## 5 Results
### Threshold Effect Analysis  
We first constructed the LR statistic and utilized the bootstrap method with 300 repetitions to determine the number of thresholds. As shown in Table 5, the statistical significance of the first threshold is below 0.1, but the second and third thresholds are not statistically significant. This indicates that when port size is considered the threshold variable, the impact of port TFP on CO2 emissions from port cities exhibits a significant single-threshold effect. Estimating the single-threshold panel model, the obtained single threshold is 7867, with a corresponding 95% confidence interval of [7854, 7889].  
According to the estimation results in Table 6, we observe a significant threshold effect of port size on the relationship between the TFP and CO2 emissions in port cities. Specifically, when the port size is below the threshold, the impact of port TFP on CO2 emissions is negligible, with a coefficient of only \(-0.008\), which lacks statistical significance. Conversely, when the port size exceeds this threshold, the positive impact of port TFP on CO2 emissions significantly strengthens, with the coefficient reaching 0.062, and it is statistically significant at the 1% level. This finding reveals an important phenomenon: in smaller ports, improvements in TFP hardly affect CO2 emissions, whereas for larger ports, an increase in TFP significantly promotes CO2 emissions in port cities.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables** & **TWFE** & **Q25** & **Q50** & **Q75** \\ \hline \multirow{2}{*}{_TFP_} & 0.078 *** & 0.020 & 0.039 * & 0.055 * \\  & (0.022) & (0.031) & (0.022) & (0.030) \\  & 0.074 & \(-\)0.116 & \(-\)0.091 & \(-\)0.071 \\  & (0.097) & (0.101) & (0.073) & (0.098) \\  & 0.351 *** & 0.217 ** & 0.155 ** & 0.104 \\  & (0.108) & (0.101) & (0.073) & (0.097) \\  & 0.141 *** & 0.070 ** & 0.090 *** & 0.106 *** \\  & (0.027) & (0.031) & (0.022) & (0.030) \\ Constant & \(-\)1.414 & - & - & - \\  & (1.606) & - & - & - \\ \hline \(F\) & 19.87 & - & - & - \\ \(N\) & 176 & 176 & 176 & 176 \\ \(R^{2}\) & 0.688 & - & - & - \\ \hline \hline \end{tabular} Note: standard errors in parentheses, *** \(p<\) 0.01, ** \(p<\) 0.05, * \(p<\) 0.1.  
\end{table}
Table 4: Baseline regression results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Threshold** & **Hypothesis** & **RSS** & **MSE** & **Fstat** & **Prob** \\ \hline \multirow{2}{*}{Single} & H0 : no threshold & \multirow{2}{*}{2.019} & \multirow{2}{*}{0.012} & \multirow{2}{*}{12.88 *} & \multirow{2}{*}{0.08} \\  & H1 : one threshold & \multirow{2}{*}{2.015} & \multirow{2}{*}{0.012} & \multirow{2}{*}{0.31} & \multirow{2}{*}{0.98} \\ Double & H0 : one threshold & \multirow{2}{*}{1.999} & \multirow{2}{*}{0.012} & \multirow{2}{*}{1.34} & \multirow{2}{*}{0.69} \\  & H1 : double threshold & \multirow{2}{*}{1.999} & \multirow{2}{*}{0.012} & \multirow{2}{*}{1.34} & \multirow{2}{*}{0.69} \\ Triple & H0 : double threshold & \multirow{2}{*}{1.999} & \multirow{2}{*}{0.012} & \multirow{2}{*}{1.34} & \multirow{2}{*}{0.69} \\  & H1 : triple threshold & & & & \\ \hline \hline \end{tabular} Note: * \(p<\) 0.1.  
\end{table}
Table 5: Threshold existence test.