*3.3. Impulse Response Analysis*

So as to further investigate the dynamic relationship between the variables in the PVAR model, the impulse response function is computed. Specifically, we set up Monte Carlo simulations for four types of subsamples and finally obtained a 4 × 4 impulse response graph, and the corresponding results are displayed in Figure 4 for the different groups: eastern (Figure 4a), central (Figure 4b), northeastern (Figure 4c), and western regions (Figure 4d), respectively.

**Figure 4.** Variable impulse responses.

For provinces in the eastern regions, only *NU* shows a positive response to a standard deviation in its own unit. These results further verify that provinces in the eastern region may have been committed to environmental protection, hence there is no dynamic relationship. For provinces in the central region, the impulse response of *EC* to *NU* is positive, which is consistent with the PVAR model regression analysis. The implication is that these provinces should pay much attention to the high-pollution industries while the pace of new-type urbanization accelerates. The impulse response of *NU* to *EC* is positive in the current period, and then it decreases in the first period and tends to be weak after the second period, which is also consistent with the PVAR model regression analysis. The implication is that the negative externality of environmental damage related to energy consumption may offset the benefit of an increase in the level of new-type urbanization from energy consumption over time. While energy consumption is not conducive to promoting the level of new-type urbanization, these provinces should adopt some conservation policies. For provinces in the northeastern region, the impulse response of *EC* to *NU* is negative, which quickly reaches the highest value and then converges to zero. The implication is that the negative externality of environmental damage related to energy consumption may gradually increase over time. The impulse response of *NU* to *EC* is positive in the current period, and then it decreases in the first period and tends to be weak after the fourth period, which is the same as the provinces in the central region. For the provinces in the western region, the impulse response of *EC* to *NU* and the impulse response of *NU* to *EC* are virtually the same as the provinces in the central region, hence it is not necessary to interpret these results. In contrast to other regions, it is noteworthy that the impulse response of EC to NU does not diminish over time. This further denotes that the urbanization process in the western region relies predominantly on high energy consumption and highly pollutant-intensive inputs, and the legacy of conventional economic development approaches remains an arduous obstacle to overcome.
