## 3 Empirical Research
### Analysis of Results
#### 3.3.1 Analysis of Cross-Efficiency Modeling Results  
First, for the decision-making units without a network structure division, the traditional CCR model was adopted to obtain the annual efficiency values of each decision-making unit. The relevant efficiency results are shown in Table 3.  
When observing the results of the CCR model from a vertical perspective of the table, it can be found that there is often more than one decision-making unit with an innovation efficiency value of 1 in each year. Specifically, in 2016, the innovation efficiency value of seven provinces was 1, namely, Beijing, Ningxia, Guangxi, Xinjiang, Jiangxi, Henan, and Gansu. In 2017, it was Yunnan, Beijing, Ningxia, Anhui, Jiangxi, Henan, and Qinghai. In 2018, it was Beijing, Guangxi, Xinjiang, Henan, and Heilongjiang. In 2019, it was Inner Mongolia, Ningxia, Xinjiang, Henan, and Qinghai. The only province that has maintained \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial Number** & **DMU** & **2016** & **2017** & **2018** & **2019** & **Average Efficiency** \\ \hline
1 & Shanghai & 0.522 & 0.481 & 0.352 & 0.230 & 0.396 \\
2 & Yunnan & 0.675 & 1 & 0.557 & 0.466 & 0.675 \\
3 & Neimenggu & 0.602 & 0.346 & 0.623 & 1 & 0.643 \\
4 & Beijing & 1 & 1 & 1 & 0.569 & 0.892 \\
5 & Jilin & 0.396 & 0.342 & 0.418 & 0.761 & 0.479 \\
6 & Sichuan & 0.571 & 0.477 & 0.479 & 0.311 & 0.459 \\
7 & Tianjin & 0.626 & 0.681 & 0.689 & 0.461 & 0.614 \\
8 & Ningxia & 1 & 1 & 0.904 & 1 & 0.976 \\
9 & Anhui & 0.927 & 1 & 0.790 & 0.545 & 0.816 \\
10 & Shandong & 0.463 & 0.564 & 0.695 & 0.555 & 0.569 \\
11 & Shanxi & 0.669 & 0.631 & 0.803 & 0.732 & 0.709 \\
12 & Guangdong & 0.948 & 0.865 & 0.533 & 0.347 & 0.673 \\
13 & Guangxi & 1 & 0.645 & 1 & 0.565 & 0.802 \\
14 & Xinjiang & 1 & 0.208 & 1 & 1 & 0.802 \\
15 & Jiangsu & 0.673 & 0.814 & 0.615 & 0.472 & 0.644 \\
16 & Jiangxi & 1 & 1 & 0.995 & 0.610 & 0.901 \\
17 & Hebei & 0.541 & 0.573 & 0.522 & 0.422 & 0.514 \\
18 & Henan & 1 & 1 & 1 & 1 & 1 \\
19 & Zhejiang & 0.840 & 0.903 & 0.696 & 0.540 & 0.745 \\
20 & Hainan & 0.131 & 0.119 & 0.182 & 0.909 & 0.335 \\
21 & Hubei & 0.796 & 0.728 & 0.427 & 0.374 & 0.581 \\
22 & Hunan & 0.533 & 0.568 & 0.599 & 0.445 & 0.536 \\
23 & Gansu & 1 & 0.413 & 0.626 & 0.348 & 0.597 \\
24 & Fujian & 0.756 & 0.627 & 0.633 & 0.335 & 0.588 \\
25 & Guizhou & 0.325 & 0.305 & 0.329 & 0.266 & 0.306 \\
26 & Liaoning & 0.372 & 0.351 & 0.404 & 0.313 & 0.360 \\
27 & Chongqing & 0.979 & 0.897 & 0.826 & 0.447 & 0.787 \\
28 & Shaanxi & 0.346 & 0.255 & 0.316 & 0.268 & 0.296 \\
29 & Qinghai & 0.705 & 1 & 0.949 & 1 & 0.913 \\
30 & Heilongjiang & 0.765 & 0.492 & 1 & 0.337 & 0.648 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Efficiency results of traditional CCR model. an innovation efficiency value of 1 for four consecutive years is Henan. Considering the actual situation of various provinces in China, although the comprehensive scientific and technological innovation level of Henan Province has significantly improved, it is not the province with the most outstanding innovation efficiency. This indicates that when the CCR model evaluates the innovation efficiency of high-tech manufacturing industries in various provinces, it may lead to an overestimation of the performance of certain decision-making units and a lack of sufficient discrimination. For this reason, the cross-efficiency model will be adopted for further analysis next. For the decision-making units without a network structure division, three types of cross-efficiency models were adopted to obtain the annual efficiency values of each decision-making unit. The relevant efficiency results are respectively presented in Tables 4-6. Overall, from Tables 4-6, it can be seen that the three types of cross-efficiency models--benevolent, neutral, and other-suppressing--show significant differences in evaluating the efficiency of each province. The benevolent model has the highest score, followed by the neutral model, and the other-suppressing model has the lowest score.