## 3 Empirical Research
### Analysis of Results
#### 3.3.1 Analysis of Cross-Efficiency Modeling Results
This phenomenon indicates that the three models have different attitudes toward efficiency assessment, and their respective emphasis on evaluation dimensions and tolerance levels also varies. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Serial Number** & **DMU** & **2016** & **2017** & **2018** & **2019** & **Average Efficiency** \\ \hline
1 & Shanghai & 0.461 & 0.424 & 0.327 & 0.192 & 0.351 \\
2 & Yunnan & 0.413 & 0.993 & 0.469 & 0.406 & 0.570 \\
3 & Neimenggu & 0.246 & 0.245 & 0.497 & 0.723 & 0.428 \\
4 & Beijing & 0.857 & 0.890 & 1.000 & 0.382 & 0.782 \\
5 & Jilin & 0.348 & 0.323 & 0.374 & 0.391 & 0.359 \\
6 & Sichuan & 0.486 & 0.455 & 0.450 & 0.276 & 0.417 \\
7 & Tianjin & 0.508 & 0.559 & 0.577 & 0.410 & 0.514 \\
8 & Ningxia & 0.967 & 0.933 & 0.833 & 0.923 & 0.914 \\
9 & Anhui & 0.827 & 0.919 & 0.773 & 0.462 & 0.745 \\
10 & Shandong & 0.391 & 0.448 & 0.543 & 0.495 & 0.469 \\
11 & Shanxi & 0.438 & 0.387 & 0.690 & 0.503 & 0.505 \\
12 & Guangdong & 0.787 & 0.766 & 0.485 & 0.290 & 0.582 \\
13 & Guangxi & 0.428 & 0.318 & 0.851 & 0.265 & 0.466 \\
14 & Xinjiang & 0.374 & 0.109 & 0.826 & 0.227 & 0.384 \\
15 & Jiangsu & 0.614 & 0.759 & 0.609 & 0.413 & 0.599 \\
16 & Jiangxi & 0.901 & 0.838 & 0.876 & 0.544 & 0.790 \\
17 & Hebei & 0.446 & 0.472 & 0.505 & 0.313 & 0.434 \\
18 & Henan & 0.831 & 0.802 & 0.997 & 0.644 & 0.819 \\
19 & Zhejiang & 0.703 & 0.770 & 0.656 & 0.457 & 0.647 \\
20 & Hainan & 0.663 & 0.106 & 0.175 & 0.222 & 0.142 \\
21 & Hubei & 0.686 & 0.647 & 0.398 & 0.325 & 0.514 \\
22 & Hunan & 0.489 & 0.497 & 0.589 & 0.393 & 0.492 \\
23 & Gansu & 0.458 & 0.384 & 0.532 & 0.294 & 0.417 \\
24 & Fujian & 0.682 & 0.582 & 0.544 & 0.296 & 0.526 \\
25 & Guizhou & 0.282 & 0.294 & 0.300 & 0.222 & 0.275 \\
26 & Liaoning & 0.334 & 0.327 & 0.377 & 0.270 & 0.327 \\
27 & Chongqing & 0.834 & 0.821 & 0.787 & 0.365 & 0.702 \\
28 & Shaanxi & 0.297 & 0.229 & 0.309 & 0.230 & 0.266 \\
29 & Qinghai & 0.552 & 0.786 & 0.701 & 0.933 & 0.743 \\
30 & Heilongjiang & 0.413 & 0.324 & 0.717 & 0.289 & 0.436 \\ \hline \end{tabular}
\end{table} 
Table 4: The benevolent cross-efficiency results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Serial Number** & **DMU** & **2016** & **2017** & **2018** & **2019** & **Average Efficiency** \\ \hline
1 & Shanghai & 0.419 & 0.399 & 0.309 & 0.173 & 0.325 \\
2 & Yunnan & 0.401 & 0.935 & 0.429 & 0.368 & 0.533 \\
3 & Neimenggu & 0.281 & 0.238 & 0.480 & 0.714 & 0.428 \\
4 & Beijing & 0.801 & 0.848 & 0.968 & 0.351 & 0.742 \\
5 & Jilin & 0.314 & 0.306 & 0.345 & 0.394 & 0.340 \\
6 & Sichuan & 0.432 & 0.428 & 0.428 & 0.257 & 0.387 \\
7 & Tianjin & 0.474 & 0.536 & 0.562 & 0.376 & 0.487 \\
8 & Ningxia & 0.915 & 0.899 & 0.799 & 0.868 & 0.870 \\
9 & Anhui & 0.745 & 0.865 & 0.732 & 0.416 & 0.689 \\
10 & Shandong & 0.361 & 0.433 & 0.533 & 0.454 & 0.445 \\
11 & Sharai & 0.390 & 0.366 & 0.637 & 0.475 & 0.467 \\
12 & Guangdong & 0.704 & 0.715 & 0.457 & 0.261 & 0.534 \\
13 & Guangxi & 0.398 & 0.305 & 0.764 & 0.252 & 0.430 \\
14 & Xinjang & 0.442 & 0.110 & 0.737 & 0.274 & 0.391 \\
15 & Jiangsu & 0.551 & 0.712 & 0.577 & 0.376 & 0.554 \\
16 & Jiangxi & 0.792 & 0.785 & 0.808 & 0.499 & 0.721 \\
17 & Hebei & 0.409 & 0.457 & 0.479 & 0.299 & 0.411 \\
18 & Henan & 0.745 & 0.762 & 0.932 & 0.615 & 0.763 \\
19 & Zhejiang & 0.650 & 0.729 & 0.622 & 0.412 & 0.603 \\
20 & Hainan & 0.069 & 0.102 & 0.164 & 0.262 & 0.149 \\
21 & Hubei & 0.624 & 0.610 & 0.383 & 0.298 & 0.479 \\
22 & Hunan & 0.447 & 0.468 & 0.556 & 0.358 & 0.457 \\
23 & Gansu & 0.512 & 0.358 & 0.514 & 0.270 & 0.413 \\
24 & Fujian & 0.624 & 0.551 & 0.527 & 0.271 & 0.493 \\
25 & Guizhou & 0.256 & 0.277 & 0.279 & 0.205 & 0.255 \\
26 & Liaoning & 0.304 & 0.307 & 0.360 & 0.245 & 0.304 \\
27 & Chongqing & 0.743 & 0.773 & 0.738 & 0.336 & 0.647 \\
28 & Shaanxi & 0.278 & 0.220 & 0.293 & 0.209 & 0.250 \\
29 & Qinghai & 0.484 & 0.837 & 0.694 & 0.861 & 0.719 \\
30 & Heilongjiang & 0.399 & 0.333 & 0.654 & 0.263 & 0.412 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The neutral cross-efficiency results.