Does carbon mitigation depend on green fiscal policy or green investment?

Does carbon mitigation depend on the force of government or the autonomy of enterprises? We should first distinguish the roles of green fiscal policy and corporate green investment to test whether they can independently guide enterprises to reduce carbon emissions. Because a clear relationship will help resolve the embarrassment caused by their different goals. Then we use theoretical and empirical methods to analyze green fiscal policies and corporate green investment mechanisms, which have nonlinear impacts on carbon mitigation in mathematics. Furthermore, we have empirically verified then in three effective paths: the promotion of green fiscal policies on green investment, the mediator of green investment in the influence of green fiscal policies on carbon mitigation and enterprise performance, and the difference in firm heterogeneity on green investment. The results show that green fiscal policies support enterprises in realizing carbon mitigation by pressure, stimulating green investment, and achieving Innovation Compensation. Carbon mitigation depends on the trigger of green fiscal policies and the catalysis of green investment. That means the green fiscal policy is an effective instrument for the government to stimulate green innovation only when they are vital in reducing carbon emissions. Finally, we can summarize the evolutionary process of carbon mitigate from mandatory green fiscal policies to independent green investment, which is helpful for green governance and the low-carbon development of enterprises.


Introduction
The concept of green and low-carbon development has basically reached a global consensus, and China has made significant achievements in environmental pollution control, energy conservation and carbon mitigation since 2005. According to the Tracking Data of Renewable Energy Investment in First Half of 2021, the carbon emission intensity of China in 2018 was 45.80% lower than that in 2005. In the first half of 2021, China's investment in renewable energy reached 45.5 billion dollars, and the global new investment was about 174.3 billion dollars. Generally speaking, green and low-carbon development is helpful for green governance and the green development of enterprises. Theoretically, there are two views on carbon governance: the Pigouvian Tax based on government intervention and the Coase Theorem based on the property rights definition. In short, the main idea of coping with carbon mitigation is to internalize external factors. Many studies mainly focus on improving green efficiency, encouraging green investment, and realizing the coordinated development of carbon mitigation and the enterprises ′ performance. As for the relationship between green fiscal policies and green investment, much research generally believes that enterprises will rarely take the intuitive measures to protect the environment or bear responsibilities if the government does not strengthen policy regulations [1]. Therefore they usually inspire green investment by a dual pressure of green fiscal policies or enterprise competition. And a green subsidy also generally compensates for the cost of green investment and encourages enterprises to accept green fiscal policies. It can stimulate corporate green investment to form a complementary cross-effect combining punitive and incentive policies in carbon mitigation [2].
Previous research adheres to the correct guiding ideology, but does not pay enough attention to the resilience of the enterprises' green innovation. In terms of guiding ideology, internalizing external factors is the main idea to deal with carbon emissions. In terms of governance measures, research mainly emphasizes the direct impact of the government green fiscal instruments, except the article. However, the article attempts to reveal the indirect effect of fiscal instruments on carbon emission, the direct impact on enterprise green innovation, and the mediating effect of green innovation in fiscal instruments on dual dividends (carbon emission and corporate performance). Firstly, green fiscal policies play a crucial role in carbon mitigation. Many studies have proved the establishment of the Weak Porter Hypothesis [3,4], and differences in the Strong Porter Hypothesis [5][6][7]. The 'Weak Porter Hypothesis' believes that environmental regulation can stimulate green innovation, while the 'Strong Porter Hypothesis' believes that environmental regulation can stimulate ecological innovation and enhance the competitiveness of enterprises. Secondly, the intensity of green fiscal policies affects the level of R&D investment and enterprise performance. As mandatory measures, green fiscal policies promote green investment and carbon mitigation. Green fiscal policies can achieve the best driving effect on green investment under moderate salary incentives [8]. Green investment has been improved by the pilot policy of carbon emission rights trading [9]. Finally, green innovation promotes carbon mitigation, and affects enterprise performance. Although green governance cannot bring short-term profits, it helps to improve long-term value [10]. Government rewards and punishments can effectively stimulate green investment and improve carbon mitigation, but there are some differences in enterprise performance [11,12]. With the incentive of subsidy policies, many enterprises are compensated for the governance cost through green investment [13]. So, enterprises with a high level of green governance will have a higher growth ability, lower risk-taking, looser financing constraints and higher long-term values.
