n=10{,}000$,
66		−18.1\% at $n=400{,}000$) --- its bias floor binds almost immediately ---
67		−while the boosting model improves monotonically through the full sample
68		−(17.6\% $\to$ 14.5\%): the machine's advantage grows from under one
69		−error point at $n = 10{,}000$ to 3.6 points at
70		−$n = 400{,}000$. Flexible methods
71		−are not a free lunch in small markets: below a few tens of thousands of
72		−training sales, the machine's edge is modest, one reason rural and thin-%
73		−market AVMs underperform \citep{bogin2020house}.
	87	+against training size from 10{,}000 to 400{,}000 sales on a fixed random
	88	+holdout. The OLS quadratic is flat from the very first step (19.1\% at
	89	+$n = 10{,}000$, 19.2\% at $n = 400{,}000$): its bias floor binds
	90	+immediately, and more data cannot lower it. The boosting model improves
	91	+monotonically through the full sample (17.6\% $\to$ 14.5\%), so its
	92	+advantage grows from 1.6 points at $n = 10{,}000$ to 4.7 points at
	93	+$n = 400{,}000$. Flexible methods are not a free lunch in small markets:
	94	+below a few tens of thousands of training sales, the learner's edge is
	95	+modest, one reason thin-market automated valuation underperforms
	96	+\citep{bogin2020house}, and a reason the provincial scale of the present
	97	+data matters for the size of the gap we measure.
74	98
75		−\begin{figure}[t]
	99	+\begin{figure}[tbp]
76	100	\centering
77	101	\includegraphics[width=0.72\textwidth]{fig_learning.png}
78	102	\caption{Learning curves: median absolute error against training-set
		`@@ -80,7 +104,7 @@ size (random holdout fixed), OLS quadratic versus gradient boosting.}`
80	104	\label{fig:learning}
81	105	\end{figure}
82	106
83		−\begin{table}[t]
	107	+\begin{table}[tbp]
84	108	\centering
85	109	\begin{threeparttable}
86	110	\caption{Learning curves}
		`@@ -98,23 +122,28 @@ seeded subsamples of the indicated size.`
98	122
99	123	Table~\ref{tab:segments} and Figure~\ref{fig:segments} decompose the
100	124	random-holdout MdAPE by property class and municipality size, and the
101		−pattern identifies the machine's edge with striking precision: it is
102		−spatial resolution. The gap is enormous for condominiums (9.1\% versus
103		−20.4\%) and in the largest cities (11.9\% versus 17.8\%) --- segments
104		−where structure is homogeneous but \emph{micro}-location varies hugely
105		−within a municipality, exactly the variation that municipality dummies
106		−cannot see and raw coordinates can. Once location is resolved, a condo
107		−is the most predictable object in the market. At the other extreme,
108		−cottages defeat both models (32.1\% versus 33.9\%): idiosyncratic,
109		−waterfront-driven stock is hard for everyone, and the machine's spatial
110		−surface cannot rescue attributes it does not observe. The complement of
111		−the assessment-inequity anatomy in \companionpaper{} is
	125	+pattern locates the learner's edge: it is spatial resolution. The gap is
	126	+largest for condominiums (9.1\% against 18.2\%) and in the largest
	127	+cities (11.9\% against 17.7\%), segments where structure is homogeneous
	128	+but \emph{micro}-location varies greatly within a municipality, exactly
	129	+the variation that municipality dummies cannot see and raw coordinates
	130	+can. Once location is resolved, a condominium is the most predictable
	131	+object in the market. The gap is also large in the thinnest
	132	+municipalities (18.7\% against 24.8\%), where a municipality effect is
	133	+estimated from few sales and the learner can borrow strength from
	134	+neighbouring municipalities through the coordinates. At the other
	135	+extreme, cottages defeat both models (32.1\% against 34.3\%):
	136	+idiosyncratic, waterfront-driven stock is hard for everyone, and a
	137	+spatial surface cannot rescue attributes it does not observe. The
	138	+complement with the assessment-inequity anatomy in \companionpaper{} is
112	139	instructive: the segments where assessors are most regressive
113	140	(heterogeneous, land-heavy stock) are also those where \emph{no}
114	141	standard technology, linear or boosted, prices accurately from roll
115		−attributes alone.
	142	+attributes alone. Section~\ref{sec:robust} examines how much of the
	143	+condominium advantage reflects genuine micro-location rather than recall
	144	+of sales in the same building.
116	145
117		−\begin{figure}[t]
	146	+\begin{figure}[tbp]
118	147	\centering
119	148	\includegraphics[width=0.8\textwidth]{fig_segments.png}
120	149	\caption{Median absolute error by market segment (random holdout):
		`@@ -122,7 +151,7 @@ OLS quadratic versus gradient boosting.}`
122	151	\label{fig:segments}
123	152	\end{figure}
124	153
125		−\begin{table}[t]
	154	+\begin{table}[tbp]
126	155	\centering
127	156	\begin{threeparttable}
128	157	\caption{Accuracy by market segment}

modified paper/sections/introduction.tex +96 −68

		`@@ -8,87 +8,115 @@ the price or not? Dummies for years or for months? Neighbourhood fixed`
8	8	effects, and how fine? Least squares or, increasingly, a gradient-boosted
9	9	ensemble? Fifty years after \citet{rosen1974hedonic} established that
10	10	theory places no restriction on the shape of the price surface, these
11		−choices are still made largely by convention --- the semi-log survives as
12		−the default \citep{sirmans2005composition}, the classic form
13		−comparisons predate the out-of-sample era \citep{halvorsen1981choice,
14		−cropper1988choice}, and the machine-learning comparisons that have
15		−multiplied since \citet{mullainathan2017machine} typically change the
16		−sample, the features and the validation scheme all at once, making it
17		−impossible to say \emph{which} ingredient buys the reported gains.
	11	+choices are still made largely by convention: the semi-log survives as
	12	+the default \citep{sirmans2005composition, khoshnoud2023evolution}, the
	13	+classic functional-form comparisons predate the out-of-sample era
	14	+\citep{halvorsen1981choice, cropper1988choice}, and the machine-learning
	15	+comparisons that have multiplied since \citet{mullainathan2017machine}
	16	+typically change the sample, the features and the validation scheme at
	17	+once, so that it is impossible to say \emph{which} ingredient buys the
	18	+reported gains.
18	19
19	20	This paper runs the comparison the way one would design an experiment.
20	21	From 514{,}212 Quebec residential sales (2021--2026) matched at the
21		−parcel level to the provincial assessment roll --- so that every model
	22	+parcel level to the provincial assessment roll---so that every model
22	23	sees the same assessor-grade attribute set: floor area, lot area, age,
23		−storeys, units, property class, physical configuration --- we estimate
24		−\textbf{twenty models organised along four axes}, varying one design
25		−choice at a time: six functional forms (linear to Box--Cox to splines),
26		−a ladder of time controls (none to month fixed effects), a ladder of
27		−spatial controls (none to a $\sim$1~km grid), and six estimation methods
28		−(OLS to random forests, gradient boosting, and a $k$-nearest-neighbour
	24	+storeys, units, property class, physical configuration---we estimate
	25	+twenty models organised along four axes, varying one design choice at a
	26	+time: six functional forms (linear to Box--Cox to splines), a ladder of
	27	+time controls (none to month fixed effects), a ladder of spatial
	28	+controls (none to a $\sim$1~km grid), and six estimation methods (OLS to
	29	+random forests, gradient boosting and a $k$-nearest-neighbour
29	30	comparables rule). Every model is scored on the same price-level
30		−scoreboard --- log models retransformed with Duan smearing, Box--Cox
31		−inverted --- and, crucially, under \textbf{two holdouts}: the standard
32		−random 80/20 split, and a forward-in-time split (train before 2025, test
33		−2025--26) that mimics how a valuation model is actually deployed.
	31	+scoreboard, with a single retransformation rule for every model whose
	32	+dependent variable is a transformed price, and under two holdouts: the
	33	+standard random 80/20 split, and a forward-in-time split (train before
	34	+2025, test 2025--26) that mimics how a valuation model is actually
	35	+deployed. Because differences of a few tenths of a point between models
	36	+evaluated on the same sales can be noise, every comparison comes with a
	37	+municipality-clustered bootstrap interval and a Diebold--Mariano-type
	38	+test of equal accuracy.
34	39
35		−Four results organise the paper.
36		−
37		−\textbf{First, functional form is a second-order choice.} Across linear,
38		−semi-log, log-log, profile-likelihood Box--Cox
39		−($\hat\lambda = 0.25$), quadratic and spline specifications --- holding
40		−controls fixed --- the median absolute error spans 16.5\% to 18.6\%.
41		−Splines beat the textbook semi-log by 1.6 points; the data-driven
42		−Box--Cox transformation, the great hope of the 1980s debate, buys
43		−nothing out of sample, vindicating \citet{cropper1988choice} and
	40	+Four results organise the paper. \emph{First, functional form is a
	41	+second-order choice.} Across linear, semi-log, log-log,
	42	+profile-likelihood Box--Cox ($\hat\lambda = 0.25$), quadratic and spline
	43	+specifications, holding controls fixed, the median absolute error spans
	44	+17.6\% to 19.2\% under the random holdout. Splines beat the textbook
	45	+semi-log by 1.4 points; the data-driven Box--Cox transformation, the
	46	+great hope of the 1980s debate, gains half a point on the median error
	47	+and nothing on the mean error, vindicating \citet{cropper1988choice} and
44	48	\citet{cassel1985cost} on modern data at scale.
45	49
46		−\textbf{Second, controls are first-order --- with a twist.} Removing all
47		−spatial controls costs ten error points (27.9\% versus 17.5\%), an order
48		−of magnitude more than any curvature decision; a $\sim$5.5~km grid beats
49		−both municipality effects and, notably, a $\sim$1.1~km grid, whose
50		−30{,}548 cells overfit --- the bias--variance trade-off in absorbing
51		−location is real and non-monotonic. Time effects show the same shape in
52		−miniature: anything beats nothing (three points), granularity beyond
53		−quarters buys nothing.
	50	+\emph{Second, controls are first-order, with a twist.} Removing all
	51	+spatial controls costs ten error points (28.8\% against 19.2\%), six
	52	+times the entire functional-form range; a $\sim$5.5~km grid is nominally
	53	+but not significantly better than municipality effects, and a
	54	+$\sim$1.1~km grid used on its own overfits (21.0\%), its 30{,}548 cells
	55	+holding three sales at the median. Nested within municipalities, so that
	56	+thin and unseen cells inherit their municipality's level, the same fine
	57	+grid becomes the most accurate linear specification in the paper
	58	+(17.3\%): the bias--variance trade-off in absorbing location is real,
	59	+and it is resolved by hierarchy rather than by coarseness. Time effects
	60	+show the same shape in miniature: anything beats nothing (three points
	61	+under the random split, six under the forward split), and granularity
	62	+beyond quarters buys nothing.
54	63
55		−\textbf{Third, under random validation the estimation method dominates.}
	64	+\emph{Third, under random validation the estimation method dominates.}
56	65	Gradient boosting reaches a median error of 14.4\% and random forests
57		−14.6\%, against 16.5\% for the best linear model --- a 13\% improvement
58		−--- and stripping the coordinates from the boosting model degrades it to
59		−23.2\%, showing that what the machine mainly learns is a flexible price
60		−surface over space \citep{bourassa2010predicting}. The na\"ive
61		−$k$-NN comparables rule (21.2\%) confirms that neither raw proximity nor
62		−raw flexibility suffices: the gains come from their combination.
	66	+14.6\%, against 17.6\% for the best linear model, an 18\% improvement
	67	+that is statistically unambiguous ($-3.2$ points, 95\% interval $-4.7$
	68	+to $-1.9$). Stripping the coordinates from the boosting model degrades
	69	+it to 23.2\%, so what the learner mainly buys is a flexible price
	70	+surface over space \citep{bourassa2010predicting, pace2020residuals};
	71	+the na\"ive $k$-NN comparables rule (21.2\%) shows that raw proximity
	72	+without attribute adjustment does not suffice either. The advantage is
	73	+not an artefact of repeat sales or of condominium units geocoded to the
	74	+same building: it survives holdouts grouped by parcel and by coordinate
	75	+pair essentially unchanged.
63	76
64		−\textbf{Fourth --- our headline --- the ranking is an artifact of the
65		−validation scheme.} Under the forward-in-time split every model degrades,
66		−but not equally: the machine-learning advantage \emph{reverses} on the
67		−median error (gradient boosting 21.2\% versus 19.1\% for the spline
68		−hedonic) and equalizes exactly on log-scale $R^2$ (0.52 for both).
69		−Random cross-validation lets flexible models interpolate the price level
70		−of their own test period; when the test period lies in the future --- the
71		−only case that matters for deployment --- that advantage is leakage, not
72		−skill. Comparisons of valuation models that report random cross-validation
73		−alone, i.e.\ most of the applied ML literature, systematically overstate
74		−the practical value of model flexibility \citep{clapp2002predicting,
75		−steurer2021metrics}.
	77	+\emph{Fourth---our headline---the advantage is a within-period
	78	+statement.} Under the forward-in-time split every model degrades, the
	79	+ensembles most: gradient boosting loses 6.8 points (to 21.2\%) and the
	80	+spline hedonic 4.1 (to 21.7\%), so the three-point gap shrinks to half a
	81	+point and loses statistical significance, while the ensembles keep a
	82	+modest lead on the mean error and on log-scale fit. Decomposing the
	83	+forward error shows why. The 2025--26 sales are not harder to price:
	84	+evaluated on the same sales, a boosting model that has seen their period
	85	+posts 13.7\%. What a frozen model loses is the \emph{level}: every
	86	+forward-split model under-prices the typical 2025--26 sale by 10--20\%,
	87	+the ensembles slightly more than the linear models because their
	88	+terminal leaf in time averages the last training months. Once each
	89	+model's level is corrected, the boosting advantage over the spline
	90	+hedonic is 2.9 points, essentially what the random split measures.
	91	+Relative pricing skill transfers forward almost intact; the price level
	92	+does not, and random cross-validation hides a staleness cost of three to
	93	+seven points of median error within eighteen months that any deployed
	94	+model, linear or boosted, must pay unless it is re-levelled by an index
	95	+or retrained. A previous version of this paper reported that the
	96	+ranking reversed in the forward split; the reversal was an artefact of
	97	+an asymmetric retransformation and is corrected here.
76	98
77	99	The paper then asks what the specification choices do to the objects
78		−economists actually extract from hedonic models. Constant-quality monthly
79		−indices implied by the month effects of four linear forms --- and by
80		−repricing a fixed portfolio with the boosting model --- agree to within a
81		−few index points across the largest housing cycle in recent Canadian
82		−history. And the boosting model's partial-dependence profiles in age and
83		−floor area track the quadratic OLS closely: the machine agrees with the
84		−economist about the gradients and disagrees mainly about the residual
85		−surface. Interpretation and prediction, in other words, conflict far less
86		−than the accuracy scoreboard suggests.
	100	+economists actually extract from hedonic models. Constant-quality
	101	+monthly indices implied by the month effects of four linear forms agree
	102	+to within 2.5 index points across the largest housing cycle in recent
	103	+Canadian history, whereas the imputation index from the boosting model
	104	+rises nine points less over five years: form does not move the index,
	105	+the estimator can. The boosting model's partial-dependence profiles in
	106	+age and floor area share the shape of the quadratic OLS gradients, with
	107	+a uniformly milder depreciation path, so the machine disagrees with the
	108	+economist about the residual surface rather than about the main
	109	+gradients. Interpretation and prediction, in other words, conflict far
	110	+less than the accuracy scoreboard suggests.
87	111
88	112	Section~\ref{sec:lit} situates the exercise in the functional-form,
89		−spatial-hedonic and ML-valuation literatures. Section~\ref{sec:data}
90		−describes the data, Section~\ref{sec:method} the experimental design.
91		−Section~\ref{sec:results} reports the horse race,
92		−Section~\ref{sec:ext} the index, implicit-price, learning-curve and
93		−segment extensions, Section~\ref{sec:disc} discusses implications, and
	113	+spatial-hedonic and machine-learning valuation literatures.
	114	+Section~\ref{sec:data} describes the data, Section~\ref{sec:method} the
	115	+experimental design, the scoreboard and the inference procedures.
	116	+Section~\ref{sec:results} reports the horse race and decomposes the
	117	+generalization gap, Section~\ref{sec:ext} the index, implicit-price,
	118	+learning-curve and segment extensions, Section~\ref{sec:robust} the
	119	+robustness analyses (retransformation rule, leakage-free holdouts, nested
	120	+spatial effects, Box--Cox grid, boosting hyper-parameters),
	121	+Section~\ref{sec:disc} discusses implications, and
94	122	Section~\ref{sec:concl} concludes.

modified paper/sections/literature.tex +92 −50

		`@@ -6,62 +6,104 @@`
6	6	\subsection{The functional-form debate}
7	7
8	8	Hedonic theory is silent about functional form. \citet{rosen1974hedonic}
9		−showed that the price surface is an equilibrium envelope of bids and
10		−offers, so nothing structural pins down its curvature ---
11		−form is an empirical choice. The classical exchange settled into a
12		−three-cornered debate: \citet{halvorsen1981choice} advocated data-driven
13		−Box--Cox transformations \citep{box1964analysis};
14		−\citet{cassel1985cost} cautioned that flexible transformations optimize
15		−in-sample fit while degrading the implicit prices researchers actually
16		−use; and \citet{cropper1988choice}, in an influential simulation study,
17		−found that simple forms --- linear and semi-log --- are the most robust to
18		−the misspecification and omitted variables that characterize real data.
19		−Fifty years on, the semi-log remains the profession's default
20		−\citep{malpezzi2003hedonic, sirmans2005composition}, but systematic
21		−head-to-head evidence on modern samples remains scarce, and the classic
22		−studies predate the out-of-sample validation culture. Two further
23		−technical strands feed our design: retransformation bias in log models
24		−\citep{duan1983smearing}, which we correct with the smearing factor so
25		−that every form competes in levels; and forecast-evaluation methodology
26		−for house prices \citep{clapp2002predicting, steurer2021metrics}.
	9	+showed that the price surface is an equilibrium envelope of bid and
	10	+offer functions, so nothing structural pins down its curvature: the form
	11	+is an empirical choice. The classical exchange settled into a
	12	+three-cornered debate. \citet{halvorsen1981choice} advocated letting the
	13	+data choose the transformation through the Box--Cox family
	14	+\citep{box1964analysis}; \citet{cassel1985cost} cautioned that flexible
	15	+transformations optimise in-sample fit while degrading the implicit
	16	+prices researchers actually use; and \citet{cropper1988choice}, in a
	17	+simulation study that remains the standard reference, found that simple
	18	+forms, linear and semi-log, are the most robust to the misspecification
	19	+and omitted variables that characterise real data. The debate has been
	20	+revisited for welfare measurement rather than prediction:
	21	+\citet{kuminoff2010which} show in a Monte Carlo design calibrated to
	22	+actual housing data that the choice of control variables (notably
	23	+spatial fixed effects) matters more for recovering marginal willingness
	24	+to pay than the choice of functional form, and \citet{bishop2020best}
	25	+codify the resulting best practice. Fifty years on, the semi-log remains
	26	+the profession's default \citep{malpezzi2003hedonic,
	27	+sirmans2005composition, khoshnoud2023evolution}, but systematic
	28	+head-to-head evidence on large modern samples remains scarce, and the
	29	+classic studies predate the out-of-sample validation culture. Two
	30	+technical strands feed our design. Retransformation bias in log models
	31	+\citep{duan1983smearing, manning2001estimating} determines how
	32	+predictions in logarithms are converted into price levels, a step that
	33	+turns out to matter for the comparison between linear models and tree
	34	+ensembles. Forecast-evaluation methodology, from the equal-accuracy tests
	35	+of \citet{diebold1995comparing} and \citet{giacomini2006tests} to their
	36	+application to house prices \citep{clapp2002predicting,
	37	+steurer2021metrics}, supplies the inferential framework we use to decide
	38	+whether differences on the scoreboard are real.
27	39
28	40	\subsection{Space and time in hedonic models}
29	41
30	42	A second literature concerns what the covariates cannot capture. House
31	43	prices are spatially autocorrelated at fine scale
32		−\citep{dubin1998spatial, anselin1988spatial}, and the practical remedies
33		−range from submarket segmentation \citep{goodman1998housing} to spatial
34		−econometrics and simple location fixed effects; comparative studies
35		−generally find that flexibly absorbing location buys more predictive
36		−accuracy than any parametric spatial process \citep{case2004modeling,
37		−bourassa2010predicting, pace1997spatial}. In the Quebec context,
	44	+\citep{anselin1988spatial, dubin1998spatial, pace1998spatiotemporal}, and
	45	+the practical remedies range from submarket segmentation
	46	+\citep{goodman1998housing, goodman2003segmentation, bourassa2003submarkets}
	47	+to spatial econometric processes, semiparametric location surfaces
	48	+\citep{clapp2003semiparametric, fik2003modeling} and simple location
	49	+fixed effects. Comparative studies generally find that flexibly
	50	+absorbing location buys more predictive accuracy than any parametric
	51	+spatial process, and that the gain depends on how submarkets are drawn
	52	+\citep{pace1997spatial, case2004modeling, bourassa2007spatial,
	53	+bourassa2010predicting}. \citet{pace2020residuals} show with tree
	54	+ensembles that the residuals of standard hedonic and spatial models
	55	+still contain exploitable spatial information, which is precisely the
	56	+margin our coordinate-based learners target. In the Quebec context,
38	57	\citet{desrosiers2000hedonic} document the importance of access and
39		−neighbourhood attributes in Quebec City. On the time dimension, hedonic
40		−price-index theory --- the time-dummy versus imputation debate ---
41		−is surveyed by \citet{hill2013hedonic} and codified in the RPPI handbook
42		−\citep{oecd2013handbook, silver2018house}; a byproduct of our month-FE
43		−models is a direct test of how sensitive a constant-quality index is to
44		−the underlying form.
	58	+neighbourhood attributes in Quebec City, and \citet{dube2013pooled}
	59	+stress that sales pooled over time are not exchangeable: a sale can
	60	+inform the price of a later neighbour but not of an earlier one, which
	61	+is the asymmetry a forward-in-time holdout respects and a random split
	62	+ignores. On the time dimension, the time-dummy versus imputation debate
	63	+in hedonic price-index theory is surveyed by \citet{hill2013hedonic} and
	64	+codified in the RPPI handbook \citep{oecd2013handbook, silver2018house};
	65	+\citet{hill2009boom} and \citet{hill2018geospatial} show that imputation
	66	+indices built from flexible, spline-based hedonic models track a boom
	67	+and bust more faithfully, and \citet{diewert2015decomposition} and
	68	+\citet{diewert2016tokyo} develop the hedonic decomposition of prices into
	69	+land and structure components. A by-product of our month-effects models
	70	+is a direct test of how sensitive a constant-quality index is to the
	71	+underlying functional form and to the estimator.
45	72
46	73	\subsection{Machine learning and automated valuation}
47	74
48		−The third strand is the rapid colonization of mass valuation by machine
49		−learning. \citet{mullainathan2017machine} frame prediction as ML's
50		−comparative advantage, with hedonic pricing as their running example;
51		−\citet{athey2019machine} survey the toolkit. Applied comparisons ---
52		−random forests \citep{breiman2001random}, gradient boosting
53		−\citep{friedman2001greedy, ke2017lightgbm} --- consistently report 20--40\%
54		−error reductions over linear hedonics \citep{mayer2019estimation,
55		−hong2020machine, kok2017big}, with accuracy degrading in thin rural
56		−markets \citep{bogin2020house}; \citet{gencay1996nonlinear} anticipated
57		−the pattern with semiparametric estimators. Three gaps motivate our
58		−design. First, most comparisons change several ingredients at once
59		−(features, sample, validation scheme), so the \emph{sources} of the ML
60		−advantage --- curvature? interactions? spatial flexibility? --- are rarely
61		−isolated; our axis design holds features constant and varies one choice
62		−at a time. Second, almost all published comparisons use random
63		−cross-validation, which leaks future price levels into training and
64		−flatters any flexible model; we score every model under a
65		−forward-in-time split as well. Third, comparisons seldom examine what the
66		−flexible models \emph{imply} --- indices, implicit prices --- which is
67		−what economists need; our extensions section does exactly that.
	75	+The third strand is the rapid adoption of machine learning in mass
	76	+valuation. \citet{mullainathan2017machine} frame prediction as the
	77	+comparative advantage of machine learning, with hedonic pricing as their
	78	+running example; \citet{athey2019machine} survey the toolkit. The
	79	+applied comparisons, from early neural networks and random forests
	80	+\citep{zurada2011comparison, antipov2012mass, mccluskey2013prediction} to
	81	+gradient boosting \citep{kok2017big, mayer2019estimation,
	82	+perezrave2019machine, hong2020machine}, consistently report error
	83	+reductions of 20--40\% over linear hedonics, with accuracy degrading in
	84	+thin rural markets \citep{bogin2020house}; \citet{gencay1996nonlinear}
	85	+anticipated the pattern with semiparametric estimators, and
	86	+\citet{lorenz2023interpretable} show that the gains come with
	87	+interpretable partial-dependence profiles that economists can read as
	88	+implicit prices. \citet{mayer2019estimation} is the closest antecedent
	89	+to our forward-in-time design: on Swiss data they compare estimation
	90	+methods together with updating rules (moving windows, weighting) and
	91	+find that the choice of updating matters as much as the estimator; we
	92	+isolate the same question by scoring frozen models on a future period.
	93	+Three gaps motivate our design. First, most comparisons change several
	94	+ingredients at once (features, sample, validation scheme), so the sources
	95	+of the machine-learning advantage---curvature, interactions, spatial
	96	+flexibility---are rarely isolated; our axis design holds the features
	97	+constant and varies one choice at a time
	98	+\citep[compare the specification exercise of][]{schulz2014automated}.
	99	+Second, almost all published comparisons use random cross-validation,
	100	+which leaks the future price level into training, and, when properties
	101	+sell repeatedly or share a building, lets a coordinate-based learner
	102	+recall a property's own earlier price; the forecasting and ecology
	103	+literatures have long documented how such temporal and spatial
	104	+dependence inflates cross-validated accuracy
	105	+\citep{bergmeir2012crossvalidation, roberts2017crossvalidation}. We score
	106	+every model under a forward-in-time split and under parcel- and
	107	+building-grouped splits as well. Third, comparisons seldom examine what
	108	+the flexible models \emph{imply}---indices, implicit prices---which is
	109	+what economists need; Section~\ref{sec:ext} does exactly that.

