<reponame>ida-j/endogenous-peer-effects
\begin{table}\caption{\footnotesize {\bf Hermite Polynomial Sieve}: Parameter values across 1000 Monte Carlo replications with $h(a)=\sin (3 a_i)$ and $K_N=8$} 
\begin{threeparttable} 
\centering \footnotesize
\scalebox{.9}{\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline 
\cellcolor{yellow}$N$&\multicolumn{5}{|c|}{\cellcolor{yellow}$100$}&\multicolumn{5}{|c|}{\cellcolor{yellow}$250$}&\\\hline 
CF&$(0)$&$(1)$&$(2)$&$(3)$&$(4)$& $(0)$ &$(1)$&$(2)$&$(3)$&$(4)$&\\\hline 
\multirow{4}{*}{$\beta_1=0$}& -6.418 & -1.467 &-0.004 &0.004 &-0.297 &-3.678& -4.572 &-0.002 &0.018& -0.489 &\textit{mean bias} \\ 
&(138.162 )&(10.632 )&(0.532 )&(0.516 )&(5.533 )&(90.996 )&(59.146 )&(0.810 )&(0.797 )&(8.549 )&\textit{std}\\ 
& 0.809 & 0.582 &0.058 &0.056 &0.037 &0.947& 0.836 &0.064 &0.062& 0.039 &\textit{size} \\ \midrule
\multirow{4}{*}{$\beta_2=1$}& 0.328 & 0.023 &-0.024 &-0.000 &0.019 &0.029& 0.054 &-0.017 &-0.001& 0.011 &\textit{mean bias} \\ 
&(8.440 )&(0.406 )&(0.036 )&(0.041 )&(0.336 )&(1.535 )&(0.849 )&(0.022 )&(0.026 )&(0.175 )&\textit{std}\\ 
& 0.291 & 0.088 &0.124 &0.068 &0.039 &0.418& 0.261 &0.125& 0.056 &0.037 &\textit{size} \\\midrule 
\multirow{4}{*}{$\beta_3=1$}& 6.152 & 1.318 &-0.005& -0.013 &0.273 &3.710 &4.375 &-0.009 &-0.027& 0.452 &\textit{mean bias} \\ 
&(133.262 )&(10.142 )&(0.522 )&(0.509 )&(5.196 )&(92.350 )&(57.346 )&(0.795 )&(0.783 )&(7.928 )&\textit{std}\\ 
& 0.659 & 0.453 &0.057 &0.054 &0.040 &0.890& 0.810& 0.069 &0.063 &0.042 &\textit{size} \\\midrule 
&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.021, median bias$=$0.008 }&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.008, median bias$=$0.003 }&\\ \hline 
\cellcolor{yellow}$N$&\multicolumn{5}{|c|}{\cellcolor{yellow}$100$}&\multicolumn{5}{|c|}{\cellcolor{yellow}$250$}&\\\hline 
CF&$(0)$&$(1)$&$(2)$&$(3)$&$(4)$& $(0)$ &$(1)$&$(2)$&$(3)$&$(4)$&\\\hline 
\multirow{4}{*}{$\beta_1=0.5$}& -0.986 & -1.028 &-0.006 &0.000 &-0.300 &-0.193& 0.182 &-0.006 &0.011& 0.786 &\textit{mean bias} \\ 
&(8.755 )&(5.485 )&(0.416 )&(0.405 )&(4.931 )&(6.819 )&(20.207 )&(0.639 )&(0.628 )&(23.932 )&\textit{std}\\ 
& 0.877 & 0.632 &0.060 &0.057 &0.041 &0.982& 0.915 &0.066 &0.065& 0.043 &\textit{size} \\ \midrule 
\multirow{4}{*}{$\beta_2=1$}& 0.033 & 0.021 &-0.024 &-0.000 &0.023 &-0.026& -0.023 &-0.017 &-0.001& -0.054 &\textit{mean bias} \\ 
&(0.592 )&(0.209 )&(0.036 )&(0.041 )&(0.342 )&(0.150 )&(0.420 )&(0.022 )&(0.026 )&(1.678 )&\textit{std}\\ 
