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}.910A long-standing academic literature has questioned whether these conventions are optimal. \citet{colwell1983} formalised the approach as a statistical estimator and showed that the familiar adjustment grid is a special case of a regression in which the coefficients are fixed a priori. \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,gau1994} extended this to the joint problem of selecting and weighting comparables, proposing a minimum-variance criterion that trades off the number of comparables against their heterogeneity. \citet{isakson1986,isakson2002} examined the nearest-neighbour logic of comparable selection and the role of distance metrics in characteristic space. \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 or illustrated on small samples---typically a few hundred sales in one city---and 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 hundreds of thousands of 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{pace1998} and \citet{pace1997} argued for non-parametric and spatial estimation of adjustments. More recent work has emphasised spatial heterogeneity in implicit prices \citep{bourassa2010,case2004} and the use of geographically weighted or locally estimated models. 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{bailey1963} and \citet{case1989} introduced repeat-sales indices and \citet{hill2013} reviews hedonic index construction; 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.1718\subsection{Automated valuation and machine learning}1920Automated 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{pagourtzi2003} survey the methods; \citet{mccluskey2013} compare neural networks with hedonic models for mass appraisal; \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{bourassa2010} and \citet{case2004} compare spatial econometric specifications; \citet{pace2020} review the state of AVMs. 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.2122Two 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.2324\subsection{Appraiser behaviour and the limits of simulation}2526Finally, a behavioural literature studies how appraisers actually select and adjust comparables and documents anchoring on contract prices, prior appraisals and assessed values \citep{diaz1990,diaz2001,northcraft1987}. 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.27