modified paper/sections/methodology.tex +264 −70

		`@@ -3,80 +3,274 @@`
3	3	\section{Methodology: the design of the horse race}
4	4	\label{sec:method}
5	5
6		−The comparison is organised so that each design choice varies while
7		−everything else is held fixed. All models price the same sales from the
8		−same attribute set; only the functional mapping changes.
	6	+The comparison is organised so that one design choice varies at a time
	7	+while everything else is held fixed. All twenty models price the same
	8	+sales from the same attribute vector; only the mapping from attributes to
	9	+price changes. This section defines the models, the retransformation rule
	10	+that puts them on a common scoreboard, the two holdouts and the inference
	11	+procedures.
	12	+
	13	+\subsection{Notation and the baseline hedonic function}
	14	+
	15	+For sale $i$ let $P_i$ denote the price, $\mathbf{x}_i$ the vector of
	16	+structural attributes supplied by the assessment roll (floor area $a_i$
	17	+in m$^2$, lot area $l_i$ in m$^2$ with an indicator $h_i = \mathbb{1}[l_i
	18	+> 0]$, building age $g_i$ in years, storeys, dwelling units, and dummies
	19	+for property class and physical configuration), $m(i)$ the municipality,
	20	+$c_5(i)$ and $c_1(i)$ the $\sim$5.5~km and $\sim$1.1~km grid cells
	21	+containing the parcel, and $y(i)$, $q(i)$, $\tau(i)$ the year, quarter and
	22	+month of sale. A linear hedonic model with a transformation $g(\cdot)$ of
	23	+the price, a set $\mathcal{S}$ of spatial fixed effects and a set
	24	+$\mathcal{T}$ of time fixed effects is
	25	+\begin{equation}
	26	+ g(P_i) \;=\; \boldsymbol{\phi}(\mathbf{x}_i)'\boldsymbol{\beta}
	27	+ \;+\; \mu_{s(i)} \;+\; \delta_{t(i)} \;+\; \varepsilon_i,
	28	+ \qquad s(i)\in\mathcal{S},\; t(i)\in\mathcal{T},
	29	+ \label{eq:hedonic}
	30	+\end{equation}
	31	+where $\boldsymbol{\phi}(\cdot)$ is a basis expansion of the attributes
	32	+(identity, logarithms, quadratics or splines), $\mu_s$ absorbs location
	33	+and $\delta_t$ the market level. Following \citet{rosen1974hedonic},
	34	+nothing in theory restricts $g$ or $\boldsymbol{\phi}$; the axes below
	35	+make those choices explicit. The baseline, used as the backbone of
	36	+axes~B and~C, takes $g = \ln$, quadratics in area and age,
	37	+$\mathcal{S}$ = municipalities and $\mathcal{T}$ = quarters.
9	38
10	39	\subsection{The four axes}
11	40
12	41	\paragraph{A. Functional form.} With municipality and quarter fixed
13		−effects and the base attributes (floor area, lot area, building age,
14		−storeys, units, property class, physical configuration), we estimate:
15		−(A1) fully linear in levels; (A2) semi-log, $\ln P$ on levels
16		−\citep{malpezzi2003hedonic}; (A3) log-log, $\ln P$ on logged areas;
17		−(A4) Box--Cox on the price, with $\lambda$ chosen by profile likelihood
18		−on the training set over a grid \citep{box1964analysis,
19		−halvorsen1981choice}; (A5) semi-log with quadratics in area and age; and
20		−(A6) semi-log with cubic $B$-splines (six knots) in area, age and lot.
21		−
22		−\paragraph{B. Time effects.} On the A5 backbone: no time controls,
23		−year fixed effects, quarter fixed effects, month fixed effects ---
24		−the granularity ladder of the time-dummy index literature
25		−\citep{hill2013hedonic}.
26		−
27		−\paragraph{C. Spatial controls.} On the A5 backbone with quarter FE:
28		−no spatial controls, municipality FE (1{,}115), a $\sim$5.5~km grid
29		−(5{,}255 cells), and a $\sim$1.1~km grid (30{,}548 cells) --- a
30		−granularity ladder that brackets the bias--variance trade-off in
31		−absorbing location \citep{case2004modeling, bourassa2010predicting}.
32		−
33		−\paragraph{D. Estimation method.} Holding the attribute set fixed:
34		−(D1) OLS with municipality and month FE; (D2) cross-validated ridge on
35		−the same standardized design; (D3) a random forest
36		−\citep{breiman2001random} and (D4) gradient boosting
37		−\citep{friedman2001greedy} on the attributes plus raw coordinates and a
38		−continuous month counter; (D5) gradient boosting \emph{without}
39		−coordinates, to price what spatial flexibility is worth to the machine;
40		−and (D6) a spatial $k$-nearest-neighbour comparables rule --- the
41		−distance-weighted price per square metre of the ten nearest training
42		−sales --- as the na\"ive appraiser benchmark.
	42	+effects held fixed, the six forms differ only in $g$ and
	43	+$\boldsymbol{\phi}$:
	44	+\begin{align}
	45	+ \text{A1 (linear):}\quad & P_i = \mathbf{x}_i'\boldsymbol{\beta}
	46	+ + \mu_{m(i)} + \delta_{q(i)} + \varepsilon_i; \label{eq:a1}\\
	47	+ \text{A2 (semi-log):}\quad & \ln P_i = \mathbf{x}_i'\boldsymbol{\beta}
	48	+ + \mu_{m(i)} + \delta_{q(i)} + \varepsilon_i; \label{eq:a2}\\
	49	+ \text{A3 (log-log):}\quad & \ln P_i = \beta_a \ln a_i
	50	+ + \beta_l\, h_i \ln l_i + \beta_h h_i + \tilde{\mathbf{x}}_i'\tilde{\boldsymbol{\beta}}
	51	+ + \mu_{m(i)} + \delta_{q(i)} + \varepsilon_i; \label{eq:a3}\\
	52	+ \text{A4 (Box--Cox):}\quad & \frac{P_i^{\lambda}-1}{\lambda}
	53	+ = \mathbf{x}_i'\boldsymbol{\beta} + \mu_{m(i)} + \delta_{q(i)}
	54	+ + \varepsilon_i; \label{eq:a4}\\
	55	+ \text{A5 (quadratics):}\quad & \ln P_i = \mathbf{x}_i'\boldsymbol{\beta}
	56	+ + \beta_{aa}\Big(\tfrac{a_i}{100}\Big)^{2}
	57	+ + \beta_{gg}\Big(\tfrac{g_i}{10}\Big)^{2}
	58	+ + \mu_{m(i)} + \delta_{q(i)} + \varepsilon_i; \label{eq:a5}\\
	59	+ \text{A6 (splines):}\quad & \ln P_i = \sum_{v\in\{a,l,g\}}
	60	+ \sum_{k=1}^{8} \beta_{vk}\, B_{vk}(v_i)
	61	+ + \tilde{\mathbf{x}}_i'\tilde{\boldsymbol{\beta}}
	62	+ + \mu_{m(i)} + \delta_{q(i)} + \varepsilon_i, \label{eq:a6}
	63	+\end{align}
	64	+where $\tilde{\mathbf{x}}_i$ collects the remaining attributes and
	65	+$B_{vk}$ are cubic $B$-spline basis functions with six uniformly spaced
	66	+knots over the training range of each variable (eight basis functions
	67	+per variable). In the Box--Cox model \citep{box1964analysis,
	68	+halvorsen1981choice} the exponent is chosen on the training sample by
	69	+maximising the profile log-likelihood
	70	+\begin{equation}
	71	+ \ell(\lambda) \;=\; -\frac{n}{2}\ln\!\Big(\frac{\mathrm{SSE}(\lambda)}{n}\Big)
	72	+ \;+\; (\lambda - 1)\sum_{i=1}^{n}\ln P_i,
	73	+ \label{eq:profile}
	74	+\end{equation}
	75	+where $\mathrm{SSE}(\lambda)$ is the residual sum of squares of
	76	+\eqref{eq:a4} at $\lambda$ and the second term is the Jacobian of the
	77	+transformation. The main grid is $\lambda \in \{-0.5, -0.25, \dots, 1\}$;
	78	+Section~\ref{sec:robust} refines it to steps of $0.05$.
	79	+
	80	+\paragraph{B. Time effects.} On the A5 backbone with municipality fixed
	81	+effects, $\mathcal{T}$ runs through the granularity ladder of the
	82	+time-dummy index literature \citep{hill2013hedonic}: no time controls
	83	+(B1), year (B2), quarter (B3 $=$ A5) and month fixed effects (B4).
	84	+
	85	+\paragraph{C. Spatial controls.} On the A5 backbone with quarter fixed
	86	+effects, $\mathcal{S}$ runs from no spatial controls (C1) to
	87	+municipality fixed effects (C2 $=$ A5; 1{,}115 cells, median 79 sales
	88	+per cell), a $0.05^{\circ}$ grid (C3; 5{,}255 cells of roughly
	89	+5.5~km, median 10 sales) and a $0.01^{\circ}$ grid (C4; 30{,}548 cells of
	90	+roughly 1.1~km, mean 17 and median 3 sales per cell). The ladder brackets
	91	+the bias--variance trade-off in absorbing location
	92	+\citep{case2004modeling, bourassa2010predicting}. Because the dummies
	93	+are one-hot encoded with a dropped reference category, a test sale in a
	94	+cell absent from the training set is priced at the reference cell's
	95	+level; this affects 0.2\% of random-holdout sales under C3 and 2.5\%
	96	+under C4. Section~\ref{sec:robust} reports nested variants (municipality
	97	+plus grid effects) in which an unseen cell falls back on its
	98	+municipality instead.
	99	+
	100	+\paragraph{D. Estimation method.} Holding the attribute set fixed, D1 is
	101	+the semi-log quadratic OLS with municipality and month fixed effects
	102	+(identical to B4); D2 replaces least squares by ridge regression on the
	103	+same standardised design,
	104	+\begin{equation}
	105	+ \hat{\boldsymbol{\beta}}_{\alpha} = \arg\min_{\boldsymbol{\beta}}
	106	+ \sum_i \big(\ln P_i - \mathbf{z}_i'\boldsymbol{\beta}\big)^2
	107	+ + \alpha \lVert \boldsymbol{\beta} \rVert_2^2,
	108	+ \qquad \alpha \in \{10^{-6}, 10^{-5.5}, \dots, 10^{2}\},
	109	+ \label{eq:ridge}
	110	+\end{equation}
	111	+with $\alpha$ selected by three-fold cross-validation within the training
	112	+set. D3 is a random forest \citep{breiman2001random} and D4 a
	113	+histogram-based gradient-boosting machine \citep{friedman2001greedy,
	114	+ke2017lightgbm}, both fitted to $\ln P_i$ on the attribute vector
	115	+augmented with the raw coordinates $(\mathrm{lat}_i, \mathrm{lng}_i)$
	116	+and a continuous month counter $t_i$ (months since January 2021), with
	117	+property class and physical configuration entered as integer codes. D5
	118	+is the boosting machine without the coordinates, which prices what
	119	+spatial flexibility is worth to the learner. D6 is a spatial
	120	+$k$-nearest-neighbour comparables rule, the na\"ive appraiser benchmark:
	121	+\begin{equation}
	122	+ \widehat{\ln P}_i \;=\; \ln a_i \;+\;
	123	+ \frac{\sum_{j\in N_{10}(i)} w_{ij}\,\big(\ln P_j - \ln a_j\big)}
	124	+ {\sum_{j\in N_{10}(i)} w_{ij}},
	125	+ \qquad w_{ij} = d_{ij}^{-1},
	126	+ \label{eq:knn}
	127	+\end{equation}
	128	+where $N_{10}(i)$ contains the ten training sales nearest to $i$ in
	129	+kilometre-scaled coordinates and $d_{ij}$ is the planar distance.
	130	+Hyper-parameters are fixed a priori at library-conventional values: the
	131	+forest uses 120 trees, a minimum leaf size of 5 and half the features
	132	+per split; the boosting machine uses 600 iterations, a learning rate of
	133	+$0.08$, at most 63 leaves per tree, a minimum leaf size of 20 and an
	134	+$\ell_2$ penalty of $0.01$. The ridge is the only method tuned on the
	135	+data, and only within the training set. The exercise therefore compares
	136	+model \emph{classes} as commonly used, not tuned frontier performance;
	137	+Section~\ref{sec:robust} shows that the ranking is insensitive to
	138	+materially different boosting configurations, including one tuned on a
	139	+time-ordered validation set.
43	140
44	141	\subsection{One scoreboard: price levels}
	142	+\label{sec:scoreboard}
	143	+
	144	+Comparing models whose dependent variables differ requires every model
	145	+to be scored on the same object. We score \emph{predicted price levels}.
	146	+Let $\hat{z}_i$ be the prediction of model~$M$ on the transformed scale
	147	+($g(P)$ for the linear forms, $\ln P$ for the tree ensembles and the
	148	+$k$-NN rule) on a test sale~$i$. Two inversion rules are available. The
	149	+\emph{median rule} inverts the fitted value as is,
	150	+\begin{equation}
	151	+ \hat{P}^{\mathrm{med}}_i = g^{-1}(\hat{z}_i)
	152	+ = \begin{cases} \exp(\hat{z}_i) & g = \ln,\\[2pt]
	153	+ (\lambda \hat{z}_i + 1)^{1/\lambda} & g = \text{Box--Cox},\end{cases}
	154	+ \label{eq:median}
	155	+\end{equation}
	156	+which under symmetric transformed-scale errors is the conditional median
	157	+price and is the quantity the tree ensembles deliver natively. The
	158	+\emph{mean rule} applies Duan's (\citeyear{duan1983smearing})
	159	+nonparametric smearing estimator of the conditional mean,
	160	+\begin{equation}
	161	+ \hat{P}^{\mathrm{mean}}_i = \frac{1}{n}\sum_{j=1}^{n}
	162	+ g^{-1}\big(\hat{z}_i + \hat{e}_j\big)
	163	+ \;\;\xrightarrow{\;g=\ln\;}\;\;
	164	+ \exp(\hat{z}_i)\cdot \hat{s}, \qquad
	165	+ \hat{s} = \frac{1}{n}\sum_{j=1}^{n} \exp(\hat{e}_j),
	166	+ \label{eq:duan}
	167	+\end{equation}
	168	+where $\hat{e}_j$ are the training residuals on the transformed scale.
	169	+The smearing factor $\hat{s}$ exceeds one and corrects the downward bias
	170	+of $\exp(\hat{z})$ as an estimator of $E[P\mid\mathbf{x}]$
	171	+\citep{manning2001estimating}; for the Box--Cox model we evaluate
	172	+\eqref{eq:duan} on a random subsample of 1{,}000 training residuals.
	173	+The main scoreboard uses the median rule for every model, for two
	174	+reasons. First, it is the only rule that treats all twenty models
	175	+identically without a model-specific calibration constant: the training
	176	+residuals of tree ensembles are shrunk by overfitting, so a smearing
	177	+factor estimated from them is not comparable to one estimated from
	178	+least-squares residuals. Second, our headline metric is a median error,
	179	+whose natural target is the conditional median, and the log-scale
	180	+metrics below are only meaningful on uncorrected log predictions.
	181	+Section~\ref{sec:robust} reports the full scoreboard under the mean rule
	182	+as well. Version~1.0 of this paper smeared the linear log models but not
	183	+the tree ensembles; the asymmetry affected the comparison between the two
	184	+families and is corrected here.
	185	+
	186	+Predictions are floored at \$20{,}000. With $\hat{P}_i$ the level
	187	+prediction and $N$ the number of test sales, the four metrics are
	188	+\begin{align}
	189	+ \mathrm{APE}_i &= \frac{\lvert \hat{P}_i - P_i\rvert}{P_i}, \qquad
	190	+ \mathrm{MdAPE} = \operatorname{median}_i \mathrm{APE}_i, \qquad
	191	+ \mathrm{MAPE} = \frac{1}{N}\sum_i \mathrm{APE}_i, \label{eq:ape}\\
	192	+ \mathrm{RMSE}_{\ln} &= \Big(\frac{1}{N}\sum_i
	193	+ \big(\ln P_i - \ln \hat{P}_i\big)^2\Big)^{1/2}, \qquad
	194	+ R^2_{\ln} = 1 - \frac{\sum_i (\ln P_i - \ln \hat{P}_i)^2}
	195	+ {\sum_i (\ln P_i - \overline{\ln P})^2}.
	196	+ \label{eq:r2}
	197	+\end{align}
	198	+MdAPE and MAPE are the accuracy standards of the automated-valuation
	199	+industry and of ratio studies \citep{iaao2013standard,
	200	+steurer2021metrics}; $R^2_{\ln}$ is an out-of-sample $R^2$ on the log
	201	+scale, well defined for every model whatever its dependent variable.
	202	+
	203	+\subsection{Two holdouts, and leakage-free variants}
	204	+\label{sec:holdouts}
	205	+
	206	+Each model is evaluated under two splits. The \emph{random} split assigns
	207	+every sale independently to the test set with probability $0.2$ (seeded;
	208	+411{,}283 training and 102{,}929 test sales). The \emph{forward-in-time}
	209	+split trains on sales dated before 1~January 2025 (355{,}824) and tests
	210	+on 2025--26 (158{,}388), the deployment situation of any valuation model
	211	+that is estimated once and applied to subsequent sales. Static models
	212	+carry no forecast of the price level, so we apply the standard
	213	+carry-forward rule: a test sale whose time category (year, quarter or
	214	+month) was never observed in training is priced at the last category
	215	+observed in training, $\hat{\delta}_{t} = \hat{\delta}_{T}$ for $t > T$.
	216	+The tree ensembles are piecewise constant in the month counter, so a
	217	+test month beyond the training range is priced by the terminal leaf in
	218	+$t$, the tree analogue of the same rule. Random cross-validation lets
	219	+every model interpolate the price level of its own test period; the
	220	+forward split reveals how much of measured accuracy depends on that
	221	+interpolation \citep{bergmeir2012crossvalidation,
	222	+roberts2017crossvalidation}.
	223	+
	224	+The random split has a second, less obvious leakage channel. One fifth of
	225	+the sales in the sample are repeat sales of a parcel that sells again
	226	+within the window, and 30\% share their exact geocoded coordinates with
	227	+another sale, 92\% among condominiums, whose units are geocoded to the
	228	+building. Under a random split, a model that reads the coordinates can
	229	+learn a parcel's or a building's price from its other sales. We
	230	+therefore also evaluate the full race under two grouped holdouts in
	231	+which 20\% of \emph{parcels}, respectively 20\% of \emph{coordinate
	232	+pairs}, are assigned to the test set, so that no property (respectively
	233	+no building) appears on both sides
	234	+\citep{roberts2017crossvalidation}.
	235	+
	236	+\subsection{Inference}
	237	+\label{sec:inference}
	238	+
	239	+Differences of a few tenths of a point between models evaluated on the
	240	+same 100{,}000 sales can be either meaningful or noise, and the sales are
	241	+not independent: they cluster in municipalities whose local shocks move
	242	+all errors together. We report two complementary tools. First, a
	243	+\emph{cluster bootstrap} for MdAPE: municipalities are resampled with
	244	+replacement ($B = 500$), each draw contributing all its test sales, and
	245	+the median APE of every model and the difference between two models'
	246	+MdAPEs are recomputed; we report percentile 95\% intervals. Second, a
	247	+test of equal predictive accuracy in the spirit of
	248	+\citet{diebold1995comparing} and \citet{giacomini2006tests}. For models
	249	+$A$ and $B$ and a loss $L$, let $d_i = L(\hat{P}^A_i, P_i) -
	250	+L(\hat{P}^B_i, P_i)$; the statistic
	251	+\begin{equation}
	252	+ t_{\mathrm{DM}} = \frac{\bar{d}}{\widehat{\mathrm{se}}(\bar{d})},
	253	+ \qquad
	254	+ \widehat{\mathrm{se}}(\bar{d})^2 = \frac{G}{G-1}\,\frac{1}{N^2}
	255	+ \sum_{g=1}^{G}\Big(\sum_{i\in g}(d_i - \bar{d})\Big)^2,
	256	+ \label{eq:dm}
	257	+\end{equation}
	258	+uses standard errors clustered by municipality ($G = 1{,}115$), the
	259	+cross-sectional analogue of the HAC variance in the time-series version.
	260	+We use the absolute percentage error (the MAPE loss) and the squared log
	261	+error (the RMSE$_{\ln}$ loss); a positive $\bar{d}$ means that $B$ is
	262	+more accurate. The mean of the APE loss differential tests MAPE, not
	263	+MdAPE; the bootstrap covers the median.
45	264
46		−Comparing forms whose dependent variables differ requires care. Every
47		−model is scored on \emph{predicted price levels}: log models are
48		−retransformed with Duan's smearing factor estimated on training
49		−residuals \citep{duan1983smearing}; Box--Cox predictions are analytically
50		−inverted; level predictions are floored at \$20{,}000. We report the
51		−median and mean absolute percentage errors (MdAPE, MAPE) --- the
52		−automated-valuation industry's standards \citep{steurer2021metrics,
53		−iaao2013standard} --- together with the RMSE and $R^2$ of log predicted
54		−versus log actual prices, which are well-defined for every model.
55		−
56		−\subsection{Two holdouts}
57		−
58		−Each model is evaluated under two splits. The \emph{random} split holds
59		−out 20\% of sales (seeded). The \emph{forward-in-time} split trains on
60		−sales before January 2025 (355{,}824) and tests on 2025--2026
61		−(158{,}388) --- the deployment situation of any valuation model. Static
62		−models carry no forecast of the price level, so we apply the standard
63		−carry-forward rule: unseen time categories in the test period are priced
64		−at the last level observed in training; the machine-learning models
65		−receive the same information through the clamped month counter. Random
66		−cross-validation lets every model interpolate the price level of its own
67		−test period --- the forward split reveals how much of measured accuracy
68		−is such leakage \citep{mullainathan2017machine, clapp2002predicting}.
69		−
70		−\subsection{Estimation details}
71		−
72		−All linear models are estimated as sparse ridge regressions with a
73		−vanishing penalty ($\alpha = 10^{-6}$) --- numerically OLS, but robust to
74		−collinear dummies, and unseen categories at prediction time are priced at
75		−the reference level. Dummies are one-hot with a dropped reference; the
76		−ridge (D2) standardizes columns and cross-validates
77		−$\alpha \in [10^{-6}, 10^{2}]$. The forest uses 120 trees
78		−(minimum leaf 5, half the features per split); the boosting machine uses
79		−600 trees of at most 63 leaves (learning rate 0.08, minimum leaf 20).
80		−Hyper-parameters were fixed a priori at library-conventional values ---
81		−the exercise compares model \emph{classes} as used in practice, not tuned
82		−frontier performance.
	265	+Finally, because the forward-in-time holdout confounds the difficulty of
	266	+the test period with the staleness of a frozen model, we decompose
	267	+forward error into an aggregate level error and relative pricing skill.
	268	+For each model, $\hat{b} = \operatorname{median}_i(\ln P_i - \ln
	269	+\hat{P}_i)$ on the test set measures the common level error; the
	270	+\emph{re-levelled} MdAPE, computed with $\hat{P}_i e^{\hat{b}}$, is the
	271	+accuracy the model would attain if the aggregate price level of the test
	272	+period were known, the time adjustment practitioners obtain from a
	273	+published index \citep{thibodeau2003marking}. We also compare the
	274	+random-split models on the 2025--26 sales of their own test set with the
	275	+forward-split models on the full 2025--26 test set, which holds the test
	276	+period fixed and varies only whether that period was seen in training.

modified paper/sections/results.tex +282 −86

		`@@ -4,9 +4,15 @@`
4	4	\label{sec:results}
5	5
6	6	Table~\ref{tab:race_random} reports the full scoreboard under the random
7		−holdout (411{,}283 training sales, 102{,}929 test sales);
8		−Table~\ref{tab:race_temporal} repeats it under the forward-in-time split.
9		−Figures~\ref{fig:forms}--\ref{fig:methods} visualize each axis.
	7	+holdout (411{,}283 training sales, 102{,}929 test sales) and
	8	+Table~\ref{tab:race_temporal} under the forward-in-time split;
	9	+Table~\ref{tab:inference} adds the cluster-bootstrap intervals and the
	10	+equal-accuracy tests against the spline hedonic (A6), and
	11	+Table~\ref{tab:pairs} the targeted comparisons along each axis.
	12	+Figures~\ref{fig:forms}--\ref{fig:methods} visualise the four axes under
	13	+the random holdout. All numbers use the median rule of
	14	+Section~\ref{sec:scoreboard}; Section~\ref{sec:robust} shows how the
	15	+Duan-smeared alternative moves them.
10	16
11	17	\begin{table}[p]
12	18	\centering
		`@@ -17,11 +23,12 @@ Figures~\ref{fig:forms}--\ref{fig:methods} visualize each axis.`
17	23	\input{../results/tables/horserace_random}
18	24	\begin{tablenotes}[flushleft]\footnotesize
19	25	\item \textit{Notes:} All metrics on the held-out 20\% (102{,}929 sales).
20		−MdAPE/MAPE: median/mean absolute percentage error on price levels (log
21		−models retransformed with Duan smearing; Box--Cox inverted).
22		−RMSE$_{\ln}$ and $R^2_{\ln}$: computed on log predicted vs.\ log actual
23		−prices. Backbone rows repeat across axes by construction (A5 $=$ B3 $=$
24		−C2; B4 $=$ D1). Bold: best in axis.
	26	+MdAPE/MAPE: median/mean absolute percentage error on price levels,
	27	+eq.~\eqref{eq:ape}; transformed-scale predictions inverted with the
	28	+median rule, eq.~\eqref{eq:median}. RMSE$_{\ln}$ and $R^2_{\ln}$:
	29	+eq.~\eqref{eq:r2}. Fit: wall-clock seconds on an 18-core workstation.
	30	+Backbone rows repeat across axes by construction (A5 $=$ B3 $=$ C2;
	31	+B4 $=$ D1). Bold: lowest MdAPE within the axis.
25	32	\end{tablenotes}
26	33	\end{threeparttable}
27	34	\end{table}
		`@@ -35,31 +42,93 @@ C2; B4 $=$ D1). Bold: best in axis.`
35	42	\input{../results/tables/horserace_temporal}
36	43	\begin{tablenotes}[flushleft]\footnotesize
37	44	\item \textit{Notes:} Training on sales before January 2025 (355{,}824);
38		−testing on 2025--2026 (158{,}388). Unseen time categories are priced at
39		−the last training period (carry-forward); the machine-learning models
40		−receive the same information through the clamped month counter.
	45	+testing on 2025--26 (158{,}388). Unseen time categories are priced at
	46	+the last training period (carry-forward); the tree ensembles are
	47	+piecewise constant in the month counter and therefore apply the same
	48	+rule through their terminal leaf. Other conventions as in
	49	+Table~\ref{tab:race_random}.
	50	+\end{tablenotes}
	51	+\end{threeparttable}
	52	+\end{table}
	53	+
	54	+\begin{table}[p]
	55	+\centering
	56	+\begin{threeparttable}
	57	+\caption{Inference: bootstrap intervals and equal-accuracy tests against the spline hedonic}
	58	+\label{tab:inference}
	59	+\scriptsize
	60	+\setlength{\tabcolsep}{3.5pt}
	61	+\input{../results/tables/inference}
	62	+\begin{tablenotes}[flushleft]\footnotesize
	63	+\item \textit{Notes:} MdAPE in percent with a 95\% percentile interval
	64	+from 500 cluster-bootstrap replicates (municipalities resampled with
	65	+replacement). $\Delta$ vs.\ A6: MdAPE of the row model minus MdAPE of
	66	+A6 on the same test sales, with its bootstrap interval; negative values
	67	+favour the row model. $t_{\mathrm{DM}}$: clustered Diebold--Mariano
	68	+statistic, eq.~\eqref{eq:dm}, for the absolute-percentage-error loss
	69	+differential (row model minus A6); positive values mean A6 is more
	70	+accurate on the mean loss. $^{}$, $^{}$, $^{**}$: $p < 0.10$,
	71	+$0.05$, $0.01$ (two-sided). 1{,}115 municipality clusters.
	72	+\end{tablenotes}
	73	+\end{threeparttable}
	74	+\end{table}
	75	+
	76	+\begin{table}[tbp]
	77	+\centering
	78	+\begin{threeparttable}
	79	+\caption{Targeted comparisons along each axis}
	80	+\label{tab:pairs}
	81	+\scriptsize
	82	+\setlength{\tabcolsep}{2.5pt}
	83	+\input{../results/tables/pairs}
	84	+\begin{tablenotes}[flushleft]\footnotesize
	85	+\item \textit{Notes:} For each pair, the MdAPE difference (first model
	86	+minus second) with its 95\% cluster-bootstrap interval and the clustered
	87	+DM statistics for the APE and squared-log losses (positive: the second
	88	+model is more accurate on the mean loss). Stars as in
	89	+Table~\ref{tab:inference}.
41	90	\end{tablenotes}
42	91	\end{threeparttable}
43	92	\end{table}
44	93
45	94	\subsection{Axis A: functional form is second-order}
46	95
47		−Under the random split (Figure~\ref{fig:forms}), the six forms span
48		−16.5--18.6\% MdAPE. The spline specification wins (16.5\%), the log-log
49		−is second (17.0\%) --- floor area enters multiplicatively, as intuition
50		−suggests --- and the linear, semi-log and quadratic forms cluster within
51		−half a point of each other. The Box--Cox transformation selects
52		−$\hat\lambda = 0.25$ by profile likelihood (Table~\ref{tab:boxcox}), i.e.\
53		−the data reject both the linear ($\lambda=1$) and the log ($\lambda=0$)
54		−--- and then \emph{underperforms} the simple semi-log out of sample
55		−(18.6\%), because optimizing curvature in-sample does not survive
56		−prediction, precisely the warning of \citet{cassel1985cost} and
57		−\citet{cropper1988choice}. The ordering is preserved under the temporal
58		−split. Two free lessons: curvature in \emph{attributes} (splines) is
59		−worth more than curvature in the \emph{price} (Box--Cox); and no form
60		−choice moves the needle by more than two points.
61		−
62		−\begin{figure}[t]
	96	+Under the random split (Figure~\ref{fig:forms}) the six forms span
	97	+17.6--19.2\% MdAPE, a range of 1.5 points. The spline specification wins
	98	+(17.6\%), the log-log is second (18.0\%)---floor area enters
	99	+multiplicatively, as intuition suggests---and the linear (18.2\%),
	100	+Box--Cox (18.6\%), semi-log (19.0\%) and quadratic (19.2\%) forms follow
	101	+within a point of each other. The spline gain over the textbook
	102	+semi-log, $-1.4$ points [$-1.8$, $-1.1$], is precisely estimated and
	103	+holds on every metric (Table~\ref{tab:pairs}). The Box--Cox
	104	+transformation selects $\hat\lambda = 0.25$ by profile likelihood
	105	+(Table~\ref{tab:boxcox}), so the data reject both the linear
	106	+($\lambda = 1$) and the logarithmic ($\lambda = 0$) specification, yet
	107	+the model gains only half a point on the semi-log's median error, loses
	108	+on the mean error (DM $t = 9.0$ in favour of the semi-log) and remains a
	109	+full point behind the splines. Optimising the curvature of the
	110	+\emph{price} in sample buys little out of sample, the warning of
	111	+\citet{cassel1985cost} and \citet{cropper1988choice}; curvature in the
	112	+\emph{attributes}, which splines supply cheaply, is worth more.
	113	+
	114	+Under the forward-in-time split (Table~\ref{tab:race_temporal}) the
	115	+range widens to 20.4--23.3\% and the ordering changes: the linear model
	116	+in levels posts the lowest median error (20.4\%), followed by the
	117	+Box--Cox (21.0\%), spline (21.7\%) and log-log (21.8\%) forms, with the
	118	+semi-log and quadratic forms last (23.2--23.3\%). The linear model's
	119	+forward-split advantage is a bias coincidence rather than a property of
	120	+the form: being a conditional-mean predictor in levels, its log
	121	+prediction over-predicts the typical sale by about 5\% under the random
	122	+split (median log residual $+0.004$ against $+0.06$ for the log models),
	123	+and in a rising market that upward tilt offsets part of the staleness of
	124	+a frozen price level. Once the common level error is removed
	125	+(Section~\ref{sec:gap}), the spline form is again the most accurate
	126	+linear specification (16.8\% against 18.0\% for the linear model).
	127	+Two lessons survive both splits: no functional-form choice moves the
	128	+median error by more than about two points, and splines dominate the
	129	+semi-log everywhere.
	130	+
	131	+\begin{figure}[tbp]
63	132	\centering
64	133	\includegraphics[width=0.85\textwidth]{fig_forms.png}
65	134	\caption{Axis A --- functional form. MdAPE on the random holdout;
		`@@ -68,7 +137,7 @@ fixed throughout.}`
68	137	\label{fig:forms}
69	138	\end{figure}
70	139
71		−\begin{table}[t]
	140	+\begin{table}[tbp]
72	141	\centering
73	142	\begin{threeparttable}
74	143	\caption{Box--Cox profile likelihood}
		`@@ -76,26 +145,36 @@ fixed throughout.}`
76	145	\small
77	146	\input{../results/tables/boxcox}
78	147	\begin{tablenotes}[flushleft]\footnotesize
79		−\item \textit{Notes:} $^{\dagger}$Thousands, relative to the maximum
80		−(zero = chosen $\lambda$). Estimated on the random-split training sample
81		−with the A-axis design.
	148	+\item \textit{Notes:} $^{\dagger}$Profile log-likelihood,
	149	+eq.~\eqref{eq:profile}, in thousands relative to the maximum (zero at
	150	+the chosen $\lambda$). Estimated on the random-split training sample
	151	+with the axis-A design. A finer grid (steps of $0.05$,
	152	+Section~\ref{sec:robust}) selects $\hat\lambda = 0.35$ and lowers the
	153	+random-holdout MdAPE from 18.6\% to 18.4\%.
82	154	\end{tablenotes}
83	155	\end{threeparttable}
84	156	\end{table}
85	157
86	158	\subsection{Axis B: time controls --- anything beats nothing}
87	159
88		−Omitting time controls entirely costs three points (21.1\% versus 18.1\%)
89		−in a window containing a boom, a correction and a recovery
90		−(Figure~\ref{fig:time}). But the granularity ladder flattens immediately:
91		−year, quarter and month effects are indistinguishable to within a quarter
92		−point under the random split. Under the temporal split the ordering
93		−inverts at the bottom --- \emph{no} time effects (25.4\%) is the worst
94		−choice again, but month effects with carry-forward (20.3\%) beat quarter
95		−effects (20.5\%) only marginally: once the level must be extrapolated,
96		−fine within-sample time resolution has little to offer.
97		−
98		−\begin{figure}[t]
	160	+Omitting time controls entirely costs three points (22.0\% against
	161	+19.2\%, difference $-2.9$ [$-3.8$, $-2.1$] for year effects against
	162	+none) in a window containing a boom, a correction and a recovery
	163	+(Figure~\ref{fig:time}). The granularity ladder then flattens at once:
	164	+year, quarter and month effects lie within 0.2 points of each other
	165	+under the random split, and month effects are, if anything, marginally
	166	+worse than quarter effects ($+0.19$ [$+0.01$, $+0.37$]), the first sign
	167	+that finer within-sample time resolution buys nothing for prediction.
	168	+Under the forward-in-time split the cost of omitting time controls rises
	169	+to six points (29.3\% against 23.3\%), because a model without time
	170	+effects prices 2025--26 sales at the \emph{average} 2021--24 level rather
	171	+than at the last observed level, and month effects with carry-forward
	172	+(22.9\%) beat quarter effects (23.3\%) by a statistically fragile margin
	173	+($-0.43$ [$-0.95$, $+0.05$]). Once the level must be extrapolated, fine
	174	+time resolution has little to offer; what matters is that the carried
	175	+level be the most recent one.
	176	+
	177	+\begin{figure}[tbp]
99	178	\centering
100	179	\includegraphics[width=0.85\textwidth]{fig_time.png}
101	180	\caption{Axis B --- time effects (quadratic semi-log backbone,
		`@@ -106,18 +185,31 @@ municipality FE). MdAPE on the random holdout.}`
106	185	\subsection{Axis C: spatial controls are first-order --- up to a point}
107	186
108	187	Location dominates every other design margin
109		−(Figure~\ref{fig:space}). Stripping all spatial controls costs
110		−\emph{ten} points (27.9\% versus 17.5\%) --- five times the entire
	188	+(Figure~\ref{fig:space}). Stripping all spatial controls costs ten
	189	+points (28.8\% against 19.2\% with municipality effects, 11.2 points
	190	+[10.1, 12.3] relative to the spline hedonic), six times the entire
111	191	functional-form range. The granularity ladder, however, is
112		−non-monotonic: the $\sim$5.5~km grid (5{,}255 cells, 17.5\%) beats
113		−municipality effects (18.1\%), but the $\sim$1.1~km grid (30{,}548
114		−cells, 19.4\%) \emph{overfits} --- its cells average seventeen K sales
115		−each, unseen cells in the holdout revert to the baseline, and estimated
116		−effects are noisy. The optimal spatial resolution is an interior
117		−solution, echoing \citet{goodman1998housing} on submarket definition:
118		−finer is better only while cells remain thick enough to estimate.
119		−
120		−\begin{figure}[t]
	192	+non-monotonic. The $\sim$5.5~km grid (5{,}255 cells) is nominally better
	193	+than municipality effects (18.7\% against 19.2\%), but the difference,
	194	+$-0.45$ [$-1.07$, $+0.37$], is within bootstrap noise and the DM tests
	195	+do not reject equal accuracy; the $\sim$1.1~km grid (30{,}548 cells)
	196	+is clearly worse ($+1.8$ [$+1.2$, $+2.3$]). Its cells contain 17 sales on
	197	+average and 3 at the median, so most cell effects are estimated from a
	198	+handful of sales, and the 2.5\% of test sales that fall in a cell with
	199	+no training sale are priced at an arbitrary reference cell. Under the
	200	+forward-in-time split the ordering becomes monotonic in the wrong
	201	+direction: finer cells are worse at every step (23.3\%, 24.3\%, 25.3\%),
	202	+because a fine spatial configuration estimated on 2021--24 prices
	203	+transfers less well than a coarse one. The optimal spatial resolution is
	204	+an interior solution that depends on market thickness, echoing
	205	+\citet{goodman1998housing} and \citet{bourassa2007spatial} on submarket
	206	+definition: finer is better only while cells remain thick enough to
	207	+estimate, and the relevant thickness is larger when the model must be
	208	+carried forward in time. Section~\ref{sec:robust} shows that nesting the
	209	+grid within municipalities, so that an unseen cell falls back on its
	210	+municipality, repairs part but not all of the fine grid's deficit.
	211	+
	212	+\begin{figure}[tbp]
121	213	\centering
122	214	\includegraphics[width=0.85\textwidth]{fig_space.png}
123	215	\caption{Axis C --- spatial controls (quadratic semi-log backbone,
		`@@ -127,22 +219,33 @@ quarter FE). MdAPE on the random holdout.}`
127	219
128	220	\subsection{Axis D: the machines --- and what they actually buy}
129	221
130		−Under the random split (Figure~\ref{fig:methods}), gradient boosting
131		−posts 14.4\% and the random forest 14.6\%, against 16.5\% for the best
132		−linear model and 18.3\% for the textbook OLS: a 13--21\% error
133		−reduction, squarely in the range reported by the AVM literature
134		−\citep{mayer2019estimation, hong2020machine}. The decomposition rows
135		−identify the source. Boosting \emph{without coordinates} collapses to
136		−23.2\% --- worse than plain OLS with municipality dummies --- so the
137		−machine's edge is overwhelmingly a flexible surface over space, not
138		−exotic structure--attribute interactions. Pure proximity without
139		−structure (the $k$-NN comparables rule, 21.2\%) fails too: it is the
140		−\emph{combination} of spatial flexibility with attribute adjustment that
141		−wins. The cross-validated ridge (16.7\%) confirms that regularizing the
142		−high-dimensional dummy design buys a little; it cannot manufacture the
143		−missing interactions.
144		−
145		−\begin{figure}[t]
	222	+Under the random split (Figure~\ref{fig:methods}) gradient boosting
	223	+posts 14.4\% [13.7, 15.7] and the random forest 14.6\%, against 17.6\%
	224	+for the best linear model and 19.3\% for the textbook OLS with
	225	+municipality and month effects: an 18--25\% reduction in the median
	226	+error, squarely in the range reported by the automated-valuation
	227	+literature \citep{mayer2019estimation, hong2020machine,
	228	+perezrave2019machine}. The boosting advantage over the spline hedonic,
	229	+$-3.2$ points [$-4.7$, $-1.9$], is statistically unambiguous on every
	230	+metric (DM $t = -3.6$ on the APE loss, $-3.0$ on the squared-log loss),
	231	+and boosting edges the forest by a quarter point ($-0.24$ [$-0.46$,
	232	+$-0.05$]). The decomposition rows identify the source. Boosting
	233	+\emph{without coordinates} collapses to 23.2\%, worse than plain OLS
	234	+with municipality dummies, so the learner's edge is overwhelmingly a
	235	+flexible surface over space rather than exotic structure--attribute
	236	+interactions, consistent with the residual-information results of
	237	+\citet{pace2020residuals}. Pure proximity without structure fails too:
	238	+the $k$-NN comparables rule (21.2\%) is three and a half points worse
	239	+than the spline hedonic. It is the \emph{combination} of spatial
	240	+flexibility with attribute adjustment that wins. The cross-validated
	241	+ridge (17.7\%) is a further lesson: on the identical design, shrinking
	242	+the 1{,}115 municipality effects and the month effects toward zero
	243	+improves on OLS by 1.7 points [1.1, 2.4] and ties the spline hedonic
	244	+(difference $+0.06$ [$-0.02$, $+0.16$]). Regularising the thin
	245	+fixed effects is as valuable as adding curvature; neither manufactures
	246	+the spatial surface the trees learn.
	247	+
	248	+\begin{figure}[tbp]
146	249	\centering
147	250	\includegraphics[width=0.85\textwidth]{fig_methods.png}
148	251	\caption{Axis D --- estimation methods on the identical attribute set.
		`@@ -151,25 +254,32 @@ MdAPE on the random holdout.}`
151	254	\end{figure}
152	255
153	256	\subsection{The generalization gap: when the test set is the future}
	257	+\label{sec:gap}
154	258
155	259	Table~\ref{tab:generalization} and Figure~\ref{fig:generalization}
156	260	contain the paper's central result. Moving from the random to the
157		−forward-in-time split degrades every model --- the price level of
158		−2025--26 must be carried forward, not interpolated --- but the
159		−degradation is systematically larger for the flexible methods.
160		−Gradient boosting loses 6.8 points of MdAPE (14.4 $\to$ 21.2) and the
161		−random forest 6.7, while the spline hedonic loses 2.6 (16.5 $\to$ 19.1)
162		−and the log-log 2.2. The ranking \emph{reverses}: the best linear models
163		−beat the machines on the median error in the deployment scenario, and
164		−tie them exactly on $R^2_{\ln}$ ($\approx 0.52$). The machines remain
165		−better on MAPE (29.7 versus 30.5), i.e.\ in the tails, but the headline
166		−random-validation gap --- the number the ML-valuation literature
167		−reports --- overstates their deployable advantage entirely. The lesson
168		−is methodological and general: for models whose job is to price the
169		−future, random cross-validation is the wrong experiment
170		−\citep{mullainathan2017machine, clapp2002predicting}.
171		−
172		−\begin{table}[t]
	261	+forward-in-time split degrades every model---the price level of 2025--26
	262	+must be carried forward, not interpolated---but the degradation is
	263	+systematically larger for the flexible methods. Gradient boosting loses
	264	+6.8 points of MdAPE (14.4 $\to$ 21.2) and the random forest 6.7, while
	265	+the spline hedonic loses 4.1 (17.6 $\to$ 21.7), the ridge 4.6 and the
	266	+linear model in levels 2.1. The ranking compresses: the five best
	267	+forward-split models, linear (20.4\%), Box--Cox (21.0\%), boosting
	268	+(21.2\%), forest (21.3\%) and splines (21.7\%), lie within 1.3 points
	269	+and are statistically indistinguishable on the median error---boosting
	270	+against splines gives $-0.51$ [$-1.68$, $+0.55$], boosting against the
	271	+linear model $+0.84$ [$-1.19$, $+2.59$]. The ensembles keep a clear lead
	272	+on the mean error (MAPE 29.7\% against 30.9\% for splines and 32.9\% for
	273	+the linear model; DM $t = -3.5$ against the linear model) and on the log
	274	+scale ($R^2_{\ln}$ 0.52 against 0.49 and 0.46). Version~1.0 of this paper
	275	+reported that the ranking \emph{reversed}; that reversal was an artefact
	276	+of smearing the linear log models but not the tree ensembles
	277	+(Section~\ref{sec:robust}). The corrected statement is weaker but still
	278	+consequential: the three-point advantage that random validation
	279	+attributes to gradient boosting shrinks to half a point, and to
	280	+insignificance, when the test set lies in the future.
	281	+
	282	+\begin{table}[tbp]
173	283	\centering
174	284	\begin{threeparttable}
175	285	\caption{Random versus forward-in-time evaluation}
		`@@ -183,7 +293,7 @@ under both splits.`
183	293	\end{threeparttable}
184	294	\end{table}
185	295
186		−\begin{figure}[t]
	296	+\begin{figure}[tbp]
187	297	\centering
188	298	\includegraphics[width=0.85\textwidth]{fig_generalization.png}
189	299	\caption{The generalization gap. MdAPE under the random holdout (filled
		`@@ -191,3 +301,89 @@ circles) and the forward-in-time holdout (open squares); the grey`
191	301	segment joins the two evaluations of the same model.}
192	302	\label{fig:generalization}
193	303	\end{figure}
	304	+
	305	+Where does the gap come from? Three further cuts of the data answer the
	306	+question (Table~\ref{tab:same_period}). First, holding the test period
	307	+fixed: evaluated on the 31{,}465 sales of 2025--26 that happen to fall in
	308	+the random test set, the random-split boosting model posts 13.7\%, so
	309	+the 2025--26 sales are not intrinsically harder to price; the entire
	310	+degradation to 21.2\% comes from not having seen their period. The
	311	+\emph{staleness cost}, defined as the forward-split minus the
	312	+same-period random-split MdAPE, is 7.5 points for boosting and 7.5 for
	313	+the forest, against 4.7 for the spline hedonic, 5.2 for the ridge and
	314	+3.3 for the linear model. Second, the level decomposition of
	315	+Section~\ref{sec:inference}: the median log residual of every
	316	+forward-split model is positive and large---$+0.16$ for the spline
	317	+hedonic, $+0.18$ for the two ensembles, $+0.10$ for the linear
	318	+model---so every frozen model under-prices the typical 2025--26 sale by
	319	+10--20\%, the ensembles slightly more because their terminal leaf in the
	320	+month counter averages the last few training months rather than the last
	321	+one. Once each model's predictions are re-levelled by its own median
	322	+ratio, the forward-split MdAPE falls to 13.9\% for boosting and 16.8\%
	323	+for the spline hedonic: a gap of 2.9 points, essentially the 3.5-point
	324	+gap measured under the random split with the same correction
	325	+(13.0\% against 16.5\%). Third, the horizon profile
	326	+(Table~\ref{tab:by_quarter}, Figure~\ref{fig:horizon}): in the first
	327	+quarter after the training window boosting still leads the spline
	328	+hedonic by 1.5 points (17.1\% against 18.6\%); the lead shrinks every
	329	+quarter and vanishes by mid-2026, when both models post about 25\%.
	330	+
	331	+The picture is therefore not that the learners have memorised something
	332	+that fails to transfer. Their \emph{relative} pricing skill---which
	333	+sales are dear and which are cheap within a period---transfers forward
	334	+almost intact. What does not transfer is the \emph{level}, and a frozen
	335	+boosted model carries a slightly staler level than a frozen linear model
	336	+with carry-forward month effects. The forward-in-time holdout thus
	337	+quantifies two things that random cross-validation hides: a level
	338	+staleness of 3--7 points of median error within eighteen months, common
	339	+to every static model and largest for the trees, and the fact that the
	340	+headline gap between learners and linear hedonics is a within-period
	341	+statement. For models whose job is to price the future, random
	342	+cross-validation is the wrong experiment \citep{bergmeir2012crossvalidation,
	343	+mullainathan2017machine}; the right one separates the level, which an
	344	+index or a retraining schedule must supply, from the relative accuracy
	345	+the estimator contributes.
	346	+
	347	+\begin{table}[tbp]
	348	+\centering
	349	+\begin{threeparttable}
	350	+\caption{Decomposing the generalization gap: same-period comparison and level error}
	351	+\label{tab:same_period}
	352	+\footnotesize
	353	+\setlength{\tabcolsep}{4pt}
	354	+\input{../results/tables/same_period}
	355	+\begin{tablenotes}[flushleft]\footnotesize
	356	+\item \textit{Notes:} MdAPE in percent. Columns 2--3: models estimated on
	357	+the random-split training sample, evaluated on all random test sales and
	358	+on the 2025--26 subset of those sales. Column 4: models estimated on
	359	+sales before 2025 and evaluated on all 2025--26 sales. Staleness cost:
	360	+column 4 minus column 3. Column 5: median of $\ln P_i - \ln\hat{P}_i$ on
	361	+the forward test set (common level error). Column 6: forward-split MdAPE
	362	+after multiplying each model's predictions by $e^{\hat{b}}$
	363	+(Section~\ref{sec:inference}).
	364	+\end{tablenotes}
	365	+\end{threeparttable}
	366	+\end{table}
	367	+
	368	+\begin{table}[tbp]
	369	+\centering
	370	+\begin{threeparttable}
	371	+\caption{Forward-in-time accuracy by test quarter}
	372	+\label{tab:by_quarter}
	373	+\small
	374	+\input{../results/tables/by_quarter}
	375	+\begin{tablenotes}[flushleft]\footnotesize
	376	+\item \textit{Notes:} MdAPE (\%) of models trained on sales before
	377	+January 2025, by quarter of the test sale. 2026Q3 covers July 2026
	378	+only.
	379	+\end{tablenotes}
	380	+\end{threeparttable}
	381	+\end{table}
	382	+
	383	+\begin{figure}[tbp]
	384	+\centering
	385	+\includegraphics[width=0.8\textwidth]{fig_horizon.png}
	386	+\caption{Forward-in-time accuracy by horizon. MdAPE by quarter of the
	387	+test sale for models trained on sales before January 2025.}
	388	+\label{fig:horizon}
	389	+\end{figure}

