2.1.2. Intermediary Effect Model

To explore the transmission mechanism of new urbanization and energy-intensive industry agglomeration to nitrogen oxides, this paper constructed an intermediary effect model by referring to the method of a stepwise testing regression coefficient proposed by Judd and Kenny [54] and Baron and Kenny [55]:

$$
\ln NE\_{il} = \theta + \theta\_0 \ln NE\_{i,l-1} + \theta\_1 \ln X\_{il} + \theta\_2 \ln \pi\_{il} + \varepsilon\_{il} \tag{3}
$$

$$
\ln M\_{it} = \omega + \omega\_0 \ln M\_{i, t-1} + \omega\_1 \ln X\_{it} + \omega\_2 \ln \pi\_{it} + \varepsilon\_{it} \tag{4}
$$

$$
\ln NE\_{it} = \rho + \rho\_0 \ln NE\_{i, t-1} + \rho\_1 \ln X\_{it} + \rho\_2 \ln M\_{it} + \rho\_3 \ln \pi\_{it} + \varepsilon\_{it} \tag{5}
$$

In the process of replacing X in the equation with *nurb*, M is regressed with energy efficiency (*ee*) and human capital (*hc*), respectively. In the process of replacing X in the equation with *hagg*, M is regressed with the industrial structure (*is*) and energy structure (*es*), respectively.

Based on the intermediary effect model: (1) if the total effect coefficient *θ*<sup>1</sup> is significant, it should be the intermediary effect; otherwise, it is the masking effect. (2) If the coefficients *ω*<sup>1</sup> and *ρ*<sup>2</sup> are significant, the indirect effect of *ω*<sup>1</sup> × *ρ*<sup>2</sup> is significant. (3) If the coefficient *ρ*<sup>1</sup> of the direct effect is significant, *ω*<sup>1</sup> × *ρ*<sup>2</sup> and *ρ*<sup>1</sup> are the same sign, which reflects the intermediary effect, and if *ω*<sup>1</sup> × *ρ*<sup>2</sup> and *ρ*<sup>1</sup> are different signs, it reflects the masking effect [56,57]. In addition, the mediating effect should satisfy that the coefficient *ρ*<sup>1</sup> is less than the coefficient *θ*1.

#### *2.2. Index Construction*

#### 2.2.1. New Urbanization

Compared with the traditional urbanization measured only by the indicator of population, as for the new urbanization, more attention should be attached to the quality of urban development. From this, referring to the existing research [58–61], this paper constructed a new comprehensive evaluation index system of the urbanization level from 13 indexes and four aspects, including population, social development, ecological environment and land, which are shown in Table 1.

Based on the variation degree of each index, the entropy method determines the index weight, and the evaluation deviation of the human factors is avoided to a certain extent. In this paper, the entropy method is applied to measure the weight for each index in the new urbanization index system. The calculation formula of the weight is as follows:

Step 1: Calculate the proportion of index *j*:

$$y\_{i\circ} = \frac{X\_{i\circ}}{\sum\_{i=1}^{n} X\_{i\circ}}, \ i = 1, 2, \dots, n, \ j = 1, 2, \dots, m \tag{6}$$

Step 2: Calculate the entropy of index *j*:

$$e\_{\vec{l}} = -\frac{1}{\ln n} \sum\_{i=1}^{n} y\_{ij} \ln y\_{ij} \tag{7}$$

Step 3: Calculate the weight of each indicator:

$$
\omega\_{\dot{j}} = \frac{\left(1 - e\_{\dot{j}}\right)}{\sum\_{j=1}^{m} \left(1 - e\_{\dot{j}}\right)} \tag{8}
$$

*Xij* is the result of the standardization of the actual value of the *j*th index in the *i*th province, *Yij* is the proportion of the actual value of the *j*th index in the *i*th province, *ej* is the information entropy of the index and *ω<sup>j</sup>* is the entropy weight. Table 1 lists the comprehensive evaluation index system of the new urbanization level.


**Table 1.** The comprehensive evaluation index system of the new urbanization levels.
