*3.1. Model Specification*

So as to fully reveal the causal on this subject, the panel vector autoregression (PVAR) model is employed to conduct empirical research. Compared with the widely used vector autoregression (VAR) model, the PVAR model has the advantage of dealing with longterm panel data and endogenous causality in the traditional linear regression model. The corresponding PVAR model is constructed as follows:

$$\mathcal{Y}\_{it} = \Gamma\_0 + \sum\_{p=1}^{n} \Gamma\_p \mathcal{Y}\_{it \cdot p} + \delta\_i + f\_t + \varepsilon\_{it}$$

where the subscripts *i* and *t* denote province and year, respectively; *Yit* is a multi-dimensional variable, which is *NU* and *EC*, representing the level of new-type urbanization and energy consumption, respectively, measured by the methods introduced hereinabove; *Yit-p* is a *p*-period lag term of *Yit*; and *δ<sup>i</sup>* and *ft* indicate individual province fixed effects and year fixed effects, respectively. *εit* is termed the random disturbance.

As the PVAR model includes the lag term of dependent variables and individual province fixed effects, it can be considered a typical dynamic panel data model. Thus, the OLS estimation will be biased and inconsistent. Therefore, the system GMM proposed by Blundell and Bond [49] is used to estimate the PVAR model. The PVAR model is commonly conducted by the following steps [50,51]. Firstly, the stationarity of the panel data and the causal relationship between *NU* and *EC* have to be tested. Secondly, the optimal lag order needs to be selected, and the PVAR model can be estimated logically. Thirdly, the impulse response graph will be displayed based on the PVAR model regression. The last step is the variance decomposition.

#### *3.2. PVAR Model Regression Analysis*

#### 3.2.1. Stationarity Tests

First of all, it is necessary to inspect the stationarity of time series variables. The IPS, Fisher-ADF, and Fisher-PP are comprehensively used to implement unit root tests, and the results are reported in Table 2. In Table 2, the *p*-values of all tests for the first-difference series of *NU* and *EC* are all 0.000, which rejects the null hypothesis at the 1% significance level. Hence, we can conclude that the first-difference series of *NU* and *EC* are stationary. In other words, these original data are integrated processes of order one.

**Table 2.** Unit root test results.


Notes: The null hypothesis is that the time series variables have a unit root process.

#### 3.2.2. Benchmark Regression Results

Before estimating the PVAR model, an optimal lag *p*-period of time series variables remains to be explored. Based on the standard procedure in empirical studies, the AIC, BIC, and HQIC are used to select the optimal lag order. The selection of two lag periods is reasonable. Therefore, 2 is the optimal lag order in this paper. The estimation results of the PVAR model are reported in Table 3. The *EC* equation reflects the effects of *EC* and *UN* on *EC*, and the *UN* equation reflects the effects of *UN* and *EC* on *UN.* The estimated results for all provinces as a whole are reported in the top line of Table 3. As shown in Table 3, in the *EC* equation, the first-period lag of *EC* has a significant positive effect on *EC,* and the second-period lag of *EC* has a significant negative effect on *EC*, which indicates that energy consumption presents the characteristics of path-dependent inertia in the short run, yet it tends to converge in the long run [4,47]. The first-period lag of *NU* has a significant negative effect on *EC* and the second-period lag of *NU* has a significant positive effect on *EC*, which indicates that new-type urbanization leads to energy consumption negatively in the short run [10–16], yet the new-type urbanization leads to energy consumption positively in the long run [6–9]. In the *NU* equation, the first-period lag of *NU* has a significant positive effect on *NU,* and the second-period lag of *NU* does not have any significant effect on *NU*, which indicates that new-type urbanization also presents the characteristics of path-dependent inertia in the short run. The first-period lag of *EC* has a significant positive effect on *NU* [33], and the second-period lag of *EC* has a significant negative effect on *NU* [45], which indicates that an increase in energy consumption brings about a further increase in the level of new-type urbanization in the short run, yet it is detrimental to new-type urbanization in the long run.


**Table 3.** Estimation results of the PVAR model.

Notes: \*\*\*, \*\*, and \* show significant levels at 1%, 5%, and 10%, respectively. The value given in parentheses is *t* statistics. The subscripts <sup>−</sup><sup>1</sup> and <sup>−</sup><sup>2</sup> represent the first-period lag and the second-period lag, respectively.

The estimated results for all provinces as a whole neglect regional heterogeneity. To explore this issue, groups of provinces are classified into four types of regions according to NBS. The estimated results for provinces in the eastern region are reported in the top second line of Table 3. As shown in Table 3, in the *EC* equation, the first-period lag of *EC* and the second-period lag of *EC* have a similar effect on *EC* compared to the whole country. The first-period lag of *NU* has a significant negative effect on *EC,* and the second-period lag of *NU* does not have any effect on *EC*, which indicates that new-type urbanization leads to energy consumption negatively in the short run [4,30], yet this inhibitory effect gradually disappears over time. In the *NU* equation, both *NU* and *EC* have a similar effect on *UN* compared to the whole country.

