## 2 Materials and Methods
### Research Methods  
This paper focuses on the impact of environmental policy on \(GTFP\), specifically testing the impact of the APCP Action Plan on regional \(GTFP\), as well as the moderating effect with industrial structure optimization and rationalization as moderating variables. Based on the research objectives, grouping dummy variable _treated_ is set in this paper according to whether a province in China belongs to the pilot regions of the APCP Action Plan policy. The provinces within the three pilot regions specified by the policies are set as the treatment group and assigned a value of 1 (i.e., \(treated=1\)); provinces that are not within the policy pilot area are the control group and assigned a value of 0 (i.e., \(treated=0\)). Meanwhile, the dummy variable \(time\) is set according to the time of policy implementation. Considering the release date of the APCP Action Plan, which is 13 September 2013, and the data are annual panel data, the data of the year 2013 cannot reflect the effect of the policy, so this paper assigns 2014 and later years to 1 (i.e., \(time=1\)), and years prior to 2014 are assigned to 0 (i.e., \(time=0\)). By referring to the practice of [PERSON] [33], this paper adds a time trend term to the regression model, i.e., \(ytreat_{it}=treated_{it}+year\), which is the interaction item of the grouping dummy variable and time. This paper employs the Panel OLS-DID model and the fixed effect model to estimate changes in the differences estimation [5]. According to Hausman test, the fixed effects model is superior to the random-effects model, so the fixed effects model is selected for regression analysis. Formulas (1) and (2) are taken as benchmark models to test whether the impacts of the APCP Action Plan on the provincial \(GTFP\) are consistent with Hypotheses 1 and 2. \[InGTPP_{it}=\alpha+\beta_{1}Policy_{it}+\gamma_{n}X_{int}+\beta_{2}ytreated _{i}+\tau_{i}+\mu_{i}+\epsilon_{it} \tag{1}\]  
\[InGTPP_{it}=\alpha+\beta_{1}Policy_{it}+\beta_{2}treated_{i}+\beta_{3}time_{ t}+\gamma_{n}X_{int}+\epsilon_{it} \tag{2}\]  
The important premise of using the DID method is that the treatment group and the control group meet the parallel trend assumption [9]; that is, before the implementation of the APCP Action Plan policy, the \(GTFP\) of each province should remain relatively steady. Therefore, Model (3) is proposed to analyze whether this paper satisfies this basic assumption. \[ \begin{split}& lnGTPP_{it}=\alpha+\beta_{1}Policy_{it}+\beta_{2} treated_{i}+\beta_{3}time_{t}+\beta_{4}ytreat_{i}+\beta_{5}Before1\\ &\qquad+\beta_{6}Before2+\beta_{7}Current+\beta_{8}After1+\beta _{9}After2+\gamma_{1}X_{it}+\epsilon_{it}\end{split}  \tag{3}\]  
In exploring the moderating effect of industrial structure optimization and rationalization on the APCP Action Plan, we adopt the following moderating effect Models (4)-(6) with interaction terms:  
\[lnGTPP_{it}=\alpha_{1}+\alpha_{2}TtR_{it}+\alpha_{3}Policy_{it}+\beta_{1} RIS_{it}+ytreat_{i}+\gamma_{n}X_{int}+\tau_{t}+\mu_{i}+\epsilon_{it} \tag{4}\]  
\[lnGTPP_{it}=\alpha_{1}+\alpha_{2}TiO1_{it}+\alpha_{3}Policy_{it}+\beta_{1} OS15_{it}+ytreat_{i}+\gamma_{n}X_{int}+\tau_{t}+\mu_{i}+\epsilon_{it} \tag{5}\]  
\[lnGTPP_{it}=\alpha_{1}+\alpha_{2}TiO2_{it}+\alpha_{3}Policy_{it}+\beta_{1} OS12_{it}+ytreat_{i}+\gamma_{n}X_{int}+\tau_{t}+\mu_{i}+\epsilon_{it} \tag{6}\]  
In the benchmark model, \(GTPP_{it}\) indicates the \(GTFP\) of province \(i\) in year \(t\). In order to analyze the impact of the APCP Action Plan policy on provincial \(GTFP\), this paper uses \(Policy_{it}=treated*time\) as a dummy variable of policy influence. In the parallel trend analysis model, \(Before2,\ Before1,\ Current,\ After1,\ After2\) indicates the policy effect variable of 2 years before, 1 year before, base year, 1 year after and 2 years after the implementation of the policy respectively.