Although scholars have agreed on the direct relationship between green facial instruments, carbon emission reduction and corporate performance, we are mainly clarifying the differences in logic and mechanism of the relationship. We want to emphasize the importance of green innovation in enterprise, and explore the logical relationship between it and green facial instruments, as well as the transmission mechanism of dual dividends. So, we study whether carbon mitigation depends on the trigger of green fiscal policies or the catalysis of green investment. The logic of this paper is to check the mechanism of green fiscal policies and green innovation in carbon mitigation. The research method is theoretical and empirical analysis. First, this study used the evolutionary game model between government and enterprises to show the mathematical conclusions are proved by empirical analysis methods. Then we obtained the nonlinear impact of green fiscal policies and green investment on the payments of two players obtained by equilibrium analysis. Finally, based on the theoretical and empirical research, the evolutionary process of green fiscal policies and green innovation is further discussed by numerical analysis.
It is different from other literature. Scholars mainly focus on the direct effect of green fiscal policies on carbon emissions and enterprise performance. Still, we are focusing so far on the indirect effect of green fiscal policies and the evolutionary process of driving force for carbon mitigation. First of all, we study the innovation in variable selection. We not only study the direct impact between single variables, but also pay more attention to the coordination effect of multiple variables, including the data of government, enterprises and environmental protection, and study the orderly causal relationship between multiple variables. Green fiscal instruments promote green innovation of enterprises, green innovation behavior helps to reduce carbon emissions rather than green fiscal instruments, green innovation improves enterprise performance, ultimately promote innovation compensation, and realize double dividends. Secondly, we study the innovation in research perspective. We regard the government's mandatory carbon reduction behavior as a guiding measure, which may be short-term effective and not sustainable. The independent green innovation behavior of enterprises will be regarded as an intermediate transmission medium, which will be effective and sustainable for a long time. The improvement of environmental quality and enterprise performance will be regarded as the result of a series of measures, which will lead to coordinated development for a longer time. So, the evolutionary process of carbon mitigate transforms mandatory green fiscal policies to independent green investment. It is meaningful that the direct effect of green fiscal policies is not to reduce carbon emissions but to stimulate green investment, which means that green fiscal policies will gradually reduce or withdraw from carbon regulations when green investment is high enough. This exciting conclusion shows green fiscal policies are not mandatory to reduce carbon, but to guide enterprises to reduce carbon independently through green investment. So this study aims to analyze the different effects of the dynamic mechanism of carbon mitigation, and prove its evolutionary process from mandatory to autonomous.
By focusing on the carbon mitigation goals of the Chinese government and listed companies, this study is a unique contribution to the existing literature in the following ways. First, the objective functions of the government and enterprises are constructed to optimize their carbon decision-making strategies. As a result, we find an evolutionary game process of driving force for carbon mitigation. Second, the evolutionary game process of green fiscal policies and corporate green investment is explored. Three effects are verified: the incentive effect of green fiscal policies on green investment, the acceleration effect of green investment on carbon mitigation, and the compensation effect of green innovation on the enterprises' profits. Finally, the incentive mechanism of green fiscal policies is also revealed. However, there is a research limitation: we have not found a threshold of green fiscal policies or inflection point of green investment, which is a topic for future research.

Theoretical analysis
The low-carbon evolutionary game model consists of a government and two types of enterprise. The supply and demand law of carbon quota is considered, which is priced in two markets: the Primary Distribution Market is dominated by the government, and the Secondary Trading Market is dominated by enterprises. We analyze the effect of green fiscal policies, and the mechanism of green efficiency and corporate performance.

