1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit misspec design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_misspec_p3}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 32$, $K = 32,768$} & \multicolumn{3}{c}{$m = 64$, $K = 16,384$} & \multicolumn{3}{c}{$m = 256$, $K = 4,096$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 135.980 & 120.303 & 0.003 & 52.024 & 130.880 & 0.007 & 12.064 & 155.047 & 0.000 & 5.968 & 159.218 & 0.000 \\11(1,1) average + 1 Newton & 13.101 & 169.121 & 0.000 & 0.900 & 164.201 & 0.000 & 0.047 & 163.574 & 0.000 & 0.011 & 163.487 & 0.000 \\12(1,2) average + 2 Newton & 0.479 & 163.566 & 0.000 & 2.65e-4 & 163.509 & 0.000 & 7.15e-7 & 163.538 & 0.000 & 4.26e-8 & 163.478 & 0.000 \\13(2,0) half-block jackknife & 7708.810 & 7813.703 & 0.001 & 41.221 & 185.011 & 0.000 & 0.879 & 163.955 & 0.000 & 0.476 & 163.571 & 0.000 \\14(2,1) half-block + 1 Newton & 4.73e+6 & 4.73e+6 & 0.001 & 1.800 & 163.824 & 0.000 & 2.93e-4 & 163.538 & 0.000 & 7.54e-5 & 163.478 & 0.000 \\15(2,2) half-block + 2 Newton & 1.75e+16 & 1.75e+16 & -- & 0.011 & 163.510 & -- & 5.96e-11 & 163.538 & -- & 5.86e-12 & 163.478 & -- \\16(3,0) quarter-block & 1.32e+4 & 1.31e+4 & -- & 2684.344 & 2590.365 & -- & 0.990 & 163.440 & -- & 0.643 & 163.457 & -- \\17(3,1) quarter-block + 1 Newton & 5.83e+7 & 5.83e+7 & 0.008 & 1.55e+5 & 1.55e+5 & 0.001 & 3.15e-4 & 163.538 & 0.000 & 1.31e-4 & 163.478 & 0.000 \\18analytic Cox--Snell + 1 Newton & 1.75e+18 & 1.75e+18 & 0.004 & 0.021 & 163.522 & 0.000 & 0.001 & 163.539 & 0.000 & 3.26e-4 & 163.478 & 0.000 \\19CSL, 1 round & 51.104 & 181.310 & -- & 12.528 & 165.985 & -- & 1.379 & 163.657 & -- & 0.464 & 163.509 & -- \\20CSL, 2 rounds & 54.317 & 157.156 & -- & 6.106 & 161.226 & -- & 0.264 & 163.414 & -- & 0.059 & 163.450 & -- \\21AEE (Lin--Xi) & 80.818 & 232.638 & -- & 41.700 & 197.944 & -- & 10.841 & 172.157 & -- & 5.470 & 167.791 & -- \\22(2,1) stale Hessian & 5379.284 & 5461.385 & -- & 4.858 & 162.149 & -- & 0.013 & 163.532 & -- & 0.004 & 163.477 & -- \\23centralized MLE & 0 & 163.528 & 0.000 & 0 & 163.509 & 0.000 & 0 & 163.538 & 0.000 & 0 & 163.478 & 0.000 \\24\bottomrule25\end{tabular}26\begin{tablenotes}\footnotesize27\item 1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$; RMSE $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \theta_0\rVert$; cov $=$ empirical coverage of nominal 95\% Wald intervals (observed information at the estimate; `--' when not computed). Monte Carlo standard errors of the gaps and RMSEs are in \texttt{results/processed/summary.csv}; coverage standard error $\approx 0.007$.28\item Fraction of workers with all local fits valid (orders 2 / 3): $m=32$: 0.972 / 0.268; $m=64$: 1.000 / 0.945; $m=128$: 1.000 / 1.000; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32