## 2 Methodology and Data
### Model Design  
Most scholars [34; 35; 36] often use two basic conceptual models to study the factors that affect carbon emissions: the IPAT (Environmental load, Population, Affluence, Technology)model and KAYA identity \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Types of Energy** & **Coal** & **Coke** & **Crude Oil** & **Gasoline** & **Kerosene** & **Diesel** & **Fuel Oil** & **Natural Gas** \\ \hline Standard Coal & 0.7143 & 0.9714 & 1.4286 & 1.4714 & 1.4717 & 1.4571 & 1.4286 & 1.3300 \\ Conversion Coefficient & & & & & & & & \\ Carbon Emissions & & & & & & & \\ Coefficient (tc/tc) & & & & & & & \\ \hline \hline \end{tabular} Note: The units for the natural gas calculated by conversion for the standard coal coefficient are kg/m\({}^{3}\), and the rest are _tc/t_.  
\end{table} 
Table 2: The value of the energy conversion standard coal coefficient and carbon emission coefficient. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Represents** \\ \hline \(lnCi\) & \(lnC_{1}\) or \(lnC_{2}\) \\ \(lnY\) (total) & the total effect regression equation \\ \(lnU\) & the mediating effect regression equation \\ \(lnY\) & the direct effect regression equation \\ \(lnY(1)\) & the total effect of the regression equation \\ \(lnY(2)\) & the direct effect of the regression equation \\ \(lnC_{1}\) & The proportion of secondary industry \\ \(lnC_{2}\) & The proportion of tertiary industry \\ \(lnG\) & Economic development level \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The explanation of variables. (First proposed by Japanese professor [PERSON] at a seminar of IPCC in 1989, decomposes carbon emissions into four influencing factors). IPAT model is created by a well-known demographer Professor [PERSON] of Stanford University in the United States, who proposed an identical equation regarding the relationship between environmental load (I) and population (P), affluence (A), and technology (T):  
\[I=P\times A\times T \tag{6}\]  
Formula (6) indicates the pressure of economic development on resources and environment, P indicates the total population, A indicates the level of per capita resource consumption or consumption (per capita GDP), T indicates the degree of environmental damage that is caused by various technologies providing consumer goods, which is also known as environmental efficiency, as expressed in material terms. The KAYA identity decomposes carbon emissions into four influencing factors. The formula is as follows:  
\[C=P\times\left(\frac{G}{P}\right)\times\left(\frac{E}{G}\right)\times\left( \frac{C}{E}\right) \tag{7}\]  
P indicates the population size, G indicates the gross national product (GDP), E indicates the energy consumption, G/P indicates the per capita GDP, E/G indicates the energy consumption intensity, and C/E indicates the energy consumption carbon intensity. Referring to these two conceptual models, based on the basic principles of economics and previous research conclusions [37; 38], this paper extracts the theoretical path of urbanization on carbon emissions. 1 Urbanization \(\rightarrow\) The proportion of secondary industry \(\rightarrow\) Carbon emissions  
2 Urbanization \(\rightarrow\) The proportion of tertiary industry \(\rightarrow\) Carbon emissions  
3 The proportion of secondary industry \(\rightarrow\) Urbanization \(\rightarrow\) Carbon emissions  
4 The proportion of tertiary industry \(\rightarrow\) Urbanization \(\rightarrow\) Carbon emissions  
5 Urbanization \(\rightarrow\) Economic development level \(\rightarrow\) Carbon emissions  
6 Economic development level \(\rightarrow\) Urbanization \(\rightarrow\) Carbon emissions  
7 Urbanization \(\rightarrow\) Social Employment Level \(\rightarrow\) Economic Development Level \(\rightarrow\) Carbon Emissions  
The _STIRPAT_ model is the basic model for decomposing carbon emissions. The specific form is as shown in Equation (8). \[I_{i}=\alpha P_{i}^{b}A_{i}^{c}T_{i}^{d}e \tag{8}\]  
\(e\) represents a random error term.