*3.4. Variance Decomposition*

In order to compare the relative contribution degree of unit standard deviation in *EC* and *NU*, we further adopt the variance decomposition. The variance decomposition results of period 5, period 10, and period 20 are displayed in Table 3 for different groups: (a) eastern, (b) central, (c) northeastern, and (d) western regions. As shown in Table 4, for provinces in the eastern, central, and western regions, the variance decomposition of *EC* is dominated by its own shock, and *NU* has a small effect. However, for provinces in the northeastern region, the variance decomposition of *EC* is dominated by the effect of *NU*, and its own shock has a small effect. For provinces in the eastern region, the variance decomposition of *NU* to its own shock is almost equal to the effect of *EC*. However, for provinces in central, northeastern, and western regions, the variance decomposition of *NU* is dominated by its own shock, and *EC* has a small effect. Combined with the variance decomposition of both variables, the effect of *EC* on *NU* is much larger than the effect of *NU* on *EC* for provinces in the eastern region, yet it is the opposite for provinces in central, northeastern, and western regions. These variance decomposition results also further confirm that energy consumption may bring about greater advantages relative to its disadvantage for provinces in the eastern region, yet it is imperative to cope with the possible cost of environmental pollution related to energy consumption for the provinces in central, northeastern, and western regions.

**Table 4.** Variance decomposition.


So as to visually display the relative contribution degree of unit standard deviation in *EC* and *NU*, we further draw the variance decomposition results of *EC* and *NU* in the form of a coordinate axis. Figure 5 shows the variance decomposition of *EC* to *NU* for different groups: variance decomposition of *EC* to *NU* (Figure 5a) and variance decomposition of *NU* to *EC* (Figure 5b)*,* respectively. As shown in Figure 5a, *NU* has a remarkable influence on *EC* for the provinces in the northeastern region, and the contribution rate is the largest among the four groups. Additionally, *NU* has an increasing contribution rate to unit standard deviation in *EC* for all groups. As explained above, these results imply that it is imperative to cope with the possible cost of environmental pollution related to energy consumption. As shown in Figure 5b, *EC* has decreasing contribution rate to unit standard deviation in *NU* for provinces in the central, northeastern, and western regions, yet *EC* has an increasing contribution rate to unit standard deviation in *NU* for provinces in the eastern region, which became the largest after the tenth forecast period. These results also imply that environmental pollution related to energy consumption may gradually increase as the pace of new-type urbanization accelerates for provinces in the central, northeastern, and western regions, which are consistent with the estimation results of the PVAR model.

**Figure 5.** Variance decomposition of *EC* and *NU*.

#### **4. In-Depth Analysis of Energy-Related Data**

Finally, the pollution-related calculations are included for an in-depth analysis. We collect supplementary data, such as carbon emissions per real CNY 10,000, energy used per real CNY 10,000 (energy consumption intensity), the ratio of output value in the tertiary industry to real GDP, and the average per capita real GDP. All the relevant data are from each year's China Statistical Yearbooks, China Energy Statistical Yearbooks, each provincial statistical yearbook, and so on. As original data for the carbon emissions can be obtained from 2003 to 2019, the sample data span from 2003 to 2019. Figure 6 shows these calculations for different groups: carbon emissions (Figure 6a), energy consumption intensity (Figure 6b), industrial structure (Figure 6c), and per capita real GDP (Figure 6d), respectively.

**Figure 6.** Some energy-related data.

As shown in Figure 6a, the largest carbon emitter appears in the western region, followed by the northeastern and central regions, and the least carbon emitter happens to be in the eastern region. As the pace of the new-type urbanization accelerates, provinces in the eastern region may make great strides to reduce the pollution of carbon emissions related to energy consumption. These results undoubtedly denote that there is an EKC relation. As shown in Figure 6b, the western region has the highest energy consumption intensity, followed by the northeastern and central regions, and finally the eastern region. As energy consumption intensity represents the efficiency of energy use, the characteristics of this variable in the four different groups denote that the energy is the most efficiently used in the eastern regions, followed by central and northeastern regions, and finally the western region. As the pace of new-type urbanization accelerates, provinces in the eastern region may successfully change their energy mix, and a decrease in carbon emissions is also can be anticipated. For example, pollution-free electrical energy can be massively put to use. To sum up, these two variables both confirm the causal relationship that new-type urbanization leads to energy consumption negatively for provinces in the eastern region, and new-type urbanization leads to energy consumption positively for provinces in the central, northeastern, and western regions over time, which seems to be in agreement with the estimation results of the PVAR model.

Figure 6c,d further provides the economic reality for the EKC relation and the causal relationship between the two. As shown in Figure 6c, the ratio of output value in the tertiary industry to real GDP in the eastern region is the highest among the four groups, followed by the northeastern region, the western region, and the central region. As shown in Figure 6d, per capita real GDP in the four groups is the same as Figure 6c. As the economy develops in the eastern region, there may be a trend toward the tertiary industry, which produces low-pollution products. Therefore, new-type urbanization leads to negative energy consumption. Provinces in the central, northeastern, and western regions are

generally eager to raise the per capita real GDP level, so standards are lax concerning relevant environmental regulations. Even some high-pollution industries are encouraged in these regions, and spontaneously their ratio of output value in the tertiary industry to real GDP is behind the eastern region. Hence, the economic reality is consistent with the EKC relation and the causal relationship between the two.
