spb/wp22_uqo

1\section{Estimation, inference, linking and publication vintages}\label{sec:estimation}23\subsection{Algorithm}45Estimation is sequential and fast enough to be rerun monthly on a workstation (Table~\ref{tab:bench_prov}, last column). Stage one is a weighted least-squares regression with absorbed location fixed effects and explicit month dummies, iterated with Huber weights; it uses the full history available at the estimation date and returns the provincial path with its standard errors and the residuals. Stage two proceeds level by level: residual means and counts are computed per cell and month; the profile likelihood of each cell on a 48-point grid of $\log\tau^2$ between $10^{-8}$ and $2\times10^{-2}$ is evaluated by the Kalman filter; the level's prior is estimated by grid EM; each cell is filtered and smoothed with its posterior-mode $\tau_g^2$ and two robustness passes; its deviation (smoothed in the retrospective mode, filtered in the real-time mode) is subtracted from the residuals of its children before the next level. The whole panel for one class (province, 16 regions with sales, up to \NMrc{} MRCs and more than a thousand municipalities, 69 months) takes between ten and forty seconds.67\subsection{Inference}89Intervals are model-based: the variance of a municipal log level is the sum of the smoothed (or filtered) state variances of the municipality, its MRC and its region, plus the squared standard error of the provincial month effect. This ignores the uncertainty in the hedonic coefficients beyond $\mu$, the estimation of $\sigma_g^2$ and $\tau_g^2$, and the covariance between levels. Two checks are reported: the empirical coverage of the intervals in the Monte Carlo experiments, where the truth is known, and a cluster bootstrap on the condominium class that resamples fine-location cells with replacement and re-estimates both stages (Section~\ref{sec:validation}). Intervals are frequentist in spirit (the prior on $\log\tau^2$ is estimated, not elicited), and we call them confidence intervals; they are not posterior credible intervals for the index. Where many municipal changes are compared, we report the share of cells whose 12-month change excludes zero rather than individual significance, and the placebo experiment gives the false-positive rate of that rule.1011\subsection{Normalisation and linking}1213The retrospective series are not spliced: they are re-estimated on the full sample and normalised to the 2021 average. Real-time series are produced by re-estimating both stages at each monthly publication date on the data available then. Three publication policies are compared on the resulting vintage database: (a) full re-estimation, in which every published value may be revised; (b) a movement splice, in which only the newest monthly change is appended to a frozen history, as in RTD; (c) a revision-limited policy, in which a month is frozen after its third release, as in HMTS. The vintage database records every release of every cell-month, so the revision statistics of Section~\ref{sec:validation} are measured, not assumed.1415\subsection{Real-time vintages}1617Publication date $v_m$ for month $m$ is the last day of $m$ plus ten days, the measured publication delay; the data available at $v_m$ are the sales dated on or before $v_m - 10$ days, so the newest month is always partial. Releases are simulated monthly from July 2022 (eighteen months of history) to October 2026 for the province, the regions and the municipalities with at least 1{,}500 sales; the location partition and the empirical-Bayes priors are rebuilt from the available data at each vintage, so that no information from the future enters any real-time value. The October 2026 observation is partial through 7 October in every mode and is flagged as such in the panel.1819\subsection{Benchmarks}2021Eleven benchmark estimators are implemented on the same samples: (A) median and mean prices; (B) a stratified median with fixed weights over floor-area terciles $\times$ age terciles $\times$ subtype; (C) pooled time dummies, ordinary and Huber; (D) rolling time dummies with 7-, 13- and 25-month windows and window, movement and mean splices; (E) chained and direct double-imputation Laspeyres, Paasche and Fisher indices from per-month hedonic regressions with coarse location effects; (F) rolling-window GEKS on bilateral Fisher links with a movement splice; (G) HMTS as described by \citet{ishaak2024hmts} and the Statistics Netherlands implementation, with a smooth-trend state-space step on each base-period series and windows of 4 and 13 months; (H) Bailey--Muth--Nourse and Case--Shiller repeat sales on pairs of the same assessment unit held at least six months; (I) static empirical-Bayes partial pooling of cell deviations, the mixed-effects benchmark, which is the special case of the state-space model with $\tau^2=0$; (J) a gradient-boosting residual index trained strictly out of time on data before each month, reported as a diagnostic because predictive accuracy is not index accuracy; and (K) a re-implementation of the production QWHPI v2.1 architecture (13-month rolling Huber time dummies with mean splice for the province, direct local time dummies for cells with a median of at least 40 sales per month, and a local-level Kalman deviation with per-cell maximum-likelihood $\tau^2$ for thin cells).22