% Author: Simon-Pierre Boucher — contact@spboucher.ai
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\section{Literature Review} \label{sec:literature}
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This paper sits at the intersection of four literatures: the hedonic pricing tradition in housing economics, the text-as-data program in empirical economics, the emerging body of work on unstructured data in real estate, and the natural language processing literature on sentence embeddings. We review each in turn and then articulate the gap this paper fills.

\subsection{Hedonic Pricing Theory and Housing Markets}

The idea that the price of a differentiated good can be decomposed into the implicit prices of its characteristics predates modern housing economics: hedonic price indexes were computed for automobiles as early as the 1930s, and the approach was systematized for quality-adjusted price measurement by \citet{griliches1971price}. Its theoretical foundations rest on \citet{lancaster1966new}, who reconceptualized consumer theory around the characteristics of goods rather than goods themselves, and \citet{rosen1974hedonic}, who formalized the framework for differentiated product markets. In Rosen's model, the observed market price of a differentiated good reflects the equilibrium of supply and demand for its constituent characteristics, allowing the researcher to recover the implicit marginal prices of individual attributes through regression analysis. \citet{palmquist1984estimating} extended the theoretical framework by showing how second-stage supply and demand identification depends on exogenous variation in household characteristics and builder cost structures, while \citet{epple1987hedonic} demonstrated that under certain conditions the hedonic price function is unique and recoverable. The modern identification literature has clarified both the power and the limits of the approach: \citet{ekeland2004identification} establish conditions under which preferences can be recovered from a single hedonic market, \citet{bajari2005demand} develop estimators that accommodate unobserved product characteristics---the very problem that listing text addresses in our setting---and \citet{kuminoff2013new} survey how equilibrium sorting across housing markets shapes the interpretation of hedonic estimates. This literature underpins the interpretive caution we adopt in Section~\ref{sec:identification}: cross-sectional hedonic coefficients are equilibrium price gradients, not structural willingness-to-pay parameters.

In the housing context, the hedonic approach yields the canonical specification:
\begin{equation}
\ln(P_i) = \alpha + \bfbeta' \bfX_i + \eps_i \label{eq:hedonic}
\end{equation}
where $P_i$ is the price of property $i$, $\bfX_i$ is a vector of structural, locational, and neighborhood attributes, and $\bfbeta$ captures the implicit marginal prices. The semi-logarithmic functional form, recommended by \citet{halvorsen1981choice} and widely adopted in the literature, allows coefficients to be interpreted as approximate percentage changes in price for a unit change in the characteristic. \citet{cropper1988choice} evaluated alternative functional forms through Monte Carlo experiments, finding that simpler parametric specifications (linear and log-linear) outperform flexible Box-Cox transformations when variables are measured with error or important attributes are omitted.

The empirical literature on hedonic housing models is vast. \citet{sirmans2005composition} surveyed the composition of hedonic models and identified bedrooms, bathrooms, lot size, age, square footage, and proximity to central business districts as the most frequently included variables. \citet{sirmans2006empirical} conducted a meta-analysis of 64 hedonic studies, finding that bathrooms, square footage, and lot size consistently exhibit the largest marginal effects. \citet{malpezzi2003hedonic} provided a comprehensive review of methodological issues, including functional form selection, spatial autocorrelation, and multicollinearity. Two extensions of the baseline framework are particularly relevant here. First, \textit{quantile hedonics}: \citet{zietz2007determinants} show that the implicit prices of housing attributes vary systematically across the conditional price distribution, with many characteristics valued more highly in upper price segments, and \citet{mcmillen2008changes} uses quantile methods to decompose changes in the entire distribution of house prices. Our quantile analysis in Section~\ref{sec:robustness} extends this logic to text-derived characteristics. Second, \textit{spatial hedonics}: housing data are spatially dependent, and a long literature---\citet{anselin1988spatial}, \citet{dubin1988estimation}, and \citet{can1992specification} among the foundations---has developed specifications that absorb spatial autocorrelation in prices and errors; \citet{dube2014spatial} adapt these methods to the Canadian and Quebec microdata context. Closer to our setting still, a sustained research program using Quebec City transactions has quantified the capitalization of property attributes ranging from landscaping to accessibility \citep{desrosiers2002landscaping}. In the amenity-capitalization literature more broadly, \citet{cheshire2004capitalisation} demonstrate school-quality capitalization in local housing markets and \citet{gibbons2014costs} documents the discount associated with visual environmental disamenities, while \citet{irwin2002effects} and \citet{tyrvainen2005benefits} establish the positive value of open space and urban vegetation.

