## 4 Results and Discussions  
### Measurement Analysis of Carbon Emissions  
It can be seen from Table 4 that for the first stage, the overall national carbon emission efficiency was 0.514, out of which 10 provinces had higher levels beyond the national average, and the remaining provinces had lower levels than the national average. This finding clearly shows that the overall carbon emission efficiency in China remains low, and the situation regarding energy conservation and emission reduction is still suboptimal. The national average of the pure technical efficiency of carbon emissions was 0.608, and provinces with a higher efficiency include Beijing, Guangdong, and Hainan. The average scale efficiency of national carbon emissions is 0.865. Apart from provinces such as Qinghai, Ningxia, and Hainan, which have a lower scale efficiency, the scale efficiency of the other provinces is generally higher. Compared with the first stage, the national average level of comprehensive carbon emissions in the third stage dropped slightly, with an average value of 0.500, and the differences in comprehensive carbon emissions across different provinces increased. Zhejiang, Guangdong, Jiangsu, and other provinces with high efficiency levels further improved their efficiency, whereas the efficiency of Ningxia, Qinghai, and other provinces with low efficiency levels further decreased. Out of these, the overall carbon emission efficiency of 17 provinces was higher than the national average, and that of 13 provinces was lower than the national average. The average value of pure technical efficiency of national carbon emissions was 0.778, which displayed an increasing trend when compared to the first stage. Provinces with a higher efficiency included Guangdong, Hainan, and Zhejiang. The national average carbon emission scale efficiency was 0.638, which displayed a decreasing trend when compared to the first stage. Qinghai, Ningxia, Hainan, and other provinces had a lower scale efficiency, whereas the rest of the provinces generally displayed a higher scale efficiency.  
It can be seen from Table 5 that between 2009 and 2018, the comprehensive carbon emission efficiency of Jiangsu, Zhejiang, Beijing, and other provinces showed a rapid rise with a high magnitude of change. The comprehensive carbon emission efficiency of Guangdong, Heilongjiang, and Liaoning displayed a fluctuating trend, whereas the rest of the provinces generally showed a slow upward trend. The national average carbon emission efficiency gradually increased, and the magnitude of the increase was about 41%. Specifically, Jiangsu's comprehensive carbon emission efficiency value in 2017 and 2018 was 1, which was at the forefront of the entire production, although it did not reach such an effective state in the remaining years. In 2018, Beijing's overall carbon emission efficiency value was 1, which was also at the forefront of the entire production. Similarly, Beijing's carbon emission efficiency in other years was relatively low. Guangdong's comprehensive carbon emission efficiency value in 2011 and 2018 was 1, which was again at the forefront of the entire production. Although the comprehensive efficiency value of the remaining years did not reach 1, it was relatively high. By contrast, the overall carbon emission efficiency of the remaining provinces did not reach the aforementioned frontier production level. It can be seen that the provinces with a low overall carbon emission efficiency (e.g., lower than the national average) throughout the year were mainly distributed around economically underdeveloped areas within the central and western regions.