1\begin{table}[p]2\centering\scriptsize\setlength{\tabcolsep}{2.6pt}3\begin{threeparttable}4\caption{Monte Carlo, logit misspec design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) 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 & median & cov & gap & median & cov & gap & median & cov & gap & median & cov \\9\midrule10(1,0) plain average & 135.980 & 120.891 & 0.232 & 52.024 & 51.973 & 0.309 & 12.064 & 12.056 & 0.339 & 5.968 & 5.971 & 0.656 \\11(1,1) average + 1 Newton & 13.101 & 5.157 & 0.679 & 0.900 & 0.898 & 0.939 & 0.047 & 0.047 & 0.951 & 0.011 & 0.011 & 0.944 \\12(1,2) average + 2 Newton & 0.479 & 0.009 & 0.949 & 2.65e-4 & 2.63e-4 & 0.944 & 7.15e-7 & 7.08e-7 & 0.951 & 4.26e-8 & 4.20e-8 & 0.944 \\13(2,0) half-block jackknife & 7708.810 & 6143.458 & 0.001 & 41.221 & 16.880 & 0.262 & 0.879 & 0.765 & 0.944 & 0.476 & 0.416 & 0.944 \\14(2,1) half-block + 1 Newton & 4.73e+6 & 7.22e+4 & 0.000 & 1.800 & 0.090 & 0.933 & 2.93e-4 & 1.47e-4 & 0.951 & 7.54e-5 & 3.69e-5 & 0.944 \\15(2,2) half-block + 2 Newton & 1.75e+16 & 7.57e+7 & -- & 0.011 & 2.65e-6 & -- & 5.96e-11 & 5.76e-12 & -- & 5.86e-12 & 5.55e-12 & -- \\16(3,0) quarter-block & 1.32e+4 & 4098.009 & -- & 2684.344 & 2013.150 & -- & 0.990 & 0.856 & -- & 0.643 & 0.574 & -- \\17(3,1) quarter-block + 1 Newton & 5.83e+7 & 2.02e+4 & 0.007 & 1.55e+5 & 3111.129 & 0.002 & 3.15e-4 & 1.54e-4 & 0.951 & 1.31e-4 & 6.72e-5 & 0.944 \\18(2,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\19(3,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\20analytic Cox--Snell + 1 Newton & 1.75e+18 & 0.094 & 0.709 & 0.021 & 0.021 & 0.944 & 0.001 & 0.001 & 0.951 & 3.26e-4 & 3.09e-4 & 0.944 \\21CSL, 1 round & 51.104 & 32.959 & -- & 12.528 & 10.118 & -- & 1.379 & 1.221 & -- & 0.464 & 0.395 & -- \\22CSL, 2 rounds & 54.317 & 13.218 & -- & 6.106 & 2.649 & -- & 0.264 & 0.158 & -- & 0.059 & 0.035 & -- \\23AEE (Lin--Xi) & 80.818 & 80.816 & -- & 41.700 & 41.694 & -- & 10.841 & 10.840 & -- & 5.470 & 5.473 & -- \\24(2,1) stale Hessian & 5379.284 & 3239.275 & -- & 4.858 & 1.102 & -- & 0.013 & 0.011 & -- & 0.004 & 0.003 & -- \\25centralized MLE & 0 & -- & 0.951 & 0 & -- & 0.944 & 0 & -- & 0.951 & 0 & -- & 0.944 \\26\bottomrule27\end{tabular}28\begin{tablenotes}\footnotesize29\item 1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$ over all replications (including those with failed local fits); median $=$ its median; 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 $\approx 0.007$ or less.30\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. Rows `valid workers only' drop the workers with a failed sub-block fit from the pilot (weights renormalized) and coincide with the corresponding rows when no fit failed.31\end{tablenotes}32\end{threeparttable}33\end{table}34