Theoretical model
The carbon decision-making order is defined. Firstly, the government evenly distributes carbon quotas to enterprises based on the maximizing green efficiency function. Then, enterprises determine carbon mitigation and green investment in turn based on the decision order and the maximization of profits. Finally, the remaining or insufficient carbon quotas can be traded in the Secondary Trading Market as shown in figure 1.
Theoretically, green investment, carbon emission and objective functions are affected by green fiscal policies. Therefore, we set the following restrictions to make mathematical results closer to reality.
Restriction 1: it is assumed that the market price is less than the profits obtained from production, to prevent enterprises from making profits by trading carbon quota.
Restriction 2: to compare the results caused by firm heterogeneity, the government equally distributes carbon quotas in the Primary Distribution Market.
Restriction 3: the government does not subsidize the remaining carbon quotas in the Secondary Trading Market, but supports green investment. Theoretically, green subsidy promotes the success rate of green investment, which can reduce carbon emissions under a certain probability. So, enterprises will have more remaining quotas to trade again in the Secondary Trading Market. So, it is assumed carbon tax on carbon emission, and green subsidy for green investment.
Restriction 4: according to the governance goal, the green efficiency function is constructed for the following three reasons: x the government wants every enterprise to pay more for carbon quotas to reduce more carbon emissions. y The government wants to minimize carbon emission given the carbon tax to increase corporate costs. z The government wants to maximize carbon mitigation given the green subsidy. Therefore, the green efficiency function is taken as the payments of governmental decision optimization, which is affected by carbon quota, carbon emission and carbon mitigation. The parameters are shown in the table 1.
In table 1, where, i = 1, 2 represents two types of enterprises. G i is carbon quota, q i is carbon mitigation, and G i − q i is carbon emission. Benjaafar et al (2012) believed that carbon quota follows the price demand law of common commodities [14]. The functional relationship between price and demand is assumed to be P G = a − bG − αT, and . Based on the above settings, the following relations are made. It can reduce carbon quota (G i ) by increasing carbon tax (T) given the price. Carbon mitigation q i can be promoted by green subsidy (S), and carbon emission (G i − q i ) can be reduced by increasing enterprise investment (I i ).

Equilibrium
Two players' objective functions of green efficiency and profits are constructed. We attempt to prove the incentive effect of green fiscal policies on green investment based on the maximization of the functions. In the Secondary Trading Market, we analyze the difference in carbon mitigation caused by the decision order determined by firm heterogeneity, which leads to the difference in green investment and two objective functions. The Cournot Game and Stackelberg Game models are designed for the two types of enterprises. The objective functions are set as shown below: The green efficiency in formula (1) is composed of three parts: P G G is income obtained from the Primary Distribution Market. To control the carbon quota, the government hopes to maximize it. T (G − q 1 − q 2 ) refers to carbon tax collected according to carbon emission, which is expected to be minimized given the tax. S (q 1 + q 2 ) is a green subsidy given to carbon mitigation, which is expected to be maximized given the subsidy. So, it is considered that the lower the carbon emission, the higher the carbon mitigation, and the higher the green efficiency [15,16].  Emission reduction and economic development can be coordinated to a certain extent [17], and have a 'double dividend' regulatory effect under carbon taxes. [18] So, we get formula (1). The profits in formula (2) are composed of six parts: R (G i − q i ) is the income obtained from production, which means the more significant the profits, and the greater the carbon emission. P C i q i is the revenue received by trading the remaining carbon quota in the Secondary Trading Market. Sq i is the subsidy for carbon mitigation. P G G i is the fee paid for carbon quota in the Primary Distribution Market. T (G i − q i ) is the tax paid for carbon emission. rI 2 i is the cost paid for green investment. According to previous research, it is found that there are many nonlinear relationships between green investment and profits, such as U, N, J, or S-shaped curves [19,20]. There may be positive or negative relationships between green investment and profits. The impact of green investment on per-unit profits is not considered, but will increase corporate costs quickly. Therefore, the earnings of per-unit carbon emission are designed as an exogenous variable (R). The increased investment is designed as a quadratic function to represent the marginal decline of green investment. So, we get formula (2).
Since there are two types of enterprise in the model, the carbon quota and emission reduction are their weighted sum, expressed as G = G 1 + G 2 , q = q 1 + q 2 in formulas (1) and (2). The Cournot game and Stackelberg game are used to optimize. The equilibrium of two game models can be obtained. So, to get the differences in decision behavior and results, carbon tax and green subsidy determine the results of the game model (as shown in table 2). In When B, C, D > 0, the appropriate conclusions are as follows: x carbon emission (G j − q j , j = C, S is the Cournot game and the Stackelberg game) is negatively correlated with carbon tax (T) and green subsidy (S). y Green investment (I j 1 and I j 2 ) is positively correlated with carbon tax (T) and green subsidy (S). z Green investment (I j 1 and I j 2 ) is negatively correlated with carbon emission (G j − q j ). { Green efficiency (E j ) has a positive U-shaped relationship with carbon tax (T) and green subsidy (S). | Profits (π j 1 and π j 2 ) have a positive U-shaped relationship with carbon tax (T) and green subsidy (S), and an inverted U-shaped relationship with green investment (I j 1 and I j 2 ). Therefore, the conclusion of the mathematical model points out that the government encourages green innovation of enterprises through carbon tax and green subsidy, and green innovation promotes carbon emission reduction and goal coordination

Cournot game
Stackelberg game Carbon emission Green efficiency Enterprises profits of the two players. That is, green innovation is the intermediate factor between government instruments and goal coordination of the two players.

