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The preferred specification of the revised paper controls for the language of the listing, \nFsa{} forward-sortation-area fixed effects, a unit-corrected lot area and missing-value indicators, encodes the full text of each description with a multilingual encoder (chunk-and-pool, so that no text is truncated), and clusters standard errors by area. In that specification the twenty similarities add \prefDeltaRsq{} to the $R^2$ of log asking price (area-cluster bootstrap 95\% interval [\prefDeltaCiLo, \prefDeltaCiHi]; block $F(20,\,\prefBlockDfDen) = \prefBlockF$), and the English contrast is \enPref\% [\enPrefLo, \enPrefHi]. Out of sample, with fixed effects estimated on the training folds, the block adds \incPrefRand{} of $R^2$ under random five-fold cross-validation and \incPrefFsa{} under folds that hold out entire forward sortation areas (twenty repetitions each; Clark--West \testCwPrefRandP{} and \testCwPrefFsaP), \incPrefLoro{} when entire administrative regions are held out, and \incPrefDist{} under distance-blocked folds with a 10~km buffer, where the fixed-effects models themselves collapse (\Cref{sec:oos}). The text carries information beyond structure and location; how much depends on how far the held-out listings are from the training data. |
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−The audit's second finding concerns the twenty named coefficients. The first version of the paper claimed that five dimensions kept their sign and significance across all specifications and both encoders. We now estimate the twenty coefficients over a grid of eleven specifications and five encoder variants, adjust for multiplicity within each cell (Holm and Romano--Wolf), and apply a criterion written down before the run: a dimension is robust if it keeps its baseline sign and is Holm-significant in at least 90\% of the cells. \nRobustHolm{} dimension meets it, Luxury (\survLuxeHolm\% of cells, \survLuxeRw\% under Romano--Wolf). Over 200 random rephrasings of the references, Luxury survives in \phrPrefLuxe\% of the draws under the preferred specification and \phrDLuxe\% under the first-version baseline; no dimension meets the criterion in both the specification grid and the phrasing multiverse. The block-level fit is stable throughout (the standard deviation of the block's $R^2$ gain over the 200 phrasings is at most \mvSdMax). Two facts explain the pattern. The fitted values of a model with twenty projections depend only on the span of the reference embeddings, so that any invertible recombination of the references leaves the fit unchanged and reparametrises the coefficients (we verify this numerically to $\spanDiffRsq$ in $R^2$); each coefficient prices the part of a reference that is orthogonal to the other nineteen, not the dimension its name suggests. And the baseline features do not discriminate what their names say: against a 300-listing sample coded by two independent passes of a large language model (LLM-coded, not human-coded), the raw baseline similarities have areas under the ROC curve between \aucMiniRawMin{} and \aucMiniRawMax{} for their own dimension, whereas the centred multilingual scores reach \aucMlCentredMin{} to \aucMlCentredMax. |
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+The audit's second finding concerns the twenty named coefficients. The first version of the paper claimed that five dimensions kept their sign and significance across all specifications and both encoders. We now estimate the twenty coefficients over a grid of eleven specifications and five encoder variants, adjust for multiplicity within each cell (Holm and Romano--Wolf), and apply a criterion written down before the run: a dimension is robust if it keeps its baseline sign and is Holm-significant in at least 90\% of the cells. The criterion is met by \nRobustHolm{} dimension, Luxury (\survLuxeHolm\% of cells, \survLuxeRw\% under Romano--Wolf). Over 200 random rephrasings of the references, Luxury survives in \phrPrefLuxe\% of the draws under the preferred specification and \phrDLuxe\% under the first-version baseline; no dimension meets the criterion in both the specification grid and the phrasing multiverse. The block-level fit is stable throughout (the standard deviation of the block's $R^2$ gain over the 200 phrasings is at most \mvSdMax). Two facts explain the pattern. The fitted values of a model with twenty projections depend only on the span of the reference embeddings, so that any invertible recombination of the references leaves the fit unchanged and reparametrises the coefficients (we verify this numerically to $\spanDiffRsq$ in $R^2$); each coefficient prices the part of a reference that is orthogonal to the other nineteen, not the dimension its name suggests. And the baseline features do not discriminate what their names say: against a 300-listing sample coded by two independent passes of a large language model (LLM-coded, not human-coded), the raw baseline similarities have areas under the ROC curve between \aucMiniRawMin{} and \aucMiniRawMax{} for their own dimension, whereas the centred multilingual scores reach \aucMlCentredMin{} to \aucMlCentredMax. |
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The paper therefore makes three contributions. First, relative to the housing literature that has used text either as unrestricted embeddings for prediction \citep{shen2020text, baur2023automated, zhang2024describe, bajari2025hedonic} or as structured attributes extracted by a language model \citep{faxvaag2025incorporating, boucher2026llmvision}, it quantifies what fixed, auditable anchors deliver for inference: a block of information that survives language controls, area fixed effects, corrected size variables and area-grouped cross-validation, but not twenty stable implicit prices. Second, it documents and corrects a confound that any multilingual text-as-data application faces when documents are scored against monolingual anchors, and shows that the apparent gain of a multilingual encoder was partly an artefact of truncation: the multilingual model cuts \truncMlFr\% of French and \truncMlEn\% of English descriptions at 128 word-pieces, symmetrically, so the confound was length, not language asymmetry. Third, it replaces the usual robustness table by a pre-specified survival analysis over specifications, encoders and reference phrasings, with multiplicity adjustment, and by out-of-sample designs ranked by how far the held-out listings are from the training data. The practical recommendations that follow for reference-based projection, and for continuous dictionaries more generally, are to report the language composition of the corpus and either control for it or use a language-aligned encoder; to state the truncation length of the encoder and encode full texts; to treat block- and domain-level tests as the primary inferential objects; and to validate individual coefficients against coded labels and random rephrasings before naming them. |
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