added paper/sections/robustness.tex +216 −0

		`@@ -0,0 +1,216 @@`
	1	+% Author: Simon-Pierre Boucher — contact@spboucher.ai
	2	+% ============================================================================
	3	+\section{Robustness}
	4	+\label{sec:robust}
	5	+
	6	+This section examines the five choices in the design that a sceptical
	7	+reader would most want varied: the rule that converts transformed-scale
	8	+predictions into price levels, the leakage channels of the random
	9	+holdout, the implementation of fine spatial effects, the resolution of
	10	+the Box--Cox grid and the hyper-parameters of the boosting machine.
	11	+
	12	+\subsection{The retransformation rule}
	13	+
	14	+Table~\ref{tab:retransformation} reports the scoreboard for the
	15	+transformed-scale models under the median rule used throughout
	16	+(eq.~\ref{eq:median}) and under Duan's mean rule
	17	+(eq.~\ref{eq:duan}). The smearing factors $\hat{s}$ lie between 1.06
	18	+and 1.07 for the least-squares models and between 1.03 and 1.05 for the
	19	+ensembles, whose in-sample residuals are shrunk by overfitting. Two
	20	+regularities stand out. First, the mean rule lowers the median error of
	21	+\emph{every} log-scale model under the random split, by about one point
	22	+for the linear models and 1.3 points for the ensembles. This is not what
	23	+a conditional-mean correction should do to a median-based metric; it
	24	+happens because the log residuals are left-skewed (skewness $-1.4$ to
	25	+$-1.8$), so that their median is $+0.06$ while their mean is zero, and
	26	+$\exp(\hat{z})$ under-prices the typical sale by about 6\%---which is,
	27	+by coincidence, the size of the smearing factor. Second, under the
	28	+forward-in-time split the mean rule lowers median errors by 2.5--3
	29	+points for all models, because the market rose after the training
	30	+window and any upward factor offsets part of the staleness. Neither
	31	+effect changes a ranking when the rule is applied uniformly: boosting
	32	+leads the spline hedonic by 3.4 points under the random split and by
	33	+0.7 points under the forward split with the mean rule, against 3.2 and
	34	+0.5 with the median rule. What does change a ranking is applying the
	35	+rule to one family only. Version~1.0 of this paper smeared the linear
	36	+log models and not the ensembles; the result was a forward-split
	37	+comparison of 19.1\% for the smeared spline hedonic against 21.2\% for
	38	+the unsmeared boosting model, reported as a reversal. The comparable
	39	+numbers are 21.7\% against 21.2\% (median rule) or 19.1\% against
	40	+18.4\% (mean rule). The log-scale metrics are affected in the same
	41	+direction: smearing adds $\ln\hat{s} \approx 0.06$ to every log
	42	+prediction, which inflates RMSE$_{\ln}$ and depresses $R^2_{\ln}$ for
	43	+the smeared family only, so that the ``identical $R^2_{\ln}$'' of the
	44	+first version (0.52 for both) becomes 0.49 against 0.52 in favour of
	45	+boosting under the uniform rule.
	46	+
	47	+\begin{table}[tbp]
	48	+\centering
	49	+\begin{threeparttable}
	50	+\caption{Median rule versus Duan smearing}
	51	+\label{tab:retransformation}
	52	+\scriptsize
	53	+\setlength{\tabcolsep}{4pt}
	54	+\input{../results/tables/retransformation}
	55	+\begin{tablenotes}[flushleft]\footnotesize
	56	+\item \textit{Notes:} Median: transformed-scale prediction inverted as
	57	+is, eq.~\eqref{eq:median} (main scoreboard). Mean: Duan smearing,
	58	+eq.~\eqref{eq:duan}; $\hat{s}$ is the smearing factor estimated on
	59	+training residuals (random split), undefined for the Box--Cox model,
	60	+whose mean prediction averages the inverse transformation over 1{,}000
	61	+training residuals. $R^2_{\ln}$ under the mean rule is computed on the
	62	+smeared log prediction.
	63	+\end{tablenotes}
	64	+\end{threeparttable}
	65	+\end{table}
	66	+
	67	+\subsection{Leakage-free holdouts}
	68	+
	69	+Table~\ref{tab:group_splits} re-runs the full race under the two grouped
	70	+holdouts of Section~\ref{sec:holdouts}, and Table~\ref{tab:leakage}
	71	+decomposes the random holdout by whether the test sale's parcel, or its
	72	+exact coordinates, also appear in training. Repeat sales are irrelevant:
	73	+the parcel-grouped race reproduces the random race to within 0.1--0.4
	74	+points for every model, and within the random holdout the boosting
	75	+model prices test sales whose parcel sold before in training (14.5\%)
	76	+no better than the others (14.4\%). Shared coordinates matter more, but
	77	+for a specific reason. Test sales that share coordinates with a training
	78	+sale are priced at 12.0\% by boosting against 15.3\% for the rest, and
	79	+at 16.7\% against 22.9\% by the $k$-NN rule, whose nearest neighbour is
	80	+then literally the same building; the linear models are unaffected
	81	+(17.8\% against 17.6\% for the splines). Condominiums account for most
	82	+of these co-located sales, and the boosting model prices them at 8.9\%
	83	+when their building is in training and 10.2\% when it is not, against
	84	+18.0\% and 20.3\% for the quadratic OLS. The condominium advantage of
	85	+Section~\ref{sec:ext} is therefore genuine micro-location, with a modest
	86	+recall component. The building-grouped race, in which no coordinate pair
	87	+straddles the split, confirms it: boosting posts 14.6\% against 17.8\%
	88	+for the spline hedonic, a 3.2-point gap identical to the random race,
	89	+and the only model that loses materially is the $k$-NN rule (22.3\%
	90	+against 21.2\%).
	91	+
	92	+\begin{table}[p]
	93	+\centering
	94	+\begin{threeparttable}
	95	+\caption{The race under random, parcel-grouped and building-grouped holdouts}
	96	+\label{tab:group_splits}
	97	+\small
	98	+\input{../results/tables/group_splits}
	99	+\begin{tablenotes}[flushleft]\footnotesize
	100	+\item \textit{Notes:} MdAPE in percent. Parcel-grouped: 20\% of
	101	+assessment-roll parcels assigned to the test set, so that repeat sales
	102	+of a property never straddle the split. Building-grouped: 20\% of exact
	103	+coordinate pairs assigned to the test set, so that units geocoded to the
	104	+same building or complex never straddle the split.
	105	+\end{tablenotes}
	106	+\end{threeparttable}
	107	+\end{table}
	108	+
	109	+\begin{table}[tbp]
	110	+\centering
	111	+\begin{threeparttable}
	112	+\caption{Random holdout: accuracy on test sales seen and unseen through their parcel or coordinates}
	113	+\label{tab:leakage}
	114	+\small
	115	+\input{../results/tables/leakage}
	116	+\begin{tablenotes}[flushleft]\footnotesize
	117	+\item \textit{Notes:} MdAPE (\%) on the random holdout. ``Same parcel in
	118	+training'': the parcel of the test sale sold at least once in the
	119	+training sample. ``Same coordinates in training'': at least one training
	120	+sale shares the exact geocoded coordinates of the test sale.
	121	+\end{tablenotes}
	122	+\end{threeparttable}
	123	+\end{table}
	124	+
	125	+\subsection{Nested spatial fixed effects}
	126	+
	127	+Section~\ref{sec:results} attributes the poor showing of the
	128	+$\sim$1.1~km grid to thin cells and to the arbitrary pricing of unseen
	129	+cells. Table~\ref{tab:nested_fe} adds two specifications in which the
	130	+grid effects enter \emph{together with} municipality effects. Because
	131	+the two sets of dummies are nearly collinear, the vanishing-penalty
	132	+ridge returns the minimum-norm least-squares solution, which assigns the
	133	+component common to a municipality to the municipality effect and only
	134	+the deviation to the cell effect---a crude form of partial pooling---and
	135	+a test sale in an unseen cell inherits its municipality's level. The
	136	+effect is large. Nested within municipalities, the 5.5~km grid improves
	137	+from 18.7\% to 17.7\% and the 1.1~km grid from 21.0\% to 17.3\%, the
	138	+lowest median error of any linear specification in the paper, below the
	139	+spline hedonic (17.6\%) with the same $R^2_{\ln}$ (0.59). Under the
	140	+forward-in-time split the nested fine grid posts 21.6\% against 23.3\%
	141	+for municipality effects alone and 25.3\% for the fine grid alone. The
	142	+conclusion for axis~C is therefore sharper than ``finer overfits'':
	143	+fine spatial effects are valuable when they are anchored to a coarser
	144	+level that supplies the prior for thin and unseen cells, and harmful
	145	+when they are not. A hierarchical or kriged location effect
	146	+\citep{case2004modeling, hill2018geospatial} would push the linear
	147	+frontier further; we leave its estimation to future work.
	148	+
	149	+\begin{table}[tbp]
	150	+\centering
	151	+\begin{threeparttable}
	152	+\caption{Nested spatial fixed effects}
	153	+\label{tab:nested_fe}
	154	+\small
	155	+\input{../results/tables/nested_fe}
	156	+\begin{tablenotes}[flushleft]\footnotesize
	157	+\item \textit{Notes:} Quadratic semi-log backbone with quarter fixed
	158	+effects. C3$'$ and C4$'$ add the grid effects to the municipality
	159	+effects; with a vanishing ridge penalty the estimator is the
	160	+minimum-norm least-squares solution and unseen cells fall back on their
	161	+municipality.
	162	+\end{tablenotes}
	163	+\end{threeparttable}
	164	+\end{table}
	165	+
	166	+\subsection{A finer Box--Cox grid}
	167	+
	168	+The main grid steps $\lambda$ by $0.25$. Refining it to steps of $0.05$
	169	+over $[-0.25, 0.75]$ moves the profile-likelihood maximum to
	170	+$\hat\lambda = 0.35$, with a profile that is flat between $0.25$ and
	171	+$0.55$ (differences of under one thousandth of the log-likelihood,
	172	+within the tolerance of the sparse iterative solver) and falls steeply
	173	+on either side. The Box--Cox model at $\hat\lambda = 0.35$ posts a
	174	+random-holdout MdAPE of 18.4\% against 18.6\% at $0.25$: the exponent is
	175	+imprecisely identified in a range that excludes both the linear and the
	176	+logarithmic case, and its exact value is immaterial for prediction.
	177	+
	178	+\subsection{Boosting hyper-parameters}
	179	+
	180	+Table~\ref{tab:hgb} re-estimates the boosting model under four
	181	+materially different configurations: shallow trees with more iterations,
	182	+deep trees, heavy regularisation (minimum leaf 200, $\ell_2 = 1$), and a
	183	+configuration whose number of iterations is chosen by early stopping on
	184	+the last 10\% of training sales in date order, the time-honest tuning
	185	+rule a careful practitioner would use for a forward-looking model.
	186	+Under the random holdout the four alternatives span 14.3--14.7\% MdAPE
	187	+against 14.4\% for the baseline, and under the forward-in-time holdout
	188	+21.2--21.6\% against 21.2\%; $R^2_{\ln}$ moves by at most 0.006. The
	189	+time-honest early-stopping rule selects 700 iterations on the random
	190	+training sample and 1{,}000 on the pre-2025 sample and reproduces the
	191	+baseline to within 0.1 point under both splits. The conclusions of Sections~\ref{sec:results}
	192	+and~\ref{sec:gap} do not depend on the particular configuration we
	193	+fixed a priori, and tuning on a time-ordered validation set does not
	194	+remove the level staleness that dominates the forward-split error,
	195	+because no choice of hyper-parameters lets a static tree extrapolate a
	196	+price level it has not seen.
	197	+
	198	+\begin{table}[tbp]
	199	+\centering
	200	+\begin{threeparttable}
	201	+\caption{Gradient-boosting hyper-parameter sensitivity}
	202	+\label{tab:hgb}
	203	+\footnotesize
	204	+\setlength{\tabcolsep}{4pt}
	205	+\input{../results/tables/hgb_sensitivity}
	206	+\begin{tablenotes}[flushleft]\footnotesize
	207	+\item \textit{Notes:} All configurations use the D4 feature set
	208	+(attributes, coordinates, month counter). Baseline: 600 iterations,
	209	+learning rate 0.08, 63 leaves, minimum leaf 20, $\ell_2 = 0.01$. Early
	210	+stopping: iterations added in blocks of 100 (learning rate 0.05) until
	211	+the squared log error on the last 10\% of training sales in date order
	212	+stops improving; the selected number of iterations is shown in brackets
	213	+for the random and forward splits.
	214	+\end{tablenotes}
	215	+\end{threeparttable}
	216	+\end{table}

added results/reproduced/boxcox_fine.csv +22 −0

		`@@ -0,0 +1,22 @@`
	1	+lambda,loglik,chosen,mdape_at_chosen
	2	+-0.25,-4938790.1592812985,False,
	3	+-0.2,-4928326.613673929,False,
	4	+-0.15,-4921149.036684653,False,
	5	+-0.1,-4911809.9533146825,False,
	6	+-0.05,-4905852.743838613,False,
	7	+-0.0,-4896133.282457808,False,
	8	+0.05,-4895821.141372284,False,
	9	+0.1,-4891760.972508729,False,
	10	+0.15,-4888345.89894094,False,
	11	+0.2,-4885580.902667309,False,
	12	+0.25,-4879097.21142742,False,
	13	+0.3,-4877690.751161514,False,
	14	+0.35,-4876918.904257714,True,18.38848861136389
	15	+0.4,-4881082.917829343,False,
	16	+0.45,-4877369.476074193,False,
	17	+0.5,-4882782.367887354,False,
	18	+0.55,-4880462.865948945,False,
	19	+0.6,-4881961.43143256,False,
	20	+0.65,-4886168.783351108,False,
	21	+0.7,-4889986.164861776,False,
	22	+0.75,-4893437.953075144,False,

added results/reproduced/by_quarter.csv +36 −0

		`@@ -0,0 +1,36 @@`
	1	+quarter,model,n,mdape
	2	+2025Q1,A5 Semi-log + quadratics,17031,20.16069824377374
	3	+2025Q1,A6 Semi-log + splines,17031,18.55293878398712
	4	+2025Q1,D2 Ridge (cross-validated),17031,18.97125923373471
	5	+2025Q1,D3 Random forest,17031,17.15973919906848
	6	+2025Q1,D4 Gradient boosting,17031,17.069787319853706
	7	+2025Q2,A5 Semi-log + quadratics,34546,21.09424889763385
	8	+2025Q2,A6 Semi-log + splines,34546,19.546001101493225
	9	+2025Q2,D2 Ridge (cross-validated),34546,20.128071582190238
	10	+2025Q2,D3 Random forest,34546,19.17503183093982
	11	+2025Q2,D4 Gradient boosting,34546,19.056435785828757
	12	+2025Q3,A5 Semi-log + quadratics,28097,22.81785959565014
	13	+2025Q3,A6 Semi-log + splines,28097,21.26342871883413
	14	+2025Q3,D2 Ridge (cross-validated),28097,21.787565277767396
	15	+2025Q3,D3 Random forest,28097,20.640199696692722
	16	+2025Q3,D4 Gradient boosting,28097,20.570509508119454
	17	+2025Q4,A5 Semi-log + quadratics,24156,23.84990757727795
	18	+2025Q4,A6 Semi-log + splines,24156,22.156927074847843
	19	+2025Q4,D2 Ridge (cross-validated),24156,22.704586080935236
	20	+2025Q4,D3 Random forest,24156,21.686460771814904
	21	+2025Q4,D4 Gradient boosting,24156,21.604075720079475
	22	+2026Q1,A5 Semi-log + quadratics,15611,24.828798398064173
	23	+2026Q1,A6 Semi-log + splines,15611,23.136954110839774
	24	+2026Q1,D2 Ridge (cross-validated),15611,23.555344810884428
	25	+2026Q1,D3 Random forest,15611,22.809749906308703
	26	+2026Q1,D4 Gradient boosting,15611,22.683544277340335
	27	+2026Q2,A5 Semi-log + quadratics,30950,25.82329388343181
	28	+2026Q2,A6 Semi-log + splines,30950,24.490104774430893
	29	+2026Q2,D2 Ridge (cross-validated),30950,25.114690369909486
	30	+2026Q2,D3 Random forest,30950,24.366584102876867
	31	+2026Q2,D4 Gradient boosting,30950,24.313275442733904
	32	+2026Q3,A5 Semi-log + quadratics,7997,25.960227538726045
	33	+2026Q3,A6 Semi-log + splines,7997,24.87544352852322
	34	+2026Q3,D2 Ridge (cross-validated),7997,25.158903757045657
	35	+2026Q3,D3 Random forest,7997,24.996277735314912
	36	+2026Q3,D4 Gradient boosting,7997,24.87390841981474

added results/reproduced/hgb_sensitivity.csv +11 −0

		`@@ -0,0 +1,11 @@`
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test,scheme
	2	+D4 Gradient boosting (baseline),S,14.388300681085338,27.766499817027036,0.3471568687492957,0.6422912683312305,13.136043786916385,28.339593011975516,0.3501358518462874,0.6361258693434015,1.0475010409695187,,,40.8,411283,102929,random
	3	+"D4 shallow (15 leaves, lr 0.05, 1500 iter)",S,14.719243860105477,28.154919687681947,0.35039008957492424,0.63559725098862,13.401236660872359,28.83674263008007,0.35391692116024087,0.6282245817693768,1.051807579516185,,,28.7,411283,102929,random
	4	+"D4 deep (255 leaves, lr 0.05, 600 iter)",S,14.289611237615919,27.61056923649104,0.34601169250653546,0.6446473438310576,13.117602210229256,28.098909164979524,0.34851529339791887,0.6394863630851599,1.043402259531175,,,121.5,411283,102929,random
	5	+"D4 regularised (min leaf 200, L2 = 1)",S,14.26217307195608,27.69234020959297,0.3467049485484332,0.6432219748599041,13.01108639038474,28.277180185855872,0.3498336625404618,0.636753690914108,1.0485848722394113,,,40.9,411283,102929,random
	6	+D4 early stopping on last 10% of training months,S,14.486038756539063,27.894520070852053,0.34801538571621565,0.6405198573634903,13.222127726623725,28.493460749856283,0.35117203837899774,0.6339689957921757,1.0488581267072552,,700.0,126.3,411283,102929,random
	7	+D4 Gradient boosting (baseline),S,21.21243467837447,29.71192710420828,0.37236811207724885,0.5214213758996993,18.362851253802294,28.605014412660662,0.3587539272757954,0.5557763676216326,1.0485637089645152,,,40.7,355824,158388,temporal
	8	+"D4 shallow (15 leaves, lr 0.05, 1500 iter)",S,21.41075901094633,29.814111901291206,0.37240688652603166,0.521321702550176,18.299953587404797,28.62964905180962,0.3577628776257503,0.5582272931995136,1.0532570669661585,,,28.7,355824,158388,temporal
	9	+"D4 deep (255 leaves, lr 0.05, 600 iter)",S,21.599331939568586,29.87909605759482,0.3738085572244618,0.5177116081480675,18.958152089809033,28.790557674838784,0.3604324382094834,0.55160984301614,1.0448264651027446,,,107.7,355824,158388,temporal
	10	+"D4 regularised (min leaf 200, L2 = 1)",S,21.53671243851688,29.763998225562823,0.37211824841062413,0.5220634249166158,18.523654776944497,28.560638550076707,0.3575714411737002,0.5586999457753024,1.0503781019780596,,,33.9,355824,158388,temporal
	11	+D4 early stopping on last 10% of training months,S,21.211205965026554,29.680715279436637,0.37128678154177347,0.5241968567695916,18.364288650180356,28.557949065565285,0.3576920591594777,0.5584021719866923,1.04834813285858,,1000.0,158.8,355824,158388,temporal

added results/reproduced/horserace_group_coord.csv +21 −0

		`@@ -0,0 +1,21 @@`
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test
	2	+A1 Linear (levels),A. Functional form,18.389455311057525,35.77737768430297,0.42150872762642705,0.4729684614765287,18.389455311057525,35.77737768430297,0.42150872762642705,0.4729684614765287,,,,0.4,411263,102949
	3	+A2 Semi-log,A. Functional form,19.45406141657741,33.53341061653312,0.3982220564706349,0.5295926664345789,18.534228750178155,35.515597429659906,0.40458544391763035,0.5144388071443484,1.0716405125795019,,,0.6,411263,102949
	4	+A3 Log-log,A. Functional form,18.09423906311878,31.5648056784115,0.3795231689636993,0.5727323131971047,17.13689016366873,33.083726302727165,0.3848295353676579,0.5607009592529427,1.0637378029740763,,,0.8,411263,102949
	5	+A4 Box-Cox,A. Functional form,18.34720115572638,33.91816652516567,0.39588027012021865,0.5351089578471608,18.01369176345465,35.11846758212266,0.4005581443205167,0.5240573822295058,,0.5,,4.4,411263,102949
	6	+A5 Semi-log + quadratics,A. Functional form,19.047250871870013,32.633713129691856,0.38879112913610764,0.5516097539820513,18.060274251722916,34.383320754266194,0.39457920958428305,0.5381596654068279,1.0678021020773296,,,0.7,411263,102949
	7	+A6 Semi-log + splines,A. Functional form,17.84160255200089,31.17235135800901,0.375404013662821,0.5819566827043615,16.719953387602672,32.5440257224398,0.38032165138598156,0.5709325567849641,1.06173604546364,,,2.3,411263,102949
	8	+B1 No time effects,B. Time effects,22.020713610007295,36.07330397660628,0.41771180424287685,0.4824206287010825,21.320623105141713,38.615749714380435,0.42497748545191755,0.4642584779943505,1.0797929429062483,,,0.5,411263,102949
	9	+B2 Year FE,B. Time effects,19.216445989382176,33.21932498640056,0.3943360634939339,0.5387286770024654,18.306678366552863,35.06233519240754,0.4003352095717885,0.5245870163050035,1.069862710157588,,,0.7,411263,102949
	10	+B3 Quarter FE,B. Time effects,19.047250871870013,32.633713129691856,0.38879112913610764,0.5516097539820513,18.060274251722916,34.383320754266194,0.39457920958428305,0.5381596654068279,1.0678021020773296,,,0.7,411263,102949
	11	+B4 Month FE,B. Time effects,19.398625101840388,33.282018368201285,0.39485525067670135,0.537513247647079,18.49481494077501,35.151184915530756,0.40092705375610255,0.5231803031914969,1.070168533613627,,,0.6,411263,102949
	12	+C1 No spatial controls,C. Spatial controls,28.689547544675424,43.840616324962724,0.48386013502120434,0.30551455745412537,27.854471463760017,48.59662417250643,0.4957431862109964,0.27098415190902636,1.1117746881974258,,,0.5,411263,102949
	13	+C2 Municipality FE,C. Spatial controls,19.047250871870013,32.633713129691856,0.38879112913610764,0.5516097539820513,18.060274251722916,34.383320754266194,0.39457920958428305,0.5381596654068279,1.0678021020773296,,,0.7,411263,102949
	14	+C3 Grid-cell FE (~5.5 km),C. Spatial controls,18.750020280736805,32.64356649270374,0.38885559208588105,0.5514610522654697,17.681345309644815,34.2696279297555,0.3942232975475682,0.538992453333233,1.0671696493930205,,,0.7,411263,102949
	15	+C4 Grid-cell FE (~1.1 km),C. Spatial controls,20.225376123786642,34.842860847732275,0.40626236607303856,0.5104053661049823,18.962836326256582,36.70306684092424,0.41241718088755186,0.49545842259587813,1.0720020497888785,,,0.8,411263,102949
	16	+D1 OLS (muni + month FE),D. Estimation method,19.398625101840388,33.282018368201285,0.39485525067670135,0.537513247647079,18.49481494077501,35.151184915530756,0.40092705375610255,0.5231803031914969,1.070168533613627,,,0.6,411263,102949
	17	+D2 Ridge (cross-validated),D. Estimation method,17.890529516201568,31.251732783077244,0.3763885157696496,0.5797611590637215,16.8893677800818,32.68394222313682,0.3814143837676687,0.5684634391789163,1.0622804510287405,,,10.1,411263,102949
	18	+D3 Random forest,D. Estimation method,14.883188133292904,28.737382658558698,0.3573031529738494,0.6212983831644259,14.053333531225153,29.108973566446117,0.35869427463082987,0.6183437740317796,1.0318463155697535,,,8.4,411263,102949
	19	+D4 Gradient boosting,D. Estimation method,14.59794086326427,28.210269818504578,0.3511407425669361,0.6342486746266742,13.424406660101518,28.85748490533166,0.35438418409430017,0.6274606736319336,1.047165791723387,,,42.1,411263,102949
	20	+"D5 Gradient boosting, no coordinates",D. Estimation method,23.288069281216877,38.626422603992054,0.44226646657865465,0.4197816156316563,22.324919746724586,41.540491694908305,0.45047464198749365,0.39804481488791,1.086467333318932,,,20.8,411263,102949
	21	+D6 Spatial k-NN comparables,D. Estimation method,22.263894535107575,37.95804725523757,0.4404191782505073,0.4246184833703136,22.194183511129985,38.13596309275768,0.44042512037220527,0.42460295720693186,1.0066905499496188,,,0.3,411263,102949