A persistent challenge in hedonic pricing is the omitted variable bias arising from unobserved quality attributes. \citet{pakes2003reconsideration} argued that standard hedonic regressions yield biased implicit price estimates when important product characteristics are unobservable to the econometrician but observable to market participants. This concern is directly relevant to our study: listing descriptions may convey quality information---about finish materials, maintenance history, or neighborhood ambiance---that is not captured by conventional structural variables but is fully observable to buyers.

More recently, machine learning methods have been applied to hedonic pricing and mass appraisal, including random forests \citep{hong2020house}, penalized variable selection \citep{yoo2012variable}, and large-feature-set automated valuation \citep{kok2017big}. While these methods typically achieve superior predictive accuracy, they sacrifice the coefficient interpretability that is central to the hedonic framework's appeal for policy analysis and market valuation---a general tension in the adoption of machine learning by applied economists \citep{varian2014big, mullainathan2017machine, athey2019machine, dell2025deep}. Our approach seeks to recover this interpretability while incorporating the rich informational content of textual data.

\subsection{Text as Data in Economics}

Our methodology is best understood as an instance of the broader \textit{text-as-data} program in empirical economics, surveyed by \citet{gentzkow2019text} and, with a focus on modern deep-learning representations, by \citet{ash2023text}. This literature organizes text-based empirical work around a common two-step structure: first, represent documents as quantitative features; second, use those features in an economic model. The representation step has evolved from hand-built dictionaries---word lists whose counts proxy for a concept of interest, the workhorse of the finance literature on disclosure tone \citep{loughran2011liability, loughran2016textual}---through topic models \citep{blei2003latent, hansen2017transparency} to dense neural embeddings.

Dictionary methods remain attractive to economists precisely because they are transparent: the researcher names the concept, and the mapping from text to feature is auditable. Their weakness is lexical brittleness---a dictionary counts only the exact words it enumerates. Embedding-based representations solve the brittleness problem but break the transparency: a 384-dimensional vector has no nameable economic content. Our reference-description approach is designed to occupy the point between these extremes: like a dictionary, each feature is defined ex ante by the researcher and carries a name and an expected sign; like an embedding method, the mapping from text to feature is semantic rather than lexical, so paraphrases and synonyms load on the same dimension. In the taxonomy of \citet{gentzkow2019text}, it is a supervised projection of an unsupervised representation, with the supervision supplied by domain knowledge rather than by labeled data. Applications elsewhere in economics illustrate the payoff of interpretable text features: \citet{hansen2017transparency} measure deliberation in central bank transcripts, and \citet{marinescu2020opening} show that the words of job postings materially affect matching in labor markets.

\subsection{Text and Unstructured Data in Real Estate}

The incorporation of textual data into real estate analysis represents a growing but still nascent literature. An early strand asked whether agent remarks matter at all: \citet{haag2000real} found that specific remark categories in MLS listings are associated with price and marketing-time differentials, and \citet{pryce2008rhetoric} documented the systematic rhetorical strategies of real estate advertising, showing that listing language is a deliberate marketing instrument rather than neutral description. \citet{goodwin2014broker} showed that broker vernacular affects both selling price and liquidity, and \citet{goodwin2018connotation} distinguished the positive and negative connotations of listing wording. Because listing text is strategically produced, its information content connects to the theory of voluntary disclosure \citep{grossman1981informational, milgrom1981good} and to the evidence that informed intermediaries exploit textual and informational advantages \citep{levitt2008information}.

