% Author: Simon-Pierre Boucher — contact@spboucher.ai
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% 9. CONCLUSION
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\section{Conclusion}
\label{sec:conclusion}

This paper has compared three approaches to hedonic housing price analysis---OLS,
quantile regression, and gradient-boosted machine learning with SHAP
interpretation---using a national sample of 788,842 U.S.\ Zillow listings. Each
framework answers a different question, and the robustness program documents the
boundaries of each framework's conclusions.

OLS provides interpretable conditional mean associations whose signs and
magnitudes align with the meta-analytic record of hedonic housing studies
\citep{sirmans2005composition}: a price-to-area elasticity of 0.63, a 22.6\%
bathroom listing-price gradient, a 33.4\% foreclosure discount, and regional
listing-price differentials of 49\%--63\% between coastal and interior markets.
The progression from region fixed effects ($R^2 = 0.634$) to ZIP3 fixed effects
($R^2 = 0.725$) demonstrates---in line with the specification advice of
\citet{kuminoff2010which}---that fine-grained geographic controls capture
substantial variation, while the imputation sensitivity analysis shows the
lot-size gradient is attenuated threefold by state-median imputation.

Quantile regression reveals that mean effects mask substantial distributional
heterogeneity, formally confirmed by inter-quantile Wald tests that reject
coefficient equality for 11 of 13 variables. The garage listing-price gradient is
ten times larger at the 10th percentile than the 90th ($z = 28.92$); the pool
gradient is insignificant below the median but reaches 9.9\% at $\tau = 0.90$.
Subsample stability analysis identifies age as the one coefficient that is
genuinely unstable across geographic subsamples.

XGBoost captures non-linearities and interactions that improve prediction from
$R^2 = 0.630$ (OLS) to $R^2 = 0.833$ under random validation. That figure,
however, substantially overstates generalization to new markets. The ablation
analysis attributes the largest predictive gain to neighborhood features
($+17.6$ pp) and shows that the full model with region dummies actively harms
geographic holdout performance ($-7.6$ pp); removing all geographic features
\emph{improves} geographic holdout $R^2$ from 0.425 to 0.519, while adding
latitude and longitude does the opposite ($+3.7$ pp random, $-5.5$ pp
geographic). Geographic features help the model memorize location-specific price
levels but do not improve---and can degrade---its ability to transfer
attribute-price relationships to unseen markets.

SHAP values identify the features contributing most to predictions---living
area, bathrooms, school quality, lot size, region---and this ranking is stable
across three tree-based models (Spearman $\rho = 0.89$--$0.99$). These remain
predictive decompositions rather than implicit prices, a distinction the
explainability literature itself insists upon \citep{rudin2019stop}. Moran's
$I = 0.27$ on OLS residuals---stable across subsamples---confirms that regional
controls leave substantial spatial dependence unaddressed.

The central contribution is methodological: model evaluation in spatially
dependent housing data hinges on validation design, and the random-versus-blocked
distinction developed in ecology \citep{roberts2017cross, ploton2020spatial,
meyer2021predicting, wadoux2021spatial} transfers directly---and consequentially
---to hedonic economics. Random splits answer the interpolation question; held-out
regions answer the extrapolation question; and the two rank both models and
feature sets differently. Studies comparing machine learning to hedonic
regression on random splits alone will systematically overstate the practical ML
advantage for any application involving new markets.

Several extensions follow naturally. Spatial econometric estimation
\citep{lesage2009introduction} would model the dependence we only diagnose;
replication on transaction prices would quantify the listing-price wedge that the
seller-behavior literature predicts \citep{genesove2001loss, han2016role};
climate-risk variables \citep{bernstein2019disaster, murfin2020risk} are a
first-order omission our residual diagnostics likely reflect; generalized
additive models would decompose the ML gain into non-linearity versus spatial
partitioning; and finer geographic blocking would map the continuum between our
two validation extremes. We would regard geographic holdout validation, reported
alongside random validation, as a reasonable default for future ML-hedonic
comparisons.

The broader lesson is not that machine learning replaces hedonic econometrics,
nor the reverse. Prediction, distributional heterogeneity, and economic
interpretation are different questions; each of the tools examined here is strong
on exactly one of them, and honest housing-market analysis will continue to
require all three---each validated against the question it is actually meant to
answer.