added results/reproduced/horserace_group_parcel.csv +21 −0

		`@@ -0,0 +1,21 @@`
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test
	2	+A1 Linear (levels),A. Functional form,18.394879964095797,35.96893018809802,0.42358366884898346,0.4688087852186674,18.394879964095797,35.96893018809802,0.42358366884898346,0.4688087852186674,,,,0.4,411369,102843
	3	+A2 Semi-log,A. Functional form,19.40388065006023,33.60742551231478,0.3991437427562464,0.5283377491612558,18.459707672156842,35.527166516466494,0.40507307833118583,0.5142204489174887,1.0716280541158298,,,0.6,411369,102843
	4	+A3 Log-log,A. Functional form,18.04901279537473,31.62346448383144,0.38036202721805884,0.5716815568957894,17.060785648509054,33.08835585008513,0.3853279508875882,0.5604244841914658,1.0636869814479837,,,0.9,411369,102843
	5	+A4 Box-Cox,A. Functional form,18.24702711324504,34.006661029680444,0.3967848815219953,0.5338961387758547,17.86556740305991,35.46526823103805,0.40274905686877965,0.5197785744597814,,0.5,,4.4,411369,102843
	6	+A5 Semi-log + quadratics,A. Functional form,19.19420945605029,33.23478458992403,0.3946076985401183,0.5389971863448217,18.178626389812674,35.017880574991494,0.40026491744886666,0.5256842765856499,1.0696108179421064,,,0.6,411369,102843
	7	+A6 Semi-log + splines,A. Functional form,17.62071626632672,31.207237958155154,0.376000477877242,0.5814481534939215,16.60974843964176,32.54559297854598,0.38074837993673477,0.5708109860855053,1.0617470052055027,,,2.3,411369,102843
	8	+B1 No time effects,B. Time effects,21.649567560303716,35.80598610682794,0.4155121629945933,0.4888599034728587,20.805949301729967,38.19532183877957,0.4222433482128658,0.47216510031035164,1.078199634331365,,,0.5,411369,102843
	9	+B2 Year FE,B. Time effects,18.990446124535953,32.997820257572705,0.3921780438977923,0.5446566268137394,18.058282132701265,34.74906901015738,0.3977502821212147,0.5316252641639805,1.068487535996415,,,0.7,411369,102843
	10	+B3 Quarter FE,B. Time effects,19.19420945605029,33.23478458992403,0.3946076985401183,0.5389971863448217,18.178626389812674,35.017880574991494,0.40026491744886666,0.5256842765856499,1.0696108179421064,,,0.6,411369,102843
	11	+B4 Month FE,B. Time effects,19.332436660424253,33.33207533297025,0.3954934330533667,0.5369253343882607,18.402816630486033,35.160733297104976,0.40121192424899693,0.5234372068832924,1.0701374458919553,,,0.6,411369,102843
	12	+C1 No spatial controls,C. Spatial controls,28.887143937365718,44.050532124221256,0.4859586541235692,0.30084879639246065,28.095541551675375,48.734151973096715,0.49707893152453125,0.2684850929794075,1.1115281859261688,,,0.4,411369,102843
	13	+C2 Municipality FE,C. Spatial controls,19.19420945605029,33.23478458992403,0.3946076985401183,0.5389971863448217,18.178626389812674,35.017880574991494,0.40026491744886666,0.5256842765856499,1.0696108179421064,,,0.6,411369,102843
	14	+C3 Grid-cell FE (~5.5 km),C. Spatial controls,18.73260474151463,32.799326462608065,0.38980765046740884,0.5501443438715339,17.53502943411876,34.40695892966617,0.3952679237455016,0.5374532717263956,1.0671611573206463,,,0.7,411369,102843
	15	+C4 Grid-cell FE (~1.1 km),C. Spatial controls,21.097621825427847,35.95310914429783,0.4147863521944663,0.49064404850887544,19.553592455622823,37.9613459138871,0.4212809812757885,0.47456841574603015,1.0757010147272146,,,0.8,411369,102843
	16	+D1 OLS (muni + month FE),D. Estimation method,19.332436660424253,33.33207533297025,0.3954934330533667,0.5369253343882607,18.402816630486033,35.160733297104976,0.40121192424899693,0.5234372068832924,1.0701374458919553,,,0.6,411369,102843
	17	+D2 Ridge (cross-validated),D. Estimation method,17.70592620550421,31.251501981456574,0.3767730607223491,0.579726356784688,16.72857367165446,32.65172599817906,0.3815465570975194,0.569009649787606,1.062317122081801,,,10.2,411369,102843
	18	+D3 Random forest,D. Estimation method,14.622820199263606,28.743565661551727,0.3582854740346365,0.6199586341211347,13.749624355032527,29.092018626347237,0.3596181757160165,0.6171261233153971,1.0317651338894,,,9.2,411369,102843
	19	+D4 Gradient boosting,D. Estimation method,14.507935468925822,28.29190277596338,0.3525188079219081,0.6320938445206743,13.24585810355578,28.915575305176098,0.3556681265266408,0.6254909102009842,1.0478640275860414,,,43.0,411369,102843
	20	+"D5 Gradient boosting, no coordinates",D. Estimation method,23.41157162533723,38.73698634397927,0.44364203470006636,0.4173096237076285,22.212467734820184,41.63446817144011,0.4514086798765861,0.39672923483220146,1.0877176588778272,,,17.5,411369,102843
	21	+D6 Spatial k-NN comparables,D. Estimation method,21.308170377003776,37.246066218610544,0.43397656727509987,0.442422771348263,21.25721677508758,37.43458435469481,0.434126877127783,0.442036465398573,1.0066433972846687,,,0.3,411369,102843

modified results/reproduced/horserace_random.csv +21 −21

		`@@ -1,21 +1,21 @@`
1		−name,group,mdape,mape,rmse_ln,r2_ln,seconds,n_train,n_test
2		−A1 Linear (levels),A. Functional form,18.247735441468322,35.554833553436424,0.4197326280373289,0.4770941777730925,0.5,411283,102929
3		−A2 Semi-log,A. Functional form,18.174885439840832,34.4795393377222,0.39663369462465925,0.5330641412991447,0.6,411283,102929
4		−A3 Log-log,A. Functional form,16.965877929132013,32.69009595755662,0.38125191583247026,0.5685782006102371,0.9,411283,102929
5		−A4 Box-Cox,A. Functional form,18.567718342220903,33.001281736849975,0.3903031252718359,0.5478504801090737,4.3,411283,102929
6		−A5 Semi-log + quadratics,A. Functional form,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,0.7,411283,102929
7		−A6 Semi-log + splines,A. Functional form,16.52578223473714,32.10851818544987,0.37644836156803374,0.5793810460819198,2.6,411283,102929
8		−B1 No time effects,B. Time effects,21.1450312090911,38.37918215557233,0.42321207728034005,0.4683888002641269,0.5,411283,102929
9		−B2 Year FE,B. Time effects,18.091245071945412,34.663597249791685,0.39704996735836223,0.5320835152583053,0.7,411283,102929
10		−B3 Quarter FE,B. Time effects,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,0.6,411283,102929
11		−B4 Month FE,B. Time effects,18.322750827125915,34.80915561246471,0.3982300277671944,0.5292980206991789,0.7,411283,102929
12		−C1 No spatial controls,C. Spatial controls,27.922352076812572,48.39219298797349,0.4944639622666287,0.2743164045351353,0.5,411283,102929
13		−C2 Municipality FE,C. Spatial controls,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,0.7,411283,102929
14		−C3 Grid-cell FE (~5.5 km),C. Spatial controls,17.53978076473437,34.03632099310664,0.3918420758470441,0.5442778333854188,0.7,411283,102929
15		−C4 Grid-cell FE (~1.1 km),C. Spatial controls,19.389847159546143,37.50800513353381,0.41828640746256024,0.48069139310554865,0.8,411283,102929
16		−D1 OLS (muni + month FE),D. Estimation method,18.322750827125915,34.80915561246471,0.3982300277671944,0.5292980206991789,0.7,411283,102929
17		−D2 Ridge (cross-validated),D. Estimation method,16.671722823569887,32.2521071548757,0.37758629277068595,0.5768343018663071,10.8,411283,102929
18		−D3 Random forest,D. Estimation method,14.62750218203232,28.181960170119,0.35257338948901984,0.6310418755396041,7.6,411283,102929
19		−D4 Gradient boosting,D. Estimation method,14.388300681085338,27.766499817027036,0.3471568687492957,0.6422912683312305,42.5,411283,102929
20		−"D5 Gradient boosting, no coordinates",D. Estimation method,23.225090677534933,38.30004358013209,0.4398837230475839,0.4256801846835939,17.7,411283,102929
21		−D6 Spatial k-NN comparables,D. Estimation method,21.18226600985226,36.73270267320528,0.43669681006238664,0.43397181715912814,0.1,411283,102929
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test
	2	+A1 Linear (levels),A. Functional form,18.247735441468322,35.554833553436424,0.4197326280373289,0.4770941777730925,18.247735441468322,35.554833553436424,0.4197326280373289,0.4770941777730925,,,,0.4,411283,102929
	3	+A2 Semi-log,A. Functional form,19.034569938583708,32.66020106922096,0.39092568564912344,0.5464069104539773,18.174885439840832,34.4795393377222,0.39663369462465925,0.5330641412991447,1.0704523740369927,,,0.6,411283,102929
	4	+A3 Log-log,A. Functional form,18.00422814105048,31.24431556205711,0.3762917738410556,0.5797308952207196,16.965877929132013,32.69009595755662,0.38125191583247026,0.5685782006102371,1.0640208207942232,,,0.9,411283,102929
	5	+A4 Box-Cox,A. Functional form,18.567718342220903,33.001281736849975,0.3903031252718359,0.5478504801090737,17.931354368937967,34.39115498001405,0.3955659580558204,0.5355747370020278,,0.25,,5.1,411283,102929
	6	+A5 Semi-log + quadratics,A. Functional form,19.15743025152905,32.8527013727642,0.3911358710025644,0.5459190210301912,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,1.0698913891782036,,,0.7,411283,102929
	7	+A6 Semi-log + splines,A. Functional form,17.6216157169721,30.791561379112448,0.37171474821867573,0.5898926040038202,16.52578223473714,32.10851818544987,0.37644836156803374,0.5793810460819198,1.0620544125859206,,,2.6,411283,102929
	8	+B1 No time effects,B. Time effects,22.038141454991422,35.894437273924325,0.4162524756898916,0.4857294257045265,21.1450312090911,38.37918215557233,0.42321207728034005,0.4683888002641269,1.0800144916543517,,,0.5,411283,102929
	9	+B2 Year FE,B. Time effects,19.12497097548873,32.91021487912301,0.3914089242770463,0.5452848088000786,18.091245071945412,34.663597249791685,0.39704996735836223,0.5320835152583053,1.06983370962192,,,0.7,411283,102929
	10	+B3 Quarter FE,B. Time effects,19.15743025152905,32.8527013727642,0.3911358710025644,0.5459190210301912,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,1.0698913891782036,,,0.7,411283,102929
	11	+B4 Month FE,B. Time effects,19.342062726308214,33.01798132147254,0.39253988395462874,0.5426532514337992,18.322750827125915,34.80915561246471,0.3982300277671944,0.5292980206991789,1.0704345170610976,,,0.7,411283,102929
	12	+C1 No spatial controls,C. Spatial controls,28.785665634746415,43.740789664459314,0.48315578380182944,0.30712900384495423,27.922352076812572,48.39219298797349,0.4944639622666287,0.2743164045351353,1.1117959257819008,,,0.4,411283,102929
	13	+C2 Municipality FE,C. Spatial controls,19.15743025152905,32.8527013727642,0.3911358710025644,0.5459190210301912,18.057575256256637,34.597939297430145,0.3967501193167754,0.5327899798098671,1.0698913891782036,,,0.7,411283,102929
	14	+C3 Grid-cell FE (~5.5 km),C. Spatial controls,18.703553400119855,32.45802918238758,0.38651653174174216,0.556581136808286,17.53978076473437,34.03632099310664,0.3918420758470441,0.5442778333854188,1.067449819592543,,,0.7,411283,102929
	15	+C4 Grid-cell FE (~1.1 km),C. Spatial controls,20.962941599826827,35.57153971188526,0.41212679150885995,0.49587328501243466,19.389847159546143,37.50800513353381,0.41828640746256024,0.48069139310554865,1.0756884611181337,,,0.9,411283,102929
	16	+D1 OLS (muni + month FE),D. Estimation method,19.342062726308214,33.01798132147254,0.39253988395462874,0.5426532514337992,18.322750827125915,34.80915561246471,0.3982300277671944,0.5292980206991789,1.0704345170610976,,,0.7,411283,102929
	17	+D2 Ridge (cross-validated),D. Estimation method,17.684559394393904,30.874200209239945,0.372797514554587,0.5874999240199299,16.671722823569887,32.2521071548757,0.37758629277068595,0.5768343018663071,1.0626009803138499,,,10.9,411283,102929
	18	+D3 Random forest,D. Estimation method,14.62750218203232,28.181960170119,0.35257338948901984,0.6310418755396041,13.68191573226618,28.50111285576457,0.3537359214449655,0.6286047502994752,1.0320010783517677,,,12.5,411283,102929
	19	+D4 Gradient boosting,D. Estimation method,14.388300681085338,27.766499817027036,0.3471568687492957,0.6422912683312305,13.136043786916385,28.339593011975516,0.3501358518462874,0.6361258693434015,1.0475010409695187,,,46.7,411283,102929
	20	+"D5 Gradient boosting, no coordinates",D. Estimation method,23.225090677534933,38.30004358013209,0.4398837230475839,0.4256801846835939,22.11744594443843,41.15658845539997,0.4476945241929057,0.4051032704375488,1.0876216107611343,,,17.3,411283,102929
	21	+D6 Spatial k-NN comparables,D. Estimation method,21.18226600985226,36.73270267320528,0.43669681006238664,0.43397181715912814,21.128130305413727,36.898833705701435,0.436786904121283,0.43373824074782497,1.0056888675291784,,,0.3,411283,102929

modified results/reproduced/horserace_temporal.csv +21 −21

		`@@ -1,21 +1,21 @@`
1		−name,group,mdape,mape,rmse_ln,r2_ln,seconds,n_train,n_test
2		−A1 Linear (levels),A. Functional form,20.369511213481317,32.86005001443525,0.39728743801570204,0.4552239614410175,0.4,355824,158388
3		−A2 Semi-log,A. Functional form,20.611640132255836,33.09824319242239,0.3964345928808567,0.45756036006756484,0.5,355824,158388
4		−A3 Log-log,A. Functional form,19.189006525695262,30.749155508273613,0.3757555688314752,0.5126744490905257,0.8,355824,158388
5		−A4 Box-Cox,A. Functional form,20.957181720703545,31.940298396980698,0.38962419749983584,0.47603753989498354,3.8,355824,158388
6		−A5 Semi-log + quadratics,A. Functional form,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,0.6,355824,158388
7		−A6 Semi-log + splines,A. Functional form,19.097413080353302,30.49261711294047,0.37228529384601217,0.5216342331571537,2.1,355824,158388
8		−B1 No time effects,B. Time effects,25.384810383977687,33.162107080537304,0.41811180324070163,0.39661683797944225,0.5,355824,158388
9		−B2 Year FE,B. Time effects,21.006054587504984,32.62538772051225,0.39253658926914514,0.46817515745089067,0.6,355824,158388
10		−B3 Quarter FE,B. Time effects,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,0.6,355824,158388
11		−B4 Month FE,B. Time effects,20.347788061301657,32.47788422275795,0.38952457659313394,0.4763054439041552,0.6,355824,158388
12		−C1 No spatial controls,C. Spatial controls,26.45586672540444,41.108374756471996,0.45691339109589413,0.2794301211279968,0.4,355824,158388
13		−C2 Municipality FE,C. Spatial controls,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,0.6,355824,158388
14		−C3 Grid-cell FE (~5.5 km),C. Spatial controls,21.279243946393596,32.712624877555356,0.39371599730320833,0.464974534611328,0.6,355824,158388
15		−C4 Grid-cell FE (~1.1 km),C. Spatial controls,22.091478382056824,36.02185035008858,0.41700099046919065,0.39981863895351477,0.7,355824,158388
16		−D1 OLS (muni + month FE),D. Estimation method,20.347788061301657,32.47788422275795,0.38952457659313394,0.4763054439041552,0.6,355824,158388
17		−D2 Ridge (cross-validated),D. Estimation method,19.520136279141678,30.594351068378263,0.3747175016019065,0.5153633136379877,8.6,355824,158388
18		−D3 Random forest,D. Estimation method,21.34011982105225,29.76443050482997,0.37332513269156825,0.5189582317282835,6.8,355824,158388
19		−D4 Gradient boosting,D. Estimation method,21.21243467837447,29.71192710420828,0.37236811207724885,0.5214213758996993,41.5,355824,158388
20		−"D5 Gradient boosting, no coordinates",D. Estimation method,26.207233073287274,35.736727341535484,0.44725743322834494,0.3095639406099918,21.1,355824,158388
21		−D6 Spatial k-NN comparables,D. Estimation method,25.63120139114109,34.234843881635754,0.4653714833711972,0.2525057333957209,0.1,355824,158388
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test
	2	+A1 Linear (levels),A. Functional form,20.369511213481317,32.86005001443525,0.39728743801570204,0.4552239614410175,20.369511213481317,32.86005001443525,0.39728743801570204,0.4552239614410175,,,,0.4,355824,158388
	3	+A2 Semi-log,A. Functional form,23.154885105735325,32.88199068728801,0.4078149103607638,0.42597007752801586,20.611640132255836,33.09824319242239,0.3964345928808567,0.45756036006756484,1.076793566376698,,,0.5,355824,158388
	4	+A3 Log-log,A. Functional form,21.769614210046917,31.036455799131453,0.38771693156325343,0.4811547262154816,19.189006525695262,30.749155508273613,0.3757555688314752,0.5126744490905257,1.0655530599282332,,,0.8,355824,158388
	5	+A4 Box-Cox,A. Functional form,20.957181720703545,31.940298396980698,0.38962419749983584,0.47603753989498354,19.571597393733516,31.96261263566212,0.3844157306522595,0.48995248826084103,,0.5,,4.0,355824,158388
	6	+A5 Semi-log + quadratics,A. Functional form,23.30291738895638,32.33980518990814,0.4022452672417709,0.4415423854252667,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,1.0711855946796898,,,0.6,355824,158388
	7	+A6 Semi-log + splines,A. Functional form,21.722504213272607,30.87403330589372,0.384133203104169,0.4907019347955833,19.097413080353302,30.49261711294047,0.37228529384601217,0.5216342331571537,1.06346689326762,,,2.0,355824,158388
	8	+B1 No time effects,B. Time effects,29.296772516609654,34.68364172805182,0.4503543461363537,0.29996936286225007,25.384810383977687,33.162107080537304,0.41811180324070163,0.39661683797944225,1.0779549442640406,,,0.5,355824,158388
	9	+B2 Year FE,B. Time effects,23.651696383010147,32.69839717790235,0.40614244890268997,0.43066865187652315,21.006054587504984,32.62538772051225,0.39253658926914514,0.46817515745089067,1.0741977461673156,,,0.6,355824,158388
	10	+B3 Quarter FE,B. Time effects,23.30291738895638,32.33980518990814,0.4022452672417709,0.4415423854252667,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,1.0711855946796898,,,0.6,355824,158388
	11	+B4 Month FE,B. Time effects,22.8719130040602,32.42550461740692,0.400924502771694,0.4452037338739415,20.347788061301657,32.47788422275795,0.38952457659313394,0.4763054439041552,1.0724108768578227,,,0.6,355824,158388
	12	+C1 No spatial controls,C. Spatial controls,29.015774167241894,38.87352353861925,0.4685413801986148,0.24228787650947192,26.45586672540444,41.108374756471996,0.45691339109589413,0.2794301211279968,1.1188483034696548,,,0.4,355824,158388
	13	+C2 Municipality FE,C. Spatial controls,23.30291738895638,32.33980518990814,0.4022452672417709,0.4415423854252667,20.4747492500219,32.08431941207347,0.3884352669819105,0.47923038313059785,1.0711855946796898,,,0.6,355824,158388
	14	+C3 Grid-cell FE (~5.5 km),C. Spatial controls,24.2625431905187,33.00942406765742,0.40874325687600593,0.42335366891858794,21.279243946393596,32.712624877555356,0.39371599730320833,0.464974534611328,1.0720367816988154,,,0.6,355824,158388
	15	+C4 Grid-cell FE (~1.1 km),C. Spatial controls,25.324930433263678,35.50206863036151,0.42919028135360904,0.3642182032203949,22.091478382056824,36.02185035008858,0.41700099046919065,0.39981863895351477,1.0921887847980092,,,0.6,355824,158388
	16	+D1 OLS (muni + month FE),D. Estimation method,22.8719130040602,32.42550461740692,0.400924502771694,0.4452037338739415,20.347788061301657,32.47788422275795,0.38952457659313394,0.4763054439041552,1.0724108768578227,,,0.6,355824,158388
	17	+D2 Ridge (cross-validated),D. Estimation method,22.257318062238202,31.071606388474528,0.38804376521331146,0.480279615769711,19.520136279141678,30.594351068378263,0.3747175016019065,0.5153633136379877,1.0640215124102546,,,8.2,355824,158388
	18	+D3 Random forest,D. Estimation method,21.340119821052188,29.76443050482997,0.37332513269156825,0.5189582317282835,19.394248052512626,28.951513572891475,0.36347962322867167,0.5439961919671212,1.0324597692592685,,,10.7,355824,158388
	19	+D4 Gradient boosting,D. Estimation method,21.21243467837447,29.71192710420828,0.37236811207724885,0.5214213758996993,18.362851253802294,28.605014412660662,0.3587539272757954,0.5557763676216326,1.0485637089645152,,,41.3,355824,158388
	20	+"D5 Gradient boosting, no coordinates",D. Estimation method,26.207233073287274,35.736727341535484,0.44725743322834494,0.3095639406099918,23.004852680221028,35.9605098787384,0.42968275070306156,0.3627583254241229,1.0912898778385383,,,21.7,355824,158388
	21	+D6 Spatial k-NN comparables,D. Estimation method,25.63120139114109,34.234843881635754,0.4653714833711972,0.2525057333957209,25.38964897166118,34.13469069386835,0.46349083531773794,0.25853503771828157,1.0043584323305443,,,0.2,355824,158388

added results/reproduced/inference_random.csv +21 −0

		`@@ -0,0 +1,21 @@`
	1	+model,mdape,ci_lo,ci_hi,boot_se,diff_vs_ref,diff_lo,diff_hi,diff_vs_d4,diff_d4_lo,diff_d4_hi,dm_ape_vs_a6_t,dm_ape_vs_a6_p,dm_ape_vs_a6_diff,dm_sqlog_vs_a6_t,dm_sqlog_vs_a6_p,dm_sqlog_vs_a6_diff,dm_ape_vs_d4_t,dm_ape_vs_d4_p,dm_ape_vs_d4_diff,dm_sqlog_vs_d4_t,dm_sqlog_vs_d4_p,dm_sqlog_vs_d4_diff,n_clusters
	2	+A1 Linear (levels),18.247735441468322,16.9113510560629,19.60250248921421,0.6798156719309989,0.6261197244962204,0.13177818927938997,1.1288670458109282,3.8594347603829835,2.3810890282818233,5.572402821114919,12.297632954401742,0.0,0.04763272174323981,7.51790454474203,5.573319583618286e-14,0.03800362499584921,10.403881445314044,0.0,0.077883337364094,11.88110067074241,0.0,0.05565758751930701,1091
	3	+A2 Semi-log,19.034569938583708,17.948468947394765,20.177409718978527,0.5933974925595471,1.4129542216116064,1.0925363990812282,1.8335429697484,4.6462692574983695,3.410686792542463,6.182775708649027,10.174542669661014,0.0,0.01868639690108518,8.898715388706915,0.0,0.014651037656963798,5.814778194584789,6.071433578114238e-09,0.04893701252193937,4.763341767974322,1.9041293313204477e-06,0.03230500018042161,1091
	4	+A3 Log-log,18.00422814105048,17.07752319183666,18.977226098783678,0.5097956635710524,0.3826124240783777,0.28563151196801645,0.48671649465618905,3.6159274599651408,2.268004875035067,5.04018984221415,4.640377326082088,3.477735786239222e-06,0.0045275418294466125,3.28780657498537,0.001009711859182305,0.0034236450171746756,3.7605346164843136,0.00016955060891321594,0.034778157450300794,3.1024469169219993,0.0019192796548725966,0.02107760754063249,1091
	5	+A4 Box-Cox,18.567718342220903,17.46589758655213,19.707557217076772,0.5895493292913278,0.9461026252488018,0.6659357616138547,1.3168750827110465,4.179417661135565,2.9293738028577057,5.753351071060692,10.694909755887176,0.0,0.02209720357737525,10.463728364076685,0.0,0.014164675553688949,6.2558305116106006,3.954059302202495e-10,0.05234781919822943,5.180699999292202,2.2105477048839361e-07,0.03181863807714676,1091
	6	+A5 Semi-log + quadratics,19.15743025152905,18.201941036517315,20.15445926287562,0.5026923733244107,1.5358145345569483,1.1398198349247033,2.1391093582834935,4.769129570443711,3.684746880089903,5.930644511229821,5.530637638741666,3.190688269150144e-08,0.020611399936517463,6.846564545749681,7.564393555981042e-12,0.014815415541661218,8.696091789215284,0.0,0.050862015557371645,7.103680897159478,1.2148060335448463e-12,0.03246937806511903,1091
	7	+A6 Semi-log + splines,17.6216157169721,16.733927881204792,18.583767461456866,0.4920101568426174,,,,3.233315035886763,1.8746102788184382,4.657062294398633,,,,,,,3.5997911983137305,0.0003184728086869093,0.030250615620854186,3.021002919921985,0.002519389304698194,0.017653962523457807,1091
	8	+B1 No time effects,22.038141454991422,21.08712269256635,23.267211253160106,0.5612291624566031,4.41652573801932,3.4200841630827816,5.582948377502827,7.649840773906083,6.748344719706512,8.338009838204949,8.206346390560523,2.220446049250313e-16,0.05102875894811877,7.860550382221196,3.774758283725532e-15,0.035094269474690284,19.848983759841108,0.0,0.08127937456897295,17.415570392509096,0.0,0.0527482319981481,1091
	9	+B2 Year FE,19.12497097548873,18.135266091728134,20.16483252720224,0.5420996135180365,1.5033552585166277,1.0652509808425514,2.1819410747332237,4.736670294403391,3.6133353152983663,5.9326990304884655,6.124427672343136,9.101013276335834e-10,0.021186535000105613,7.1455155771433745,8.966161146872764e-13,0.015029091960441074,8.76902162424838,0.0,0.0514371506209598,7.29281506461723,3.035349749325178e-13,0.03268305448389889,1091
	10	+B3 Quarter FE,19.15743025152905,18.201941036517315,20.15445926287562,0.5026923733244107,1.5358145345569483,1.1398198349247033,2.1391093582834935,4.769129570443711,3.684746880089903,5.930644511229821,5.530637638741666,3.190688269150144e-08,0.020611399936517463,6.846564545749681,7.564393555981042e-12,0.014815415541661218,8.696091789215284,0.0,0.050862015557371645,7.103680897159478,1.2148060335448463e-12,0.03246937806511903,1091
	11	+B4 Month FE,19.342062726308214,18.41666765136561,20.381917170225584,0.5186977109248657,1.7204470093361124,1.2291247555472724,2.4534949420758574,4.953762045222875,3.8934157966761633,6.07316437462031,5.731933731822563,9.929206790104672e-09,0.02226419942360097,6.544042648781664,5.987765838710857e-11,0.0159157064518399,9.414342745938619,0.0,0.052514815044455154,7.726539400085093,1.1102230246251565e-14,0.033569668975297715,1091
	12	+C1 No spatial controls,28.785665634746415,27.341346218160815,30.074976710188,0.7025099701791481,11.164049917774314,10.142872490107974,12.280345112224204,14.397364953661077,12.691537820133453,15.890935706600027,7.742609666008332,9.769962616701378e-15,0.12949228285346864,15.131594441078725,0.0,0.09526765737788669,14.938137987865796,0.0,0.15974289847432283,13.859739811417462,0.0,0.1129216199013445,1091
	13	+C2 Municipality FE,19.15743025152905,18.201941036517315,20.15445926287562,0.5026923733244107,1.5358145345569483,1.1398198349247033,2.1391093582834935,4.769129570443711,3.684746880089903,5.930644511229821,5.530637638741666,3.190688269150144e-08,0.020611399936517463,6.846564545749681,7.564393555981042e-12,0.014815415541661218,8.696091789215284,0.0,0.050862015557371645,7.103680897159478,1.2148060335448463e-12,0.03246937806511903,1091
	14	+C3 Grid-cell FE (~5.5 km),18.703553400119855,17.78729355112193,20.032142200057542,0.5678254955514357,1.0819376831477534,0.21901537947672517,2.308285560296583,4.3152527190345165,3.6452950369483923,5.089221243343746,2.5295453955100333,0.011421039859825566,0.01666467803275125,2.356369638453933,0.01845454380735978,0.01122317526639169,14.03126557996909,0.0,0.04691529365360543,13.706499864516653,0.0,0.0288771377898495,1091
	15	+C4 Grid-cell FE (~1.1 km),20.962941599826827,20.085903076339296,21.854065484343828,0.4556213754459016,3.3413258828547256,2.8904906643605672,3.837012817774882,6.574640918741489,5.336615577939174,7.744405878759988,6.7530133957275,1.4480638910185917e-11,0.04779978332772806,7.5711644369648194,3.68594044175552e-14,0.03167663823611381,13.14987798988361,0.0,0.07805039894858226,12.025634909259105,0.0,0.049330600759571616,1091
	16	+D1 OLS (muni + month FE),19.342062726308214,18.41666765136561,20.381917170225584,0.5186977109248657,1.7204470093361124,1.2291247555472724,2.4534949420758574,4.953762045222875,3.8934157966761633,6.07316437462031,5.731933731822563,9.929206790104672e-09,0.02226419942360097,6.544042648781664,5.987765838710857e-11,0.0159157064518399,9.414342745938619,0.0,0.052514815044455154,7.726539400085093,1.1102230246251565e-14,0.033569668975297715,1091
	17	+D2 Ridge (cross-validated),17.684559394393904,16.768330917331383,18.6836218961783,0.5035043504152524,0.06294367742180285,-0.01676159248276264,0.1637807429146053,3.296258713308566,1.9811849496440535,4.724217428807863,2.6118019768463383,0.009006640622825302,0.0008263883012749337,2.7683584874087472,0.005633944669363622,0.0008061328148040056,3.6535115239679725,0.0002586781730240517,0.03107700392212912,3.060857865195947,0.002207038376347503,0.018460095338261817,1091
	18	+D3 Random forest,14.62750218203232,13.737999221508268,16.19555708116927,0.6178221405912262,-2.994113534939782,-4.555739590156278,-1.4648756603277908,0.23920150094698123,0.0513885363794455,0.4588555165642077,-2.85524195730287,0.00430040529118747,-0.02609601208993448,-2.205886325821924,0.027391959893569684,-0.01386385906749741,4.672835254507822,2.970700491378153e-06,0.004154603530919706,6.693591526753016,2.177591440499782e-11,0.003790103455960403,1091
	19	+D4 Gradient boosting,14.388300681085338,13.681350877219709,15.743536219678433,0.5263969787549507,-3.233315035886763,-4.657062294398633,-1.8746102788184382,,,,-3.5997911983137305,0.0003184728086869093,-0.030250615620854186,-3.021002919921985,0.002519389304698194,-0.017653962523457807,,,,,,,1091
	20	+"D5 Gradient boosting, no coordinates",23.225090677534933,22.138529223958216,25.069137709119865,0.7566123985799357,5.603474960562831,3.9352537791374327,7.507040455957043,8.836789996449594,8.10748542572112,9.787971484731155,4.50536824487449,6.625793987247164e-06,0.07508482201019637,6.433439358856359,1.2474843380516631e-10,0.055325835758930006,10.594870291718431,0.0,0.10533543763105055,16.137980864260527,0.0,0.07297979828238782,1091
	21	+D6 Spatial k-NN comparables,21.18226600985226,19.390028219965146,23.548071796694504,1.100889921651293,3.560650292880158,0.9519338843862455,5.8622156243977095,6.793965328766921,5.527326690571327,8.03181255741793,4.798111691143396,1.6016846118294126e-06,0.05941141294092833,5.960580367571443,2.513436569984151e-09,0.05253224987539075,19.297132345753973,0.0,0.08966202856178251,20.248240203175722,0.0,0.07018621239884855,1091

