spb/wp10_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3\section{Data and sample construction}4\label{sec:data}56\subsection{Sources and matching}78We start from a compiled registry of 745{,}119 residential-market9transactions recorded in Quebec between January 2021 and July 2026, each10carrying the sale price, sale date, civic address, geographic coordinates,11and a listing-derived property type. Each transaction has been matched at12the parcel level to the municipal assessment roll in force on the sale date.13The match keys on geographic proximity between the transaction's coordinates14and the roll unit's coordinates and is validated against the roll's recorded15value; a composite score (maximum 220) summarizes the quality of the16address, distance and value agreement. Matches are extremely tight: the17median distance between the transaction and the matched roll unit is180.6~metres, and every observation retained in the estimation sample19reproduces the roll's assessed value exactly.2021From the roll we observe the taxable value of the property22($AV$, \texttt{valeur immeuble}), its land and building components, lot23area, total floor area, year of construction, number of dwelling units, the24standardized use code (CUBF), the roll vintage, and the statutory25market-condition reference date discussed in Section~\ref{sec:inst}.2627\subsection{Sample restrictions}2829Table~\ref{tab:sumstats} describes the estimation sample; the selection30cascade is as follows. We keep sales of residential use codes ---31dwellings (CUBF 1000), cottages (1100), mobile homes (1211) and other32residential (1990) --- which removes vacant land, commercial property and33construction-in-progress (672{,}276 sales remain). We require a34high-confidence roll match (distance $\le 50$~m and score $\ge 150$;35568{,}711 sales), a positive assessed value and a price of at least36\$50{,}000 --- the floor of the source registry, which also screens out37most non-arm's-length transfers. Assessment ratios $r_i = AV_i/SP_i$ are38trimmed at the 1st and 99th percentiles \emph{within each roll vintage}, so39that the mechanical drift of ratio levels across vintages is not trimmed40asymmetrically (557{,}325 sales). Finally, since all estimates compare41sales within a municipality $\times$ roll $\times$ sale-year block42(``cell''), we require at least 20 sales per cell. The estimation sample43contains \textbf{522{,}769 sales} in 625 municipalities and 2{,}884 cells:44345{,}053 single-family homes, 81{,}693 plexes (2--5 units), 81{,}46145condominiums, 9{,}287 cottages and 4{,}701 mobile homes.4647\begin{table}[t]48\centering49\begin{threeparttable}50\caption{Summary statistics, estimation sample}51\label{tab:sumstats}52\small53\input{../results/tables/summary_stats}54\begin{tablenotes}[flushleft]\footnotesize55\item \textit{Notes:} 522{,}769 residential sales, January 2021 -- July562026, matched at the parcel level to the assessment roll in force at the57sale date. The assessment ratio is assessed value divided by sale price.58Roll lag is the number of months between the roll's statutory59market-condition reference date (July 1) and the sale date. The assessed60land share is the roll's land value divided by total assessed value.61\end{tablenotes}62\end{threeparttable}63\end{table}6465\subsection{The raw pattern}6667The median assessment ratio is 0.78: the typical dwelling sells for about6828\% more than its rolled value, the expected imprint of a rising market on69back-dated rolls. Figure~\ref{fig:ratiodist} shows the distribution and its70decomposition by roll lag: sales occurring within two years of the71reference date centre near 0.87, while sales more than four years out72centre near 0.64 --- the mechanical staleness gradient that our fixed73effects absorb. Figure~\ref{fig:time} traces the same mechanics in74calendar time: each roll vintage enters near parity with the market it was75referenced on, then drifts down as prices rise, and the 2022--2023 rate76shock is visible as a flattening of the drift. Everything that follows77nets out this timing structure and asks a sharper question: \emph{within} a78given municipality, roll, and year, do cheap and expensive homes face the79same ratio?8081\begin{figure}[t]82\centering83\includegraphics[width=\textwidth]{fig_ratio_dist.png}84\caption{Assessment ratios. Panel A: distribution of $AV/SP$ across the85estimation sample; the median is 0.78 and the dashed line marks parity.86Panel B: kernel of the same distribution split by the number of months87between the roll's market-condition reference date and the sale; older88rolls sit systematically further below parity.}89\label{fig:ratiodist}90\end{figure}9192\begin{figure}[t]93\centering94\includegraphics[width=\textwidth]{fig_time.png}95\caption{Median assessment ratio by sale month and roll vintage. Each line96follows sales assessed under one triennial vintage (labelled by entry97year); monthly medians with fewer than 100 sales are suppressed. Vintages98enter near their reference-date market level and drift down as prices99rise; the flattening after 2022 reflects the interest-rate correction.}100\label{fig:time}101\end{figure}102