The estimated results for provinces in the central region are reported in the top third line of Table 3. As shown in Table 3, in the *EC* equation, the first-period lag of *EC* and the second-period lag of *EC* have a similar effect on *EC* compared to the whole country. Both the first-period lag of *NU* and the second-period lag of *NU* do not have any significant effect on *EC*, which indicates that an increase in the level of new-type urbanization does not bring about energy consumption [52]. In the *NU* equation, the first-period lag of *NU* has a significant positive effect on *NU,* and the second-period lag of *NU* has a significant negative effect on *NU*. The first-period lag of *EC* and the second-period lag of *EC* have a similar effect on *UN* compared to the whole country.

The estimated results for provinces in the northeastern region are reported in the fourth line of Table 3. As shown in Table 3, in the *EC* equation, the first-period lag of *EC* and the second-period lag of *EC* have a similar effect on *EC* compared to the whole country. Both the first-period lag of *NU* and the second-period lag of *NU* do not have any significant effect on *EC*, which also indicates that an increase in the level of new-type urbanization does not bring about energy consumption [52]. In the *NU* equation, both *NU* and *EC* have a similar effect on *UN* compared to the whole country.

The estimated results for provinces in the western region are reported in the fifth line of Table 3. As shown in Table 3, in the *EC* equation, the first-period lag of *EC* and the second-period lag of *EC* have a similar effect on *EC* compared to the whole country. The first-period lag of *NU* and the second-period lag of *NU* have a similar effect on *EC* as the eastern region, which indicates that new-type urbanization leads to energy consumption negatively in the short run [4,30], yet this inhibitory effect gradually disappears over time. In the *NU* equation, the first-period lag of *NU* and the second-period lag of *NU* have a similar effect on *NU* compared to the whole country. The first-period lag of *EC* does not have any effect on *UN,* and the second-period lag of *EC* has a significantly negative effect on *UN*, which indicates that an increase in energy consumption is detrimental to new-type urbanization.

#### 3.2.3. Discussions with Concept of EKC

According to existing studies, energy consumption may lead to economic development and environmental pollution simultaneously [53–55]. Since new-type urbanization is widely considered a symbol of economic development [38], the critical issue is whether energy consumption can bring about larger benefits with respect to its cost. This basic benefit–cost tradeoff can be inferred from the causal relationship between the two. When energy consumption is conducive to promoting the level of new-type urbanization, it may indicate that the benefit of an increase in the level of new-type urbanization resulting from energy consumption is larger than the negative externality of environmental damage related to energy consumption. On the contrary, if the new-type urbanization leads to energy consumption positively, it may indicate that the advantage of energy consumption exceeds its disadvantage. From the estimated results for all provinces as a whole, we can conclude that the advantage of energy consumption is larger than its disadvantage in the short run, yet the relationship is opposite over time. From the estimated results for provinces in the eastern region, we can conclude that the advantage of energy consumption is always larger than its disadvantage over time. This again proves that those provinces in the eastern region may have started to cope with the possible environmental damage related to energy consumption. From the estimated results for provinces in the central, northeastern, and western regions, the advantages of energy consumption and its disadvantages are similar to the whole country, where the negative externality of environmental damage exceeds its benefit over time.

The PVAR model regression results can also be interpreted with the concept of the EKC, which assumes that economic growth and environmental pollution present an "inverted U" relationship [56]. Initially, as the level of new-type urbanization is relatively low, there are not too many industrial activities that lead to environmental pollution. Therefore, an increase in the level of new-type urbanization is conducive to reducing energy consumption for all samples in the short run. As the pace of new-type urbanization accelerates, there will be more and more high-pollution industries, and environmental pollution

may gradually increase. As the estimation results indicated, an increase in the level of new-type urbanization may enhance energy consumption in the long run for the central, northeast, and western regions. Even so, for provinces in the eastern region, new-type urbanization is not conducive to increasing energy consumption over time. As the economy improves, these provinces may start to focus on the possible environmental damage related to energy consumption and attempt to take some remedial actions [57]. Generally speaking, as long as new-type urbanization reaches a high level as the eastern region, more resources may be dedicated to environmental protection. Consequently, an increase in the level of new-type urbanization will be conducive to reducing environmental pollution. Our main target is not to explore the EKC, yet the implications of the estimated results are compatible with the EKC prediction. To sum up, as the pace of new-type urbanization accelerates, a negative externality, such as environmental pollution related to energy consumption, gradually increases. Once a province reaches a high level of new-type urbanization, it may conversely reduce the negative externality related to energy consumption, as indicated by the EKC assumption.
