## 6 Empirical Results and Analysis
### Endogenous Problems  
In this paper, we controlled a series of features that affect the number of urban green patent applications per 10,000 people in the baseline model regression. Therefore, it is considered that the location choice of a high-speed rail connection is unlikely to depend on the spatial pattern of green innovation output. However, some endogenous variables that affect local green technology innovation may still be omitted in the process of setting a model, leading to deviations in the estimation results. It is necessary for the instrumental variables to meet the conditions of correlation and exogeneity; thus, for this article, we applied the average altitude in urban geographic information to construct instrumental variables for high-speed rail by referring to the method used by [PERSON] et al. (2015). There is a negative relationship between altitude and high-speed rail construction, and altitude is an  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** \\ \hline
**Variables** & **Exclude Outlier** & **dumHSR** & **L\_InHSRFreq1** \\ \hline lnHSRFreq1 & 0.093 *** & & \\  & (3.89) & & \\ sci\_GDP & 0.771 * & 0.871 ** & 0.555 ** \\  & (1.96) & (2.32) & (2.19) \\ lnbooks\_100\_1 & 0.142 ** & 0.144 *** & 0.118 *** \\  & (2.85) & (3.08) & (2.59) \\ lnmobile1 & \(-\)0.084 ** & \(-\)0.086 ** & \(-\)0.054 * \\  & (\(-\)2.16) & (\(-\)2.43) & (\(-\)1.81) \\ Fin\_GDP & \(-\)0.133 ** & \(-\)0.119 ** & \(-\)0.123 ** \\  & (\(-\)2.33) & (\(-\)2.32) & (\(-\)2.18) \\ unemp\_Pop & \(-\)0.101 ** & \(-\)0.084 ** & \(-\)0.086 * \\  & (\(-\)2.34) & (\(-\)2.29) & (\(-\)1.76) \\ gyfs\_GDP & \(-\)0.066 ** & \(-\)0.060 ** & \(-\)0.047 * \\  & (\(-\)2.49) & (\(-\)2.32) & (\(-\)1.80) \\ dumHSR & & 0.356 *** & \\  & & (5.36) & \\ L\_InHSRFreq1 & & & 0.084 *** \\  & & & (4.05) \\ Constant & \(-\)3.234 *** & \(-\)3.106 *** & \(-\)2.961 *** \\  & (\(-\)12.70) & (\(-\)12.89) & (\(-\)12.08) \\ Observations & 2640 & 2840 & 2556 \\ R-squared & 0.335 & 0.361 & 0.346 \\ Number of the cities & 264 & 284 & 284 \\ City FE & Yes & Yes & Yes \\ Time FE & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 7: The results of the robustness test.  
exogenous geographic information variable that will not directly affect the level of green technology innovation in a city. Moreover, the average altitude generally does not change in a short period. As a result, after comprehensively considering the above factors, we finally selected the data of the last year of the sample (the year of 2013) for the regression of instrumental variables. The specific regression results are presented in Table 8. Column (1) reports the first-stage regression result of high-speed rail service frequency to the average altitude, confirming that they are negatively correlated. From column (2), it is observed that the regression results of the instrumental variable match the baseline model regression results; that is, the supply of high-speed rail services appreciably improves a city's green technology innovation level. In addition, it is observed that the F statistic value is 24.51, which is greater than 10; this indicates that the hypothesis of weak instrumental variables is rejected, proving that the instrumental variable is effective.