spb/wp3_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2%3% ═══════════════════════════════════════════════════════════════════════4% 9. CONCLUSION5% ═══════════════════════════════════════════════════════════════════════6\section{Conclusion}7\label{sec:conclusion}89This paper has compared three approaches to hedonic housing price analysis---OLS,10quantile regression, and gradient-boosted machine learning with SHAP11interpretation---using a national sample of 788,842 U.S.\ Zillow listings. Each12framework answers a different question, and the robustness program documents the13boundaries of each framework's conclusions.1415OLS provides interpretable conditional mean associations whose signs and16magnitudes align with the meta-analytic record of hedonic housing studies17\citep{sirmans2005composition}: a price-to-area elasticity of 0.63, a 22.6\%18bathroom listing-price gradient, a 33.4\% foreclosure discount, and regional19listing-price differentials of 49\%--63\% between coastal and interior markets.20The progression from region fixed effects ($R^2 = 0.634$) to ZIP3 fixed effects21($R^2 = 0.725$) demonstrates---in line with the specification advice of22\citet{kuminoff2010which}---that fine-grained geographic controls capture23substantial variation, while the imputation sensitivity analysis shows the24lot-size gradient is attenuated threefold by state-median imputation.2526Quantile regression reveals that mean effects mask substantial distributional27heterogeneity, formally confirmed by inter-quantile Wald tests that reject28coefficient equality for 11 of 13 variables. The garage listing-price gradient is29ten times larger at the 10th percentile than the 90th ($z = 28.92$); the pool30gradient is insignificant below the median but reaches 9.9\% at $\tau = 0.90$.31Subsample stability analysis identifies age as the one coefficient that is32genuinely unstable across geographic subsamples.3334XGBoost captures non-linearities and interactions that improve prediction from35$R^2 = 0.630$ (OLS) to $R^2 = 0.833$ under random validation. That figure,36however, substantially overstates generalization to new markets. The ablation37analysis attributes the largest predictive gain to neighborhood features38($+17.6$ pp) and shows that the full model with region dummies actively harms39geographic holdout performance ($-7.6$ pp); removing all geographic features40\emph{improves} geographic holdout $R^2$ from 0.425 to 0.519, while adding41latitude and longitude does the opposite ($+3.7$ pp random, $-5.5$ pp42geographic). Geographic features help the model memorize location-specific price43levels but do not improve---and can degrade---its ability to transfer44attribute-price relationships to unseen markets.4546SHAP values identify the features contributing most to predictions---living47area, bathrooms, school quality, lot size, region---and this ranking is stable48across three tree-based models (Spearman $\rho = 0.89$--$0.99$). These remain49predictive decompositions rather than implicit prices, a distinction the50explainability literature itself insists upon \citep{rudin2019stop}. Moran's51$I = 0.27$ on OLS residuals---stable across subsamples---confirms that regional52controls leave substantial spatial dependence unaddressed.5354The central contribution is methodological: model evaluation in spatially55dependent housing data hinges on validation design, and the random-versus-blocked56distinction developed in ecology \citep{roberts2017cross, ploton2020spatial,57meyer2021predicting, wadoux2021spatial} transfers directly---and consequentially58---to hedonic economics. Random splits answer the interpolation question; held-out59regions answer the extrapolation question; and the two rank both models and60feature sets differently. Studies comparing machine learning to hedonic61regression on random splits alone will systematically overstate the practical ML62advantage for any application involving new markets.6364Several extensions follow naturally. Spatial econometric estimation65\citep{lesage2009introduction} would model the dependence we only diagnose;66replication on transaction prices would quantify the listing-price wedge that the67seller-behavior literature predicts \citep{genesove2001loss, han2016role};68climate-risk variables \citep{bernstein2019disaster, murfin2020risk} are a69first-order omission our residual diagnostics likely reflect; generalized70additive models would decompose the ML gain into non-linearity versus spatial71partitioning; and finer geographic blocking would map the continuum between our72two validation extremes. We would regard geographic holdout validation, reported73alongside random validation, as a reasonable default for future ML-hedonic74comparisons.7576The broader lesson is not that machine learning replaces hedonic econometrics,77nor the reverse. Prediction, distributional heterogeneity, and economic78interpretation are different questions; each of the tools examined here is strong79on exactly one of them, and honest housing-market analysis will continue to80require all three---each validated against the question it is actually meant to81answer.82