& 0.278 & 0.086 &0.127 &0.067 &0.043 &0.370& 0.201 &0.127& 0.057 &0.048 &\textit{size} \\\midrule 
\multirow{4}{*}{$\beta_3=1$}& 0.977 & 0.942 &-0.001& -0.007 &0.274 &0.200 &-0.164 &-0.003 &-0.018& -0.748 &\textit{mean bias} \\ 
&(8.727 )&(4.609 )&(0.427 )&(0.418 )&(4.492 )&(6.527 )&(19.443 )&(0.639 )&(0.629 )&(22.786 )&\textit{std}\\ 
& 0.586 & 0.418 &0.062 &0.054 &0.049 &0.786& 0.816& 0.066 &0.063 &0.048 &\textit{size} \\\midrule 
&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.021, median bias$=$0.008 }&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.008, median bias$=$0.003 }&\\ \hline 
\cellcolor{yellow}$N$&\multicolumn{5}{|c|}{\cellcolor{yellow}$100$}&\multicolumn{5}{|c|}{\cellcolor{yellow}$250$}&\\\hline 
CF&$(0)$&$(1)$&$(2)$&$(3)$&$(4)$& $(0)$ &$(1)$&$(2)$&$(3)$&$(4)$&\\\hline 
\multirow{4}{*}{$\beta_1=0.8$}& -0.500 & -0.329 &-0.006 &-0.001 &-0.091 &-0.252& -1.173 &-0.007 &0.007& 0.070 &\textit{mean bias} \\ 
&(10.164 )&(3.866 )&(0.334 )&(0.324 )&(1.972 )&(2.808 )&(15.161 )&(0.523 )&(0.514 )&(1.557 )&\textit{std}\\ 
& 0.914 & 0.651 &0.060 &0.059 &0.045 &0.990& 0.961 &0.065 &0.065& 0.048 &\textit{size} \\\midrule 
\multirow{4}{*}{$\beta_2=1$}& 0.007 & -0.008 &-0.024 &-0.000 &0.016 &-0.023& 0.006 &-0.017 &-0.001& -0.002 &\textit{mean bias} \\ 
&(0.850 )&(0.157 )&(0.035 )&(0.041 )&(0.398 )&(0.083 )&(0.335 )&(0.022 )&(0.026 )&(0.061 )&\textit{std}\\ 
& 0.231 & 0.094 &0.126 &0.066 &0.047 &0.430& 0.195 &0.130& 0.057 &0.057 &\textit{size} \\ \midrule
\multirow{4}{*}{$\beta_3=1$}& 0.520 & 0.315 &0.002& -0.004 &0.097 &0.255 &1.135 &-0.001 &-0.013& -0.065 &\textit{mean bias} \\ 
&(10.718 )&(3.369 )&(0.365 )&(0.357 )&(2.206 )&(2.733 )&(14.296 )&(0.537 )&(0.529 )&(1.488 )&\textit{std}\\ 
& 0.366 & 0.255 &0.064 &0.053 &0.053 &0.426& 0.545& 0.066 &0.062 &0.059 &\textit{size} \\\midrule 
&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.021, median bias$=$0.008 }&\multicolumn{5}{|c|}{$\hat{a}$ - mean bias$=$0.008, median bias$=$0.003 }&\\ \hline 
\end{tabular}} 
\begin{tablenotes}\tiny 
\item CF - control function. $(0)$ - none, $(1)$ - $\hat{a}_i$,  $(2)$ - $\hat{h}(\hat{a}_i)$, $(3)$ - $\hat{h}(\widehat{deg}_i,x_{2i})$, $(4)$ - $h(a_i)$. 
\item Average number of links for $N=100$ is $24.1$, for $N=250$ it is $60.2$. 
\item The bias of $\hat{a}_i$ is calculated as $a_i-\hat{a}_i$ 
\item $K^*_{100,0.2}=3$, $K^*_{100,0.5}=5$, $K^*_{100,0.8}=4$ 
\item $K^*_{250,0.2}=8$, $K^*_{250,0.5}=3$, $K^*_{250,0.8}=8$ 
  \end{tablenotes} 
\end{threeparttable} 
\end{table} 