A second strand quantifies the price-relevant information in the text itself. \citet{nowak2017quality} were among the first to embed listing-comment features in formal hedonic estimation, showing that words in agent comments proxy for unobserved quality and materially reduce omitted variable bias in the estimates of other coefficients. \citet{shen2020text} pushed this agenda furthest to date: applying machine learning to property descriptions, they show that text contains substantial information about otherwise unobserved property quality and that this information predicts prices beyond structured attributes. Sentiment-based approaches summarize the tone of housing narratives \citep{zhu2023sentiment}, and recent automated-valuation work incorporates full description text into machine learning pipelines \citep{baur2023automated}. Listing language also encodes neighborhood characteristics beyond the property itself: \citet{delmelle2021language} show that the text of property advertisements predicts neighborhood socioeconomic composition and change, a reminder that text features may capture locational as well as structural variation---a theme central to our identification discussion in Section~\ref{sec:identification}.

Text is not the only unstructured signal attached to a listing. A parallel literature extracts quality information from listing \textit{photographs}: \citet{glaeser2018computer} show that exterior appearance predicts prices and renovation returns, \citet{poursaeed2018vision} estimate interior quality from listing photos and improve price prediction, and \citet{law2019take} combine street-view and satellite imagery with structured attributes. We view text and images as complementary members of the same family: both reveal quality dimensions that structured fields omit, and both raise the same interpretability challenge when processed by deep networks. Topic models offer one interpretable middle ground for text \citep{blei2003latent}, but their latent factors are difficult to name ex ante and are unstable in short, formulaic documents such as listings; our reference-based projection provides an alternative whose dimensions are fixed and named by design.

The tension between prediction and interpretation in text-augmented hedonic models mirrors a broader debate in applied econometrics. \citet{athey2019machine} provide a framework for thinking about when machine learning methods complement rather than replace traditional econometric approaches---specifically, they are most useful for constructing features (as in our reference-based approach) rather than for final-stage inference. Our work builds on these contributions while addressing the interpretability limitation that pervades existing NLP-based approaches in real estate economics.

\subsection{Sentence Embeddings and Semantic Textual Similarity}

Sentence embeddings map variable-length text into fixed-dimensional vector spaces where semantic similarity corresponds to geometric proximity. The development of contextual word representations through architectures such as ELMo \citep{peters2018deep} and subsequently BERT \citep{devlin2019bert} represented a paradigm shift from static word vectors \citep{mikolov2013distributed} to context-dependent representations. However, these models require cross-encoding for pairwise comparison, which scales quadratically with corpus size.

The Sentence-BERT framework \citep{reimers2019sentence} addressed this limitation by fine-tuning pre-trained transformer models using siamese and triplet network structures to produce embeddings optimized for cosine similarity comparisons. This approach enables efficient comparison of text pairs without requiring cross-encoding, which is computationally prohibitive for large-scale applications. Subsequent work by \citet{gao2021simcse} proposed contrastive learning objectives (SimCSE) that further improved embedding quality, while \citet{li2020sentence} demonstrated that sentence embeddings suffer from anisotropy---a geometric degeneration where embeddings occupy a narrow cone in the vector space---and proposed whitening transformations as a remedy.

The all-MiniLM-L6-v2 model \citep{wang2020minilm} is a distilled version of the MiniLM architecture that produces 384-dimensional embeddings. The model employs self-attention distillation, transferring knowledge from a larger teacher model to a compact student network. Despite its compact size (22.7M parameters), it achieves competitive performance on standard semantic textual similarity benchmarks while being substantially faster than BERT-base encoders \citep{wang2020minilm, muennighoff2023mteb}, which makes it suitable for encoding large corpora of property listings. For French text, the model's multilingual coverage---derived from its training on paraphrase data spanning multiple languages---provides adequate performance, though dedicated French models such as CamemBERT \citep{martin2020camembert} or FlauBERT \citep{le2020flaubert} could potentially improve semantic resolution for domain-specific vocabulary.

Our use of reference descriptions as fixed semantic anchors is also related to zero-shot classification, where label descriptions serve as textual anchors against which documents are scored without task-specific training \citep{yin2019benchmarking}. The difference is that we retain the continuous similarity scores as regression covariates rather than converting them into discrete class assignments, preserving the marginal-effect interpretation required by the hedonic framework.

