spb/wp16_uqo

1% ============================================================================2\section{Related literature}3\label{sec:literature}4% ============================================================================56\subsection{The sales comparison approach and its conventions}78The sales comparison approach rests on the principle of substitution: a buyer will pay no more for a property than the cost of acquiring an equally desirable substitute \citep{appraisal2020}. Its implementation follows a sequence that has barely changed since the method was formalised: identify comparable sales, verify that they are arm's-length, adjust each sale price for differences in transaction conditions, market conditions (time), location and physical characteristics, and reconcile the adjusted indications into a point estimate. Professional texts and standards give guidance on each step but rarely quantify it. The Appraisal Institute recommends ``a sufficient number'' of comparables and treats three as a practical minimum; the International Association of Assessing Officers' standard on automated valuation models recommends that comparable-sales algorithms use ``three to ten'' sales and weight them by similarity \citep{iaao2018}. Adjustments are to be ``market-derived,'' typically through paired-sales analysis, but in practice they are frequently taken from rules of thumb, published grids, or the appraiser's experience \citep{diaz1990,diaz2001}. \citet{lipscomb1990} compared four market-derived adjustment methods on a single-market sample and found that the choice of method materially changes the adjustments, which is itself an argument for testing them.910A long-standing academic literature has treated the approach as a statistical estimator and questioned whether its conventions are optimal. \citet{colwell1983} showed that the familiar adjustment grid is a special case of a regression in which the coefficients are fixed a priori, so that its accuracy depends on how close the pre-set coefficients are to the implicit prices. \citet{isakson1986,isakson1988} proposed a nearest-neighbour technique in characteristic space as an alternative to the grid, and \citet{isakson2002} set out the linear algebra that unifies the two. \citet{quan1991} modelled the appraiser as a Bayesian signal extractor who combines noisy comparable prices with a prior; in that framework the number of comparables and their weights follow from the relative variances of the signals. \citet{vandell1991} derived the optimal weights to assign to comparables as a function of their adjustment variance and showed that equal weighting is optimal only under restrictive conditions; \citet{gau1992} extended the problem to the joint selection and weighting of comparables under a minimum-variance criterion, which trades off the number of comparables against their heterogeneity, and the exchange with \citet{green1994} and \citet{gau1994} clarified the role of the covariance between adjustment errors. \citet{epley1997} noted that these optimal rules require variance estimates that practitioners rarely possess. \citet{pace1996} is the closest antecedent to our design: he interprets the grid estimator as a combination of a nearest-neighbour estimator and a parametric estimator and shows, analytically and by Monte Carlo simulation, that ordinary least squares dominates the grid, which dominates the nearest neighbour, under correct specification, and that the ranking is fragile under misspecification; \citet{pacegilley1998} generalise the two estimators into a single family. \citet{lai2008} propose a ``replication'' estimator that selects comparables so as to reproduce the subject's characteristics in combination rather than one at a time. \citet{lentz1998} survey the appraisal issues raised by the lending process, including the reliance on a small number of comparables and on judgemental adjustments. These contributions are theoretical, simulated, or illustrated on a few hundred sales in one city; none evaluates the rules out of sample on a large, heterogeneous market. Our design implements their estimators (nearest, most similar, minimum-adjustment selection; equal, distance, recency and similarity weights; median and mean reconciliation) as configurations of a single engine and measures their accuracy on more than a hundred thousand masked sales.1112\subsection{Estimating adjustments: grids, hedonics and local models}1314The estimation of adjustment magnitudes is where the sales comparison approach meets hedonic price theory. Since \citet{rosen1974}, the hedonic regression of price on characteristics has been the canonical tool for recovering implicit prices, and its coefficients are natural candidates for adjustment factors \citep{kang1991,pace1998}. \citet{kang1991} compared hedonic regression with grid-adjustment techniques on sales in a single county and found hedonic adjustments superior; \citet{cannaday1986} showed how depreciation adjustments can be estimated from the same regressions; \citet{pace1998} and \citet{pace1997} argued for non-parametric and spatial estimation of adjustments. A large literature has since emphasised spatial heterogeneity in implicit prices and the value of submarket definitions for prediction \citep{desrosiers2000,bourassa2003,goodman2003,case2004,bourassa2007,bourassa2010}, and \citet{dube2013,dube2014} have stressed that spatial dependence in housing data is also temporal, since only prior sales can influence a current price. Whether locally estimated adjustments improve on a global grid in practice is an empirical question that depends on the bias--variance trade-off: local models track heterogeneity but are noisy where sales are few. We estimate adjustments at four levels of locality---a global within-municipality hedonic grid, a regional grid