## 3 Methods and Data Sources
### Construction of the Spatial Econometric Model
#### 3.4.2 Variable Descriptions  
(1) Dependent variable: Carbon emissions (CE). After the industrial revolution, human society began to use fossil fuels in large quantities, and greenhouse gas emissions increased dramatically [50]. The burning of fossil energy has become a major source of carbon emissions. Currently, there is still a lack of official statistics for the estimation of carbon emissions, and it mainly relies on the existing fossil energy consumption to estimate the possible carbon emissions [51; 52]. Therefore, on the basis of referring to related research results, three types of energy such as coal, oil, and natural gas are selected. The calculation formula is as follows: Since the existing energy is counted in physical quantity and has different units, it needs to be uniformly converted into standard coal and calculated based on the carbon emission coefficient. In the above formula, \(ce_{j}\) represents the carbon emissions of province \(j\), and \(e_{ij}\) represents the physical amount of energy consumed by province \(j\) in a certain period of time for the \(i\). \(f_{i}\) represents the conversion coefficient of standard coal, and ci represents the type of energy. \[ce_{j}=\sum_{i=1}^{3}e_{ij}\times f_{i}\times c_{i}(i=1,2,3) \tag{10}\]  
The carbon emission factor of energy. Among them, the standard coal conversion coefficient refers to the China Energy Statistical Yearbook (2019). The carbon emission coefficient refers to the existing research results, combined with the General Principles for Comprehensive Energy Consumption Calculation (GB/T2589-2008) and Provincial Greenhouse Documents such as Guide to Compilation of Gas Inventory to be determined. Standard coal conversion coefficient and carbon emission coefficient are shown in Table 1.  
(2) Independent variable: Producer service industry agglomeration index (ser). The producer service industry is an emerging industry that arises and develops independently, and does not provide services directly to consumers. It is a guarantee service industry for the sustainable development of the manufacturing industry, promoting technological progress and industrial upgrading, and improving production efficiency. Due to the rapid development, the academic community has not yet reached a consensus on its connotation and extension. This paper systematically sorts relevant research and refers to current policies. The calculation of the agglomeration index has been explained in the research method part. (3) Control variables: There are many factors that affect carbon emissions [53; 54]. In order to avoid estimation bias due to missing variables, the following variables are selected as control variable:  
1. Industrial structure (ecbz). It is said that whether the industrial structure is advanced or not affects carbon emissions directly. Generally speaking, advanced industrial structure can effectively reduce carbon emissions. This article uses the proportion of secondary industry output value to represent it [55]. 2. The level of economic development (pgdp). According to the STIRPAT model, the level of economic development is another important factor that affects carbon emissions. Here, PGDP is selected to measure [56]. 3. Traffic conditions (glmd). Transportation is an important channel for consuming a large amount of fossil energy in addition to industrial production. It will bring a lot of carbon emissions and cause serious pollution to the environment. The road density is used here to measure [17]. 4. The population size (rkgm). The increase in the number of people will lead to an increase in the demand for production and consumption, which will expand the scale of energy consumption to a certain extent, which will lead directly to an increase in carbon emissions. Here we choose the population at the end of the year to be measured [57]. 5. Environmental regulations (rdry).