## 3 Empirical Research
### Analysis of Results
#### 3.3.1 Analysis of Cross-Efficiency Modeling Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial Number** & **DMU** & **2016** & **2017** & **2018** & **2019** & **Average Efficiency** \\ \hline
1 & Shanghai & 0.396 & 0.375 & 0.297 & 0.168 & 0.309 \\
2 & Yunnan & 0.408 & 0.924 & 0.409 & 0.360 & 0.525 \\
3 & Neimenggu & 0.269 & 0.225 & 0.448 & 0.739 & 0.420 \\
4 & Beijing & 0.742 & 0.798 & 0.927 & 0.333 & 0.700 \\
5 & Jilin & 0.304 & 0.297 & 0.334 & 0.412 & 0.337 \\
6 & Sichuan & 0.408 & 0.413 & 0.414 & 0.250 & 0.371 \\
7 & Tianjin & 0.455 & 0.522 & 0.540 & 0.360 & 0.469 \\
8 & Ningxia & 0.886 & 0.860 & 0.763 & 0.833 & 0.836 \\
9 & Anhui & 0.715 & 0.832 & 0.703 & 0.400 & 0.663 \\
10 & Shandong & 0.345 & 0.418 & 0.510 & 0.434 & 0.427 \\
11 & Shanxi & 0.396 & 0.383 & 0.640 & 0.475 & 0.474 \\
12 & Guangdong & 0.663 & 0.673 & 0.439 & 0.251 & 0.506 \\
13 & Guangxi & 0.424 & 0.309 & 0.788 & 0.277 & 0.450 \\
14 & Xinjang & 0.468 & 0.109 & 0.656 & 0.330 & 0.391 \\
15 & Jiangsu & 0.532 & 0.686 & 0.556 & 0.361 & 0.534 \\
16 & Jiangxi & 0.780 & 0.759 & 0.785 & 0.487 & 0.703 \\
17 & Hebei & 0.400 & 0.453 & 0.462 & 0.294 & 0.402 \\
18 & Henan & 0.747 & 0.762 & 0.916 & 0.599 & 0.756 \\
19 & Zhejiang & 0.628 & 0.708 & 0.595 & 0.393 & 0.581 \\
20 & Hainan & 0.068 & 0.097 & 0.157 & 0.268 & 0.148 \\
21 & Hubei & 0.587 & 0.574 & 0.369 & 0.286 & 0.454 \\
22 & Hunan & 0.434 & 0.460 & 0.538 & 0.350 & 0.446 \\
23 & Gansu & 0.517 & 0.343 & 0.481 & 0.264 & 0.401 \\
24 & Fujian & 0.594 & 0.529 & 0.505 & 0.259 & 0.471 \\
25 & Guizhou & 0.249 & 0.270 & 0.267 & 0.197 & 0.246 \\
26 & Liaoning & 0.289 & 0.299 & 0.345 & 0.237 & 0.293 \\
27 & Chongqing & 0.719 & 0.748 & 0.722 & 0.327 & 0.629 \\
28 & Shaanxi & 0.265 & 0.211 & 0.280 & 0.200 & 0.239 \\
29 & Qinghai & 0.467 & 0.813 & 0.687 & 0.873 & 0.710 \\
30 & Heilongjiang & 0.400 & 0.327 & 0.636 & 0.255 & 0.404 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The adversarial cross-efficiency results. Meanwhile, in order to better observe the results of the CCR model and the cross-efficiency model, the comparison of the annual efficiency values of the 30 decision-making units using the four models is shown in Figure 3.  
As can be seen from Tables 3-6 and Figure 3, for each decision unit, the cross-efficiency values of the three types are generally lower than those in the traditional CCR model. In the CCR model, there is usually more than one decision unit with an efficiency value of 1, which may lead to overestimation of the performance of certain decision units and a lack of differentiation. The three-category cross-efficiency model, on the other hand, can provide a more detailed and comprehensive evaluation and ranking of all the provinces, avoiding the situation where the efficiency value is too concentrated at 1, thus improving the differentiation and usefulness of the model. Meanwhile, among the three types of cross-efficiency values, the neutral cross-efficiency value is usually located between the benevolent cross-efficiency value and the adversarial cross-efficiency value, which indicates that the neutral model neither favors any party nor overly oppresses the other decision-making units in its evaluation of decision-making units, thus presenting a relatively balanced evaluation method. Compared with the benevolent and adversarial models, the neutral cross-efficiency model is more suitable for evaluating those decision-making units that need to consider the cooperation and game relationship in a comprehensive way, in which it can more accurately reflect the actual efficiency of each decision-making unit in interaction and competition.