added results/reproduced/inference_temporal.csv +21 −0

		`@@ -0,0 +1,21 @@`
	1	+model,mdape,ci_lo,ci_hi,boot_se,diff_vs_ref,diff_lo,diff_hi,diff_vs_d4,diff_d4_lo,diff_d4_hi,dm_ape_vs_a6_t,dm_ape_vs_a6_p,dm_ape_vs_a6_diff,dm_sqlog_vs_a6_t,dm_sqlog_vs_a6_p,dm_sqlog_vs_a6_diff,dm_ape_vs_d4_t,dm_ape_vs_d4_p,dm_ape_vs_d4_diff,dm_sqlog_vs_d4_t,dm_sqlog_vs_d4_p,dm_sqlog_vs_d4_diff,n_clusters
	2	+A1 Linear (levels),20.369511213481317,19.050772109018073,21.69348139159165,0.6849601233930911,-1.3529929997912902,-2.2770702594184407,-0.42539919706467916,-0.8429234648931541,-2.5898121968575603,1.1895847489303906,6.317663783346769,2.6554691778812867e-10,0.01986016708541528,6.164003649673723,7.092830767163605e-10,0.010278990678011518,3.520049279845853,0.0004314666251414856,0.03148122910226971,3.9079109150864686,9.309761836728825e-05,0.0191792975131057,1071
	3	+A2 Semi-log,23.154885105735325,21.6887719627368,24.674870127680457,0.7875237764863192,1.4323808924627173,0.7670651228422551,2.2976528083716783,1.9424504273608534,0.5295622515203463,3.4375141515059062,7.796357304870725,6.439293542825908e-15,0.020079573813942913,7.223963685447007,5.049294315995212e-13,0.01875468338548904,3.965893940282591,7.312137370973915e-05,0.03170063583079734,5.055071810178792,4.3022885698462687e-07,0.02765499022058323,1071
	4	+A3 Log-log,21.769614210046917,20.51940280719328,23.227311337108237,0.6739267745802049,0.04710999677431005,-0.04315938950036894,0.18763013229223433,0.5571795316724462,-0.5423402505386862,1.8391490439319191,1.804661231143382,0.07112771002474405,0.0016242249323772874,2.543121816787227,0.010986691828438477,0.0027661012937557784,1.646327603990528,0.09969632924843053,0.013245286949231714,2.098866610291465,0.03582866095871928,0.011666408128849963,1071
	5	+A4 Box-Cox,20.957181720703545,19.742168516904147,22.156377541760673,0.6381565190731153,-0.7653224925690623,-1.4473333084469813,-0.09482024347911353,-0.25525295767092615,-1.7949341953230935,1.4690422686693982,4.264381230833118,2.0045693571724144e-05,0.010662650910869802,2.2871023500844068,0.022189849754430613,0.004248697550322327,2.5043936657330677,0.012266146996653404,0.022283712927724228,2.2903116877035994,0.02200325477123455,0.01314900438541651,1071
	6	+A5 Semi-log + quadratics,23.30291738895638,21.869038097481326,24.922485533073313,0.8102019586928445,1.5804131756837734,1.0783669250409043,2.22065102463182,2.0904827105819095,0.9486003551587855,3.181577878834679,6.065811464275289,1.3128906850568e-09,0.014657718840144185,7.152656593716022,8.51096970677645e-13,0.014242937291334905,4.603816313944034,4.148183673891026e-06,0.026278780856998613,6.444665276370954,1.1585576942252374e-10,0.023143244126429093,1071
	7	+A6 Semi-log + splines,21.722504213272607,20.45126930153131,23.100552763771457,0.6610274998462855,,,,0.5100695348981361,-0.5516760349102061,1.677839052305929,,,,,,,1.615823456025302,0.1061324886702475,0.011621062016854429,1.9765879301563614,0.04808822757633413,0.008900306835094185,1071
	8	+B1 No time effects,29.296772516609654,27.25307447396948,31.453026176290106,1.0868368852006105,7.574268303337046,6.039750998516674,9.027043210519999,8.084337838235182,7.297235701980839,9.07468513889715,5.307042338766459,1.1141830524863394e-07,0.03809608422158093,9.288145872580824,0.0,0.05526071935683395,19.75478536885888,0.0,0.04971714623843536,16.92421738378873,0.0,0.06416102619192815,1071
	9	+B2 Year FE,23.651696383010147,22.215432187910814,25.268875459898798,0.8096188915960055,1.92919216973754,1.3131800189892668,2.7530865495071235,2.439261704635676,1.3173521256992164,3.562209825093329,6.1579767061896264,7.368019527831393e-10,0.018243638720086247,6.017796983225028,1.7680674702091892e-09,0.017393371073605394,5.139555821884859,2.7538867297671743e-07,0.029864700736940673,7.23985001734488,4.4919623576333834e-13,0.026293677908699582,1071
	10	+B3 Quarter FE,23.30291738895638,21.869038097481326,24.922485533073313,0.8102019586928445,1.5804131756837734,1.0783669250409043,2.22065102463182,2.0904827105819095,0.9486003551587855,3.181577878834679,6.065811464275289,1.3128906850568e-09,0.014657718840144185,7.152656593716022,8.51096970677645e-13,0.014242937291334905,4.603816313944034,4.148183673891026e-06,0.026278780856998613,6.444665276370954,1.1585576942252374e-10,0.023143244126429093,1071
	11	+B4 Month FE,22.8719130040602,21.532938038433826,24.438984492545977,0.7619484470830038,1.149408790787593,0.6893140083694228,1.8098306190197673,1.659478325685729,0.5920810512262819,2.7576763092148138,5.991209061016688,2.082866767949554e-09,0.015514713115132013,5.990884007795864,2.0870345451839967e-09,0.013182139195661349,4.567473208327871,4.936387487219918e-06,0.027135775131986443,6.024141823255467,1.7000925112142795e-09,0.02208244603075553,1071
	12	+C1 No spatial controls,29.015774167241894,27.422211588155974,30.325868927192477,0.7462222947018358,7.293269953969286,4.96861955562622,9.193766804289842,7.803339488867422,4.996711778534667,10.324147123803586,11.088323777905881,0.0,0.07999490232725531,7.508284601340977,5.995204332975845e-14,0.07197270723135413,17.010072661797665,0.0,0.09161596434410973,6.338419778689569,2.3213364563900996e-10,0.08087301406644831,1071
	13	+C2 Municipality FE,23.30291738895638,21.869038097481326,24.922485533073313,0.8102019586928445,1.5804131756837734,1.0783669250409043,2.22065102463182,2.0904827105819095,0.9486003551587855,3.181577878834679,6.065811464275289,1.3128906850568e-09,0.014657718840144185,7.152656593716022,8.51096970677645e-13,0.014242937291334905,4.603816313944034,4.148183673891026e-06,0.026278780856998613,6.444665276370954,1.1585576942252374e-10,0.023143244126429093,1071
	14	+C3 Grid-cell FE (~5.5 km),24.2625431905187,22.503220945710353,26.363285194699493,1.0301736045564578,2.540038977246091,1.5785786294135338,3.4839259747851203,3.0501085121442273,2.0572172007955043,3.9118766585912756,4.503146745467939,6.695461754135934e-06,0.02135390761763703,4.450105287824345,8.582820140379255e-06,0.019512732314535812,8.314219574865609,0.0,0.03297496963449146,12.3741576283692,0.0,0.028413039149629993,1071
	15	+C4 Grid-cell FE (~1.1 km),25.324930433263678,24.251360863509277,26.29352775446495,0.49390977597366215,3.60242621999107,2.1189111166682935,4.91703661788902,4.112495754889206,2.25480020889692,5.928810388694186,12.43144220323286,0.0,0.046280353244677816,9.969202355421647,0.0,0.03664597988132135,7.149992224263942,8.677503160470224e-13,0.057901415261532245,6.861875584202508,6.796341267545358e-12,0.045546286716415536,1071
	16	+D1 OLS (muni + month FE),22.8719130040602,21.532938038433826,24.438984492545977,0.7619484470830038,1.149408790787593,0.6893140083694228,1.8098306190197673,1.659478325685729,0.5920810512262819,2.7576763092148138,5.991209061016688,2.082866767949554e-09,0.015514713115132013,5.990884007795864,2.0870345451839967e-09,0.013182139195661349,4.567473208327871,4.936387487219918e-06,0.027135775131986443,6.024141823255467,1.7000925112142795e-09,0.02208244603075553,1071
	17	+D2 Ridge (cross-validated),22.257318062238202,20.96191993033077,23.668021827486456,0.6692303373351438,0.5348138489655945,0.48101405213608955,0.6088791910137628,1.0448833838637306,0.0012400068282902282,2.185150952674026,6.580369386315953,4.692801702788074e-11,0.0019757308258080398,16.00748490968894,0.0,0.0030196459938548717,1.9584584383888557,0.05017624333623605,0.01359679284266247,2.647413747037119,0.008111004795629206,0.011919952828949056,1071
	18	+D3 Random forest,21.340119821052188,19.907687448517617,22.980295616439495,0.8411843763724454,-0.38238439222041976,-1.5015448169575225,0.5571785755217394,0.12768514267771636,-0.14568791249818178,0.36811779443404413,-1.568790205531711,0.11669683137166498,-0.011096028010637537,-1.9109037795897155,0.05601694727646822,-0.008186663027891686,0.9790991544458619,0.3275309894032459,0.0005250340062168912,1.2895287248262932,0.19721433670042376,0.0007136438072025015,1071
	19	+D4 Gradient boosting,21.21243467837447,19.70747318840484,22.945391194003907,0.8986037102049517,-0.5100695348981361,-1.6778390523059303,0.551676034910206,,,,-1.615823456025302,0.1061324886702475,-0.011621062016854429,-1.9765879301563614,0.04808822757633413,-0.008900306835094185,,,,,,,1071
	20	+"D5 Gradient boosting, no coordinates",26.207233073287274,25.23007220277521,27.506849996204814,0.608040527286014,4.484728860014666,2.8779728042965105,6.210941230892228,4.994798394912802,3.1215058615470648,6.500510794984376,5.875060368764621,4.2268928357458435e-09,0.04862694035641765,9.378346817879406,0.0,0.05248089385093869,13.890923788390463,0.0,0.06024800237327208,11.078685604065148,0.0,0.06138120068603288,1071
	21	+D6 Spatial k-NN comparables,25.63120139114109,23.14828800408425,28.333593401968223,1.407855973507387,3.9086971778684827,1.7817973469367552,5.637733529113384,4.418766712766619,3.332669523407553,5.470721729412763,4.036460402580431,5.4263679257982034e-05,0.0336081057574204,7.832489620597485,4.884981308350689e-15,0.0690122998080397,26.494126476851566,0.0,0.04522916777427483,15.848240562584424,0.0,0.0779126066431339,1071

added results/reproduced/leakage.csv +37 −0

		`@@ -0,0 +1,37 @@`
	1	+key,seen_in_training,segment,n,model,mdape
	2	+in_train_parcel,True,all,17219,A5 Semi-log + quadratics,19.786608950655705
	3	+in_train_parcel,True,all,17219,A6 Semi-log + splines,18.27278654110786
	4	+in_train_parcel,True,all,17219,D2 Ridge (cross-validated),18.21506909664557
	5	+in_train_parcel,True,all,17219,D3 Random forest,14.568143855697022
	6	+in_train_parcel,True,all,17219,D4 Gradient boosting,14.494590514304903
	7	+in_train_parcel,True,all,17219,"D5 Gradient boosting, no coordinates",22.887248058209508
	8	+in_train_parcel,True,all,17219,D6 Spatial k-NN comparables,22.21141825253498
	9	+in_train_parcel,True,condo,3374,A5 Semi-log + quadratics,17.414213423610217
	10	+in_train_parcel,True,condo,3374,D4 Gradient boosting,9.035672175351072
	11	+in_train_parcel,False,all,85710,A5 Semi-log + quadratics,19.05005201781079
	12	+in_train_parcel,False,all,85710,A6 Semi-log + splines,17.48581012929675
	13	+in_train_parcel,False,all,85710,D2 Ridge (cross-validated),17.576292121577303
	14	+in_train_parcel,False,all,85710,D3 Random forest,14.639597756778661
	15	+in_train_parcel,False,all,85710,D4 Gradient boosting,14.368856147710904
	16	+in_train_parcel,False,all,85710,"D5 Gradient boosting, no coordinates",23.28075103236257
	17	+in_train_parcel,False,all,85710,D6 Spatial k-NN comparables,20.990025690392308
	18	+in_train_parcel,False,condo,11474,A5 Semi-log + quadratics,18.43144280197513
	19	+in_train_parcel,False,condo,11474,D4 Gradient boosting,9.080011346798681
	20	+in_train_coord,True,all,27475,A5 Semi-log + quadratics,19.16845806222931
	21	+in_train_coord,True,all,27475,A6 Semi-log + splines,17.776290704974276
	22	+in_train_coord,True,all,27475,D2 Ridge (cross-validated),17.859099147831706
	23	+in_train_coord,True,all,27475,D3 Random forest,11.74898846453675
	24	+in_train_coord,True,all,27475,D4 Gradient boosting,11.994995797797987
	25	+in_train_coord,True,all,27475,"D5 Gradient boosting, no coordinates",20.04914260589526
	26	+in_train_coord,True,all,27475,D6 Spatial k-NN comparables,16.652769091793402
	27	+in_train_coord,True,condo,13261,A5 Semi-log + quadratics,17.97470023475135
	28	+in_train_coord,True,condo,13261,D4 Gradient boosting,8.934702433522762
	29	+in_train_coord,False,all,75454,A5 Semi-log + quadratics,19.15384674472759
	30	+in_train_coord,False,all,75454,A6 Semi-log + splines,17.555794642798645
	31	+in_train_coord,False,all,75454,D2 Ridge (cross-validated),17.625875167760007
	32	+in_train_coord,False,all,75454,D3 Random forest,15.749377923105962
	33	+in_train_coord,False,all,75454,D4 Gradient boosting,15.321150846402826
	34	+in_train_coord,False,all,75454,"D5 Gradient boosting, no coordinates",24.512690151286638
	35	+in_train_coord,False,all,75454,D6 Spatial k-NN comparables,22.907703956528476
	36	+in_train_coord,False,condo,1587,A5 Semi-log + quadratics,20.34309569440084
	37	+in_train_coord,False,condo,1587,D4 Gradient boosting,10.243202880340052

modified results/reproduced/learning.csv +6 −6

		`@@ -1,13 +1,13 @@`
1	1	n_train,model,mdape,mape,rmse_ln,r2_ln
2		−10000,OLS quadratic (muni+quarter FE),18.38436183742385,34.439941317616764,0.39722768960842764,0.531664536345561
	2	+10000,OLS quadratic (muni+quarter FE),19.136226571989205,32.82348826216586,0.39279102092321205,0.5420678667536525
3	3	10000,Gradient boosting,17.55817415103931,31.777076909845096,0.386462587914794,0.5567048988691092
4		−25000,OLS quadratic (muni+quarter FE),18.13123412223344,34.71752541710843,0.3987497135923394,0.5280686972389094
	4	+25000,OLS quadratic (muni+quarter FE),19.056034269404236,32.98471009782084,0.39338974517982517,0.5406707674234809
5	5	25000,Gradient boosting,16.117235891494122,29.823687390173077,0.36598650222996054,0.6024349909662393
6		−50000,OLS quadratic (muni+quarter FE),17.85098430954251,34.291813175933555,0.394668048572139,0.5376807754235925
	6	+50000,OLS quadratic (muni+quarter FE),18.801486657084954,32.60613267913101,0.38924551758611076,0.5502975469627178
7	7	50000,Gradient boosting,15.46029775645706,29.149938590306927,0.3602557920963508,0.6147878645125984
8		−100000,OLS quadratic (muni+quarter FE),17.858528109660003,33.97231033671203,0.39154828747222153,0.5449609437080014
	8	+100000,OLS quadratic (muni+quarter FE),18.79513254400627,32.30474782180091,0.3861646547014708,0.5573881289110587
9	9	100000,Gradient boosting,15.201224181879457,28.789207604531935,0.35629888749041316,0.6232034228186022
10		−200000,OLS quadratic (muni+quarter FE),17.926781291106366,34.286171684612285,0.3940853634933891,0.5390448972702662
	10	+200000,OLS quadratic (muni+quarter FE),18.95754804582277,32.59698579952596,0.3886557888504686,0.5516591634684497
11	11	200000,Gradient boosting,14.75286425569271,28.18065043214689,0.3510692811837181,0.6341831746695208
12		−400000,OLS quadratic (muni+quarter FE),18.06403273608106,34.590640697337626,0.3967353319490308,0.5328248061516689
	12	+400000,OLS quadratic (muni+quarter FE),19.163049017655457,32.85043942607389,0.3911538943677605,0.5458771723710507
13	13	400000,Gradient boosting,14.485229661097984,27.850855998019064,0.3478423367115942,0.640877268082553

added results/reproduced/nested_fe.csv +5 −0

		`@@ -0,0 +1,5 @@`
	1	+name,group,mdape,mape,rmse_ln,r2_ln,mdape_mean,mape_mean,rmse_ln_mean,r2_ln_mean,smear,lambda,best_iter,seconds,n_train,n_test,scheme
	2	+C3' Municipality + grid-cell FE (~5.5 km),R. Nested spatial FE,17.665652290445884,31.12198554971308,0.37510903497229636,0.5823686750564678,16.57229702106549,32.4806122435959,0.37992439164733227,0.5715774026320801,1.0631574832813349,,,0.8,411283,102929,random
	3	+C4' Municipality + grid-cell FE (~1.1 km),R. Nested spatial FE,17.29729629720419,30.733211555044505,0.3721271623880836,0.5889820782402844,16.375718827618094,32.05295192430275,0.3767837714918572,0.5786311816346446,1.0618679756677316,,,0.9,411283,102929,random
	4	+C3' Municipality + grid-cell FE (~5.5 km),R. Nested spatial FE,21.540172002578217,31.319651378571518,0.387790697263982,0.4809572799709757,18.969417428034074,31.146859757968027,0.3774487316843718,0.5082727550291839,1.0655936591628847,,,0.7,355824,158388,temporal
	5	+C4' Municipality + grid-cell FE (~1.1 km),R. Nested spatial FE,21.551985610380243,31.053622599219104,0.3860253906004687,0.48567211222806106,19.040236558535824,30.77780074936307,0.37492649963695734,0.5148225523371934,1.063943524835854,,,0.8,355824,158388,temporal

added results/reproduced/pairs.csv +27 −0

		`@@ -0,0 +1,27 @@`
	1	+scheme,model_a,model_b,mdape_a,mdape_b,diff,diff_lo,diff_hi,dm_ape_t,dm_ape_p,dm_sqlog_t,dm_sqlog_p
	2	+random,A2 Semi-log,A1 Linear (levels),19.034569938583708,18.247735441468322,0.786834497115386,0.41777153663505734,1.2226677871864655,-10.686601368220524,0.0,-4.195670171129506,2.720659259725089e-05
	3	+random,A6 Semi-log + splines,A2 Semi-log,17.6216157169721,19.034569938583708,-1.4129542216116064,-1.8335429697484,-1.0925363990812282,-10.174542669661014,0.0,-8.898715388706915,0.0
	4	+random,A4 Box-Cox,A2 Semi-log,18.567718342220903,19.034569938583708,-0.4668515963628046,-0.5884632595730912,-0.3515787120379936,8.968814092671723,0.0,-0.6913546659882105,0.48934268588585117
	5	+random,A3 Log-log,A2 Semi-log,18.00422814105048,19.034569938583708,-1.0303417975332287,-1.4512106300041965,-0.7229610971299634,-7.8961780030161535,2.886579864025407e-15,-10.077109850055015,0.0
	6	+random,B2 Year FE,B1 No time effects,19.12497097548873,22.038141454991422,-2.9131704795026927,-3.840391706025526,-2.058685463008183,-8.108170173583066,4.440892098500626e-16,-7.414195626155693,1.2234657731369225e-13
	7	+random,B4 Month FE,B3 Quarter FE,19.342062726308214,19.15743025152905,0.1846324747791641,0.009302948022620466,0.36545434556285866,2.8512317585347584,0.0043550214198446735,2.8914469178564333,0.003834723670044893
	8	+random,C3 Grid-cell FE (~5.5 km),C2 Municipality FE,18.703553400119855,19.15743025152905,-0.45387685140919487,-1.0674805259265627,0.36564802296516835,-1.1325549920922209,0.25740117846477517,-1.1710051289695664,0.24159671553609452
	9	+random,C4 Grid-cell FE (~1.1 km),C2 Municipality FE,20.962941599826827,19.15743025152905,1.8055113482977774,1.2410975614274538,2.3151293348045763,7.123073216501024,1.0556000518135988e-12,7.327255973885574,2.349231920106831e-13
	10	+random,D2 Ridge (cross-validated),D1 OLS (muni + month FE),17.684559394393904,19.342062726308214,-1.6575033319143095,-2.3738182373546737,-1.1306026474848994,-5.474659566022061,4.383534979446324e-08,-5.9766089127788495,2.278302435598789e-09
	11	+random,D4 Gradient boosting,D3 Random forest,14.388300681085338,14.62750218203232,-0.23920150094698123,-0.45885551656420775,-0.0513885363794455,-4.672835254507822,2.970700491378153e-06,-6.693591526753016,2.177591440499782e-11
	12	+random,D4 Gradient boosting,"D5 Gradient boosting, no coordinates",14.388300681085338,23.225090677534933,-8.836789996449594,-9.787971484731155,-8.10748542572112,-10.594870291718431,0.0,-16.137980864260527,0.0
	13	+random,D4 Gradient boosting,A1 Linear (levels),14.388300681085338,18.247735441468322,-3.8594347603829835,-5.572402821114921,-2.3810890282818233,-10.403881445314044,0.0,-11.88110067074241,0.0
	14	+random,A6 Semi-log + splines,A1 Linear (levels),17.6216157169721,18.247735441468322,-0.6261197244962204,-1.1288670458109282,-0.13177818927939008,-12.297632954401742,0.0,-7.51790454474203,5.573319583618286e-14
	15	+temporal,A2 Semi-log,A1 Linear (levels),23.154885105735325,20.369511213481317,2.7853738922540074,1.7788182735293514,3.8803663265918216,0.12007360831229617,0.9044248386245604,3.5326533859479348,0.00041141148678836004
	16	+temporal,A6 Semi-log + splines,A2 Semi-log,21.722504213272607,23.154885105735325,-1.4323808924627173,-2.2976528083716783,-0.7670651228422554,-7.796357304870725,6.439293542825908e-15,-7.223963685447007,5.049294315995212e-13
	17	+temporal,A4 Box-Cox,A2 Semi-log,20.957181720703545,23.154885105735325,-2.1977033850317795,-3.1466875936389673,-1.4637657862566353,-5.293840398286759,1.197739760705474e-07,-6.972682156866287,3.1095126473701384e-12
	18	+temporal,A3 Log-log,A2 Semi-log,21.769614210046917,23.154885105735325,-1.3852708956884072,-2.2367115754092746,-0.7387385691927764,-7.105911135498072,1.1952661083114435e-12,-6.302689050518644,2.9252533728651997e-10
	19	+temporal,B2 Year FE,B1 No time effects,23.651696383010147,29.296772516609654,-5.645076133599506,-6.510622685144795,-4.523812050946931,-3.8445189114832927,0.00012078917028457425,-10.351974415660491,0.0
	20	+temporal,B4 Month FE,B3 Quarter FE,22.8719130040602,23.30291738895638,-0.4310043848961804,-0.9466994932147289,0.049163437435324885,0.7433560498426371,0.45726614558734036,-0.8851075462469108,0.37609862982402076
	21	+temporal,C3 Grid-cell FE (~5.5 km),C2 Municipality FE,24.2625431905187,23.30291738895638,0.9596258015623178,0.16372589677996133,1.8087259847256496,2.296878919423751,0.02162567786746883,1.6301068446540665,0.1030789173649842
	22	+temporal,C4 Grid-cell FE (~1.1 km),C2 Municipality FE,25.324930433263678,23.30291738895638,2.022013044307297,0.1532742784899062,3.589326531283127,8.122062031800938,4.440892098500626e-16,4.79314541245226,1.6418652810656909e-06
	23	+temporal,D2 Ridge (cross-validated),D1 OLS (muni + month FE),22.257318062238202,22.8719130040602,-0.6145949418219985,-1.25927559041227,-0.16597374782475421,-5.560559072361206,2.6891181059696123e-08,-4.694048528809288,2.6785044802135616e-06
	24	+temporal,D4 Gradient boosting,D3 Random forest,21.21243467837447,21.340119821052188,-0.12768514267771636,-0.36811779443404413,0.1456879124981816,-0.9790991544458619,0.3275309894032459,-1.2895287248262932,0.19721433670042376
	25	+temporal,D4 Gradient boosting,"D5 Gradient boosting, no coordinates",21.21243467837447,26.207233073287274,-4.994798394912802,-6.500510794984377,-3.1215058615470657,-13.890923788390463,0.0,-11.078685604065148,0.0
	26	+temporal,D4 Gradient boosting,A1 Linear (levels),21.21243467837447,20.369511213481317,0.8429234648931541,-1.1895847489303917,2.58981219685756,-3.520049279845853,0.0004314666251414856,-3.9079109150864686,9.309761836728825e-05
	27	+temporal,A6 Semi-log + splines,A1 Linear (levels),21.722504213272607,20.369511213481317,1.3529929997912902,0.42539919706467916,2.27707025941844,-6.317663783346769,2.6554691778812867e-10,-6.164003649673723,7.092830767163605e-10

added results/reproduced/relevel.csv +41 −0

		`@@ -0,0 +1,41 @@`
	1	+scheme,model,median_log_resid,mdape,mdape_relevelled,mape_relevelled,rmse_ln_centered
	2	+random,A1 Linear (levels),0.003941579311327104,18.247735441468322,18.23004891488436,35.69297195166703,0.4202401848567488
	3	+random,A2 Semi-log,0.05718358954988467,19.034569938583708,18.231160761954637,34.0869684129567,0.3949373865541228
	4	+random,A3 Log-log,0.058544005681735456,18.00422814105048,16.999353648099166,32.573565774441384,0.380703144661566
	5	+random,A4 Box-Cox,0.04130325060083884,18.567718342220903,17.954579371141705,34.12392448255233,0.3943404790319506
	6	+random,A5 Semi-log + quadratics,0.060482363271615824,19.15743025152905,18.11709775973182,34.346470692604235,0.39562549011238385
	7	+random,A6 Semi-log + splines,0.05992694422787537,17.6216157169721,16.524937550487323,32.09956942745145,0.37640447767238644
	8	+random,B1 No time effects,0.05783820151938279,22.038141454991422,21.21973153779817,37.60444848077603,0.42017760445683755
	9	+random,B2 Year FE,0.060634056819226956,19.12497097548873,18.120790003428947,34.4190972555926,0.39595399652847946
	10	+random,B3 Quarter FE,0.060482363271615824,19.15743025152905,18.11709775973182,34.346470692604235,0.39562549011238385
	11	+random,B4 Month FE,0.05989058589285712,19.342062726308214,18.354164512138155,34.515768803825544,0.39693480132805525
	12	+random,C1 No spatial controls,0.064660279848761,28.785665634746415,28.084183838836008,46.280530679601654,0.4873531649156765
	13	+random,C2 Municipality FE,0.060482363271615824,19.15743025152905,18.11709775973182,34.346470692604235,0.39562549011238385
	14	+random,C3 Grid-cell FE (~5.5 km),0.06211418728747908,18.703553400119855,17.560654074769303,33.92747210229044,0.3913354959102772
	15	+random,C4 Grid-cell FE (~1.1 km),0.07346052233407185,20.962941599826827,19.37902139629324,37.526713965938505,0.41837214294707703
	16	+random,D1 OLS (muni + month FE),0.05989058589285712,19.342062726308214,18.354164512138155,34.515768803825544,0.39693480132805525
	17	+random,D2 Ridge (cross-validated),0.05859458753725022,17.684559394393904,16.68303730586329,32.182831210501654,0.377254725760277
	18	+random,D3 Random forest,0.059849487924283906,14.62750218203232,13.315627506545855,29.149851711862564,0.3571621747065756
	19	+random,D4 Gradient boosting,0.06070519978533717,14.388300681085338,12.968025826820522,28.70404274157882,0.3522826247099593
	20	+random,"D5 Gradient boosting, no coordinates",0.06518367898153521,23.225090677534933,22.231894512368584,40.34607372325065,0.4445804591769491
	21	+random,D6 Spatial k-NN comparables,0.031091961266028534,21.18226600985226,21.08883377849876,37.76094936816919,0.43809139600270497
	22	+temporal,A1 Linear (levels),0.1023593997120793,20.369511213481317,17.983628345464886,34.78005470885447,0.4002842762670569
	23	+temporal,A2 Semi-log,0.1537984152326084,23.154885105735325,19.250951132236665,34.93065853825993,0.39945237558539437
	24	+temporal,A3 Log-log,0.15909109773775665,21.769614210046917,17.266368727247855,32.391262877862694,0.377692222226945
	25	+temporal,A4 Box-Cox,0.1258160183976118,20.957181720703545,17.619997411558572,33.74049661940829,0.3889147051380237
	26	+temporal,A5 Semi-log + quadratics,0.17129196839132454,23.30291738895638,18.276550062146548,33.989570593169596,0.39008182451924517
	27	+temporal,A6 Semi-log + splines,0.1614247324548579,21.722504213272607,16.82576888128111,32.08286270087081,0.37439667304872754
	28	+temporal,B1 No time effects,0.2826557411184121,29.296772516609654,19.01095994641687,34.65256914399475,0.3950407735178907
	29	+temporal,B2 Year FE,0.17007926384480498,23.651696383010147,18.99713708925793,34.63025036534526,0.39482039546313313
	30	+temporal,B3 Quarter FE,0.17129196839132454,23.30291738895638,18.276550062146548,33.989570593169596,0.39008182451924517
	31	+temporal,B4 Month FE,0.15736851631187143,22.8719130040602,18.68918931880011,34.336746664507935,0.3927079521397681
	32	+temporal,C1 No spatial controls,0.16321364030035745,29.015774167241894,25.986670604102326,42.99352712008042,0.4606526213784797
	33	+temporal,C2 Municipality FE,0.17129196839132454,23.30291738895638,18.276550062146548,33.989570593169596,0.39008182451924517
	34	+temporal,C3 Grid-cell FE (~5.5 km),0.18220234989278072,24.2625431905187,18.814878020376376,34.76783893858608,0.3949793249194573
	35	+temporal,C4 Grid-cell FE (~1.1 km),0.1709061348026415,25.324930433263678,20.522125855535506,38.230322256162516,0.42231730885691315
	36	+temporal,D1 OLS (muni + month FE),0.15736851631187143,22.8719130040602,18.68918931880011,34.336746664507935,0.3927079521397681
	37	+temporal,D2 Ridge (cross-validated),0.17022474494589535,22.257318062238202,17.037619921036498,32.23095939217706,0.3756435542037618
	38	+temporal,D3 Random forest,0.18360250057646788,21.340119821052188,13.905947637222784,29.094464580355663,0.3542908632942389
	39	+temporal,D4 Gradient boosting,0.18339005785301854,21.21243467837447,13.865439528037044,29.06582352581495,0.35369501531983066
	40	+temporal,"D5 Gradient boosting, no coordinates",0.18807982851052696,26.207233073287274,21.276298850287766,38.44281213948979,0.431047370174503
	41	+temporal,D6 Spatial k-NN comparables,0.22093905599935848,25.63120139114109,19.23963333094165,34.78903287000047,0.41913080372044065

added results/reproduced/same_period.csv +21 −0

		`@@ -0,0 +1,21 @@`
	1	+model,mdape_random_all,mdape_random_2025_26,mdape_forward_2025_26,n_random_2025_26,n_forward
	2	+A1 Linear (levels),18.247735441468322,17.09006288548948,20.369511213481317,31465,158388
	3	+A2 Semi-log,19.034569938583708,18.049772389120093,23.154885105735325,31465,158388
	4	+A3 Log-log,18.00422814105048,17.301575106616333,21.769614210046917,31465,158388
	5	+A4 Box-Cox,18.567718342220903,17.63772856887288,20.957181720703545,31465,158388
	6	+A5 Semi-log + quadratics,19.15743025152905,18.496565926231643,23.30291738895638,31465,158388
	7	+A6 Semi-log + splines,17.6216157169721,16.986964776398153,21.722504213272607,31465,158388
	8	+B1 No time effects,22.038141454991422,25.46195922621089,29.296772516609654,31465,158388
	9	+B2 Year FE,19.12497097548873,18.587477688637772,23.651696383010147,31465,158388
	10	+B3 Quarter FE,19.15743025152905,18.496565926231643,23.30291738895638,31465,158388
	11	+B4 Month FE,19.342062726308214,18.91583380701899,22.8719130040602,31465,158388
	12	+C1 No spatial controls,28.785665634746415,26.419945359140563,29.015774167241894,31465,158388
	13	+C2 Municipality FE,19.15743025152905,18.496565926231643,23.30291738895638,31465,158388
	14	+C3 Grid-cell FE (~5.5 km),18.703553400119855,18.261595423633086,24.2625431905187,31465,158388
	15	+C4 Grid-cell FE (~1.1 km),20.962941599826827,19.84981063507152,25.324930433263678,31465,158388
	16	+D1 OLS (muni + month FE),19.342062726308214,18.91583380701899,22.8719130040602,31465,158388
	17	+D2 Ridge (cross-validated),17.684559394393904,17.098506259471893,22.257318062238202,31465,158388
	18	+D3 Random forest,14.62750218203232,13.8581263765865,21.340119821052188,31465,158388
	19	+D4 Gradient boosting,14.388300681085338,13.704684482746913,21.21243467837447,31465,158388
	20	+"D5 Gradient boosting, no coordinates",23.225090677534933,20.99193671205706,26.207233073287274,31465,158388
	21	+D6 Spatial k-NN comparables,21.18226600985226,22.55888464294253,25.63120139114109,31465,158388

modified results/reproduced/segments.csv +7 −7

		`@@ -1,15 +1,15 @@`
1	1	segment,model,n,mdape,mape,rmse_ln,r2_ln
2		−Class: single_family,OLS quadratic,69835,17.15697828017771,35.09144196354416,0.4018837509330969,0.5269797760968626
	2	+Class: single_family,OLS quadratic,69835,18.818747368969795,33.62957142912425,0.39648525503248905,0.5396025632666579
3	3	Class: single_family,Gradient boosting,69835,15.08887366879076,29.429305197147464,0.3608165339944521,0.6187132829338855
4		−Class: condo,OLS quadratic,14848,20.42743440870622,27.094418864984917,0.32651881058598764,0.4074914996647663
	4	+Class: condo,OLS quadratic,14848,18.197646141652584,24.35300386684896,0.32154382366324963,0.4254093992708138
5	5	Class: condo,Gradient boosting,14848,9.071686847966884,14.485209967611992,0.20596083242967297,0.7642523075225905
6		−Class: plex,OLS quadratic,15115,18.50099130749293,36.98046001501068,0.41103973211699246,0.5454994242149013
	6	+Class: plex,OLS quadratic,15115,20.245072332644707,35.37422177148882,0.4052926027997528,0.5581201635953541
7	7	Class: plex,Gradient boosting,15115,16.52761611544543,30.817583909526963,0.36806946728568257,0.635559683430239
8		−Class: cottage,OLS quadratic,2109,33.91947109274449,53.22661347754297,0.5482899168598493,0.3136130552394867
	8	+Class: cottage,OLS quadratic,2109,34.25391889121872,49.5560691019703,0.5417910818656525,0.32978799887448207
9	9	Class: cottage,Gradient boosting,2109,32.09640332106328,45.661889354803385,0.5034612691648649,0.4212638262473417
10		−Muni < 1k sales,OLS quadratic,29253,23.257955712558935,42.00606759369818,0.4521889409919308,0.4895905571585859
	10	+Muni < 1k sales,OLS quadratic,29253,24.83881625772472,39.847712541492584,0.44558852842475133,0.5043822749230567
11	11	Muni < 1k sales,Gradient boosting,29253,18.686729079471053,32.7580249582477,0.38939943295154483,0.621496886358641
12		−Muni 1k–10k sales,OLS quadratic,37419,15.193131785630404,32.29520768278317,0.3776824491741606,0.5133709854088806
	12	+Muni 1k–10k sales,OLS quadratic,37419,16.825938909928517,31.11245095169157,0.3718321556965634,0.5283299710327505
13	13	Muni 1k–10k sales,Gradient boosting,37419,14.504639160801878,28.498332907599565,0.3521566764912874,0.576926089020657
14		−Muni > 10k sales,OLS quadratic,36257,17.82460628493704,30.99741904583036,0.3669850806325136,0.46899139390723055
	14	+Muni > 10k sales,OLS quadratic,36257,17.685506151376927,29.004985587875904,0.3625286510651555,0.48180954127111475
15	15	Muni > 10k sales,Gradient boosting,36257,11.91348390081652,22.983932385296278,0.30299483947274597,0.6380278097783667

added results/tables/by_quarter.tex +13 −0

		`@@ -0,0 +1,13 @@`
	1	+\begin{tabular}{lrccccc}
	2	+\toprule
	3	+Test quarter & $n$ & A5 Quadratics & A6 Splines & D2 Ridge & D3 Random forest & D4 Boosting \\
	4	+\midrule
	5	+2025Q1 & 17,031 & 20.2 & 18.6 & 19.0 & 17.2 & 17.1 \\
	6	+2025Q2 & 34,546 & 21.1 & 19.5 & 20.1 & 19.2 & 19.1 \\
	7	+2025Q3 & 28,097 & 22.8 & 21.3 & 21.8 & 20.6 & 20.6 \\
	8	+2025Q4 & 24,156 & 23.8 & 22.2 & 22.7 & 21.7 & 21.6 \\
	9	+2026Q1 & 15,611 & 24.8 & 23.1 & 23.6 & 22.8 & 22.7 \\
	10	+2026Q2 & 30,950 & 25.8 & 24.5 & 25.1 & 24.4 & 24.3 \\
	11	+2026Q3 & 7,997 & 26.0 & 24.9 & 25.2 & 25.0 & 24.9 \\
	12	+\bottomrule
	13	+\end{tabular}
		\ No newline at end of file

modified results/tables/generalization.tex +5 −5

		`@@ -4,11 +4,11 @@`
4	4	\cmidrule{2-3}\cmidrule{5-6}
5	5	Model & MdAPE (\%) & $R^2_{\ln}$ & & MdAPE (\%) & $R^2_{\ln}$ \\
6	6	\midrule
7		−A5 Semi-log + quadratics & 18.1 & 0.533 & & 20.5 & 0.479 \\
8		−B4 Month FE & 18.3 & 0.529 & & 20.3 & 0.476 \\
9		−C4 Grid-cell FE ($\sim$1.1 km) & 19.4 & 0.481 & & 22.1 & 0.400 \\
10		−D1 OLS (muni + month FE) & 18.3 & 0.529 & & 20.3 & 0.476 \\
11		−D2 Ridge (cross-validated) & 16.7 & 0.577 & & 19.5 & 0.515 \\
	7	+A5 Semi-log + quadratics & 19.2 & 0.546 & & 23.3 & 0.442 \\
	8	+B4 Month FE & 19.3 & 0.543 & & 22.9 & 0.445 \\
	9	+C4 Grid-cell FE ($\sim$1.1 km) & 21.0 & 0.496 & & 25.3 & 0.364 \\
	10	+D1 OLS (muni + month FE) & 19.3 & 0.543 & & 22.9 & 0.445 \\
	11	+D2 Ridge (cross-validated) & 17.7 & 0.587 & & 22.3 & 0.480 \\
12	12	D3 Random forest & 14.6 & 0.631 & & 21.3 & 0.519 \\
13	13	D4 Gradient boosting & 14.4 & 0.642 & & 21.2 & 0.521 \\
14	14	D5 Gradient boosting, no coordinates & 23.2 & 0.426 & & 26.2 & 0.310 \\

