## 3 Research Design
### Framework and Variable Description
\begin{split}\text{API}_{\text{it}}=\beta_{1}(\text{AT}_{\text{it}} )+\beta_{2}(\text{SH}_{\text{it}})+\beta_{3}(\text{ARH}_{\text{it}})+\beta_{4}( \text{AA}_{\text{it}})+\beta_{5}(\text{MWS}_{\text{it}})+\beta_{6}(\text{AWS}_ {\text{it}})+\beta_{7}(\text{MDP}_{\text{it}})+\beta_{8}(\text{AP}_{\text{it}} )+\beta_{9}(\text{DP}_{\text{it}})+\\ \beta_{10}(\text{BUA}_{\text{it}})+\beta_{11}(\text{PD}_{\text{it}} )+\beta_{12}(\text{GRB}_{\text{it}})+\beta_{13}(\text{WA}_{\text{it}})\end{split}  \tag{3}\]  
where \(\beta\) stands for the weight of different indicators, i stands for city, and t stands for year. The values in brackets are the standardized values of different indicator data, which can be obtained by standardizing the collected data. The standardization processing formula of the indicator is \((\text{y}-\text{y}_{\text{min}})/(\text{y}_{\text{max}}-\text{y}_{\text{min}})\), in which \(\text{y}_{\text{min}}\) means the minimum value of the indicator data and \(\text{y}_{\text{max}}\) means the maximum value of the indicator data. In terms of the choice of the control variable, this paper follows the practice of [PERSON] et al. (2016) [33] and chooses population density (den) to represent the concentration degree of the urban population, follows the research of [PERSON] et al. (2019) [35] and chooses built-up area (bua) to represent the area that has actually been developed and constructed in a block with public facilities in the prefecture-level administrative region, and follows the research of [PERSON] et al. (2020) [36] and chooses per capita GDP of prefecture-level cities to represent the economic development level (ey) of the research region. The above three factors mirror the urbanization process of various regions from different angles. The deepening of urbanization increases the underlying-surface roughness, which reduces the ground wind speed and weakens atmospheric self-purification capacity ([PERSON] et al., 2017) [17]. This paper chooses the proportion of the secondary industry to GDP to demonstrate the impact of industrial structure (in) on environmental pollution ([PERSON] et al., 2017) [34]. The reason lies in that the secondary industry dominates the heavy industry, and sulfur dioxide formed by fossil-fuel combustion in heavy industry and smoke and dust from the construction industry clearly constitutes important sources of environmental pollution, thus affecting the emission of pollutants ([PERSON], 2015) [37]. In terms of the choice of the threshold variable, this paper chooses environmental regulation (er). This paper follows the research conclusion of [PERSON] and [PERSON] (2001) [38] and uses the removal amount of industrial sulfur dioxide to measure environmental regulation. On the relationship between environmental regulation and environmental pollution, there are two views. The first one admits that environmental regulation urges enterprises to engage in technological and organizational innovation, improve their production efficiency and market competitiveness, and ultimately achieve a win-win result of environmental protection and economic growth ([PERSON], 2017) [39]. The second view oppugns that environmental regulation can effectively reduce environmental pollution, and proposes a \"green paradox\" ([PERSON], 2018) [40].