shrunk towards the global one, a per-valuation local regression on the candidate pool, and a non-linear gradient-boosting model---and test the trade-off directly across density strata.1516Time adjustments raise a separate issue. Price indices are routinely estimated with the full sample and applied retroactively, which leaks information from the future into every ``historical'' valuation; \citet{clapham2006} document how much repeat-sales and hedonic indices are revised as later data arrive. \citet{bailey1963} and \citet{case1989} introduced repeat-sales indices, \citet{hill2013} reviews hedonic index construction and \citet{hillscholz2018} show the gains from geospatial information in hedonic imputation; we follow the hedonic route but re-estimate the regional monthly index every month using only prior sales, so that the time adjustment applied to a comparable on a given valuation date is one that could actually have been computed on that date. The seasonality of housing markets documented by \citet{ngai2014} matters here: because the price level of the valuation month is never observed, every point-in-time method inherits a seasonal error that we report rather than remove.1718The assessed value is a further source of information that the appraisal literature treats ambiguously. \citet{clapp1992} showed that assessed values can be used to construct price indices, and \citet{thibodeau2003} that marking assessed values to market with a small number of sales yields accurate estimates. Assessors' sales-ratio methods rest on the same idea. We treat the assessment ratio as one adjustment scheme among eight and quantify what the assessed value adds to both the traditional and the machine-learning methods.1920\subsection{Automated valuation and machine learning}2122Automated valuation models (AVMs) have moved from mass appraisal \citep{gloudemans1999} to lending and consumer applications, and the literature comparing them with traditional valuation has grown rapidly. \citet{shiller1999} set out the logic of evaluating valuation systems on their out-of-sample forecast errors rather than on in-sample fit. \citet{pagourtzi2003} survey the methods; \citet{zurada2011} and \citet{mccluskey2013} compare neural networks and other learners with hedonic models for mass appraisal; \citet{kok2017} document the move from manual appraisal to automated valuation in institutional practice; \citet{mayer2019} evaluate several machine-learning algorithms on a large Swiss dataset and find that gradient boosting and random forests dominate linear hedonics, with mixed-effects and spatial models close behind; \citet{pace2020} show that tree ensembles extract information from the residuals of hedonic and spatial models; \citet{bogin2020} find that both AVMs and appraisers are less accurate in rural areas, where comparables are scarce. \citet{steurer2021} review the metrics used to evaluate AVMs and argue for reporting medians, shares within tolerance bands and coverage together, which is the convention we follow; \citet{krause2020} compare error-based and model-based measures of AVM uncertainty, a question we take up when calibrating value intervals; \citet{lorenz2023} show how interpretable machine learning can recover implicit prices from tree ensembles, which narrows but does not close the gap between opaque and transparent methods. A consistent finding is that tree ensembles with location features achieve median absolute errors of roughly 8--15\% on residential sales, depending on market and data richness. Comparable-sales algorithms are themselves a major class of AVM \citep{iaao2018}, and hybrid approaches that use a model to adjust comparables are common in industry but rarely evaluated in the academic literature.2324Two features of this literature motivate our design. First, machine-learning benchmarks are usually trained on random splits of the data, which overstate accuracy relative to a temporal split \citep{mayer2019}; we use strict chronological separation and quarterly retraining, which is how such models are deployed. Second, the information set is rarely held constant: AVMs often exploit variables (assessed values, listing information) that the traditional method in the same study does not. We give every method the same characteristics and the same point-in-time index, and we separately quantify the value of the assessed value as an input to both the traditional and the machine-learning methods. Our inference draws on the forecast-evaluation literature: paired comparisons of losses on common targets \citep{diebold1995,giacomini2006}, the median as the loss-minimising point forecast under absolute error \citep{gneiting2011,hyndman2006}, the protection against data snooping that a separate selection sample affords when many specifications are searched \citep{white2000,hansen2005}, and distribution-free calibration of prediction intervals on a hold-out sample \citep{lei2018}.2526\subsection{Appraiser behaviour and the limits of simulation}2728Finally, a behavioural literature studies how appraisers actually select and adjust comparables and documents anchoring on contract prices, prior appraisals and assessed values \citep{northcraft1987,diaz1990,diaz2001}; on administrative data, \citet{eriksen2019} and \citet{calem2021} show that purchase appraisals cluster at or just above the contract price. We do not observe appraisers' files, and our results concern the predictive accuracy of \emph{rules}, not of practitioners. The distinction matters in both directions: a practitioner may do better than any rule by using information we do not observe (condition, renovations, listing history), and worse by anchoring. Our contribution is to establish what the observable record supports, so that professional rules and training can be benchmarked against it.29