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1\begin{table}[htbp]2\centering\small3\caption{Monte Carlo: timing diagnostics at the municipality level}\label{tab:mc_lag}4\begin{threeparttable}56\begin{tabular}{lrrrrr}7\toprule8Scenario & Reps & SHARP lag (months) & SHARP revision RMSE & QHPI lag & sec./rep \\9\midrule10baseline & 80 & +0.01 & 2.36 & +0.01 & — \\11turning point & 80 & +0.00 & 2.36 & +0.02 & — \\12flat quality up & 80 & +0.01 & 2.37 & +0.03 & — \\13rising quality down & 80 & +0.01 & 2.37 & +0.02 & — \\14drifting hedonics & 80 & +0.01 & 2.39 & +0.01 & — \\15heavy tails & 80 & -0.01 & 4.80 & -0.00 & — \\16sparse & 80 & +0.02 & 3.16 & +0.01 & — \\17no local dynamics & 80 & +0.00 & 2.20 & -0.00 & — \\18idiosyncratic towns & 80 & +0.02 & 3.10 & -0.00 & — \\19\bottomrule20\end{tabular}21\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}22\end{threeparttable}23\end{table}24