\begin{table}[!ht]
\caption{Pre-trends under a universal base period and long differences}\label{table:referee_long2}
\centering
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lcccccc}\hline\hline
Neighbour outcome (log) & \(e=-4\) & \(e=-3\) & \(e=-2\) & Post avg. & p (leads) & p (all cells) \\ \hline
Population &     -0.89 (     0.36) &     -1.14 (     0.32) &     -0.97 (     0.30) &      0.27 (     0.20) &     0.005 &     0.000 \\
Current expenditure &     -0.37 (     0.67) &      0.52 (     0.59) &      0.04 (     0.40) &      1.04 (     0.45) &     0.535 &     0.003 \\
Education expenditure &     -0.76 (     0.97) &      1.27 (     0.82) &      0.22 (     0.70) &      2.93 (     0.73) &     0.156 &     0.003 \\
Public-sector employment &     -0.24 (     1.31) &     -0.25 (     0.97) &     -1.31 (     0.75) &      2.20 (     0.94) &     0.310 &     0.031 \\
Private-sector employment &     -0.14 (     1.40) &      0.56 (     1.15) &      0.63 (     0.97) &     -1.74 (     1.07) &     0.864 &     0.515 \\
Number of firms &     -0.11 (     0.76) &      0.58 (     0.57) &      0.11 (     0.45) &     -1.19 (     0.63) &     0.602 &     0.126 \\
Firms (services) &     -1.13 (     0.90) &     -0.72 (     0.70) &     -0.39 (     0.54) &     -1.11 (     0.68) &     0.631 &     0.114 \\
Federal transfers (ex-FPM) &      1.82 (     2.82) &      4.65 (     3.06) &      1.59 (     2.12) &      4.28 (     2.23) &     0.507 &     0.015 \\
\hline\hline
\end{tabular}
\end{adjustbox}\par
\begin{tablenotes}\footnotesize
\item Callaway--Sant'Anna event studies re-estimated with a universal base period and long differences (csdid option \texttt{long2}): every coefficient, pre- and post-event, is a long difference relative to the period before treatment (\(g-1\)), the specification suited to assessing parallel trends and closest to the conventional linear event-study regression. Coefficients in percent (log \(\times 100\)); influence-function standard errors clustered at the neighbour level in parentheses. Post avg.: average of the post-event coefficients. p (leads): p-value of the joint Wald test that the three aggregated event-time leads shown (\(e=-4,-3,-2\), cohort-size weighted) are zero --- the test aligned with the reported event-study exhibits. p (all cells): p-value of the joint Wald test that every disaggregated pre-treatment ATT(g,t) cell equals zero (65 restrictions); with this many restrictions the cluster-robust chi-squared statistic is known to over-reject in finite samples, and scattered single-cell deviations can produce rejection even when the aggregated leads are flat, so the two tests are reported side by side. Estimation sample identical to the headline results.
\end{tablenotes}\end{table}