% Author: Simon-Pierre Boucher — contact@spboucher.ai
% ============================================================================
\section{Discussion}
\label{sec:disc}

\subsection{Mechanisms}

The evidence assembles into a coherent mechanism story with three layers.

\paragraph{1. Hedonic difficulty, not assessor idiosyncrasy.} The
heterogeneity profile tracks the difficulty of the valuation problem with
almost embarrassing fidelity: condominiums (homogeneous, comparable-rich)
are nearly equitable; old houses, plexes, cottages and high-land-share
properties (heterogeneous, comparable-poor, unanchored by construction
costs) are severely regressive. This is the pattern predicted if assessors
run reasonable hedonic models whose unexplained component is largest ---
and most value-correlated --- where the housing bundle is hardest to price
\citep{amornsiripanitch2022residential, gloudemans2011fundamentals,
bostic2007land}. Regression toward the mean in any imperfect valuation
model over-values the cheap tail and under-values the expensive tail;
our quantile profile, with proportionality holding at the bottom and
collapsing at the top ($\beta(0.90) = 0.49$), shows Quebec's failure is
concentrated where comparables are thinnest.

\paragraph{2. Staleness amplifies the gap.} The doubling of the
province-wide PRB in 2021--2022 shows that triennial rolls interact
perversely with fast markets: when prices move 30--40\% between reference
dates, the cross-sectional dispersion of appreciation --- which is itself
correlated with price segment --- loads directly into measured inequity.
Jurisdictions cannot control housing cycles, but they control revaluation
frequency; annual-cycle systems mechanically cap this channel
\citep{berry2021reassessing, ross2012assessor}.

\paragraph{3. Scale helps: the Montr\'eal exception.} Montr\'eal ---
the largest sales sample, a dedicated in-house assessment service, dense
comparable markets in every segment --- is the only large jurisdiction
with progressive assessments, in all six years. Mid-sized and small
municipalities, many relying on contracted regional evaluators with
limited modelling capacity, are uniformly regressive. The thin-market
mechanism of \citet{mcmillen2008thin} operates within a single provincial
rulebook: identical statutes, divergent outcomes, sorted by market depth
and assessment resources. We note one caveat: Montr\'eal's measured
progressivity may partly reflect within-city composition (its cell is the
whole city, pooling boroughs), and borough-level analysis is a natural
extension.

\subsection{Policy implications}

Three levers follow directly from the diagnosis, in increasing order of
ambition. First, \textbf{shorten the cycle}: moving from triennial to
annual (or indexed) rolls would eliminate the staleness component that
dominated 2021--2022; several U.S. states and British Columbia already
operate annual cycles. Second, \textbf{pool assessment capacity}: the
regressivity gradient by municipality size argues for regional or
provincial mass-appraisal services --- scale is the cheapest known
technology for assessment quality. Third, \textbf{audit vertically, not
just horizontally}: Quebec's oversight regime monitors median ratios and
CODs but sets no explicit PRB requirement; adding the IAAO vertical
standard to the ministry's audit criteria, with published
municipality-level statistics like those in this paper, would make the
equity dimension visible and contestable. Because low-priced-segment
owners appeal least \citep{avenancio2022assessment, plummer2014evidence},
supply-side correction --- better models --- will do more than
demand-side remedies.

\subsection{Limitations}

Four limitations bound the interpretation. First, sale prices below
\$50{,}000 are absent from the source registry and some residual
non-arm's-length transfers may survive our screens; the robustness
battery (dropping sub-\$100k sales, tightening trims) shows the
conclusions survive, but the bottom-decile tax-shift magnitude should be
read as an upper bound on that decile. Second, our data cover 2021--2026,
an unusually turbulent market; the within-market elasticity is stable
across the window, but levels statistics from calmer periods would differ.
Third, we observe no appeals, renovations between assessment and sale, or
conditions of sale; some of what we call horizontal noise is genuine
unobserved quality change. Fourth, without owner demographics we cannot
speak to the distributional incidence across income or racial groups as
\citet{avenancio2022assessment} do --- linking these assessments to census
tract characteristics is the obvious next step.