added results/tables/group_splits.tex +34 −0

		`@@ -0,0 +1,34 @@`
	1	+\begin{tabular}{l cc c cc c cc}
	2	+\toprule
	3	+ & \multicolumn{2}{c}{Random 80/20} & & \multicolumn{2}{c}{Parcel-grouped} & & \multicolumn{2}{c}{Building-grouped} \\
	4	+\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}
	5	+Model & MdAPE & $R^2_{\ln}$ & & MdAPE & $R^2_{\ln}$ & & MdAPE & $R^2_{\ln}$ \\
	6	+\midrule
	7	+\multicolumn{9}{l}{\itshape A. Functional form}\\
	8	+\quad A1 Linear & 18.2 & 0.477 & & 18.4 & 0.469 & & 18.4 & 0.473 \\
	9	+\quad A2 Semi-log & 19.0 & 0.546 & & 19.4 & 0.528 & & 19.5 & 0.530 \\
	10	+\quad A3 Log-log & 18.0 & 0.580 & & 18.0 & 0.572 & & 18.1 & 0.573 \\
	11	+\quad A4 Box--Cox & 18.6 & 0.548 & & 18.2 & 0.534 & & 18.3 & 0.535 \\
	12	+\quad A5 Quadratics & 19.2 & 0.546 & & 19.2 & 0.539 & & 19.0 & 0.552 \\
	13	+\quad A6 Splines & 17.6 & 0.590 & & 17.6 & 0.581 & & 17.8 & 0.582 \\
	14	+\multicolumn{9}{l}{\itshape B. Time effects}\\
	15	+\quad B1 No time FE & 22.0 & 0.486 & & 21.6 & 0.489 & & 22.0 & 0.482 \\
	16	+\quad B2 Year FE & 19.1 & 0.545 & & 19.0 & 0.545 & & 19.2 & 0.539 \\
	17	+\quad B3 Quarter FE & 19.2 & 0.546 & & 19.2 & 0.539 & & 19.0 & 0.552 \\
	18	+\quad B4 Month FE & 19.3 & 0.543 & & 19.3 & 0.537 & & 19.4 & 0.538 \\
	19	+\multicolumn{9}{l}{\itshape C. Spatial controls}\\
	20	+\quad C1 No spatial FE & 28.8 & 0.307 & & 28.9 & 0.301 & & 28.7 & 0.306 \\
	21	+\quad C2 Municipality FE & 19.2 & 0.546 & & 19.2 & 0.539 & & 19.0 & 0.552 \\
	22	+\quad C3 Grid 5.5 km & 18.7 & 0.557 & & 18.7 & 0.550 & & 18.8 & 0.551 \\
	23	+\quad C4 Grid 1.1 km & 21.0 & 0.496 & & 21.1 & 0.491 & & 20.2 & 0.510 \\
	24	+\multicolumn{9}{l}{\itshape D. Estimation method}\\
	25	+\quad D1 OLS & 19.3 & 0.543 & & 19.3 & 0.537 & & 19.4 & 0.538 \\
	26	+\quad D2 Ridge & 17.7 & 0.587 & & 17.7 & 0.580 & & 17.9 & 0.580 \\
	27	+\quad D3 Random forest & 14.6 & 0.631 & & 14.6 & 0.620 & & 14.9 & 0.621 \\
	28	+\quad D4 Boosting & 14.4 & 0.642 & & 14.5 & 0.632 & & 14.6 & 0.634 \\
	29	+\quad D5 Boosting, no coord. & 23.2 & 0.426 & & 23.4 & 0.417 & & 23.3 & 0.420 \\
	30	+\quad D6 $k$-NN comparables & 21.2 & 0.434 & & 21.3 & 0.442 & & 22.3 & 0.425 \\
	31	+\midrule
	32	+Test sales & 102,929 & & & 102,843 & & & 102,949 & \\
	33	+\bottomrule
	34	+\end{tabular}
		\ No newline at end of file

added results/tables/hgb_sensitivity.tex +13 −0

		`@@ -0,0 +1,13 @@`
	1	+\begin{tabular}{l cc c cc}
	2	+\toprule
	3	+ & \multicolumn{2}{c}{Random holdout} & & \multicolumn{2}{c}{Forward-in-time} \\
	4	+\cmidrule{2-3}\cmidrule{5-6}
	5	+Gradient-boosting configuration & MdAPE (\%) & $R^2_{\ln}$ & & MdAPE (\%) & $R^2_{\ln}$ \\
	6	+\midrule
	7	+Gradient boosting (baseline) & 14.4 & 0.642 & & 21.2 & 0.521 \\
	8	+Shallow (15 leaves, lr 0.05, 1500 iter) & 14.7 & 0.636 & & 21.4 & 0.521 \\
	9	+Deep (255 leaves, lr 0.05, 600 iter) & 14.3 & 0.645 & & 21.6 & 0.518 \\
	10	+Regularised (min leaf 200, L2 = 1) & 14.3 & 0.643 & & 21.5 & 0.522 \\
	11	+Early stopping on last 10\% of training months [700 / 1000 it.] & 14.5 & 0.641 & & 21.2 & 0.524 \\
	12	+\bottomrule
	13	+\end{tabular}
		\ No newline at end of file

modified results/tables/horserace_random.tex +18 −18

		`@@ -4,30 +4,30 @@ Model & MdAPE (\%) & MAPE (\%) & RMSE$_{\ln}$ & $R^2_{\ln}$ & Fit (s) \\`
4	4	\midrule
5	5	\multicolumn{6}{l}{\itshape A. Functional form}\\
6	6	\quad A1 Linear (levels) & 18.2 & 35.6 & 0.420 & 0.477 & 0 \\
7		−\quad A2 Semi-log & 18.2 & 34.5 & 0.397 & 0.533 & 1 \\
8		−\quad A3 Log-log & 17.0 & 32.7 & 0.381 & 0.569 & 1 \\
9		−\quad A4 Box-Cox & 18.6 & 33.0 & 0.390 & 0.548 & 4 \\
10		−\quad A5 Semi-log + quadratics & 18.1 & 34.6 & 0.397 & 0.533 & 1 \\
11		−\quad A6 Semi-log + splines & \textbf{16.5} & 32.1 & 0.376 & 0.579 & 3 \\
	7	+\quad A2 Semi-log & 19.0 & 32.7 & 0.391 & 0.546 & 1 \\
	8	+\quad A3 Log-log & 18.0 & 31.2 & 0.376 & 0.580 & 1 \\
	9	+\quad A4 Box-Cox & 18.6 & 33.0 & 0.390 & 0.548 & 5 \\
	10	+\quad A5 Semi-log + quadratics & 19.2 & 32.9 & 0.391 & 0.546 & 1 \\
	11	+\quad A6 Semi-log + splines & \textbf{17.6} & 30.8 & 0.372 & 0.590 & 3 \\
12	12	\midrule
13	13	\multicolumn{6}{l}{\itshape B. Time effects}\\
14		−\quad B1 No time effects & 21.1 & 38.4 & 0.423 & 0.468 & 0 \\
15		−\quad B2 Year FE & 18.1 & 34.7 & 0.397 & 0.532 & 1 \\
16		−\quad B3 Quarter FE & \textbf{18.1} & 34.6 & 0.397 & 0.533 & 1 \\
17		−\quad B4 Month FE & 18.3 & 34.8 & 0.398 & 0.529 & 1 \\
	14	+\quad B1 No time effects & 22.0 & 35.9 & 0.416 & 0.486 & 0 \\
	15	+\quad B2 Year FE & \textbf{19.1} & 32.9 & 0.391 & 0.545 & 1 \\
	16	+\quad B3 Quarter FE & 19.2 & 32.9 & 0.391 & 0.546 & 1 \\
	17	+\quad B4 Month FE & 19.3 & 33.0 & 0.393 & 0.543 & 1 \\
18	18	\midrule
19	19	\multicolumn{6}{l}{\itshape C. Spatial controls}\\
20		−\quad C1 No spatial controls & 27.9 & 48.4 & 0.494 & 0.274 & 0 \\
21		−\quad C2 Municipality FE & 18.1 & 34.6 & 0.397 & 0.533 & 1 \\
22		−\quad C3 Grid-cell FE ($\sim$5.5 km) & \textbf{17.5} & 34.0 & 0.392 & 0.544 & 1 \\
23		−\quad C4 Grid-cell FE ($\sim$1.1 km) & 19.4 & 37.5 & 0.418 & 0.481 & 1 \\
	20	+\quad C1 No spatial controls & 28.8 & 43.7 & 0.483 & 0.307 & 0 \\
	21	+\quad C2 Municipality FE & 19.2 & 32.9 & 0.391 & 0.546 & 1 \\
	22	+\quad C3 Grid-cell FE ($\sim$5.5 km) & \textbf{18.7} & 32.5 & 0.387 & 0.557 & 1 \\
	23	+\quad C4 Grid-cell FE ($\sim$1.1 km) & 21.0 & 35.6 & 0.412 & 0.496 & 1 \\
24	24	\midrule
25	25	\multicolumn{6}{l}{\itshape D. Estimation method}\\
26		−\quad D1 OLS (muni + month FE) & 18.3 & 34.8 & 0.398 & 0.529 & 1 \\
27		−\quad D2 Ridge (cross-validated) & 16.7 & 32.3 & 0.378 & 0.577 & 11 \\
28		−\quad D3 Random forest & 14.6 & 28.2 & 0.353 & 0.631 & 8 \\
29		−\quad D4 Gradient boosting & \textbf{14.4} & 27.8 & 0.347 & 0.642 & 42 \\
30		−\quad D5 Gradient boosting, no coordinates & 23.2 & 38.3 & 0.440 & 0.426 & 18 \\
	26	+\quad D1 OLS (muni + month FE) & 19.3 & 33.0 & 0.393 & 0.543 & 1 \\
	27	+\quad D2 Ridge (cross-validated) & 17.7 & 30.9 & 0.373 & 0.587 & 11 \\
	28	+\quad D3 Random forest & 14.6 & 28.2 & 0.353 & 0.631 & 12 \\
	29	+\quad D4 Gradient boosting & \textbf{14.4} & 27.8 & 0.347 & 0.642 & 47 \\
	30	+\quad D5 Gradient boosting, no coordinates & 23.2 & 38.3 & 0.440 & 0.426 & 17 \\
31	31	\quad D6 Spatial k-NN comparables & 21.2 & 36.7 & 0.437 & 0.434 & 0 \\
32	32	\bottomrule
33	33	\end{tabular}
		\ No newline at end of file

modified results/tables/horserace_temporal.tex +18 −18

		`@@ -3,31 +3,31 @@`
3	3	Model & MdAPE (\%) & MAPE (\%) & RMSE$_{\ln}$ & $R^2_{\ln}$ & Fit (s) \\
4	4	\midrule
5	5	\multicolumn{6}{l}{\itshape A. Functional form}\\
6		−\quad A1 Linear (levels) & 20.4 & 32.9 & 0.397 & 0.455 & 0 \\
7		−\quad A2 Semi-log & 20.6 & 33.1 & 0.396 & 0.458 & 0 \\
8		−\quad A3 Log-log & 19.2 & 30.7 & 0.376 & 0.513 & 1 \\
	6	+\quad A1 Linear (levels) & \textbf{20.4} & 32.9 & 0.397 & 0.455 & 0 \\
	7	+\quad A2 Semi-log & 23.2 & 32.9 & 0.408 & 0.426 & 0 \\
	8	+\quad A3 Log-log & 21.8 & 31.0 & 0.388 & 0.481 & 1 \\
9	9	\quad A4 Box-Cox & 21.0 & 31.9 & 0.390 & 0.476 & 4 \\
10		−\quad A5 Semi-log + quadratics & 20.5 & 32.1 & 0.388 & 0.479 & 1 \\
11		−\quad A6 Semi-log + splines & \textbf{19.1} & 30.5 & 0.372 & 0.522 & 2 \\
	10	+\quad A5 Semi-log + quadratics & 23.3 & 32.3 & 0.402 & 0.442 & 1 \\
	11	+\quad A6 Semi-log + splines & 21.7 & 30.9 & 0.384 & 0.491 & 2 \\
12	12	\midrule
13	13	\multicolumn{6}{l}{\itshape B. Time effects}\\
14		−\quad B1 No time effects & 25.4 & 33.2 & 0.418 & 0.397 & 0 \\
15		−\quad B2 Year FE & 21.0 & 32.6 & 0.393 & 0.468 & 1 \\
16		−\quad B3 Quarter FE & 20.5 & 32.1 & 0.388 & 0.479 & 1 \\
17		−\quad B4 Month FE & \textbf{20.3} & 32.5 & 0.390 & 0.476 & 1 \\
	14	+\quad B1 No time effects & 29.3 & 34.7 & 0.450 & 0.300 & 0 \\
	15	+\quad B2 Year FE & 23.7 & 32.7 & 0.406 & 0.431 & 1 \\
	16	+\quad B3 Quarter FE & 23.3 & 32.3 & 0.402 & 0.442 & 1 \\
	17	+\quad B4 Month FE & \textbf{22.9} & 32.4 & 0.401 & 0.445 & 1 \\
18	18	\midrule
19	19	\multicolumn{6}{l}{\itshape C. Spatial controls}\\
20		−\quad C1 No spatial controls & 26.5 & 41.1 & 0.457 & 0.279 & 0 \\
21		−\quad C2 Municipality FE & \textbf{20.5} & 32.1 & 0.388 & 0.479 & 1 \\
22		−\quad C3 Grid-cell FE ($\sim$5.5 km) & 21.3 & 32.7 & 0.394 & 0.465 & 1 \\
23		−\quad C4 Grid-cell FE ($\sim$1.1 km) & 22.1 & 36.0 & 0.417 & 0.400 & 1 \\
	20	+\quad C1 No spatial controls & 29.0 & 38.9 & 0.469 & 0.242 & 0 \\
	21	+\quad C2 Municipality FE & \textbf{23.3} & 32.3 & 0.402 & 0.442 & 1 \\
	22	+\quad C3 Grid-cell FE ($\sim$5.5 km) & 24.3 & 33.0 & 0.409 & 0.423 & 1 \\
	23	+\quad C4 Grid-cell FE ($\sim$1.1 km) & 25.3 & 35.5 & 0.429 & 0.364 & 1 \\
24	24	\midrule
25	25	\multicolumn{6}{l}{\itshape D. Estimation method}\\
26		−\quad D1 OLS (muni + month FE) & 20.3 & 32.5 & 0.390 & 0.476 & 1 \\
27		−\quad D2 Ridge (cross-validated) & \textbf{19.5} & 30.6 & 0.375 & 0.515 & 9 \\
28		−\quad D3 Random forest & 21.3 & 29.8 & 0.373 & 0.519 & 7 \\
29		−\quad D4 Gradient boosting & 21.2 & 29.7 & 0.372 & 0.521 & 42 \\
30		−\quad D5 Gradient boosting, no coordinates & 26.2 & 35.7 & 0.447 & 0.310 & 21 \\
	26	+\quad D1 OLS (muni + month FE) & 22.9 & 32.4 & 0.401 & 0.445 & 1 \\
	27	+\quad D2 Ridge (cross-validated) & 22.3 & 31.1 & 0.388 & 0.480 & 8 \\
	28	+\quad D3 Random forest & 21.3 & 29.8 & 0.373 & 0.519 & 11 \\
	29	+\quad D4 Gradient boosting & \textbf{21.2} & 29.7 & 0.372 & 0.521 & 41 \\
	30	+\quad D5 Gradient boosting, no coordinates & 26.2 & 35.7 & 0.447 & 0.310 & 22 \\
31	31	\quad D6 Spatial k-NN comparables & 25.6 & 34.2 & 0.465 & 0.253 & 0 \\
32	32	\bottomrule
33	33	\end{tabular}
		\ No newline at end of file

added results/tables/inference.tex +32 −0

		`@@ -0,0 +1,32 @@`
	1	+\begin{tabular}{l ccc c ccc}
	2	+\toprule
	3	+ & \multicolumn{3}{c}{Random holdout} & & \multicolumn{3}{c}{Forward-in-time holdout} \\
	4	+\cmidrule{2-4}\cmidrule{6-8}
	5	+Model & MdAPE [95\% CI] & $\Delta$ vs.\ A6 [95\% CI] & $t_{\mathrm{DM}}$ & & MdAPE [95\% CI] & $\Delta$ vs.\ A6 [95\% CI] & $t_{\mathrm{DM}}$ \\
	6	+\midrule
	7	+\multicolumn{8}{l}{\itshape A. Functional form}\\
	8	+\quad A1 Linear & 18.2 [16.9, 19.6] & +0.6 [+0.1, +1.1] & 12.3$^{*}$ & & 20.4 [19.1, 21.7] & -1.4 [-2.3, -0.4] & 6.3$^{*}$ \\
	9	+\quad A2 Semi-log & 19.0 [17.9, 20.2] & +1.4 [+1.1, +1.8] & 10.2$^{*}$ & & 23.2 [21.7, 24.7] & +1.4 [+0.8, +2.3] & 7.8$^{*}$ \\
	10	+\quad A3 Log-log & 18.0 [17.1, 19.0] & +0.4 [+0.3, +0.5] & 4.6$^{**}$ & & 21.8 [20.5, 23.2] & +0.0 [-0.0, +0.2] & 1.8$^{}$ \\
	11	+\quad A4 Box--Cox & 18.6 [17.5, 19.7] & +0.9 [+0.7, +1.3] & 10.7$^{*}$ & & 21.0 [19.7, 22.2] & -0.8 [-1.4, -0.1] & 4.3$^{*}$ \\
	12	+\quad A5 Quadratics & 19.2 [18.2, 20.2] & +1.5 [+1.1, +2.1] & 5.5$^{*}$ & & 23.3 [21.9, 24.9] & +1.6 [+1.1, +2.2] & 6.1$^{*}$ \\
	13	+\quad A6 Splines & 17.6 [16.7, 18.6] & --- & --- & & 21.7 [20.5, 23.1] & --- & --- \\
	14	+\multicolumn{8}{l}{\itshape B. Time effects}\\
	15	+\quad B1 No time FE & 22.0 [21.1, 23.3] & +4.4 [+3.4, +5.6] & 8.2$^{*}$ & & 29.3 [27.3, 31.5] & +7.6 [+6.0, +9.0] & 5.3$^{*}$ \\
	16	+\quad B2 Year FE & 19.1 [18.1, 20.2] & +1.5 [+1.1, +2.2] & 6.1$^{*}$ & & 23.7 [22.2, 25.3] & +1.9 [+1.3, +2.8] & 6.2$^{*}$ \\
	17	+\quad B3 Quarter FE & 19.2 [18.2, 20.2] & +1.5 [+1.1, +2.1] & 5.5$^{*}$ & & 23.3 [21.9, 24.9] & +1.6 [+1.1, +2.2] & 6.1$^{*}$ \\
	18	+\quad B4 Month FE & 19.3 [18.4, 20.4] & +1.7 [+1.2, +2.5] & 5.7$^{*}$ & & 22.9 [21.5, 24.4] & +1.1 [+0.7, +1.8] & 6.0$^{*}$ \\
	19	+\multicolumn{8}{l}{\itshape C. Spatial controls}\\
	20	+\quad C1 No spatial FE & 28.8 [27.3, 30.1] & +11.2 [+10.1, +12.3] & 7.7$^{*}$ & & 29.0 [27.4, 30.3] & +7.3 [+5.0, +9.2] & 11.1$^{*}$ \\
	21	+\quad C2 Municipality FE & 19.2 [18.2, 20.2] & +1.5 [+1.1, +2.1] & 5.5$^{*}$ & & 23.3 [21.9, 24.9] & +1.6 [+1.1, +2.2] & 6.1$^{*}$ \\
	22	+\quad C3 Grid 5.5 km & 18.7 [17.8, 20.0] & +1.1 [+0.2, +2.3] & 2.5$^{}$ & & 24.3 [22.5, 26.4] & +2.5 [+1.6, +3.5] & 4.5$^{*}$ \\
	23	+\quad C4 Grid 1.1 km & 21.0 [20.1, 21.9] & +3.3 [+2.9, +3.8] & 6.8$^{*}$ & & 25.3 [24.3, 26.3] & +3.6 [+2.1, +4.9] & 12.4$^{*}$ \\
	24	+\multicolumn{8}{l}{\itshape D. Estimation method}\\
	25	+\quad D1 OLS & 19.3 [18.4, 20.4] & +1.7 [+1.2, +2.5] & 5.7$^{*}$ & & 22.9 [21.5, 24.4] & +1.1 [+0.7, +1.8] & 6.0$^{*}$ \\
	26	+\quad D2 Ridge & 17.7 [16.8, 18.7] & +0.1 [-0.0, +0.2] & 2.6$^{*}$ & & 22.3 [21.0, 23.7] & +0.5 [+0.5, +0.6] & 6.6$^{*}$ \\
	27	+\quad D3 Random forest & 14.6 [13.7, 16.2] & -3.0 [-4.6, -1.5] & -2.9$^{***}$ & & 21.3 [19.9, 23.0] & -0.4 [-1.5, +0.6] & -1.6 \\
	28	+\quad D4 Boosting & 14.4 [13.7, 15.7] & -3.2 [-4.7, -1.9] & -3.6$^{***}$ & & 21.2 [19.7, 22.9] & -0.5 [-1.7, +0.6] & -1.6 \\
	29	+\quad D5 Boosting, no coord. & 23.2 [22.1, 25.1] & +5.6 [+3.9, +7.5] & 4.5$^{*}$ & & 26.2 [25.2, 27.5] & +4.5 [+2.9, +6.2] & 5.9$^{*}$ \\
	30	+\quad D6 $k$-NN comparables & 21.2 [19.4, 23.5] & +3.6 [+1.0, +5.9] & 4.8$^{*}$ & & 25.6 [23.1, 28.3] & +3.9 [+1.8, +5.6] & 4.0$^{*}$ \\
	31	+\bottomrule
	32	+\end{tabular}
		\ No newline at end of file

added results/tables/leakage.tex +21 −0

		`@@ -0,0 +1,21 @@`
	1	+\begin{tabular}{l cc c cc}
	2	+\toprule
	3	+ & \multicolumn{2}{c}{Same parcel in training} & & \multicolumn{2}{c}{Same coordinates in training} \\
	4	+\cmidrule{2-3}\cmidrule{5-6}
	5	+Model & Yes & No & & Yes & No \\
	6	+\midrule
	7	+\multicolumn{6}{l}{\itshape All test sales}\\
	8	+\quad A5 Quadratics & 19.8 & 19.1 & & 19.2 & 19.2 \\
	9	+\quad A6 Splines & 18.3 & 17.5 & & 17.8 & 17.6 \\
	10	+\quad D3 Random forest & 14.6 & 14.6 & & 11.7 & 15.7 \\
	11	+\quad D4 Boosting & 14.5 & 14.4 & & 12.0 & 15.3 \\
	12	+\quad D5 Boosting, no coord. & 22.9 & 23.3 & & 20.0 & 24.5 \\
	13	+\quad D6 $k$-NN comparables & 22.2 & 21.0 & & 16.7 & 22.9 \\
	14	+\quad Test sales & 17,219 & 85,710 & & 27,475 & 75,454 \\
	15	+\midrule
	16	+\multicolumn{6}{l}{\itshape Condominiums only}\\
	17	+\quad A5 Quadratics & 17.4 & 18.4 & & 18.0 & 20.3 \\
	18	+\quad D4 Boosting & 9.0 & 9.1 & & 8.9 & 10.2 \\
	19	+\quad Test sales & 3,374 & 11,474 & & 13,261 & 1,587 \\
	20	+\bottomrule
	21	+\end{tabular}
		\ No newline at end of file

modified results/tables/learning.tex +6 −6

		`@@ -2,11 +2,11 @@`
2	2	\toprule
3	3	Training sales & Gradient boosting & OLS quadratic (muni+quarter FE) \\
4	4	\midrule
5		−10,000 & 17.6 & 18.4 \\
6		−25,000 & 16.1 & 18.1 \\
7		−50,000 & 15.5 & 17.9 \\
8		−100,000 & 15.2 & 17.9 \\
9		−200,000 & 14.8 & 17.9 \\
10		−400,000 & 14.5 & 18.1 \\
	5	+10,000 & 17.6 & 19.1 \\
	6	+25,000 & 16.1 & 19.1 \\
	7	+50,000 & 15.5 & 18.8 \\
	8	+100,000 & 15.2 & 18.8 \\
	9	+200,000 & 14.8 & 19.0 \\
	10	+400,000 & 14.5 & 19.2 \\
11	11	\bottomrule
12	12	\end{tabular}
		\ No newline at end of file

added results/tables/nested_fe.tex +13 −0

		`@@ -0,0 +1,13 @@`
	1	+\begin{tabular}{l cc c cc}
	2	+\toprule
	3	+ & \multicolumn{2}{c}{Random holdout} & & \multicolumn{2}{c}{Forward-in-time} \\
	4	+\cmidrule{2-3}\cmidrule{5-6}
	5	+Spatial controls & MdAPE (\%) & $R^2_{\ln}$ & & MdAPE (\%) & $R^2_{\ln}$ \\
	6	+\midrule
	7	+C2 Municipality FE (1,115 cells) & 19.2 & 0.546 & & 23.3 & 0.442 \\
	8	+C3 Grid 5.5 km (5,255 cells) & 18.7 & 0.557 & & 24.3 & 0.423 \\
	9	+C4 Grid 1.1 km (30,548 cells) & 21.0 & 0.496 & & 25.3 & 0.364 \\
	10	+C3$'$ Municipality + grid 5.5 km & 17.7 & 0.582 & & 21.5 & 0.481 \\
	11	+C4$'$ Municipality + grid 1.1 km & 17.3 & 0.589 & & 21.6 & 0.486 \\
	12	+\bottomrule
	13	+\end{tabular}
		\ No newline at end of file

added results/tables/pairs.tex +21 −0

		`@@ -0,0 +1,21 @@`
	1	+\begin{tabular}{ll c cc c cc}
	2	+\toprule
	3	+ & & & \multicolumn{2}{c}{Random holdout} & & \multicolumn{2}{c}{Forward-in-time} \\
	4	+\cmidrule{4-5}\cmidrule{7-8}
	5	+Comparison & & MdAPE & $\Delta$MdAPE [95\% CI] & $t_{\mathrm{DM}}$ APE / sq.\ log & & $\Delta$MdAPE [95\% CI] & $t_{\mathrm{DM}}$ APE / sq.\ log \\
	6	+\midrule
	7	+A2 Semi-log vs. & A1 Linear & 19.0 / 18.2 & +0.79 [+0.42, +1.22] & -10.7$^{*}$ / -4.2$^{}$ & & +2.79 [+1.78, +3.88] & 0.1 / 3.5$^{**}$ \\
	8	+A6 Splines vs. & A2 Semi-log & 17.6 / 19.0 & -1.41 [-1.83, -1.09] & -10.2$^{*}$ / -8.9$^{}$ & & -1.43 [-2.30, -0.77] & -7.8$^{}$ / -7.2$^{*}$ \\
	9	+A4 Box--Cox vs. & A2 Semi-log & 18.6 / 19.0 & -0.47 [-0.59, -0.35] & 9.0$^{*}$ / -0.7 & & -2.20 [-3.15, -1.46] & -5.3$^{}$ / -7.0$^{**}$ \\
	10	+A3 Log-log vs. & A2 Semi-log & 18.0 / 19.0 & -1.03 [-1.45, -0.72] & -7.9$^{*}$ / -10.1$^{}$ & & -1.39 [-2.24, -0.74] & -7.1$^{}$ / -6.3$^{*}$ \\
	11	+B2 Year FE vs. & B1 No time FE & 19.1 / 22.0 & -2.91 [-3.84, -2.06] & -8.1$^{*}$ / -7.4$^{}$ & & -5.65 [-6.51, -4.52] & -3.8$^{}$ / -10.4$^{*}$ \\
	12	+B4 Month FE vs. & B3 Quarter FE & 19.3 / 19.2 & +0.18 [+0.01, +0.37] & 2.9$^{*}$ / 2.9$^{*}$ & & -0.43 [-0.95, +0.05] & 0.7 / -0.9 \\
	13	+C3 Grid 5.5 km vs. & C2 Municipality FE & 18.7 / 19.2 & -0.45 [-1.07, +0.37] & -1.1 / -1.2 & & +0.96 [+0.16, +1.81] & 2.3$^{**}$ / 1.6 \\
	14	+C4 Grid 1.1 km vs. & C2 Municipality FE & 21.0 / 19.2 & +1.81 [+1.24, +2.32] & 7.1$^{*}$ / 7.3$^{}$ & & +2.02 [+0.15, +3.59] & 8.1$^{}$ / 4.8$^{*}$ \\
	15	+D2 Ridge vs. & D1 OLS & 17.7 / 19.3 & -1.66 [-2.37, -1.13] & -5.5$^{*}$ / -6.0$^{}$ & & -0.61 [-1.26, -0.17] & -5.6$^{}$ / -4.7$^{*}$ \\
	16	+D4 Boosting vs. & D3 Random forest & 14.4 / 14.6 & -0.24 [-0.46, -0.05] & -4.7$^{*}$ / -6.7$^{*}$ & & -0.13 [-0.37, +0.15] & -1.0 / -1.3 \\
	17	+D4 Boosting vs. & D5 Boosting, no coord. & 14.4 / 23.2 & -8.84 [-9.79, -8.11] & -10.6$^{*}$ / -16.1$^{}$ & & -4.99 [-6.50, -3.12] & -13.9$^{}$ / -11.1$^{*}$ \\
	18	+D4 Boosting vs. & A1 Linear & 14.4 / 18.2 & -3.86 [-5.57, -2.38] & -10.4$^{*}$ / -11.9$^{}$ & & +0.84 [-1.19, +2.59] & -3.5$^{}$ / -3.9$^{*}$ \\
	19	+A6 Splines vs. & A1 Linear & 17.6 / 18.2 & -0.63 [-1.13, -0.13] & -12.3$^{*}$ / -7.5$^{}$ & & +1.35 [+0.43, +2.28] & -6.3$^{}$ / -6.2$^{*}$ \\
	20	+\bottomrule
	21	+\end{tabular}
		\ No newline at end of file

added results/tables/retransformation.tex +18 −0

		`@@ -0,0 +1,18 @@`
	1	+\begin{tabular}{l c cc cc c cc cc}
	2	+\toprule
	3	+ & & \multicolumn{4}{c}{Random holdout} & & \multicolumn{4}{c}{Forward-in-time holdout} \\
	4	+\cmidrule{3-6}\cmidrule{8-11}
	5	+ & & \multicolumn{2}{c}{MdAPE (\%)} & \multicolumn{2}{c}{$R^2_{\ln}$} & & \multicolumn{2}{c}{MdAPE (\%)} & \multicolumn{2}{c}{$R^2_{\ln}$} \\
	6	+\cmidrule{3-4}\cmidrule{5-6}\cmidrule{8-9}\cmidrule{10-11}
	7	+Model & $\hat{s}$ & Median & Mean & Median & Mean & & Median & Mean & Median & Mean \\
	8	+\midrule
	9	+A2 Semi-log & 1.070 & 19.0 & 18.2 & 0.546 & 0.533 & & 23.2 & 20.6 & 0.426 & 0.458 \\
	10	+A3 Log-log & 1.064 & 18.0 & 17.0 & 0.580 & 0.569 & & 21.8 & 19.2 & 0.481 & 0.513 \\
	11	+A4 Box--Cox & --- & 18.6 & 17.9 & 0.548 & 0.536 & & 21.0 & 19.6 & 0.476 & 0.490 \\
	12	+A5 Quadratics & 1.070 & 19.2 & 18.1 & 0.546 & 0.533 & & 23.3 & 20.5 & 0.442 & 0.479 \\
	13	+A6 Splines & 1.062 & 17.6 & 16.5 & 0.590 & 0.579 & & 21.7 & 19.1 & 0.491 & 0.522 \\
	14	+D2 Ridge & 1.063 & 17.7 & 16.7 & 0.587 & 0.577 & & 22.3 & 19.5 & 0.480 & 0.515 \\
	15	+D3 Random forest & 1.032 & 14.6 & 13.7 & 0.631 & 0.629 & & 21.3 & 19.4 & 0.519 & 0.544 \\
	16	+D4 Boosting & 1.048 & 14.4 & 13.1 & 0.642 & 0.636 & & 21.2 & 18.4 & 0.521 & 0.556 \\
	17	+\bottomrule
	18	+\end{tabular}
		\ No newline at end of file

added results/tables/same_period.tex +21 −0

		`@@ -0,0 +1,21 @@`
	1	+\begin{tabular}{l cc c c c c}
	2	+\toprule
	3	+ & \multicolumn{2}{c}{Random split} & Forward split & Staleness & Level error & Re-levelled \\
	4	+\cmidrule{2-3}\cmidrule{4-4}
	5	+Model & All test sales & 2025--26 sales & 2025--26 sales & cost & $\hat{b}$ & MdAPE \\
	6	+\midrule
	7	+A1 Linear & 18.2 & 17.1 & 20.4 & +3.3 & +0.102 & 18.0 \\
	8	+A5 Quadratics & 19.2 & 18.5 & 23.3 & +4.8 & +0.171 & 18.3 \\
	9	+A6 Splines & 17.6 & 17.0 & 21.7 & +4.7 & +0.161 & 16.8 \\
	10	+B4 Month FE & 19.3 & 18.9 & 22.9 & +4.0 & +0.157 & 18.7 \\
	11	+C3 Grid 5.5 km & 18.7 & 18.3 & 24.3 & +6.0 & +0.182 & 18.8 \\
	12	+C4 Grid 1.1 km & 21.0 & 19.8 & 25.3 & +5.5 & +0.171 & 20.5 \\
	13	+D2 Ridge & 17.7 & 17.1 & 22.3 & +5.2 & +0.170 & 17.0 \\
	14	+D3 Random forest & 14.6 & 13.9 & 21.3 & +7.5 & +0.184 & 13.9 \\
	15	+D4 Boosting & 14.4 & 13.7 & 21.2 & +7.5 & +0.183 & 13.9 \\
	16	+D5 Boosting, no coord. & 23.2 & 21.0 & 26.2 & +5.2 & +0.188 & 21.3 \\
	17	+D6 $k$-NN comparables & 21.2 & 22.6 & 25.6 & +3.1 & +0.221 & 19.2 \\
	18	+\midrule
	19	+Test sales & 102,929 & 31,465 & 158,388 & & & \\
	20	+\bottomrule
	21	+\end{tabular}
		\ No newline at end of file

