*5.1. Scenario Design*

The Porter hypothesis is an important issue related to carbon constraint. The weak version of the hypothesis describes how appropriate environmental regulations will stimulate technological innovation, while the strong version expresses that environmental regulation positively affects total factor productivity (TFP) or business performance by stimulating technological innovation. This paper focuses on TFP to test the boundary of the Porter hypothesis rather than green productivity, such as in many papers [61] because the definition of the strong version of the hypothesis is productivity.

The two types of carbon pricing models studied in this paper belong to environmental regulation. Therefore, the article wants to simulate the border of the Porter hypothesis in the CT and ETS scenarios. In the CGE model, the TFP of the sector is given exogenously. Therefore, the CGE model implies a critical assumption: the carbon pricing strategy will not affect the change in TFP. Thus, the model cannot use the CGE model to directly verify whether the Porter hypothesis is valid in a region. However, it can study the boundary of the Porter hypothesis through modeling technology: the changes in endogenous and exogenous variables. This section intends to discuss how much additional TFP is needed to increase and meet economic neutrality under carbon neutrality. In other words, what the study wants to know in this section is how much more TFP the enterprise needs to improve and meet the carbon neutrality target without reducing GDP.

Based on this idea, additional research and designs are carried out. We first add the endogenous TFP exchange rates to the scale factor in the CES production function in a value-added bundle and make GDP exogenous to be the same as BAU's GDP. Specifically, the modeling technology changes can be described in the CES production function and GDP calculation, as presented in Equations (1) and (2):

$$\mathcal{Y}\_{it} = \mathcal{A}\_{it} \left(\sum\_{j} \delta\_{ij} Input\_{ijt}^{\rho\_i} \right)^{1/\rho\_i} \tag{1}$$

$$\text{GDP}\_{l} = \sum\_{i} (XP\_{it} + XG\_{it} + XV\_{it} + EX\_{it} - IM\_{it}) \tag{2}$$

where Y*it* is the gross output in sector *i* and period *t*. The sector produces goods and services through the CES production function technology. A*it* is the TFP in sector *i* and period *t*. *δij* is the share parameter of input *j* in the production process by sector *i*, and *ρ<sup>i</sup>* is the elasticity parameter. *Inputijt* is the total input of factor *j* in period *t*. GDP*<sup>t</sup>* is the gross domestic product in period *t*, while *XPit*, *XGit*, *XVit*, *EXit*, and *IMit* are household consumption, government consumption, investment, export, and import.

Usually, A*it* is the exogenous variable and GDP*<sup>t</sup>* is the endogenous variable in the model, which means that we performed the comparative analysis based on the same technology level, and we can analyze different external shocks on GDP or other endogenous variables. However, this section wants to explore the border of the strong version of the Porter hypothesis. So, the TFP should be the endogenous variable, and GDP should be controlled to be equal to BAU's GDP in other scenarios. Therefore, the paper changes the model by Equations (3) and (4):

$$Y\_{it}^{cf} = (1 + \theta) \mathbf{A}\_{it} \left(\sum\_{j} \delta\_{ij} \ln p u t\_{it}^{cf \rho\_i}\right)^{1/\rho\_i} \tag{3}$$

$$\overline{\text{GDP}\_{t}} = \sum\_{i} \left( X P\_{it}^{cf} + X G\_{it}^{cf} + X V\_{it}^{cf} + E X\_{it}^{cf} - I M\_{it}^{cf} \right) \tag{4}$$

where *ϑ*, which is an endogenous variable that catches the changes in TFP in the condition of the same GDP. The variables with superscript *c f* denote that they are endogenous variables in this section whose values are different from those in the previous section. GDP*t* is an exogenous variable, which is the same in all scenarios in this section. Other settings are the same as in Section 4. The scenario design in this section is described in Table 3.

**Table 3.** The second scenario design.

