spb/wp22_uqo

1\section{Introduction}\label{sec:intro}23A house price index answers a deceptively simple question: by how much has the price of a dwelling of constant quality changed between two dates? For a province, the question is well posed and the data abundant. For a municipality of three thousand inhabitants that records four sales a month, the question is the same but the evidence is thin, the sold dwellings differ from month to month, and any estimator must decide how much to trust the local sales and how much to borrow from neighbouring and encompassing markets. Statistical agencies have answered this trade-off with rules of thumb (minimum counts, suppression) or with methods designed for liquid markets. This paper treats the trade-off as an estimation problem.45We propose SHARP-HPI, a two-stage framework for monthly, quality-adjusted price indices across a geographic hierarchy. The first stage is a robust pooled hedonic regression in which log prices are explained by structural characteristics, fine-scale location fixed effects (a nested metric grid whose resolution adapts to the density of sales), provincial month effects, and quality prices allowed to drift smoothly over time. The second stage treats each geography's monthly mean residual as a noisy observation of a latent deviation from its parent's path and estimates that deviation with a heteroskedastic local-level state-space model. The innovation variance of each cell, which governs how quickly the deviation is allowed to move and therefore how much weight a month of local sales receives, is calibrated by empirical Bayes across all cells of a level rather than estimated from each cell's own handful of observations. The result is a panel of indices for the province, \NMrc{} regional county municipalities (MRCs) and \NMunWithSales{} municipalities by property class, each with a count of actual sales, an effective sample size, a local-data weight, an interval, and a reliability grade.67The paper makes four contributions. First, it builds the index on an audited population: \NRawTx{} registered sales published by the Quebec land registry feed between January 2021 and October 2026, matched to the provincial assessment roll, with an exclusion ledger (Table~\ref{tab:exclusions}), a measured publication lag and a classification of dwellings into mutually exclusive classes. Second, it compares the proposed estimator with eleven benchmarks spanning the hedonic, multilateral, repeat-sales, machine-learning and production-index traditions on the same data. Third, it evaluates all estimators in Monte Carlo experiments on synthetic markets with known quality-constant price paths, including markets where the quality of sold homes rises while prices are flat, markets with heavy-tailed noise, and two counter-examples designed so that the adaptive hierarchy should not win. Fourth, it simulates the real-time publication process with monthly vintages and quantifies revisions, timeliness and publication policies.89We are explicit about novelty. The verified literature (Section~\ref{sec:lit}) contains every ingredient: structural time-series index levels \citep{francke2010thin}, hierarchical common-plus-deviation trends with heavy-tailed errors \citep{francke2017hierarchical}, small-area shrinkage with estimated weights \citep{fayherriot1979,raomolina2015}, rolling-window hedonics with low-volume safeguards \citep{hill2022rtd}, and hedonic multilateral time-series smoothing for small domains in official statistics \citep{ishaak2024hmts}. What we did not find in a single published estimator is the combination of a single-sale hedonic observation equation, a multi-level administrative hierarchy, empirical-Bayes calibration of the pooling strength across cells, reliability accounting for every cell-month, and real-time vintage evaluation with a measured registration lag. The paper should be read as an integration and empirical assessment of these components, not as a new class of model.1011Three findings matter for practice. In the Monte Carlo experiments the hierarchical state-space estimator reduces the root mean squared error of municipal monthly changes to \MCmunicipalitySsharpbaselineRmse{} log points, against \MCmunicipalityKqhpibaselineRmse{} for per-cell state-space estimation, \MCmunicipalityCpooledtdbaselineRmse{} for a cell-level time dummy and \MCmunicipalityAmedianbaselineRmse{} for the median; the empirical-Bayes calibration of the innovation variance matters for interval coverage rather than for point accuracy; the local-linear-trend and Gaussian variants do not improve on the robust local level; and two counter-examples show where the design loses: with heavy-tailed contamination a coarser location partition is more robust, and at the regional level, where sales are plentiful, estimating each region's own hedonic coefficients beats pooled coefficients plus a smoothed deviation. On the Quebec data the provincial house index rises from 100 in 2021 to \ProvSephouse{} in September 2026, condominiums to \ProvSepcondo{} and plexes to \ProvSepplex{}; the dispersion across municipalities is wide and largely reliable only for cells graded A to C. In real time, first-release monthly changes at the provincial level are revised by a mean absolute \RevFirsthouseprovince{} log points (houses), and municipal first releases by \RevFirsthousemunicipality{}; publishing without revision costs about half a log point per month at the municipal level.1213The remainder of the paper follows the protocol in which it was pre-specified. Section~\ref{sec:lit} reviews the literature and states the gap. Section~\ref{sec:data} describes the data, the institutional setting and the population definition. Section~\ref{sec:estimand} defines the estimand and the measurement challenges. Section~\ref{sec:framework} presents the SHARP-HPI model and identification. Section~\ref{sec:estimation} covers estimation, inference, linking and vintages. Section~\ref{sec:simulation} reports the Monte Carlo evidence. Section~\ref{sec:empirical} presents the Quebec indices, Section~\ref{sec:validation} the benchmarks, validation, ablations and robustness, Section~\ref{sec:implications} the implications, and Section~\ref{sec:conclusion} the limitations and conclusion. Code, the index panel, the vintage database and every table and figure are generated by the accompanying repository.14