# WP21 — Pre-registered analysis protocol (written before data construction, 2026-10-20)

# 1. Objectives

Quantitative synthesis of implicit prices of residential characteristics (RQ1–RQ8 of CLAUDE.md), extending Sirmans, Macpherson & Zietz (2005) and Sirmans, MacDonald, Macpherson & Zietz (2006) in coverage (global, 1970–2026), harmonisation (effect-size families), econometrics (multilevel/robust/Bayesian meta-regression, publication selection) and scope (spatial and AI-enhanced models).

# 2. Primary characteristics (pre-specified; pooled only if ≥10 independent studies with usable SEs)

Living area (elasticity or % per unit), lot size, age, bedrooms, bathrooms, garage/parking, swimming pool, fireplace, air conditioning, basement, number of storeys, distance to CBD, distance to transit, school quality, crime, air pollution, noise, flood risk, green space/parks, water view/waterfront, energy efficiency rating. Secondary characteristics: everything else in the taxonomy (reported descriptively; pooled when ≥5 studies).

# 3. Primary effect-size family per characteristic

Binary attributes (pool, garage, AC, fireplace, basement, waterfront, view, flood zone, energy label): percentage premium 100[exp(β)−1] from log-price models (Kennedy-type adjustment reported as sensitivity); level-price models converted only when a sample mean price is reported (flagged). Continuous attributes (area, lot, age, bedrooms, bathrooms, distances, pollution, crime, income): semi-elasticities (% per unit) from log-linear models and elasticities from log-log models, kept in separate families; units harmonised (m², km, years). Partial correlations r = t/sqrt(t²+df) computed for all estimates as a unit-free secondary family.

# 4. Models (pre-specified)

M1 random-effects REML per characteristic × family (metafor rma.uni, Python cross-check). M2 three-level model (estimates within studies) rma.mv with study and estimate random effects; RVE (clubSandwich CR2) inference. M3 meta-regression with moderators: continent, income group (World Bank), data-period midpoint (not publication year), property type, outcome type (price/listing/rent), estimator (OLS / spatial / ML-derived), FE for time/location, publication type, sample size (log). M4 publication selection: funnel asymmetry (Egger), PET-PEESE on families with ≥20 estimates, selection-model sensitivity (Vevea–Hedges step function) when k ≥ 30; published vs working-paper contrast. M5 Bayesian hierarchical model (weakly informative priors: effect ~ N(0, 10²) on the % scale, τ ~ half-Cauchy(0, 5)) for the primary characteristics; R-hat and ESS reported. M6 exploratory ML meta-regression (random forest, gradient boosting) with study-grouped cross-validation; reported as exploratory.

# 5. Hypotheses (directional, pre-specified)

H1 living area, bathrooms, garage, pool, AC, fireplace, waterfront/view: positive; age, distance to CBD (in monocentric samples), pollution, noise, crime, flood zone: negative; bedrooms: ambiguous conditional on area. H2 Heterogeneity (I²) above 75 % for every characteristic. H3 Spatial and ML-derived marginal effects do not differ systematically from OLS once moderators are controlled (null tested). H4 Small-study effects present for "signature" amenities (pool, view, waterfront) but not for area. H5 Implicit prices of energy efficiency and green space rise over data periods after 2008.

# 6. Validation

Independent double extraction of a random 15 % of included studies (minimum 20); report agreement on coefficient, SE, sign, variable mapping; primary synthesis restricted to validated or high-confidence extractions; sensitivity including all.

# 7. Deviations

Any deviation from this protocol is logged in reports/methodological_decisions.md with its reason and date.