modified results/tables/segments.tex +7 −7

		`@@ -2,12 +2,12 @@`
2	2	\toprule
3	3	Segment & $n$ (test) & OLS quadratic & Gradient boosting \\
4	4	\midrule
5		−Condo & 14,848 & 20.4 & 9.1 \\
6		−Cottage & 2,109 & 33.9 & 32.1 \\
7		−Plex & 15,115 & 18.5 & 16.5 \\
8		−Single family & 69,835 & 17.2 & 15.1 \\
9		−Muni 1k--10k sales & 37,419 & 15.2 & 14.5 \\
10		−Muni $<$ 1k sales & 29,253 & 23.3 & 18.7 \\
11		−Muni $>$ 10k sales & 36,257 & 17.8 & 11.9 \\
	5	+Condo & 14,848 & 18.2 & 9.1 \\
	6	+Cottage & 2,109 & 34.3 & 32.1 \\
	7	+Plex & 15,115 & 20.2 & 16.5 \\
	8	+Single family & 69,835 & 18.8 & 15.1 \\
	9	+Muni 1k--10k sales & 37,419 & 16.8 & 14.5 \\
	10	+Muni $<$ 1k sales & 29,253 & 24.8 & 18.7 \\
	11	+Muni $>$ 10k sales & 36,257 & 17.7 & 11.9 \\
12	12	\bottomrule
13	13	\end{tabular}
		\ No newline at end of file

modified scripts/02_horserace.py +7 −2

		`@@ -7,7 +7,9 @@ Fits the twenty registry models under (i) a random 80/20 holdout and`
7	7	Box–Cox profile likelihood and summary statistics.
8	8
9	9	Writes: horserace_random.csv, horserace_temporal.csv, boxcox.csv,
10		−summary_stats.csv, sample_counts.csv
	10	+summary_stats.csv, sample_counts.csv, and the test-set predictions of
	11	+every model (data/processed/predictions_<scheme>.parquet, not committed)
	12	+used by scripts/06_robustness.py for the inference and leakage analyses.
11	13
12	14	Usage: python scripts/02_horserace.py
13	15	"""
		`@@ -56,8 +58,11 @@ def main() -> None:`
56	58
57	59	# ------------------------------------------------------------ the race
58	60	for scheme in ("random", "temporal"):
59		− res = models.run_horserace(df, scheme)
	61	+ res, preds = models.run_horserace(df, scheme,
	62	+ return_predictions=True)
60	63	res.to_csv(out / f"horserace_{scheme}.csv", index=False)
	64	+ preds.to_parquet(config.PROCESSED / f"predictions_{scheme}.parquet",
	65	+ index=False)
61	66
62	67
63	68	if __name__ == "__main__":

modified scripts/04_make_figures.py +33 −0

		`@@ -186,6 +186,38 @@ def fig_segments():`
186	186	_save(fig, "fig_segments.png")
187	187
188	188
	189	+# ---------------------------------------------------------------- fig 10
	190	+def fig_horizon():
	191	+ """Forward-in-time MdAPE by test quarter (distance from the last
	192	+ training month), selected models."""
	193	+ f = RES / "by_quarter.csv"
	194	+ if not f.exists():
	195	+ return
	196	+ q = pd.read_csv(f)
	197	+ fig, ax = plt.subplots(figsize=(0.8 * TEXTWIDTH, 3.2))
	198	+ series = (("A6 Semi-log + splines", BLUE, "o", "-", "A6 Splines"),
	199	+ ("A5 Semi-log + quadratics", BLUES[2], "o", (0, (5, 2)),
	200	+ "A5 Quadratics"),
	201	+ ("D2 Ridge (cross-validated)", BLUES[5], "^", (0, (1, 1.2)),
	202	+ "D2 Ridge"),
	203	+ ("D4 Gradient boosting", RED, "s", "-", "D4 Boosting"),
	204	+ ("D3 Random forest", "#e08a8a", "s", (0, (5, 2)),
	205	+ "D3 Random forest"))
	206	+ for m, color, mk, ls, label in series:
	207	+ g = q[q["model"] == m].sort_values("quarter")
	208	+ ax.plot(range(len(g)), g["mdape"], marker=mk, ms=4, color=color,
	209	+ ls=ls, lw=1.1, mfc="white" if mk == "s" else color,
	210	+ label=label)
	211	+ g = q[q["model"] == series[0][0]].sort_values("quarter")
	212	+ ax.set_xticks(range(len(g)))
	213	+ ax.set_xticklabels(g["quarter"], fontsize=8, rotation=0)
	214	+ ax.set_xlabel("Test quarter (training ends December 2024)")
	215	+ ax.set_ylabel("Median absolute error (%)")
	216	+ ax.legend(fontsize=7.5, ncol=2, loc="upper left")
	217	+ ygrid(ax)
	218	+ _save(fig, "fig_horizon.png")
	219	+
	220	+
189	221	def main() -> None:
190	222	config.ensure_dirs()
191	223	apply_style()
		`@@ -195,6 +227,7 @@ def main() -> None:`
195	227	fig_profiles()
196	228	fig_learning()
197	229	fig_segments()
	230	+ fig_horizon()
198	231	made = sorted(p.name for p in OUT.glob("fig_*.png"))
199	232	print(f"{len(made)} figures written:", ", ".join(made))
200	233

modified scripts/05_make_tables.py +306 −0

		`@@ -133,6 +133,305 @@ def t_segments():`
133	133	(TAB / "segments.tex").write_text("\n".join(lines))
134	134
135	135
	136	+# ---------------------------------------------------------------- revision 1.1
	137	+SHORT = {"A1 Linear (levels)": "A1 Linear", "A2 Semi-log": "A2 Semi-log",
	138	+ "A3 Log-log": "A3 Log-log", "A4 Box-Cox": "A4 Box--Cox",
	139	+ "A5 Semi-log + quadratics": "A5 Quadratics",
	140	+ "A6 Semi-log + splines": "A6 Splines",
	141	+ "B1 No time effects": "B1 No time FE", "B2 Year FE": "B2 Year FE",
	142	+ "B3 Quarter FE": "B3 Quarter FE", "B4 Month FE": "B4 Month FE",
	143	+ "C1 No spatial controls": "C1 No spatial FE",
	144	+ "C2 Municipality FE": "C2 Municipality FE",
	145	+ "C3 Grid-cell FE (~5.5 km)": "C3 Grid 5.5 km",
	146	+ "C4 Grid-cell FE (~1.1 km)": "C4 Grid 1.1 km",
	147	+ "D1 OLS (muni + month FE)": "D1 OLS", "D2 Ridge (cross-validated)":
	148	+ "D2 Ridge", "D3 Random forest": "D3 Random forest",
	149	+ "D4 Gradient boosting": "D4 Boosting",
	150	+ "D5 Gradient boosting, no coordinates": "D5 Boosting, no coord.",
	151	+ "D6 Spatial k-NN comparables": "D6 $k$-NN comparables"}
	152	+A6, D4 = "A6 Semi-log + splines", "D4 Gradient boosting"
	153	+
	154	+
	155	+def _stars(p):
	156	+ return "$^{*}$" if p < 0.01 else "$^{}$" if p < 0.05 else \
	157	+ "$^{*}$" if p < 0.10 else ""
	158	+
	159	+
	160	+def t_inference():
	161	+ """MdAPE with cluster-bootstrap 95% CI, difference versus the spline
	162	+ hedonic (A6) with its CI, and the clustered DM t statistic on the APE
	163	+ loss differential, under both holdouts."""
	164	+ lines = [r"\begin{tabular}{l ccc c ccc}", r"\toprule",
	165	+ r" & \multicolumn{3}{c}{Random holdout} & &"
	166	+ r" \multicolumn{3}{c}{Forward-in-time holdout} \\",
	167	+ r"\cmidrule{2-4}\cmidrule{6-8}",
	168	+ r"Model & MdAPE [95\% CI] & $\Delta$ vs.\ A6 [95\% CI] & "
	169	+ r"$t_{\mathrm{DM}}$ & & MdAPE [95\% CI] & "
	170	+ r"$\Delta$ vs.\ A6 [95\% CI] & $t_{\mathrm{DM}}$ \\",
	171	+ r"\midrule"]
	172	+ R = {s: pd.read_csv(RES / f"inference_{s}.csv").set_index("model")
	173	+ for s in ("random", "temporal")}
	174	+ groups = {"A": "A. Functional form", "B": "B. Time effects",
	175	+ "C": "C. Spatial controls", "D": "D. Estimation method"}
	176	+ cur = None
	177	+ for m in SHORT:
	178	+ if m[0] != cur:
	179	+ cur = m[0]
	180	+ lines.append(r"\multicolumn{8}{l}{\itshape " + groups[cur]
	181	+ + r"}\\")
	182	+ cells = [r"\quad " + SHORT[m]]
	183	+ for s in ("random", "temporal"):
	184	+ x = R[s].loc[m]
	185	+ cells.append(f"{x['mdape']:.1f} [{x['ci_lo']:.1f}, "
	186	+ f"{x['ci_hi']:.1f}]")
	187	+ if m == A6:
	188	+ cells += ["---", "---"]
	189	+ else:
	190	+ cells.append(f"{x['diff_vs_ref']:+.1f} [{x['diff_lo']:+.1f}, "
	191	+ f"{x['diff_hi']:+.1f}]")
	192	+ cells.append(f"{x['dm_ape_vs_a6_t']:.1f}"
	193	+ + _stars(x['dm_ape_vs_a6_p']))
	194	+ if s == "random":
	195	+ cells.append("")
	196	+ lines.append(" & ".join(cells) + r" \\")
	197	+ lines += [r"\bottomrule", r"\end{tabular}"]
	198	+ (TAB / "inference.tex").write_text("\n".join(lines))
	199	+
	200	+
	201	+def t_retransformation():
	202	+ """Median-consistent versus Duan-smeared (mean-consistent) predictions."""
	203	+ sel = ["A2 Semi-log", "A3 Log-log", "A4 Box-Cox",
	204	+ "A5 Semi-log + quadratics", "A6 Semi-log + splines",
	205	+ "D2 Ridge (cross-validated)", "D3 Random forest",
	206	+ "D4 Gradient boosting"]
	207	+ R = {s: pd.read_csv(RES / f"horserace_{s}.csv").set_index("name")
	208	+ for s in ("random", "temporal")}
	209	+ lines = [r"\begin{tabular}{l c cc cc c cc cc}", r"\toprule",
	210	+ r" & & \multicolumn{4}{c}{Random holdout} & &"
	211	+ r" \multicolumn{4}{c}{Forward-in-time holdout} \\",
	212	+ r"\cmidrule{3-6}\cmidrule{8-11}",
	213	+ r" & & \multicolumn{2}{c}{MdAPE (\%)} & "
	214	+ r"\multicolumn{2}{c}{$R^2_{\ln}$} & & "
	215	+ r"\multicolumn{2}{c}{MdAPE (\%)} & "
	216	+ r"\multicolumn{2}{c}{$R^2_{\ln}$} \\",
	217	+ r"\cmidrule{3-4}\cmidrule{5-6}\cmidrule{8-9}\cmidrule{10-11}",
	218	+ r"Model & $\hat{s}$ & Median & Mean & Median & Mean & & "
	219	+ r"Median & Mean & Median & Mean \\", r"\midrule"]
	220	+ for m in sel:
	221	+ a, b = R["random"].loc[m], R["temporal"].loc[m]
	222	+ sm = "---" if pd.isna(a["smear"]) else f"{a['smear']:.3f}"
	223	+ lines.append(
	224	+ f"{SHORT[m]} & {sm} & {a['mdape']:.1f} & {a['mdape_mean']:.1f} & "
	225	+ f"{a['r2_ln']:.3f} & {a['r2_ln_mean']:.3f} & & "
	226	+ f"{b['mdape']:.1f} & {b['mdape_mean']:.1f} & "
	227	+ f"{b['r2_ln']:.3f} & {b['r2_ln_mean']:.3f} \\\\")
	228	+ lines += [r"\bottomrule", r"\end{tabular}"]
	229	+ (TAB / "retransformation.tex").write_text("\n".join(lines))
	230	+
	231	+
	232	+def t_same_period():
	233	+ sp = pd.read_csv(RES / "same_period.csv").set_index("model")
	234	+ rl = pd.read_csv(RES / "relevel.csv")
	235	+ rl = rl[rl["scheme"] == "temporal"].set_index("model")
	236	+ sel = ["A1 Linear (levels)", "A5 Semi-log + quadratics",
	237	+ "A6 Semi-log + splines", "B4 Month FE",
	238	+ "C3 Grid-cell FE (~5.5 km)", "C4 Grid-cell FE (~1.1 km)",
	239	+ "D2 Ridge (cross-validated)", "D3 Random forest",
	240	+ "D4 Gradient boosting", "D5 Gradient boosting, no coordinates",
	241	+ "D6 Spatial k-NN comparables"]
	242	+ lines = [r"\begin{tabular}{l cc c c c c}", r"\toprule",
	243	+ r" & \multicolumn{2}{c}{Random split} & Forward split & "
	244	+ r"Staleness & Level error & Re-levelled \\",
	245	+ r"\cmidrule{2-3}\cmidrule{4-4}",
	246	+ r"Model & All test sales & 2025--26 sales & 2025--26 sales & "
	247	+ r"cost & $\hat{b}$ & MdAPE \\", r"\midrule"]
	248	+ for m in sel:
	249	+ x = sp.loc[m]
	250	+ lines.append(f"{SHORT[m]} & {x['mdape_random_all']:.1f} & "
	251	+ f"{x['mdape_random_2025_26']:.1f} & "
	252	+ f"{x['mdape_forward_2025_26']:.1f} & "
	253	+ f"{x['mdape_forward_2025_26'] - x['mdape_random_2025_26']:+.1f} & "
	254	+ f"{rl.loc[m, 'median_log_resid']:+.3f} & "
	255	+ f"{rl.loc[m, 'mdape_relevelled']:.1f} \\\\")
	256	+ n1, n2 = int(sp["n_random_2025_26"].iloc[0]), int(sp["n_forward"].iloc[0])
	257	+ lines += [r"\midrule", f"Test sales & 102,929 & {n1:,} & {n2:,} & & & \\\\",
	258	+ r"\bottomrule", r"\end{tabular}"]
	259	+ (TAB / "same_period.tex").write_text("\n".join(lines))
	260	+
	261	+
	262	+def t_pairs():
	263	+ pr = pd.read_csv(RES / "pairs.csv")
	264	+ lines = [r"\begin{tabular}{ll c cc c cc}", r"\toprule",
	265	+ r" & & & \multicolumn{2}{c}{Random holdout} & &"
	266	+ r" \multicolumn{2}{c}{Forward-in-time} \\",
	267	+ r"\cmidrule{4-5}\cmidrule{7-8}",
	268	+ r"Comparison & & MdAPE & $\Delta$MdAPE [95\% CI] & "
	269	+ r"$t_{\mathrm{DM}}$ APE / sq.\ log & & "
	270	+ r"$\Delta$MdAPE [95\% CI] & $t_{\mathrm{DM}}$ APE / sq.\ log \\",
	271	+ r"\midrule"]
	272	+ pairs = list(dict.fromkeys(zip(pr["model_a"], pr["model_b"])))
	273	+ for a, b in pairs:
	274	+ r = pr[(pr["model_a"] == a) & (pr["model_b"] == b)].set_index("scheme")
	275	+ x, y = r.loc["random"], r.loc["temporal"]
	276	+ cells = [SHORT[a] + " vs.", SHORT[b],
	277	+ f"{x['mdape_a']:.1f} / {x['mdape_b']:.1f}",
	278	+ f"{x['diff']:+.2f} [{x['diff_lo']:+.2f}, {x['diff_hi']:+.2f}]",
	279	+ f"{x['dm_ape_t']:.1f}{_stars(x['dm_ape_p'])} / "
	280	+ f"{x['dm_sqlog_t']:.1f}{_stars(x['dm_sqlog_p'])}", "",
	281	+ f"{y['diff']:+.2f} [{y['diff_lo']:+.2f}, {y['diff_hi']:+.2f}]",
	282	+ f"{y['dm_ape_t']:.1f}{_stars(y['dm_ape_p'])} / "
	283	+ f"{y['dm_sqlog_t']:.1f}{_stars(y['dm_sqlog_p'])}"]
	284	+ lines.append(" & ".join(cells) + r" \\")
	285	+ lines += [r"\bottomrule", r"\end{tabular}"]
	286	+ (TAB / "pairs.tex").write_text("\n".join(lines))
	287	+
	288	+
	289	+def t_group_splits():
	290	+ R = {s: pd.read_csv(RES / f"horserace_{s}.csv").set_index("name")
	291	+ for s in ("random", "group_parcel", "group_coord")}
	292	+ lines = [r"\begin{tabular}{l cc c cc c cc}", r"\toprule",
	293	+ r" & \multicolumn{2}{c}{Random 80/20} & &"
	294	+ r" \multicolumn{2}{c}{Parcel-grouped} & &"
	295	+ r" \multicolumn{2}{c}{Building-grouped} \\",
	296	+ r"\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}",
	297	+ r"Model & MdAPE & $R^2_{\ln}$ & & MdAPE & $R^2_{\ln}$ & & "
	298	+ r"MdAPE & $R^2_{\ln}$ \\", r"\midrule"]
	299	+ groups = {"A": "A. Functional form", "B": "B. Time effects",
	300	+ "C": "C. Spatial controls", "D": "D. Estimation method"}
	301	+ cur = None
	302	+ for m in SHORT:
	303	+ if m[0] != cur:
	304	+ cur = m[0]
	305	+ lines.append(r"\multicolumn{9}{l}{\itshape " + groups[cur]
	306	+ + r"}\\")
	307	+ cells = [r"\quad " + SHORT[m]]
	308	+ for i, s in enumerate(("random", "group_parcel", "group_coord")):
	309	+ x = R[s].loc[m]
	310	+ cells += [f"{x['mdape']:.1f}", f"{x['r2_ln']:.3f}"]
	311	+ if i < 2:
	312	+ cells.append("")
	313	+ lines.append(" & ".join(cells) + r" \\")
	314	+ ns = [f"{int(R[s]['n_test'].iloc[0]):,}" for s in
	315	+ ("random", "group_parcel", "group_coord")]
	316	+ lines += [r"\midrule",
	317	+ f"Test sales & {ns[0]} & & & {ns[1]} & & & {ns[2]} & \\\\",
	318	+ r"\bottomrule", r"\end{tabular}"]
	319	+ (TAB / "group_splits.tex").write_text("\n".join(lines))
	320	+
	321	+
	322	+def t_leakage_decomp():
	323	+ L = pd.read_csv(RES / "leakage.csv")
	324	+ sel = ["A5 Semi-log + quadratics", "A6 Semi-log + splines",
	325	+ "D3 Random forest", "D4 Gradient boosting",
	326	+ "D5 Gradient boosting, no coordinates",
	327	+ "D6 Spatial k-NN comparables"]
	328	+ lines = [r"\begin{tabular}{l cc c cc}", r"\toprule",
	329	+ r" & \multicolumn{2}{c}{Same parcel in training} & &"
	330	+ r" \multicolumn{2}{c}{Same coordinates in training} \\",
	331	+ r"\cmidrule{2-3}\cmidrule{5-6}",
	332	+ r"Model & Yes & No & & Yes & No \\", r"\midrule"]
	333	+ def cell(key, flag, m, seg="all"):
	334	+ x = L[(L["key"] == key) & (L["seen_in_training"] == flag)
	335	+ & (L["model"] == m) & (L["segment"] == seg)]
	336	+ return f"{x['mdape'].iloc[0]:.1f}" if len(x) else "---"
	337	+ def n(key, flag, seg="all"):
	338	+ x = L[(L["key"] == key) & (L["seen_in_training"] == flag)
	339	+ & (L["segment"] == seg)]
	340	+ return f"{int(x['n'].iloc[0]):,}"
	341	+ lines.append(r"\multicolumn{6}{l}{\itshape All test sales}\\")
	342	+ for m in sel:
	343	+ lines.append(f"\\quad {SHORT[m]} & {cell('in_train_parcel', True, m)} & "
	344	+ f"{cell('in_train_parcel', False, m)} & & "
	345	+ f"{cell('in_train_coord', True, m)} & "
	346	+ f"{cell('in_train_coord', False, m)} \\\\")
	347	+ lines.append(f"\\quad Test sales & {n('in_train_parcel', True)} & "
	348	+ f"{n('in_train_parcel', False)} & & {n('in_train_coord', True)} & "
	349	+ f"{n('in_train_coord', False)} \\\\")
	350	+ lines.append(r"\midrule")
	351	+ lines.append(r"\multicolumn{6}{l}{\itshape Condominiums only}\\")
	352	+ for m in ("A5 Semi-log + quadratics", "D4 Gradient boosting"):
	353	+ lines.append(f"\\quad {SHORT[m]} & {cell('in_train_parcel', True, m, 'condo')} & "
	354	+ f"{cell('in_train_parcel', False, m, 'condo')} & & "
	355	+ f"{cell('in_train_coord', True, m, 'condo')} & "
	356	+ f"{cell('in_train_coord', False, m, 'condo')} \\\\")
	357	+ lines.append(f"\\quad Test sales & {n('in_train_parcel', True, 'condo')} & "
	358	+ f"{n('in_train_parcel', False, 'condo')} & & "
	359	+ f"{n('in_train_coord', True, 'condo')} & "
	360	+ f"{n('in_train_coord', False, 'condo')} \\\\")
	361	+ lines += [r"\bottomrule", r"\end{tabular}"]
	362	+ (TAB / "leakage.tex").write_text("\n".join(lines))
	363	+
	364	+
	365	+def t_nested_fe():
	366	+ N = pd.read_csv(RES / "nested_fe.csv")
	367	+ R = {s: pd.read_csv(RES / f"horserace_{s}.csv").set_index("name")
	368	+ for s in ("random", "temporal")}
	369	+ rows = [("C2 Municipality FE", "C2 Municipality FE (1,115 cells)"),
	370	+ ("C3 Grid-cell FE (~5.5 km)", "C3 Grid 5.5 km (5,255 cells)"),
	371	+ ("C4 Grid-cell FE (~1.1 km)", "C4 Grid 1.1 km (30,548 cells)"),
	372	+ ("C3' Municipality + grid-cell FE (~5.5 km)",
	373	+ "C3$'$ Municipality + grid 5.5 km"),
	374	+ ("C4' Municipality + grid-cell FE (~1.1 km)",
	375	+ "C4$'$ Municipality + grid 1.1 km")]
	376	+ lines = [r"\begin{tabular}{l cc c cc}", r"\toprule",
	377	+ r" & \multicolumn{2}{c}{Random holdout} & &"
	378	+ r" \multicolumn{2}{c}{Forward-in-time} \\",
	379	+ r"\cmidrule{2-3}\cmidrule{5-6}",
	380	+ r"Spatial controls & MdAPE (\%) & $R^2_{\ln}$ & & MdAPE (\%) & "
	381	+ r"$R^2_{\ln}$ \\", r"\midrule"]
	382	+ for key, label in rows:
	383	+ vals = []
	384	+ for s in ("random", "temporal"):
	385	+ if key in R[s].index:
	386	+ x = R[s].loc[key]
	387	+ else:
	388	+ x = N[(N["name"] == key) & (N["scheme"] == s)].iloc[0]
	389	+ vals += [f"{x['mdape']:.1f}", f"{x['r2_ln']:.3f}"]
	390	+ lines.append(f"{label} & {vals[0]} & {vals[1]} & & {vals[2]} & "
	391	+ f"{vals[3]} \\\\")
	392	+ lines += [r"\bottomrule", r"\end{tabular}"]
	393	+ (TAB / "nested_fe.tex").write_text("\n".join(lines))
	394	+
	395	+
	396	+def t_hgb_sensitivity():
	397	+ H = pd.read_csv(RES / "hgb_sensitivity.csv")
	398	+ names = list(dict.fromkeys(H["name"]))
	399	+ lines = [r"\begin{tabular}{l cc c cc}", r"\toprule",
	400	+ r" & \multicolumn{2}{c}{Random holdout} & &"
	401	+ r" \multicolumn{2}{c}{Forward-in-time} \\",
	402	+ r"\cmidrule{2-3}\cmidrule{5-6}",
	403	+ r"Gradient-boosting configuration & MdAPE (\%) & $R^2_{\ln}$ & & "
	404	+ r"MdAPE (\%) & $R^2_{\ln}$ \\", r"\midrule"]
	405	+ for nm in names:
	406	+ a = H[(H["name"] == nm) & (H["scheme"] == "random")].iloc[0]
	407	+ b = H[(H["name"] == nm) & (H["scheme"] == "temporal")].iloc[0]
	408	+ label = _esc(nm.replace("D4 ", "").replace("%", r"\%"))
	409	+ label = label[0].upper() + label[1:]
	410	+ if not pd.isna(b.get("best_iter", float("nan"))):
	411	+ label += f" [{int(a['best_iter'])} / {int(b['best_iter'])} it.]"
	412	+ lines.append(f"{label} & {a['mdape']:.1f} & {a['r2_ln']:.3f} & & "
	413	+ f"{b['mdape']:.1f} & {b['r2_ln']:.3f} \\\\")
	414	+ lines += [r"\bottomrule", r"\end{tabular}"]
	415	+ (TAB / "hgb_sensitivity.tex").write_text("\n".join(lines))
	416	+
	417	+
	418	+def t_by_quarter():
	419	+ Q = pd.read_csv(RES / "by_quarter.csv")
	420	+ piv = Q.pivot_table(index="quarter", columns="model", values="mdape")
	421	+ ns = Q.groupby("quarter")["n"].first()
	422	+ cols = ["A5 Semi-log + quadratics", "A6 Semi-log + splines",
	423	+ "D2 Ridge (cross-validated)", "D3 Random forest",
	424	+ "D4 Gradient boosting"]
	425	+ lines = [r"\begin{tabular}{lr" + "c" * len(cols) + "}", r"\toprule",
	426	+ r"Test quarter & $n$ & " + " & ".join(SHORT[c] for c in cols)
	427	+ + r" \\", r"\midrule"]
	428	+ for q, row in piv.iterrows():
	429	+ lines.append(f"{q} & {ns[q]:,.0f} & "
	430	+ + " & ".join(f"{row[c]:.1f}" for c in cols) + r" \\")
	431	+ lines += [r"\bottomrule", r"\end{tabular}"]
	432	+ (TAB / "by_quarter.tex").write_text("\n".join(lines))
	433	+
	434	+
136	435	def main() -> None:
137	436	config.ensure_dirs()
138	437	t_summary()
		`@@ -142,6 +441,13 @@ def main() -> None:`
142	441	t_boxcox()
143	442	t_learning()
144	443	t_segments()
	444	+ for fn in (t_inference, t_retransformation, t_same_period, t_pairs,
	445	+ t_group_splits, t_leakage_decomp, t_nested_fe,
	446	+ t_hgb_sensitivity, t_by_quarter):
	447	+ try:
	448	+ fn()
	449	+ except FileNotFoundError as e: # step 06 not run yet
	450	+ print(f" skipped {fn.__name__}: {e}")
145	451	made = sorted(p.name for p in TAB.glob("*.tex"))
146	452	print(f"{len(made)} tables written:", ", ".join(made))
147	453

added scripts/06_robustness.py +274 −0

		`@@ -0,0 +1,274 @@`
	1	+#!/usr/bin/env python3
	2	+# Author: Simon-Pierre Boucher — contact@spboucher.ai
	3	+"""Step 06 — Inference and robustness (added in the 2026-10-17 revision).
	4	+
	5	+Reads the test-set predictions stored by step 02 and runs the additional
	6	+analyses requested by the editorial review:
	7	+
	8	+1. cluster-bootstrap confidence intervals (municipality clusters) for the
	9	+ MdAPE of every model, and Diebold–Mariano / Giacomini–White-type tests
	10	+ of equal accuracy against the spline hedonic (A6) and gradient
	11	+ boosting (D4), under both holdouts -> inference_<scheme>.csv
	12	+2. same-period comparison: random-split models evaluated on the 2025–26
	13	+ sales of the random test set versus forward-in-time models on the
	14	+ full 2025–26 test set -> same_period.csv
	15	+3. forward-in-time accuracy by test quarter -> by_quarter.csv
	16	+4. leakage decomposition of the random holdout: accuracy on test sales
	17	+ whose parcel / coordinate pair also appears in training versus the
	18	+ others -> leakage.csv
	19	+5. leakage-free holdouts: the full race under parcel-grouped and
	20	+ coordinate-grouped 80/20 splits -> horserace_group_parcel.csv,
	21	+ horserace_group_coord.csv
	22	+6. nested spatial fixed effects (municipality + grid) -> nested_fe.csv
	23	+7. Box–Cox on a finer lambda grid -> boxcox_fine.csv
	24	+8. gradient-boosting hyper-parameter sensitivity -> hgb_sensitivity.csv
	25	+10. targeted pairwise comparisons along each axis (bootstrap CI of the
	26	+ MdAPE difference and clustered DM tests) -> pairs.csv
	27	+9. level-bias decomposition: median log residual (aggregate level error)
	28	+ and MdAPE after re-levelling predictions by the test-set median ratio
	29	+ (relative pricing skill net of the level error) -> relevel.csv
	30	+
	31	+Usage: python scripts/06_robustness.py (about 15 min)
	32	+"""
	33	+import sys
	34	+import time
	35	+from pathlib import Path
	36	+
	37	+import numpy as np
	38	+import pandas as pd
	39	+
	40	+sys.path.insert(0, str(Path(__file__).resolve().parents[1] / "src"))
	41	+
	42	+from wp11 import config, inference, models, sample # noqa: E402
	43	+
	44	+OUT = config.REPRODUCED
	45	+MODEL_NAMES = [m["name"] for m in models.model_registry()]
	46	+A6, D4, A5 = ("A6 Semi-log + splines", "D4 Gradient boosting",
	47	+ "A5 Semi-log + quadratics")
	48	+
	49	+
	50	+def _mdape(y, p):
	51	+ return float(np.median(np.abs(p - y) / y) * 100)
	52	+
	53	+
	54	+def step_inference(P: dict):
	55	+ for scheme, Ps in P.items():
	56	+ t0 = time.time()
	57	+ boot = inference.cluster_bootstrap_mdape(Ps, MODEL_NAMES, ref=A6)
	58	+ boot_d4 = inference.cluster_bootstrap_mdape(Ps, MODEL_NAMES, ref=D4)
	59	+ boot = boot.merge(boot_d4[["model", "diff_vs_ref", "diff_lo",
	60	+ "diff_hi"]]
	61	+ .rename(columns={"diff_vs_ref": "diff_vs_d4",
	62	+ "diff_lo": "diff_d4_lo",
	63	+ "diff_hi": "diff_d4_hi"}),
	64	+ on="model", how="left")
	65	+ rows = []
	66	+ for m in MODEL_NAMES:
	67	+ r = {"model": m}
	68	+ for ref, tag in ((A6, "a6"), (D4, "d4")):
	69	+ if m == ref:
	70	+ continue
	71	+ for loss, ltag in ((inference.ape, "ape"),
	72	+ (inference.sq_log, "sqlog")):
	73	+ t = inference.dm_test(Ps, m, ref, loss=loss)
	74	+ r[f"dm_{ltag}_vs_{tag}_t"] = t["t"]
	75	+ r[f"dm_{ltag}_vs_{tag}_p"] = t["p"]
	76	+ r[f"dm_{ltag}_vs_{tag}_diff"] = t["mean_diff"]
	77	+ rows.append(r)
	78	+ res = boot.merge(pd.DataFrame(rows), on="model")
	79	+ res["n_clusters"] = Ps["muni"].nunique()
	80	+ res.to_csv(OUT / f"inference_{scheme}.csv", index=False)
	81	+ print(f" inference [{scheme}] done in {time.time() - t0:.0f}s")
	82	+
	83	+
	84	+def step_same_period(P: dict):
	85	+ cut = pd.Timestamp(config.TEMPORAL_CUTOFF)
	86	+ Pr = P["random"][P["random"]["sale_date"] >= cut]
	87	+ Pt = P["temporal"]
	88	+ rows = []
	89	+ for m in MODEL_NAMES:
	90	+ rows.append({"model": m,
	91	+ "mdape_random_all": _mdape(P["random"]["price"].to_numpy(),
	92	+ P["random"][m].to_numpy()),
	93	+ "mdape_random_2025_26": _mdape(Pr["price"].to_numpy(),
	94	+ Pr[m].to_numpy()),
	95	+ "mdape_forward_2025_26": _mdape(Pt["price"].to_numpy(),
	96	+ Pt[m].to_numpy()),
	97	+ "n_random_2025_26": len(Pr), "n_forward": len(Pt)})
	98	+ pd.DataFrame(rows).to_csv(OUT / "same_period.csv", index=False)
	99	+ print(" same-period comparison done")
	100	+
	101	+
	102	+def step_by_quarter(P: dict):
	103	+ Pt = P["temporal"].copy()
	104	+ Pt["q"] = Pt["sale_date"].dt.to_period("Q").astype(str)
	105	+ rows = []
	106	+ for q, g in Pt.groupby("q"):
	107	+ for m in (A5, A6, "D2 Ridge (cross-validated)", "D3 Random forest",
	108	+ D4):
	109	+ rows.append({"quarter": q, "model": m, "n": len(g),
	110	+ "mdape": _mdape(g["price"].to_numpy(),
	111	+ g[m].to_numpy())})
	112	+ pd.DataFrame(rows).to_csv(OUT / "by_quarter.csv", index=False)
	113	+ print(" by-quarter accuracy done")
	114	+
	115	+
	116	+def step_leakage(P: dict):
	117	+ Pr = P["random"]
	118	+ rows = []
	119	+ for key in ("in_train_parcel", "in_train_coord"):
	120	+ for flag in (True, False):
	121	+ g = Pr[Pr[key] == flag]
	122	+ for m in (A5, A6, "D2 Ridge (cross-validated)",
	123	+ "D3 Random forest", D4,
	124	+ "D5 Gradient boosting, no coordinates",
	125	+ "D6 Spatial k-NN comparables"):
	126	+ rows.append({"key": key, "seen_in_training": flag,
	127	+ "segment": "all", "n": len(g), "model": m,
	128	+ "mdape": _mdape(g["price"].to_numpy(),
	129	+ g[m].to_numpy())})
	130	+ gc = g[g["prop_class"] == "condo"]
	131	+ for m in (A5, D4):
	132	+ rows.append({"key": key, "seen_in_training": flag,
	133	+ "segment": "condo", "n": len(gc), "model": m,
	134	+ "mdape": _mdape(gc["price"].to_numpy(),
	135	+ gc[m].to_numpy())})
	136	+ pd.DataFrame(rows).to_csv(OUT / "leakage.csv", index=False)
	137	+ print(" leakage decomposition done")
	138	+
	139	+
	140	+def step_relevel(P: dict):
	141	+ """Decompose forward-in-time error into an aggregate level error and
	142	+ relative pricing skill. For each model the median log residual
	143	+ b = median(ln y - ln p) measures the common level error (staleness);
	144	+ the re-levelled MdAPE uses p * exp(b), i.e. an oracle time adjustment
	145	+ of the kind practitioners obtain from a published index."""
	146	+ rows = []
	147	+ for scheme, Ps in P.items():
	148	+ y = Ps["price"].to_numpy(float)
	149	+ for m in MODEL_NAMES:
	150	+ p = Ps[m].to_numpy(float)
	151	+ b = float(np.median(np.log(y) - np.log(p)))
	152	+ rows.append({"scheme": scheme, "model": m,
	153	+ "median_log_resid": b,
	154	+ "mdape": _mdape(y, p),
	155	+ "mdape_relevelled": _mdape(y, p * np.exp(b)),
	156	+ "mape_relevelled": float(np.mean(
	157	+ np.abs(p * np.exp(b) - y) / y) * 100),
	158	+ "rmse_ln_centered": float(np.sqrt(np.mean(
	159	+ (np.log(y) - np.log(p) - b) ** 2)))})
	160	+ pd.DataFrame(rows).to_csv(OUT / "relevel.csv", index=False)
	161	+ print(" level-bias decomposition done")
	162	+
	163	+
	164	+PAIRS = [("A2 Semi-log", "A1 Linear (levels)"),
	165	+ ("A6 Semi-log + splines", "A2 Semi-log"),
	166	+ ("A4 Box-Cox", "A2 Semi-log"),
	167	+ ("A3 Log-log", "A2 Semi-log"),
	168	+ ("B2 Year FE", "B1 No time effects"),
	169	+ ("B4 Month FE", "B3 Quarter FE"),
	170	+ ("C3 Grid-cell FE (~5.5 km)", "C2 Municipality FE"),
	171	+ ("C4 Grid-cell FE (~1.1 km)", "C2 Municipality FE"),
	172	+ ("D2 Ridge (cross-validated)", "D1 OLS (muni + month FE)"),
	173	+ ("D4 Gradient boosting", "D3 Random forest"),
	174	+ ("D4 Gradient boosting", "D5 Gradient boosting, no coordinates"),
	175	+ ("D4 Gradient boosting", "A1 Linear (levels)"),
	176	+ ("A6 Semi-log + splines", "A1 Linear (levels)")]
	177	+
	178	+
	179	+def step_pairs(P: dict):
	180	+ """Targeted comparisons: for each (A, B) the MdAPE difference A - B
	181	+ with its cluster-bootstrap interval and the clustered DM statistics
	182	+ on the APE and squared-log losses (positive t = B more accurate)."""
	183	+ rows = []
	184	+ for scheme, Ps in P.items():
	185	+ for a, b in PAIRS:
	186	+ boot = inference.cluster_bootstrap_mdape(Ps, [a, b], ref=b)
	187	+ x = boot.set_index("model").loc[a]
	188	+ t1 = inference.dm_test(Ps, a, b, loss=inference.ape)
	189	+ t2 = inference.dm_test(Ps, a, b, loss=inference.sq_log)
	190	+ rows.append({"scheme": scheme, "model_a": a, "model_b": b,
	191	+ "mdape_a": x["mdape"],
	192	+ "mdape_b": boot.set_index("model").loc[b, "mdape"],
	193	+ "diff": x["diff_vs_ref"], "diff_lo": x["diff_lo"],
	194	+ "diff_hi": x["diff_hi"],
	195	+ "dm_ape_t": t1["t"], "dm_ape_p": t1["p"],
	196	+ "dm_sqlog_t": t2["t"], "dm_sqlog_p": t2["p"]})
	197	+ pd.DataFrame(rows).to_csv(OUT / "pairs.csv", index=False)
	198	+ print(" targeted pairwise comparisons done")
	199	+
	200	+
	201	+def step_group_splits(df):
	202	+ for scheme in ("group_parcel", "group_coord"):
	203	+ res = models.run_horserace(df, scheme)
	204	+ res.to_csv(OUT / f"horserace_{scheme}.csv", index=False)
	205	+
	206	+
	207	+def step_nested_fe(df):
	208	+ rows = []
	209	+ for scheme in ("random", "temporal"):
	210	+ res = models.run_horserace(df, scheme,
	211	+ registry=models.robustness_registry())
	212	+ res["scheme"] = scheme
	213	+ rows.append(res)
	214	+ pd.concat(rows).to_csv(OUT / "nested_fe.csv", index=False)
	215	+
	216	+
	217	+def step_boxcox_fine(df):
	218	+ d = models.add_derived(df)
	219	+ d["sale_year_c"] = d["sale_year"].astype(str)
	220	+ train, test = models.split(d, "random")
	221	+ grid = [round(x, 2) for x in np.arange(-0.25, 0.751, 0.05)]
	222	+ lam, prof = models.fit_boxcox(train, models.NUM_LEVELS,
	223	+ models.CATS + ["muni", "quarter"],
	224	+ grid=grid)
	225	+ prof["chosen"] = prof["lambda"] == lam
	226	+ # out-of-sample accuracy of the Box–Cox model at the refined lambda
	227	+ spec = dict(name="A4 fine", group="x", kind="boxcox",
	228	+ numeric=models.NUM_LEVELS, fe=["muni", "quarter"],
	229	+ boxcox_grid=[lam])
	230	+ pred, _ = models.fit_predict(spec, train, test)
	231	+ prof.attrs = {}
	232	+ prof["mdape_at_chosen"] = np.where(prof["chosen"],
	233	+ _mdape(test["price"].to_numpy(float),
	234	+ np.clip(pred, config.PRED_FLOOR,
	235	+ None)), np.nan)
	236	+ prof.to_csv(OUT / "boxcox_fine.csv", index=False)
	237	+ print(f" Box–Cox fine grid: lambda* = {lam}")
	238	+
	239	+
	240	+def step_hgb_sensitivity(df):
	241	+ rows = []
	242	+ for scheme in ("random", "temporal"):
	243	+ reg = [dict(name="D4 Gradient boosting (baseline)", group="S",
	244	+ kind="hgb")]
	245	+ reg += [dict(name=f"D4 {label}", group="S", kind="hgb",
	246	+ hgb_params=params)
	247	+ for label, params in models.HGB_ALTERNATIVES.items()]
	248	+ res = models.run_horserace(df, scheme, registry=reg)
	249	+ res["scheme"] = scheme
	250	+ rows.append(res)
	251	+ pd.concat(rows).to_csv(OUT / "hgb_sensitivity.csv", index=False)
	252	+
	253	+
	254	+def main() -> None:
	255	+ config.ensure_dirs()
	256	+ df = sample.load()
	257	+ P = {s: pd.read_parquet(config.PROCESSED / f"predictions_{s}.parquet")
	258	+ for s in ("random", "temporal")}
	259	+ t0 = time.time()
	260	+ step_inference(P)
	261	+ step_same_period(P)
	262	+ step_by_quarter(P)
	263	+ step_leakage(P)
	264	+ step_relevel(P)
	265	+ step_pairs(P)
	266	+ step_group_splits(df)
	267	+ step_nested_fe(df)
	268	+ step_boxcox_fine(df)
	269	+ step_hgb_sensitivity(df)
	270	+ print(f"Robustness step finished in {(time.time() - t0) / 60:.1f} min")
	271	+
	272	+
	273	+if __name__ == "__main__":
	274	+ main()