Cosine similarity between two $L_2$-normalized embedding vectors $\mathbf{u}$ and $\mathbf{v}$ is defined as:
\begin{equation}
\text{sim}(\mathbf{u}, \mathbf{v}) = \frac{\mathbf{u} \cdot \mathbf{v}}{||\mathbf{u}|| \cdot ||\mathbf{v}||} = \mathbf{u} \cdot \mathbf{v} \label{eq:cosine}
\end{equation}
This measure ranges from $-1$ to $1$, with higher values indicating greater semantic similarity. For normalized vectors, cosine similarity reduces to the dot product, enabling efficient computation via matrix multiplication. The geometric interpretation is straightforward: cosine similarity measures the angle between two vectors in the embedding space, with a value of 1 indicating identical direction (perfect semantic alignment) and 0 indicating orthogonality (semantic independence). Negative values, while theoretically possible, are rare in practice for sentence embeddings due to the positivity bias inherent in transformer representations \citep{ethayarajh2019contextual}.

\subsection{Research Gap and Contribution}

The literatures above leave a two-sided gap. On the economics side, the text-as-data toolkit offers either transparent-but-brittle dictionaries or powerful-but-opaque embeddings, and the housing applications to date have prioritized prediction over the estimation of named implicit prices. On the NLP side, interpretable machine learning has developed post hoc explanation tools \citep{ribeiro2016why, lundberg2017unified} and arguments for inherently interpretable models in high-stakes settings \citep{rudin2019stop}, but these have not been adapted to the requirements of hedonic inference, where features must be defined ex ante, carry economic names, and enter a linear model with valid standard errors. Table~\ref{tab:literature_comparison} summarizes how our approach compares with existing methods along five dimensions.

\begin{table}[!htbp]
\centering
\caption{Comparison of text-based approaches in hedonic pricing.}
\label{tab:literature_comparison}
\small
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lC{1.8cm}C{1.8cm}C{1.8cm}C{1.8cm}C{2.4cm}}
\toprule
\textbf{Method} & \textbf{Semantic Depth} & \textbf{Interpret-ability} & \textbf{Scalability} & \textbf{Multi-lingual} & \textbf{Key Reference} \\
\midrule
Keyword counts & Low & High & High & No & \citet{nowak2017quality} \\
Broker vernacular / connotation & Low & High & High & No & \citet{goodwin2018connotation} \\
ML on text features & Low & Moderate & High & No & \citet{shen2020text} \\
Sentiment indices & Low & High & High & Yes & \citet{zhu2023sentiment} \\
LDA topics & Moderate & Low & Moderate & No & \citet{blei2003latent} \\
Neural embeddings (black-box) & High & None & Low & Limited & \citet{baur2023automated} \\
PCA on embeddings & High & None & High & Yes & --- \\
\textbf{Reference cosine} & \textbf{High} & \textbf{High} & \textbf{High} & \textbf{Yes} & \textbf{This paper} \\
\bottomrule
\end{tabular}
\end{adjustbox}
\end{table}

Our reference-based cosine similarity approach resolves the depth-interpretability tension by leveraging the deep semantic representations of transformer embeddings while producing features with clear economic interpretation. Each similarity score measures the degree to which a property's description resembles a researcher-defined qualitative archetype, yielding features that are both semantically meaningful and directly usable as right-hand-side variables in a hedonic regression.

This approach contributes to a broader methodological trend in applied economics where machine learning tools are used for feature construction rather than final-stage estimation \citep{athey2019machine, mullainathan2017machine, gentzkow2019text}. By treating embeddings as an intermediate representation and projecting them onto economically meaningful axes, we preserve the inferential advantages of OLS while exploiting the representational power of deep learning. The reference-based projection is also related to the concept of ``concept bottleneck models'' in interpretable machine learning \citep{koh2020concept}, where high-dimensional representations are channeled through human-interpretable intermediate concepts before reaching the prediction stage.
