spb/wp10_uqo Public

1% Author: Simon-Pierre Boucher — contact@spboucher.ai2% ============================================================================3\section{Robustness}4\label{sec:robust}56Table~\ref{tab:robust} and Figure~\ref{fig:robust} re-estimate the two7headline elasticities --- $\gamma_{\text{FE}}$ and the Clapp8$\gamma_{\text{IV}}$ --- across ten sample and measurement variants;9Table~\ref{tab:quantile} reports the quantile coefficients underlying10Figure~\ref{fig:quantile}.1112\begin{table}[t]13\centering14\begin{threeparttable}15\caption{Robustness of the vertical-inequity elasticities}16\label{tab:robust}17\small18\input{../results/tables/robustness}19\begin{tablenotes}[flushleft]\footnotesize20\item \textit{Notes:} Each row re-estimates the Cheng fixed-effects and21Clapp IV regressions on the indicated variant; cells with fewer than 2022sales after restriction are dropped. Municipality-clustered standard23errors in parentheses. *, **, *** denote significance at 10\%, 5\%, 1\%24against $\gamma = 0$.25\end{tablenotes}26\end{threeparttable}27\end{table}2829\begin{figure}[t]30\centering31\includegraphics[width=0.85\textwidth]{fig_robustness.png}32\caption{Stability of $\gamma$ across sample variants. Filled circles:33fixed-effects estimates; open squares: Clapp IV. Whiskers are 95\%34confidence intervals, municipality-clustered.}35\label{fig:robust}36\end{figure}3738\begin{table}[t]39\centering40\begin{threeparttable}41\caption{Quantile-regression coefficients}42\label{tab:quantile}43\small44\input{../results/tables/quantile}45\begin{tablenotes}[flushleft]\footnotesize46\item \textit{Notes:} Quantile regressions of within-cell demeaned47$\ln AV$ on demeaned $\ln SP$, estimated on a seeded 250{,}000-sale48subsample. Stars test $H_0\!:\beta(\tau)=1$.49\end{tablenotes}50\end{threeparttable}51\end{table}5253\paragraph{Match quality.} Requiring the maximum matcher score of 22054(210{,}820 sales) or a match distance under 10~metres changes55$\gamma_{\text{FE}}$ to $-0.41$ and $-0.36$ respectively, and56$\gamma_{\text{IV}}$ to $-0.10$ and $-0.09$: if anything, the cleanest57matches show \emph{more} regressivity, ruling out mismatch noise as the58source.5960\paragraph{Extreme sales.} Dropping all sales under \$100{,}000 --- the61segment most likely to harbour residual non-arm's-length transfers ---62attenuates the FE estimate modestly ($-0.30$) and the IV to $-0.05$, both63still overwhelmingly significant. Tightening the ratio trim to the 5th--95th64percentiles, which mechanically compresses dispersion, cuts65$\gamma_{\text{FE}}$ to $-0.15$ and $\gamma_{\text{IV}}$ to $-0.04$; the66qualitative conclusion is unchanged, and the ordering67$|\gamma_{\text{IV}}| < |\gamma_{\text{FE}}|$ is preserved in every68variant, as the measurement-error logic requires.6970\paragraph{Composition.} Single-family homes alone give71$\gamma_{\text{FE}} = -0.45$; condominiums alone $-0.12$ (with an IV72estimate indistinguishable from zero), confirming that the aggregate73result is not an artefact of pooling heterogeneous property classes ---74each class is regressive or neutral on its own, none is progressive.7576\paragraph{Time and market depth.} Splitting the window into 2021--202377and 2024--2026 yields $-0.35$ and $-0.34$ (FE); restricting to78municipalities with at least 300 sales, or to cells with at least 50,79moves the estimates by less than 0.005. The phenomenon is stable across80the largest housing-cycle swing in recent Canadian history.8182\paragraph{Inference.} With 625 municipality clusters, the83cluster-robust $t$-statistics on $\gamma_{\text{FE}}$ exceed 11 in every84variant; the IV first stage is enormous (the rank instrument correlates85with within-cell log price at $F$ far above conventional thresholds), so86weak-instrument concerns do not arise.87