% Author: Simon-Pierre Boucher — contact@spboucher.ai % % ═══════════════════════════════════════════════════════════════════════ % 1. INTRODUCTION % ═══════════════════════════════════════════════════════════════════════ \section{Introduction} \label{sec:introduction} Housing is the dominant asset in the typical American household's portfolio, the collateral underpinning the largest class of household debt, and a central object of study in urban economics, household finance, and public policy. How housing attributes map into prices matters far beyond academia: property-tax assessment, mortgage underwriting, and the automated valuation models (AVMs) that increasingly mediate transactions all rest on some version of that mapping. The hedonic pricing framework---formalized by \citet{rosen1974hedonic} on the consumer-theoretic foundations of \citet{lancaster1966new}, with empirical roots stretching back to \citet{waugh1928quality} and \citet{court1939hedonic}---provides the canonical approach: decompose observed prices into the implicit valuations of constituent characteristics. Yet after five decades of applied hedonic research, three methodological tensions remain unresolved, and the arrival of machine-learning valuation has sharpened rather than settled them. First, the standard OLS hedonic model imposes a (log-)linear relationship between attributes and prices, an assumption chosen largely for robustness under attribute omission \citep{cropper1988choice} but one that may poorly approximate the non-linear, interactive structure of housing markets. Second, by estimating conditional mean effects, OLS constrains implicit prices to be constant across the price distribution---a restriction the quantile-regression literature has shown to be empirically untenable \citep{zietz2008determinants, mcmillen2008changes, liao2012hedonic}. Third, while gradient-boosted models deliver large predictive gains in property valuation \citep{bourassa2010predicting, kok2017big}, their black-box character limits adoption where economic interpretation matters \citep{mullainathan2017machine, athey2019machine}---and, as this paper documents, their headline accuracy can be a partial illusion created by the way they are evaluated. This paper confronts the three tensions on a single dataset of 788,842 active Zillow listings covering all 50 U.S. states and the District of Columbia, with 62 regressors spanning structural attributes, lot characteristics, amenities, neighborhood quality, market status, and six interaction terms. We estimate three families of models, each answering a distinct question: \begin{enumerate}[nosep] \item \textbf{Semi-log OLS} with HC3 robust standard errors---and progressively finer geographic fixed effects---for interpretable conditional mean associations; \item \textbf{Quantile regression} at five quantiles, with formal inter-quantile Wald tests, for distribution-specific listing-price gradients; \item \textbf{Gradient-boosted ensembles} (XGBoost, LightGBM) with SHAP-based interpretation \citep{lundberg2017unified} for non-linear prediction. \end{enumerate} The core methodological contribution is a systematic examination of \textbf{spatial leakage} in hedonic model evaluation. Housing data are spatially dependent: nearby properties share unobserved local price determinants \citep{dubin1998spatial, basu1998analysis}. Standard random train-test splits therefore allow information to leak from training to test sets through spatial proximity, inflating out-of-sample performance---a phenomenon documented in ecology and geostatistics \citep{roberts2017cross, ploton2020spatial, meyer2021predicting} but rarely confronted in housing economics. We quantify its consequences through three complementary designs: (i) a \emph{geographic holdout} in which ten entire states (438,315 listings) are withheld from training; (ii) a six-stage \emph{ablation cascade} that traces the XGBoost predictive gain to specific feature groups under both validation schemes and reveals that region dummies actively \emph{harm} geographic generalization; and (iii) a \emph{coordinate experiment} in which adding raw latitude and longitude boosts random-split $R^2$ by 3.7 percentage points while \emph{reducing} geographic holdout $R^2$ by 5.5 percentage points. Together these designs show that the gap between random and geographic validation is not a matter of degree: the two protocols measure qualitatively different model capabilities---interpolation within observed markets versus extrapolation to new ones---and they rank feature sets differently. Our contribution is methodological and empirical, not causal. Following the identification literature \citep{bartik1987estimation, ekeland2004identification, kuminoff2013new, bishop2020best}, we interpret all estimates as conditional associations in \emph{listing} prices---capitalization gradients in asking prices---rather than structural willingness-to-pay parameters, and we engage the listing-price microstructure literature \citep{horowitz1992role, genesove2001loss, han2016role} when drawing that distinction. Within that discipline, the paper makes four contributions: \begin{enumerate}[nosep] \item \textbf{Geographic granularity in OLS.} Progressively finer spatial fixed effects (region $\rightarrow$ state $\rightarrow$ ZIP3) raise $R^2$ from 0.634 to 0.725, providing national-scale, prediction-oriented evidence for the specification advice of \citet{kuminoff2010which}; residual Moran's $I$ of 0.27 shows that even ZIP3 controls leave substantial spatial structure unabsorbed. \item \textbf{Formal distributional heterogeneity.} Inter-quantile Wald tests reject coefficient equality between the 10th and 90th conditional percentiles for 11 of 13 key attributes; the pattern (garage and living-area gradients concentrated at the bottom of the distribution, pool and lot-size gradients at the top) is stable across ten independent subsamples. \item \textbf{Anatomy of the ML advantage.} XGBoost's $R^2 = 0.833$ under random validation falls to 0.425--0.547 under state-level holdout; removing all geographic features \emph{improves} geographic holdout $R^2$ to 0.519. The ablation traces the random-validation gain primarily to neighborhood-quality variables ($+17.6$ pp) and shows their contribution largely fails to transfer across states. \item \textbf{Cross-model stability of SHAP.} Importance rankings correlate at $\rho = 0.89$--$0.99$ across XGBoost, LightGBM, and random forests, supporting SHAP as a description of predictive structure while our framing---informed by the explainability debate \citep{rudin2019stop}---keeps it distinct from Rosen's implicit prices. \end{enumerate} For practitioners, the message is direct: in AVM deployment contexts that require generalization to unfamiliar markets, validation design is not a technicality but the difference between a model that appears excellent and one that actually transfers; and geographic features, however helpful in-sample, can be counterproductive out-of-market \citep{steurer2021metrics}. For researchers, the results argue that random-split accuracy comparisons between ML and hedonic models---now common in the literature---systematically overstate the ML advantage whenever the deployment question involves new locations. The remainder of the paper is organized as follows. Section~\ref{sec:literature} situates the study in the hedonic, quantile, machine-learning, and spatial-validation literatures. Section~\ref{sec:data} describes the data, sample construction, variable coding, and the listing-price caveat. Section~\ref{sec:methodology} presents the econometric and machine-learning methodology, the three validation designs, and the interpretation framework. Section~\ref{sec:results} reports estimation results across the three model families. Section~\ref{sec:robustness} presents imputation, winsorization, and subsample-stability checks. Section~\ref{sec:discussion} interprets the findings against the literature, Section~\ref{sec:limitations} enumerates limitations, and Section~\ref{sec:conclusion} concludes.