Numerical analysis
Although we have obtained the equilibrium of green fiscal policies and green investment of the two players, we are more interested in the evolutionary process of decision situation and their payments in a repeated game. Therefore, we simulate the process of two players' strategies (carbon tax and green investment) and payments (green efficiency and enterprise performance) using numerical analysis. Theoretically, it is assumed the government decides under the complete rationality. Usually, the government cannot obtain all information, but make decisions according to the marginal effect signal under bounded rationality. We were referring to the hypothesis of Bischi et al (2004) and Sheng (2019) on bounded rationality [21,22]. If the marginal revenue is positive in a period, decisions will be added in the next period; on the contrary, if the marginal revenue is negative in a period, decisions will be reduced in the next period. Therefore, the governmental dynamic game system on green fiscal policies can be expressed using the following different formulas where ∂E j / ∂S j is the marginal green efficiency function of the subsidy (S j ). θ S , θ T ⩾ 0 is the adjustment frequency of the tax and subsidy. ∂E j / ∂T j is marginal green efficiency function of the tax (T j ), which is obtained from the equilibrium in table 2, and substituted into formula (3), the dynamic function can be obtained as below The dynamic formula (4) describes the change in government decisions. The adjustment frequency θ j is more easily influenced by subjective factors. So they are the key parameters that need to be tested.
Let, S j (t + 1) = S j (t), T j (t + 1) = T j (t), then four equilibrium points are obtained in the two-game models, and ( S j * , T j * ) are the only non-zero Nash equilibrium.
It can be seen from formula (5) the adjustment frequency θ j has no impact on the equilibrium, and the formula of green efficiency and enterprise profits is positive U-shaped. Coordinated development can be realized when the tax and subsidy cross the equilibrium point in the formula (5). It can be seen from the functional nature that increasing the tax and subsidy can improve green efficiency. Therefore, the role of tax and subsidy in improving green efficiency is consistent. Taking T j ⩾ S j , which is to ensure that green subsidies can be payable within the scope of carbon tax. Taking T j = S j , which is to maximize green efficiency through the maximization of green subsidy. To show the influence of the adjustment frequency on enterprises, the numerical analysis is used to simulate. Take a = 12, b = 2.5, c = 14, d = 3.4, R = 14.5, α = 0.5, β = 0.2, µ = 0.6, r = 0.16, and the Jacobian Matrix can be obtained from the formula (4), which meets the necessary and sufficient condition of equilibrium stability according to the Jury Judgment Condition of a nonlinear dynamic system. The above parameters are substituted into formula (3), and the evolutionary process of carbon mitigation can be obtained in a long-term repeated game, which can explain the change of the two players' strategies and their payments using the following four figures. Figure 2 shows the change in carbon tax. In the stable period, there is no difference in the tax level of enterprises. From the double period, the tax of homogeneous enterprises has increased significantly, while the tax of heterogeneous firms has not. It shows that the competition of heterogeneous firms help to reduce carbon tax, which is consistent with the following empirical analysis. Figure 3 shows the change in green investment, which has not increased considerably in homogeneous enterprises. However, the green investment in the two types of enterprises has increased significantly in the competitive environment of heterogeneous enterprises. It shows that the competition of heterogeneous enterprises can stimulate green investment. Figure 4 shows that heterogeneous carbon emission is more minor than that of homogeneous enterprises. It has a rapid downward trend after a double period, which is consistent with the change in green investment. So, green investment accelerates energy conservation and carbon mitigation.
In figure 5, the profits of enterprise 1 is reduced at a higher investment. The profits of enterprise 2   does not decrease at a lower investment, and shows an evident growth in the double period, which is consistent with the change of green investment. It shows that green investment can realize Innovation Compensation under an appropriate investment. Therefore, it is important to subsidize the increased costs of enterprise due to green innovation and help them survive the 'cold winter' .  The bifurcation and chaos of carbon tax, green investment, carbon emission and profits successively experience three states (stability, periods and divergence) with the increased adjustment frequency of government decisions. In conclusion, the firm heterogeneity has different performances in green investment, carbon mitigation, and performance, which reflects the triggering effect of green fiscal policies and the catalytic impact of green investment. Therefore, the evolution process of carbon emission reduction can be obtained. Carbon tax can be considered as a mandatory means of carbon reduction, which is conducive to improving environmental quality, but is detrimental to enterprise performance and is not conducive to green innovation. Green subsidies can be considered as incentive carbon reduction means, which is conducive to improving environmental quality and damaging enterprise performance, but can stimulate the green innovation behavior of enterprises. Green innovation can be considered as an independent means of carbon reduction, which can realize the coordinated growth of environmental quality and enterprise performance. Nevertheless, we still want to explore and verify this evolution process through empirical data.

