## 4 Estimation Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**External Links**} & \multicolumn{2}{c}{**Internal Links**} & \multicolumn{2}{c}{**Meta-Frontier**} \\ \hline  & \multicolumn{2}{c}{**Estimate**} & \multicolumn{2}{c}{**Estimate**} & \multicolumn{2}{c}{**LP**} & \multicolumn{1}{c}{**QP**} \\  & \multicolumn{2}{c}{**(t-Value)**} & \multicolumn{2}{c}{**(t-Value)**} & \multicolumn{1}{c}{**} & \\ \hline Constant & 7.8800 *** & 4.9212 * & \multirow{2}{*}{8.527865} & \multirow{2}{*}{2.321221} \\  & (7.9329) & (1.9257) & & \\ \hline \multirow{2}{*}{\(\ln\text{x}_{1}\)} & \(-8.3936\) *** & \(-0.6238\) & \multirow{2}{*}{\(-7.29096\)} & \multirow{2}{*}{\(-4.23376\)} \\  & (\(-9.9765\)) & (\(-0.7143\)) & & \\ \hline \multirow{2}{*}{\(\ln\text{x}_{2}\)} & 0.8574 & 2.2875 *** & \multirow{2}{*}{1.492447} & \multirow{2}{*}{1.682885} \\  & (1.0575) & (7.0512) & & \\ \hline \multirow{2}{*}{\(\ln\text{x}_{3}\)} & 6.6566 *** & \(-1.5367\) * & \multirow{2}{*}{4.8524} & \multirow{2}{*}{3.009739} \\  & (8.1108) & (\(-1.7420\)) & & \\ \hline \multirow{2}{*}{\(\left(\ln\text{x}_{1}\right)^{2}\)} & 2.0083 *** & \(-0.4737\) *** & \multirow{2}{*}{2.443998} & \multirow{2}{*}{1.433955} \\  & (4.0657) & (\(-3.2088\)) & & \\ \hline \multirow{2}{*}{\(\left(\ln\text{x}_{2}\right)^{2}\)} & \(-0.0670\) & \(-0.0447\) & \multirow{2}{*}{0.061414} & \multirow{2}{*}{0.075224} \\  & (\(-0.3118\)) & (\(-1.2368\)) & & \\ \hline \multirow{2}{*}{\(\left(\ln\text{x}_{3}\right)^{2}\)} & 1.7391 *** & \(-0.6738\) *** & \multirow{2}{*}{1.903512} & \multirow{2}{*}{1.209849} \\  & (3.3376) & (\(-2.7980\)) & & \\ \hline \multirow{2}{*}{\(\ln\text{x}_{1}\)*} & 0.7445 & \(-0.3822\) *** & \multirow{2}{*}{0.172138} & \multirow{2}{*}{0.119306} \\  & (1.3961) & (\(-3.6890\)) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimation results of group and meta-frontier production functions. Table 3 below shows the average, standard deviation, minimum and maximum values of TE, MTR, and TE* calculated using frontier production functions and meta-frontier production functions. As a result of the analysis, the TE value showed that the efficiency of the internal links group (0.7226) was higher than that of the external links group (0.6782). However, in the case of two groups using different production technologies, the MTR values and the TE* values should be compared rather than basing the comparison on the TE values. In the case of TE*, the difference between the external links group (0.6268) and the internal links group (0.6309) was very small in terms of LP. In other words, whether providing news articles within a search engine or providing news articles by connecting users to their website, the meta-frontier efficiency was similar. However, the MTR of the external links group (0.9279) was much higher than the MTR of the internal links group (0.8776), and the result was completely opposite to that of the TE. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**External Links**} & \multicolumn{2}{c}{**Internal Links**} & \multicolumn{2}{c}{**Meta-Frontier**} \\ \hline  & \multicolumn{2}{c}{**Estimate (t-Value)**} & \multicolumn{2}{c}{**Estimate (t-Value)**} & \multicolumn{1}{c}{**LP**} & \multicolumn{1}{c}{**QP**} \\ \hline \(\ln\mathrm{x}_{2}\) * & \(-0.6328\) & \(0.2641\)* (1.8826) & \(-0.40439\) & \(-0.41082\) \\ \hline \(\ln\mathrm{x}_{3}\) * & \(-3.6687\)*** (\(-4.3971\)) & \(1.3540\)*** (3.5107) & \(-4.05277\) & \(-2.38309\) \\ \hline \end{tabular} Note: * \(p<0.1\), *** \(p<0.01\).  
\end{table} 
Table 2: _Cont._