spb/wp3_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2%3% ═══════════════════════════════════════════════════════════════════════4% 1. INTRODUCTION5% ═══════════════════════════════════════════════════════════════════════6\section{Introduction}7\label{sec:introduction}89Housing is the dominant asset in the typical American household's portfolio, the10collateral underpinning the largest class of household debt, and a central object11of study in urban economics, household finance, and public policy. How housing12attributes map into prices matters far beyond academia: property-tax assessment,13mortgage underwriting, and the automated valuation models (AVMs) that increasingly14mediate transactions all rest on some version of that mapping. The hedonic pricing15framework---formalized by \citet{rosen1974hedonic} on the consumer-theoretic16foundations of \citet{lancaster1966new}, with empirical roots stretching back to17\citet{waugh1928quality} and \citet{court1939hedonic}---provides the canonical18approach: decompose observed prices into the implicit valuations of constituent19characteristics. Yet after five decades of applied hedonic research, three20methodological tensions remain unresolved, and the arrival of machine-learning21valuation has sharpened rather than settled them.2223First, the standard OLS hedonic model imposes a (log-)linear relationship between24attributes and prices, an assumption chosen largely for robustness under attribute25omission \citep{cropper1988choice} but one that may poorly approximate the26non-linear, interactive structure of housing markets. Second, by estimating27conditional mean effects, OLS constrains implicit prices to be constant across the28price distribution---a restriction the quantile-regression literature has shown to29be empirically untenable \citep{zietz2008determinants, mcmillen2008changes,30liao2012hedonic}. Third, while gradient-boosted models deliver large predictive31gains in property valuation \citep{bourassa2010predicting, kok2017big}, their32black-box character limits adoption where economic interpretation matters33\citep{mullainathan2017machine, athey2019machine}---and, as this paper documents,34their headline accuracy can be a partial illusion created by the way they are35evaluated.3637This paper confronts the three tensions on a single dataset of 788,842 active38Zillow listings covering all 50 U.S. states and the District of Columbia, with 6239regressors spanning structural attributes, lot characteristics, amenities,40neighborhood quality, market status, and six interaction terms. We estimate three41families of models, each answering a distinct question:42\begin{enumerate}[nosep]43    \item \textbf{Semi-log OLS} with HC3 robust standard errors---and progressively44    finer geographic fixed effects---for interpretable conditional mean45    associations;46    \item \textbf{Quantile regression} at five quantiles, with formal47    inter-quantile Wald tests, for distribution-specific listing-price gradients;48    \item \textbf{Gradient-boosted ensembles} (XGBoost, LightGBM) with SHAP-based49    interpretation \citep{lundberg2017unified} for non-linear prediction.50\end{enumerate}5152The core methodological contribution is a systematic examination of53\textbf{spatial leakage} in hedonic model evaluation. Housing data are spatially54dependent: nearby properties share unobserved local price determinants55\citep{dubin1998spatial, basu1998analysis}. Standard random train-test splits56therefore allow information to leak from training to test sets through spatial57proximity, inflating out-of-sample performance---a phenomenon documented in58ecology and geostatistics \citep{roberts2017cross, ploton2020spatial,59meyer2021predicting} but rarely confronted in housing economics. We quantify its60consequences through three complementary designs: (i) a \emph{geographic holdout}61in which ten entire states (438,315 listings) are withheld from training; (ii) a62six-stage \emph{ablation cascade} that traces the XGBoost predictive gain to63specific feature groups under both validation schemes and reveals that region64dummies actively \emph{harm} geographic generalization; and (iii) a65\emph{coordinate experiment} in which adding raw latitude and longitude boosts66random-split $R^2$ by 3.7 percentage points while \emph{reducing} geographic67holdout $R^2$ by 5.5 percentage points. Together these designs show that the gap68between random and geographic validation is not a matter of degree: the two69protocols measure qualitatively different model capabilities---interpolation70within observed markets versus extrapolation to new ones---and they rank feature71sets differently.7273Our contribution is methodological and empirical, not causal. Following the74identification literature \citep{bartik1987estimation, ekeland2004identification,75kuminoff2013new, bishop2020best}, we interpret all estimates as conditional76associations in \emph{listing} prices---capitalization gradients in asking77prices---rather than structural willingness-to-pay parameters, and we engage the78listing-price microstructure literature \citep{horowitz1992role, genesove2001loss,79han2016role} when drawing that distinction. Within that discipline, the paper80makes four contributions:8182\begin{enumerate}[nosep]83    \item \textbf{Geographic granularity in OLS.} Progressively finer spatial84    fixed effects (region $\rightarrow$ state $\rightarrow$ ZIP3) raise $R^2$ from85    0.634 to 0.725, providing national-scale, prediction-oriented evidence for the86    specification advice of \citet{kuminoff2010which}; residual Moran's $I$ of87    0.27 shows that even ZIP3 controls leave substantial spatial structure88    unabsorbed.89    \item \textbf{Formal distributional heterogeneity.} Inter-quantile Wald tests90    reject coefficient equality between the 10th and 90th conditional percentiles91    for 11 of 13 key attributes; the pattern (garage and living-area gradients92    concentrated at the bottom of the distribution, pool and lot-size gradients at93    the top) is stable across ten independent subsamples.94    \item \textbf{Anatomy of the ML advantage.} XGBoost's $R^2 = 0.833$ under95    random validation falls to 0.425--0.547 under state-level holdout; removing96    all geographic features \emph{improves} geographic holdout $R^2$ to 0.519.97    The ablation traces the random-validation gain primarily to98    neighborhood-quality variables ($+17.6$ pp) and shows their contribution99    largely fails to transfer across states.100    \item \textbf{Cross-model stability of SHAP.} Importance rankings correlate at101    $\rho = 0.89$--$0.99$ across XGBoost, LightGBM, and random forests, supporting102    SHAP as a description of predictive structure while our framing---informed by103    the explainability debate \citep{rudin2019stop}---keeps it distinct from104    Rosen's implicit prices.105\end{enumerate}106107For practitioners, the message is direct: in AVM deployment contexts that require108generalization to unfamiliar markets, validation design is not a technicality but109the difference between a model that appears excellent and one that actually110transfers; and geographic features, however helpful in-sample, can be111counterproductive out-of-market \citep{steurer2021metrics}. For researchers, the112results argue that random-split accuracy comparisons between ML and hedonic113models---now common in the literature---systematically overstate the ML advantage114whenever the deployment question involves new locations.115116The remainder of the paper is organized as follows.117Section~\ref{sec:literature} situates the study in the hedonic, quantile,118machine-learning, and spatial-validation literatures.119Section~\ref{sec:data} describes the data, sample construction, variable coding,120and the listing-price caveat. Section~\ref{sec:methodology} presents the121econometric and machine-learning methodology, the three validation designs, and122the interpretation framework. Section~\ref{sec:results} reports estimation123results across the three model families. Section~\ref{sec:robustness} presents124imputation, winsorization, and subsample-stability checks.125Section~\ref{sec:discussion} interprets the findings against the literature,126Section~\ref{sec:limitations} enumerates limitations, and127Section~\ref{sec:conclusion} concludes.128