added src/wp11/inference.py +95 −0

		`@@ -0,0 +1,95 @@`
	1	+# Author: Simon-Pierre Boucher — contact@spboucher.ai
	2	+"""Inference for out-of-sample accuracy comparisons.
	3	+
	4	+Two tools, both operating on the stored test-set predictions:
	5	+
	6	+* a cluster bootstrap (resampling municipalities with replacement) for
	7	+ the MdAPE of each model and for the MdAPE difference between two
	8	+ models evaluated on the same test sales;
	9	+* a Diebold–Mariano / Giacomini–White-type test of equal predictive
	10	+ accuracy: the mean of the per-sale loss differential d_i = L(e_i^A) -
	11	+ L(e_i^B) is tested against zero with standard errors clustered by
	12	+ municipality (the cross-sectional analogue of the HAC-robust DM
	13	+ statistic). Losses: absolute percentage error (the MAPE loss) and the
	14	+ squared log error (the RMSE_ln loss).
	15	+"""
	16	+from __future__ import annotations
	17	+
	18	+import numpy as np
	19	+import pandas as pd
	20	+
	21	+from . import config
	22	+
	23	+
	24	+def ape(y: np.ndarray, p: np.ndarray) -> np.ndarray:
	25	+ return np.abs(p - y) / y
	26	+
	27	+
	28	+def sq_log(y: np.ndarray, p: np.ndarray) -> np.ndarray:
	29	+ return (np.log(y) - np.log(p)) ** 2
	30	+
	31	+
	32	+def cluster_bootstrap_mdape(P: pd.DataFrame, models: list[str],
	33	+ cluster: str = "muni", B: int = 500,
	34	+ ref: str \| None = None,
	35	+ seed: int = config.SEED) -> pd.DataFrame:
	36	+ """Percentile 95% intervals for MdAPE (and MdAPE minus the reference
	37	+ model's MdAPE) from B cluster-bootstrap replicates.
	38	+
	39	+ Clusters are municipalities; each replicate draws clusters with
	40	+ replacement (so a drawn municipality contributes all its test sales,
	41	+ possibly several times) and recomputes the median APE.
	42	+ """
	43	+ y = P["price"].to_numpy(float)
	44	+ A = {m: ape(y, P[m].to_numpy(float)) for m in models}
	45	+ codes, uniq = pd.factorize(P[cluster])
	46	+ G = len(uniq)
	47	+ rng = np.random.default_rng(seed)
	48	+ # pre-compute row indices per cluster
	49	+ order = np.argsort(codes, kind="stable")
	50	+ bounds = np.searchsorted(codes[order], np.arange(G + 1))
	51	+ rows_by_cluster = [order[bounds[g]:bounds[g + 1]] for g in range(G)]
	52	+ reps = {m: np.empty(B) for m in models}
	53	+ for b in range(B):
	54	+ draw = rng.integers(0, G, G)
	55	+ idx = np.concatenate([rows_by_cluster[g] for g in draw])
	56	+ for m in models:
	57	+ reps[m][b] = np.median(A[m][idx])
	58	+ out = []
	59	+ for m in models:
	60	+ point = float(np.median(A[m]) * 100)
	61	+ lo, hi = np.percentile(reps[m], [2.5, 97.5]) * 100
	62	+ row = {"model": m, "mdape": point, "ci_lo": lo, "ci_hi": hi,
	63	+ "boot_se": float(reps[m].std(ddof=1) * 100)}
	64	+ if ref is not None and m != ref:
	65	+ d = (reps[m] - reps[ref]) * 100
	66	+ row.update({"diff_vs_ref": point - float(np.median(A[ref]) * 100),
	67	+ "diff_lo": float(np.percentile(d, 2.5)),
	68	+ "diff_hi": float(np.percentile(d, 97.5))})
	69	+ out.append(row)
	70	+ return pd.DataFrame(out)
	71	+
	72	+
	73	+def dm_test(P: pd.DataFrame, model_a: str, model_b: str,
	74	+ loss=ape, cluster: str = "muni") -> dict:
	75	+ """Clustered test of E[d_i] = 0 for d_i = L_A(i) - L_B(i).
	76	+
	77	+ Returns the mean differential (positive = A has larger loss, i.e.
	78	+ B is more accurate), its cluster-robust standard error, the t
	79	+ statistic and the two-sided normal p-value.
	80	+ """
	81	+ y = P["price"].to_numpy(float)
	82	+ d = loss(y, P[model_a].to_numpy(float)) - loss(y, P[model_b].to_numpy(float))
	83	+ codes, _ = pd.factorize(P[cluster])
	84	+ n, G = len(d), codes.max() + 1
	85	+ dbar = d.mean()
	86	+ # cluster-robust variance of the mean: sum over clusters of squared
	87	+ # within-cluster sums of demeaned d, divided by n^2
	88	+ sums = np.bincount(codes, weights=d - dbar, minlength=G)
	89	+ var = (sums 2).sum() / n 2 * G / (G - 1)
	90	+ se = float(np.sqrt(var))
	91	+ t = float(dbar / se) if se > 0 else np.nan
	92	+ from math import erf, sqrt
	93	+ p = 2 * (1 - 0.5 * (1 + erf(abs(t) / sqrt(2)))) if np.isfinite(t) else np.nan
	94	+ return {"model_a": model_a, "model_b": model_b, "mean_diff": float(dbar),
	95	+ "se": se, "t": t, "p": float(p), "n_clusters": int(G)}

modified src/wp11/models.py +220 −43

		`@@ -6,8 +6,8 @@ Twenty hedonic models organised along four design axes:`
6	6	A. functional form — linear, semi-log, log-log, Box–Cox, quadratic,
7	7	splines (linear estimator, muni + quarter FE)
8	8	B. time effects — none / year / quarter / month FE (quadratic backbone)
9		− C. spatial controls — none / municipality / ~1.1 km grid / neighbourhood
10		− unit FE (quadratic backbone, quarter FE)
	9	+ C. spatial controls — none / municipality / ~5.5 km grid / ~1.1 km
	10	+ grid FE (quadratic backbone, quarter FE)
11	11	D. estimation method — OLS, ridge, random forest, gradient boosting
12	12	(with and without coordinates), spatial k-NN
13	13	comparables
		`@@ -16,9 +16,25 @@ Every linear model is estimated as a sparse ridge with a vanishing penalty`
16	16	(numerically OLS, but it (i) survives collinear dummies and (ii) predicts
17	17	unseen categories at the reference level via ``handle_unknown='ignore'``).
18	18	Every model is evaluated on identical train/test splits, and all metrics
19		−are computed on price levels — log models are retransformed with Duan's
20		−smearing factor, Box–Cox by analytic inversion — so that functional forms
21		−compete on the same scoreboard.
	19	+are computed on price levels so that functional forms compete on the
	20	+same scoreboard. Two retransformation rules are available for every model
	21	+whose dependent variable is a transformation of the price:
	22	+
	23	+ * ``"median"`` (main scoreboard) — the fitted transformed value is
	24	+ inverted as is: exp(.) for log models, the analytic inverse for
	25	+ Box–Cox. Under symmetric transformed-scale errors this is the
	26	+ conditional median price, the target that MdAPE/MAPE reward and the
	27	+ quantity the tree ensembles (fit on ln P) deliver natively. Log-scale
	28	+ metrics (RMSE_ln, R2_ln) are always computed on this prediction.
	29	+ * ``"mean"`` (robustness) — Duan's (1983) smearing estimator of the
	30	+ conditional mean: exp(z_hat) * mean(exp(e_i)) for log models and
	31	+ mean_i g^{-1}(z_hat + e_i) over training residuals e_i for Box–Cox;
	32	+ tree ensembles receive the same correction from their (in-sample)
	33	+ training residuals.
	34	+
	35	+Version 1.0 of the paper smeared the linear log models but not the tree
	36	+ensembles, which penalised the linear models on every metric; the
	37	+``"median"`` rule applied uniformly is the scoreboard of version 1.1.
22	38	"""
23	39	from __future__ import annotations
24	40
		`@@ -62,6 +78,16 @@ def split(df: pd.DataFrame, scheme: str):`
62	78	if scheme == "temporal":
63	79	cut = pd.Timestamp(config.TEMPORAL_CUTOFF)
64	80	return df[df["sale_date"] < cut], df[df["sale_date"] >= cut]
	81	+ if scheme in ("group_parcel", "group_coord"):
	82	+ # Leakage-free random holdouts: 20% of groups (parcels, or exact
	83	+ # coordinate pairs = buildings/complexes) go to the test set, so
	84	+ # that no property (resp. building) is seen on both sides.
	85	+ key = "parcel" if scheme == "group_parcel" else "coord"
	86	+ rng = np.random.default_rng(config.SEED)
	87	+ groups = df[key].unique()
	88	+ test_groups = set(groups[rng.random(len(groups)) < config.TEST_SHARE])
	89	+ mask = df[key].isin(test_groups).to_numpy()
	90	+ return df[~mask], df[mask]
65	91	raise ValueError(scheme)
66	92
67	93
		`@@ -118,13 +144,30 @@ def _inv_boxcox(z: np.ndarray, lam: float) -> np.ndarray:`
118	144	return base ** (1.0 / lam)
119	145
120	146
121		−def fit_boxcox(train: pd.DataFrame, numeric: list[str], cats: list[str]):
	147	+def _smear_boxcox(z_hat: np.ndarray, resid: np.ndarray, lam: float,
	148	+ n_resid: int = 1000) -> np.ndarray:
	149	+ """Duan's smearing estimator of E[P \| X] for a Box–Cox model:
	150	+ the average of g^{-1}(z_hat + e_i) over (a subsample of) the training
	151	+ residuals e_i. Reduces to exp(z_hat) * mean(exp(e)) when lam = 0."""
	152	+ rng = np.random.default_rng(config.SEED)
	153	+ e = resid if len(resid) <= n_resid else rng.choice(resid, n_resid,
	154	+ replace=False)
	155	+ out = np.zeros_like(z_hat)
	156	+ for chunk in np.array_split(np.arange(len(z_hat)),
	157	+ max(1, len(z_hat) // 5000)):
	158	+ out[chunk] = _inv_boxcox(z_hat[chunk, None] + e[None, :],
	159	+ lam).mean(axis=1)
	160	+ return out
	161	+
	162	+
	163	+def fit_boxcox(train: pd.DataFrame, numeric: list[str], cats: list[str],
	164	+ grid: list[float] \| None = None):
122	165	"""Profile-likelihood choice of λ on the training sample."""
123	166	y = train["price"].to_numpy(float)
124	167	n = len(y)
125	168	sum_ln_y = np.log(y).sum()
126	169	rows = []
127		− for lam in config.BOXCOX_GRID:
	170	+ for lam in (grid if grid is not None else config.BOXCOX_GRID):
128	171	pipe = _linear_pipeline(numeric, cats)
129	172	z = _boxcox(y, lam)
130	173	pipe.fit(train, z)
		`@@ -136,6 +179,43 @@ def fit_boxcox(train: pd.DataFrame, numeric: list[str], cats: list[str]):`
136	179	return lam_star, prof
137	180
138	181
	182	+HGB_PARAMS = dict(max_iter=600, learning_rate=0.08, max_leaf_nodes=63,
	183	+ min_samples_leaf=20, l2_regularization=1e-2)
	184	+
	185	+# Alternative gradient-boosting configurations for the hyper-parameter
	186	+# sensitivity analysis (Section "Robustness"). ``early_stopping`` holds out
	187	+# the last 10% of the training rows in time order as a validation set,
	188	+# i.e. a time-honest tuning rule.
	189	+HGB_ALTERNATIVES = {
	190	+ "shallow (15 leaves, lr 0.05, 1500 iter)":
	191	+ dict(max_iter=1500, learning_rate=0.05, max_leaf_nodes=15,
	192	+ min_samples_leaf=20, l2_regularization=1e-2),
	193	+ "deep (255 leaves, lr 0.05, 600 iter)":
	194	+ dict(max_iter=600, learning_rate=0.05, max_leaf_nodes=255,
	195	+ min_samples_leaf=20, l2_regularization=1e-2),
	196	+ "regularised (min leaf 200, L2 = 1)":
	197	+ dict(max_iter=600, learning_rate=0.08, max_leaf_nodes=63,
	198	+ min_samples_leaf=200, l2_regularization=1.0),
	199	+ "early stopping on last 10% of training months":
	200	+ dict(max_iter=2000, learning_rate=0.05, max_leaf_nodes=63,
	201	+ min_samples_leaf=20, l2_regularization=1e-2,
	202	+ early_stopping=True),
	203	+}
	204	+
	205	+
	206	+def robustness_registry() -> list[dict]:
	207	+ """Additional specifications: nested spatial FE (unseen grid cells fall
	208	+ back to their municipality instead of an arbitrary reference cell)."""
	209	+ return [
	210	+ dict(name="C3' Municipality + grid-cell FE (~5.5 km)",
	211	+ group="R. Nested spatial FE", kind="linear_log",
	212	+ numeric=NUM_QUAD, fe=["muni", "grid5", "quarter"]),
	213	+ dict(name="C4' Municipality + grid-cell FE (~1.1 km)",
	214	+ group="R. Nested spatial FE", kind="linear_log",
	215	+ numeric=NUM_QUAD, fe=["muni", "grid", "quarter"]),
	216	+ ]
	217	+
	218	+
139	219	# ---------------------------------------------------------------- registry
140	220	def model_registry() -> list[dict]:
141	221	"""The twenty models. ``fe`` lists categorical FE columns appended to
		`@@ -193,10 +273,27 @@ def model_registry() -> list[dict]:`
193	273
194	274
195	275	# ---------------------------------------------------------------- fit/eval
196		−def fit_predict(spec: dict, train: pd.DataFrame, test: pd.DataFrame):
197		− """Fit one registry entry, return level predictions on the test set."""
	276	+def fit_predict(spec: dict, train: pd.DataFrame, test: pd.DataFrame,
	277	+ retransform: str = "median"):
	278	+ """Fit one registry entry, return level predictions on the test set.
	279	+
	280	+ ``retransform`` is ``"median"`` (plain inversion of the transformed
	281	+ prediction) or ``"mean"`` (Duan smearing). ``spec`` is updated in
	282	+ place with ``smear`` (log models), ``lambda`` (Box–Cox) and, when
	283	+ ``retransform="mean"`` is requested, both predictions are returned
	284	+ through ``spec["pred_median"]`` / ``spec["pred_mean"]``.
	285	+ """
198	286	kind = spec["kind"]
199	287	y_train = train["price"].to_numpy(float)
	288	+ both = retransform == "mean"
	289	+
	290	+ def _log_out(z_hat_test, z_hat_train, model):
	291	+ resid = np.log(y_train) - z_hat_train
	292	+ smear = float(np.mean(np.exp(resid))) # Duan (1983)
	293	+ spec["smear"] = smear
	294	+ p_med = np.exp(z_hat_test)
	295	+ spec["pred_median"], spec["pred_mean"] = p_med, p_med * smear
	296	+ return (p_med * smear if both else p_med), model
200	297
201	298	if kind in ("linear_level", "linear_log", "boxcox", "ridge"):
202	299	cats = CATS + spec.get("fe", [])
		`@@ -204,7 +301,9 @@ def fit_predict(spec: dict, train: pd.DataFrame, test: pd.DataFrame):`
204	301	spline_cols=spec.get("spline"))
205	302	if kind == "linear_level":
206	303	pipe.fit(train, y_train)
207		− return pipe.predict(test), pipe
	304	+ p = pipe.predict(test)
	305	+ spec["pred_median"] = spec["pred_mean"] = p
	306	+ return p, pipe
208	307	if kind in ("linear_log", "ridge"):
209	308	if kind == "ridge":
210	309	from sklearn.preprocessing import StandardScaler
		`@@ -212,32 +311,72 @@ def fit_predict(spec: dict, train: pd.DataFrame, test: pd.DataFrame):`
212	311	("sc", StandardScaler(with_mean=False)),
213	312	("reg", RidgeCV(alphas=np.logspace(-6, 2, 17),
214	313	cv=3))]
215		− z = np.log(y_train)
216		− pipe.fit(train, z)
217		− resid = z - pipe.predict(train)
218		− smear = float(np.mean(np.exp(resid))) # Duan (1983)
219		− return np.exp(pipe.predict(test)) * smear, pipe
220		− lam, _ = fit_boxcox(train, spec["numeric"], cats)
	314	+ pipe.fit(train, np.log(y_train))
	315	+ return _log_out(pipe.predict(test), pipe.predict(train), pipe)
	316	+ lam, _ = fit_boxcox(train, spec["numeric"], cats,
	317	+ grid=spec.get("boxcox_grid"))
221	318	pipe = _linear_pipeline(spec["numeric"], cats)
222		− pipe.fit(train, _boxcox(y_train, lam))
	319	+ z = _boxcox(y_train, lam)
	320	+ pipe.fit(train, z)
223	321	spec["lambda"] = lam
224		− return _inv_boxcox(pipe.predict(test), lam), pipe
	322	+ z_hat = pipe.predict(test)
	323	+ p_med = _inv_boxcox(z_hat, lam)
	324	+ spec["pred_median"] = p_med
	325	+ if both:
	326	+ resid = z - pipe.predict(train)
	327	+ spec["pred_mean"] = _smear_boxcox(z_hat, resid, lam)
	328	+ return spec["pred_mean"], pipe
	329	+ return p_med, pipe
225	330
226	331	if kind == "rf":
227	332	m = RandomForestRegressor(n_estimators=120, min_samples_leaf=5,
228	333	max_features=0.5, n_jobs=-1,
229	334	random_state=config.SEED)
230	335	m.fit(_ml_frame(train), np.log(y_train))
231		− return np.exp(m.predict(_ml_frame(test))), m
	336	+ return _log_out(m.predict(_ml_frame(test)),
	337	+ m.predict(_ml_frame(train)) if both
	338	+ else np.log(y_train), m)
232	339
233	340	if kind in ("hgb", "hgb_nogeo"):
234	341	geo = kind == "hgb"
235		− m = HistGradientBoostingRegressor(
236		− max_iter=600, learning_rate=0.08, max_leaf_nodes=63,
237		− min_samples_leaf=20, l2_regularization=1e-2,
238		− random_state=config.SEED)
239		− m.fit(_ml_frame(train, geo), np.log(y_train))
240		− return np.exp(m.predict(_ml_frame(test, geo))), m
	342	+ params = dict(spec.get("hgb_params", HGB_PARAMS))
	343	+ tr = train
	344	+ if params.pop("early_stopping", False):
	345	+ # time-honest validation: the last 10% of training rows in
	346	+ # sale-date order serve as the early-stopping set
	347	+ tr = train.sort_values("sale_date")
	348	+ n_val = int(0.1 * len(tr))
	349	+ Xv, yv = _ml_frame(tr.tail(n_val), geo), np.log(
	350	+ tr.tail(n_val)["price"].to_numpy(float))
	351	+ tr = tr.head(len(tr) - n_val)
	352	+ m = HistGradientBoostingRegressor(random_state=config.SEED,
	353	+ **params)
	354	+ # scikit-learn's early stopping draws a random validation
	355	+ # split; emulate a time-ordered one by staged fitting
	356	+ m.set_params(early_stopping=False)
	357	+ best, best_iter = np.inf, params["max_iter"]
	358	+ m.set_params(warm_start=True, max_iter=100)
	359	+ for it in range(100, params["max_iter"] + 1, 100):
	360	+ m.set_params(max_iter=it)
	361	+ m.fit(_ml_frame(tr, geo),
	362	+ np.log(tr["price"].to_numpy(float)))
	363	+ mse = float(np.mean((yv - m.predict(Xv)) ** 2))
	364	+ if mse < best - 1e-5:
	365	+ best, best_iter = mse, it
	366	+ elif it - best_iter >= 300:
	367	+ break
	368	+ spec["best_iter"] = best_iter
	369	+ m = HistGradientBoostingRegressor(random_state=config.SEED,
	370	+ {params,
	371	+ "max_iter": best_iter})
	372	+ tr = train
	373	+ else:
	374	+ m = HistGradientBoostingRegressor(random_state=config.SEED,
	375	+ **params)
	376	+ m.fit(_ml_frame(tr, geo), np.log(tr["price"].to_numpy(float)))
	377	+ return _log_out(m.predict(_ml_frame(test, geo)),
	378	+ m.predict(_ml_frame(train, geo)) if both
	379	+ else np.log(y_train), m)
241	380
242	381	if kind == "knn":
243	382	# price-per-m2 of the 10 nearest sold neighbours (lat/lng, km-scaled)
		`@@ -245,21 +384,17 @@ def fit_predict(spec: dict, train: pd.DataFrame, test: pd.DataFrame):`
245	384	Xte = test[["lat", "lng"]].to_numpy() * np.array([111.0, 78.0])
246	385	m = KNeighborsRegressor(n_neighbors=10, weights="distance", n_jobs=-1)
247	386	m.fit(Xtr, np.log(y_train) - train["ln_area"].to_numpy())
248		− return np.exp(m.predict(Xte) + test["ln_area"].to_numpy()), m
	387	+ z_te = m.predict(Xte) + test["ln_area"].to_numpy()
	388	+ z_tr = (m.predict(Xtr) + train["ln_area"].to_numpy() if both
	389	+ else np.log(y_train))
	390	+ return _log_out(z_te, z_tr, m)
249	391
250	392	raise ValueError(kind)
251	393
252	394
253		−def run_horserace(df: pd.DataFrame, scheme: str) -> pd.DataFrame:
254		− """Evaluate the full registry under one split scheme.
255		−
256		− Under the forward-in-time split, test-period time categories (months,
257		− quarters, years) were never seen in training. A one-hot encoder would
258		− silently price them at the baseline period; the honest forecasting
259		− rule for a static model is to freeze the price level at the last
260		− period observed in training, so unseen time labels are remapped to the
261		− latest training label before prediction.
262		− """
	395	+def prepare(df: pd.DataFrame, scheme: str):
	396	+ """Derived columns, split, and the carry-forward rule for the
	397	+ forward-in-time scheme. Returns (train, test)."""
263	398	d = add_derived(df)
264	399	d["sale_year_c"] = d["sale_year"].astype(str)
265	400	train, test = split(d, scheme)
		`@@ -268,16 +403,58 @@ def run_horserace(df: pd.DataFrame, scheme: str) -> pd.DataFrame:`
268	403	for col in ("quarter", "month", "sale_year_c"):
269	404	last = train[col].max()
270	405	test.loc[~test[col].isin(train[col].unique()), col] = last
	406	+ return train, test
	407	+
	408	+
	409	+def run_horserace(df: pd.DataFrame, scheme: str,
	410	+ registry: list[dict] \| None = None,
	411	+ return_predictions: bool = False):
	412	+ """Evaluate a registry (default: the twenty models) under one split.
	413	+
	414	+ Under the forward-in-time split, test-period time categories (months,
	415	+ quarters, years) were never seen in training. A one-hot encoder would
	416	+ silently price them at the baseline period; the honest forecasting
	417	+ rule for a static model is to freeze the price level at the last
	418	+ period observed in training, so unseen time labels are remapped to the
	419	+ latest training label before prediction. Tree ensembles are piecewise
	420	+ constant in the month counter, so a test month beyond the training
	421	+ range is priced by the terminal leaf — the tree analogue of the same
	422	+ carry-forward rule.
	423	+
	424	+ Metrics are reported for the median-consistent prediction (main
	425	+ scoreboard, suffix none) and for the Duan-smeared mean prediction
	426	+ (suffix ``_mean``). With ``return_predictions`` the test-set
	427	+ predictions of every model are returned as a second DataFrame.
	428	+ """
	429	+ train, test = prepare(df, scheme)
271	430	y_test = test["price"].to_numpy(float)
272		− rows = []
273		− for spec in model_registry():
	431	+ rows, preds = [], {}
	432	+ for spec in (registry if registry is not None else model_registry()):
	433	+ spec = dict(spec)
274	434	t0 = time.time()
275		− pred, _ = fit_predict(dict(spec), train, test)
276		− met = _metrics(y_test, pred)
	435	+ fit_predict(spec, train, test, retransform="mean")
	436	+ p_med, p_mean = spec["pred_median"], spec["pred_mean"]
	437	+ met = _metrics(y_test, p_med)
	438	+ met_mean = {f"{k}_mean": v for k, v in
	439	+ _metrics(y_test, p_mean).items()}
277	440	rows.append({"name": spec["name"], "group": spec["group"],
278		− **met, "seconds": round(time.time() - t0, 1),
	441	+ met, met_mean,
	442	+ "smear": spec.get("smear", np.nan),
	443	+ "lambda": spec.get("lambda", np.nan),
	444	+ "best_iter": spec.get("best_iter", np.nan),
	445	+ "seconds": round(time.time() - t0, 1),
279	446	"n_train": len(train), "n_test": len(test)})
280		− print(f" [{scheme}] {spec['name']:<38} "
	447	+ preds[spec["name"]] = np.clip(p_med, config.PRED_FLOOR, None)
	448	+ print(f" [{scheme}] {spec['name']:<44} "
281	449	f"MdAPE={met['mdape']:5.1f}% R2_ln={met['r2_ln']:.3f} "
282	450	f"({rows[-1]['seconds']}s)")
283		− return pd.DataFrame(rows)
	451	+ res = pd.DataFrame(rows)
	452	+ if not return_predictions:
	453	+ return res
	454	+ P = test[["id", "sale_date", "price", "muni", "prop_class", "grid",
	455	+ "parcel", "coord"]].reset_index(drop=True)
	456	+ P["in_train_parcel"] = P["parcel"].isin(set(train["parcel"]))
	457	+ P["in_train_coord"] = P["coord"].isin(set(train["coord"]))
	458	+ for k, v in preds.items():
	459	+ P[k] = v
	460	+ return res, P

modified src/wp11/sample.py +8 −2

		`@@ -73,6 +73,12 @@ def build(raw: pd.DataFrame \| None = None) -> pd.DataFrame:`
73	73	df["prop_class"] = _property_class(df)
74	74	df["link"] = df["role_lien_physique"].map(LINK_MAP).fillna("unknown")
75	75	df["muni"] = df["role_code_mun"]
	76	+ # Grouping keys for leakage-free holdouts: the assessment-roll parcel
	77	+ # identifier (repeat sales of the same property) and the exact
	78	+ # geocoded coordinate pair (units sharing a building or complex).
	79	+ df["parcel"] = df["role_id_provinc"].astype(str)
	80	+ df["coord"] = (df["lat"].round(6).astype(str) + "_"
	81	+ + df["lng"].round(6).astype(str))
76	82	df["grid"] = ((df["lat"] / config.GRID_DEG).round().astype(int).astype(str)
77	83	+ "_" + (df["lng"] / config.GRID_DEG).round().astype(int).astype(str))
78	84	df["grid5"] = ((df["lat"] / config.GRID5_DEG).round().astype(int).astype(str)
		`@@ -91,8 +97,8 @@ def build(raw: pd.DataFrame \| None = None) -> pd.DataFrame:`
91	97	keep = ["id", "sale_date", "sale_year", "month", "quarter", "t",
92	98	"price", "ln_price", "area", "ln_area", "lot", "ln_lot", "has_lot",
93	99	"age", "floors", "units", "prop_class", "link",
94		− "muni", "grid", "grid5", "lat", "lng", "city",
95		− "role_municipalite"]
	100	+ "muni", "grid", "grid5", "parcel", "coord", "lat", "lng",
	101	+ "city", "role_municipalite"]
96	102	return df[keep].reset_index(drop=True)
97	103
98	104
99	105

spb/wp11_uqo

révision scientifique complète (editorial board, 2026-10-17)

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