spb/wp22_uqo

1\section{Literature and research gap}\label{sec:lit}23\subsection{Quality adjustment: hedonic time dummies, imputation and multilateral methods}45The hedonic approach to constant-quality price measurement goes back to \citet{court1939} and \citet{griliches1961}, with the theoretical foundation in \citet{rosen1974}. For housing, \citet{hill2013survey} surveys and classifies the hedonic index methods, and the Eurostat et al.\ handbook \citep{eurostat2013handbook} codifies them for official statistics. Two families dominate. The \emph{time-dummy} method pools transactions across periods and reads the index off period dummies; the \emph{hedonic imputation} method estimates a separate hedonic function per period and imputes the price of a fixed basket of dwellings at each period's prices, yielding Laspeyres, Paasche and Fisher variants \citep{hillmelser2008,diewert2009imputation,dehaan2010hedonic,silverheravi2007}. \citet{hill2018geospatial} show that flexible geospatial controls materially improve hedonic imputation indices. The time-dummy method revises its history whenever new periods are added; the \emph{rolling time dummy} (RTD) of \citet{hill2022rtd} estimates the model on a rolling window and chains only the newest movement, with options for choosing the window length, the linking rule and for handling periods with few transactions. Multilateral methods designed for scanner data have been transferred to housing: GEKS on bilateral hedonic links with rolling windows and splicing \citep{ivancic2011scanner,dehaan2014scanner,diewertfox2022substitution} and the hedonic multilateral time-series method (HMTS) of \citet{ishaak2024hmts}, which smooths the series of imputed average prices of each base period with a state-space model and splices a window of them, producing stable and limited-revisable indices for small domains of commercial property in the Netherlands. \citet{hill2026survey} review the developments in real estate price measurement since the global financial crisis.67\subsection{Repeat sales, hybrids and thin markets}89The repeat-sales method \citep{bailey1963,caseshiller1987,caseshiller1989,shiller1991arithmetic} avoids the need for characteristics by comparing successive sales of the same dwelling, at the cost of discarding single sales and of selection and renovation biases \citep{clapp1991alltransactions,gatzlaffhaurin1997,gatzlaffhaurin1998,hwangquigley2004}. Hybrid models combine single and repeated sales \citep{casequigley1991,quigley1995hybrid}, and \citet{wallacemeese1997} and \citet{dorsey2010hedonic} compare the families empirically. For thin markets, \citet{schwann1998thin} and \citet{francke2010thin} replace period dummies by structural time-series models in which the index level follows a random walk or a local linear trend, so that periods with no sales still receive an estimate. \citet{francke2017hierarchical} extend this to a hierarchical model with one common trend and cluster-specific deviations and Student-$t$ errors, obtaining reliable indices at a granular level from few observations; \citet{francke2025censustract} add spatially varying loadings on latent factors to produce census-tract indices; \citet{bogin2019local} and \citet{contatlarson2024} build large panels of local repeat-sales indices; \citet{renfoxbruce2017} cluster sparse tract series in a Bayesian nonparametric model; \citet{lopezhewings2018} propose a matching Fisher index for small areas; \citet{bourassa2013robust,bourassa2016robusthedonic} study robust repeat-sales and hedonic indices. \citet{nowaksmith2020} document that the constant-quality assumption of repeat-sales indices fails in a time-varying way.1011\subsection{Small-area estimation, state-space models and reconciliation}1213The statistical treatment of ``borrowing strength'' is the small-area estimation literature: the area-level model of \citet{fayherriot1979} shrinks a direct estimate toward a synthetic one with a weight equal to the ratio of model variance to total variance, and its mean squared error is well understood \citep{dattalahiri2000,datta2005variability,pfeffermann2013sae,raomolina2015}; the empirical-Bayes roots are \citet{efronmorris1973,efronmorris1975}, and \citet{gelman2006prior} discusses priors for variance parameters in hierarchical models. State-space methods \citep{kalman1960,harvey1989,durbinkoopman2012} provide filtered (one-sided) and smoothed (two-sided) estimates of latent levels with exact variances. Coherent combination of estimates across a hierarchy is the subject of forecast reconciliation \citep{hyndman2011hierarchical,wickramasuriya2019mint,athanasopoulos2024reconciliation}.1415\subsection{Timeliness, revisions and real-time evaluation}1617Indices built from deeds are published with a lag and revised as late registrations arrive. \citet{clappgiaccotto1999} and \citet{clapham2006revision} analyse revisions in repeat-sales indices; \citet{vandeminne2020revisions} use revisions as a quality criterion; \citet{sayag2022nowcasts} nowcast late-reported transactions to cut revisions; \citet{anenberg2017timely} date transactions at the contract date using listings; \citet{croushore2011realtime} surveys real-time data analysis. In Canada, the Teranet--National Bank index is a repeat-sales index on registry transfers \citep{teranet2017methodology}, the CREA MLS Home Price Index is a benchmark hedonic index on brokered resales \citep{crea2023hpi}, and Statistics Canada's resale index component used an arithmetic repeat-sales method \citep{statcan2019rppi}.1819\subsection{The gap}2021Table~\ref{tab:lit_gap} summarises what the closest predecessors do and what remains. RTD and HMTS treat each geography separately and obtain stability from windows and splices rather than from an estimated signal-to-noise ratio; the Francke hierarchy and the small-area models estimate the pooling weight but with a repeat-sales observation equation, time-constant hyper-parameters and a single deviation level; reconciliation operates on forecasts of additive series. The combination examined here is (i) a single-sale hedonic observation equation with fine location control, (ii) a four-level administrative hierarchy, (iii) innovation variances calibrated across cells by empirical Bayes so that the pooling weight is both cell-specific and time-varying through the Kalman gain, (iv) explicit reliability accounting, and (v) real-time evaluation with a measured registration lag. We establish by simulation and on the data whether this combination improves on its components; we do not claim that any component is new.2223\begin{table}[htbp]\centering\footnotesize24\caption{Closest predecessors and the remaining space}\label{tab:lit_gap}25\begin{tabular}{p{3.4cm}p{5.6cm}p{5.6cm}}26\toprule27Approach & What it does & What SHARP-HPI adds or changes \\28\midrule29Rolling time dummy \citep{hill2022rtd} & Pooled hedonic on a rolling window; only the newest movement is chained; low-volume safeguards & Cell-specific, estimated pooling across a hierarchy; model-based intervals; revisions measured rather than avoided by construction \\30HMTS \citep{ishaak2024hmts} & Imputed average prices by base period smoothed series-by-series with a state-space model, windows spliced & One joint hierarchy with cross-cell calibration of the signal-to-noise ratio; robust innovations; single-sale observation equation \\31Hierarchical repeat sales \citep{francke2017hierarchical} & Common trend plus cluster deviations, Student-$t$ errors, repeat-sales pairs & Hedonic single sales (no pair selection), four nested levels, empirical-Bayes calibration of $\tau^2$ across cells, reliability grades \\32Fay--Herriot / SAE \citep{fayherriot1979,raomolina2015} & Static area-level shrinkage with estimated variance components and MSE & Dynamic (state-space) version across a geographic hierarchy; direct, model-assisted and unidentified cells reported \\33Forecast reconciliation \citep{wickramasuriya2019mint} & Coherent forecasts of additive hierarchies & Tested as an aggregation diagnostic for log-linear stock-weighted aggregates; reported when it smooths rather than improves \\34\bottomrule35\end{tabular}36\end{table}37