\begin{table}[htbp]
\centering\small
\caption{Monte Carlo: timing diagnostics at the municipality level}\label{tab:mc_lag}
\begin{threeparttable}

\begin{tabular}{lrrrrr}
\toprule
Scenario & Reps & SHARP lag (months) & SHARP revision RMSE & QHPI lag & sec./rep \\
\midrule
baseline & 80 & +0.01 & 2.36 & +0.01 & — \\
turning point & 80 & +0.00 & 2.36 & +0.02 & — \\
flat quality up & 80 & +0.01 & 2.37 & +0.03 & — \\
rising quality down & 80 & +0.01 & 2.37 & +0.02 & — \\
drifting hedonics & 80 & +0.01 & 2.39 & +0.01 & — \\
heavy tails & 80 & -0.01 & 4.80 & -0.00 & — \\
sparse & 80 & +0.02 & 3.16 & +0.01 & — \\
no local dynamics & 80 & +0.00 & 2.20 & -0.00 & — \\
idiosyncratic towns & 80 & +0.02 & 3.10 & -0.00 & — \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize\item Lag = argmax of the cross-correlation between estimated and true 3-month changes (negative = estimate lags). Revision RMSE = RMSE between filtered (real-time) and smoothed monthly changes (×100).\end{tablenotes}
\end{threeparttable}
\end{table}