Empirical analysis
Carbon tax and green subsidy are important decision variables of government, and the impact on green efficiency and profits is a concern for government and enterprises. In table 2, the environmental tax, subsidy, and other relevant parameters affect carbon emission, green investment, efficiency, and profits.

Empirical hypothesis
The above conclusions show that green fiscal policies affect green investment, carbon mitigation and enterprise profits. Enterprises realize the importance of green investment facing the pressure of green fiscal policies. Therefore, green fiscal policies are the trigger of green investment. The empirical model (as shown in figure 6) and related hypotheses are designed based on theoretical conclusions. Data from China are used to verify the consistency between the theoretical model and empirical data. Hypotheses are as follows: H 1 : green fiscal policies (carbon tax and subsidy) positively affect green investment.

Empirical model
The empirical model is constructed based on the theoretical analysis, formulas (1) and (2) are combined, and the Fixed-effect model and Intermediary Effect test method are considered as follows: Formula (6) shows the impact of carbon tax and subsidy on green investment. If the effect of green investment on green efficiency and EV is considered, and the quadratic of green investment exists, we can get the formula (7): where the dependent variable of DE is green efficiency (measured by carbon emission (CO 2 )) and corporate performance (measured by EV). Substituting formula (6) into the formula (7), and comprehensively considering the effect of green fiscal policies on green efficiency and enterprise value, formula (8) is obtained: where Etax is the carbon tax. Gsub is the green subsidy. GTI is green technology innovation. Controls represent the control variable group, f is the year Fixed-effect, λ is the enterprise Fixed-effect, and ε is the residual.

Variable selection
We conducted empirical research using panel data of Chinese A-share listed companies and their regions from 2006 to 2017. The data are from the CSMAR Figure 6. Empirical model.

