*3.3. Pollution Function*

To update the pollution function [62], innovation input and climate change have been included in the pollution function as follows:

$$pol\_{\rm it} = \gamma\_0 + \gamma\_1 \text{geg}\_{\rm it} + \gamma\_2 \text{geg}\_{\rm it}^2 + \gamma\_3 \varepsilon\_{\rm it} + \gamma\_4 ino + \gamma\_5 \text{step}\_{\rm it} + \gamma\_6 \text{wtemp}\_{\rm it} + \gamma\_7 \text{wrb}\_{\rm it} + \gamma\_8 poli + \varepsilon\_{3, \rm t} \tag{6}$$

where *pol* denotes greenhouse gas emissions; *geg* denotes green economic growth; *geg*<sup>2</sup> denotes geg squared; *e* denotes the proportion of renewable energy consumption; *urb* denotes urbanization; *poli* denotes climate policy measured by whether the Kyoto Protocol is signed before 2016 or participation in the Paris Agreement after 2016. If the sample has participated in the above two agreements, we will record it as 1, on the contrary, we will record it as 0. Besides, stemp and wtemp respectively represent the average temperature of three months in summer and winter; and ε is the error term. All variables are logarithmic except stemp and wtemp.

From Equations (4)–(6), A three-dimensional simultaneous equation framework is used to analyze the energy-environment-growth nexus. In conclusion, the structural equations look as follows:

$$
\begin{aligned}
\text{geg}\_{it} &= a\_0 + a\_1 k\_{it} + a\_2 c\_{it} + a\_3 i n o\_{it} + \varepsilon\_{1,it} \\
\varepsilon\_{it} &= \beta\_0 + \beta\_1 \text{geg}\_{it} + \beta\_2 i n d\_{it} + \beta\_3 i n o\_{it} + \beta\_4 \text{stemp}\_{it} + \beta\_5 \text{wtemp}\_{it} + \varepsilon\_{2,it}
\end{aligned}
\tag{7}
$$

*polit* = *γ*<sup>0</sup> + *γ*1*gegit* + *γ*2*geg*<sup>2</sup> *it* + *γ*3*eit* + *γ*4*ino* + *γ*5*stempit* + *γ*6*wtempit* + *γ*7*urbit* + *γ*<sup>8</sup> *poli* + *ε*3,*it*