Database, RESSET Database, China Statistical Yearbook, Provincial Statistical Yearbooks and Annual
Reports of listed companies. After matching and sorting, 11 532 effective samples are obtained.
The proxy variable of the carbon tax is the atmospheric pollutant discharge fee (Etax). At present, there is environmental tax (or air pollution tax) data in China, and there is no carbon tax. This paper uses the data of air pollution tax as the proxy variable of carbon tax. Environmental tax refers to the general designation of all taxes collected to achieve the goal of environmental protection. Compared with the three, environmental tax has the largest extension, including energy tax and carbon tax, as well as other taxes related to environmental protection, such as sulfur tax, nitrogen tax, sewage tax, etc. Before the implementing of the carbon tax in 2018, China had paid sewage charges. According to the relevant provisions of the measures for the administration of standards for collecting of sewage charges, the equivalent price of air pollutants is 0.6 yuan kg −1 , and the equal-cost of solid waste is 25 yuan t −1 . Firstly, the proportion coefficient δ 1 C and δ 1 P air pollution discharge fee of the whole country and each region are obtained, multiplied by the unit cost of the industrial sulfur dioxide emission, industrial oxide emission and industrial solid waste emission, respectively. Then, the correction coefficient δ 2 C is obtained, which is based on the actual proportion of air pollution discharge fees in the Annual Environmental Statistics Report from 2005 to 2010. Next, the proportion coefficient of the national air pollution discharge fee from 2011 to 2017 is adjusted with the standard deviation. Finally, the coefficient δ 2 P of air pollution discharge fees in each region after adjustment is obtained by using the for- The estimated value of the carbon tax is obtained by multiplying the pollutant discharge fees.
The carbon tax variable (Etax) uses air and solid waste emission data. Therefore, the air pollution discharge fee is multiplied by the unit cost of the industrial sulfur dioxide, industrial oxide, and solid waste emission, which was downloaded from the Annual Environmental Statistics Report.
Carbon emission (CO 2 ) is calculated by the formula 'Industrial Output Coefficient of Enterprise × Adjustment Coefficient of Regional Pollution Indicators (δ 2 P ) × Regional Carbon Emission' . Where, 'Regional Carbon Emission' downloads from IPCC Sectoral Approach, which is a regional coefficient. 'Adjustment Coefficient of Regional Pollution Indicators' is obtained by using the formula ( × δ 1 P , which is a regional coefficient too. 'Industrial Output Coefficient of Enterprise' is a ratio of enterprise output to regional output. So carbon emission is an enterprise coefficient. Generally, the social contributions of enterprises determine the differences in taxation and subsidy. Therefore, we take firm heterogeneity as control variables (Controls), including three aspects. Employment (Size) is measured by the number of employees. Taxation (Tax) is measured by the taxes payable by enterprises. Enterprise nature (SOE) is measured by state-owned or private enterprises. Table 3 shows the descriptive statistical results of variables obtained after logarithm of the original data.

Empirical results
To verify the hypothesis of H 1 -H 4 , the regression analysis of formulas (6)-(8) is carried out using the sorted data. The regression results of empirical models are shown in table 4.
The results in table 4 can be analyzed in the following four ways: Firstly, the hypothesis H 1 assumes that carbon tax and green subsidy positively effect on green technology innovation. The Fixed-effect model tests the formula (6). The results of models 1 and 2 in table 4 show that both the tax and subsidy have a negative effect on green innovation at the significance level of 0.01., which means the smaller the subsidy and tax, the higher the green investment. GTI is expressed by the ratio of carbon emission to industrial-added value. The smaller the proportion, the higher the level of green technology innovation. GPT is expressed by the ratio of energy consumption to sales revenue of new products. The smaller the proportion, the higher the level of green product innovation. It shows that the level of green innovation is improving with the increasing of tax and subsidy. Furthermore, the policy intensity of tax is higher than that of the subsidy at a 0.11 standard deviation. Therefore, the hypothesis H 1 is supported.
Secondly, the hypothesis H 2 assumes that green technology innovation plays a positive role in green efficiency. Unfortunately, due to the limitation of data availability, no suitable alternative variable has been found for the green innovation variable in formula (7). Therefore, there is not enough empirical results to support H2. Thirdly, the hypothesis H 3 assumes that green technology innovation plays a positive role in the enterprise performance. Model 5 shows a positive Ushaped relationship between EV and green technology innovation, indicating that EV has two stages with the improvement of green technology innovation. In the first stage, EV gradually decreases because of the cost of coping with carbon emissions. In the second stage, EV can be increased when the Innovation Compensation Effect is obtained. Therefore, the hypothesis H 2 and H 3 are supported.
Fourthly, the hypothesis H 4 assumes that green innovation plays a mediator role in the double effect model of green efficiency and corporate performance. Models 6 and 7 show that the quadratic coefficients of the tax and subsidy are significantly positive, and they have a positive U-shaped relationship with the carbon emission and EV. Models 8 and 9 show that green fiscal policies and green technology innovation mainly relates to carbon emission and EV. Similarly, models 5 and model 9 show that the impact of green fiscal policies on EV is first reduced and then increased, reflecting the lag of Innovation Compensation Effect. So, the hypothesis H 4 is supported.
Fifthly, the robustness of the models is tested.
x The two-stage System GMM model is used. The first lag phase of carbon tax, green subsidy and green technology innovation is used respectively as instrumental variables in the models. The results are shown in table 4, they passed the Weak Instrumental Variable test and Preliminary Identification test and explained the endogenous problem. y In the System GMM test, the significance and coefficients of models 1-9 are consistent with table 4, indicating the stability of the econometric test conclusions.
In short, the hypotheses H 1 , H 3 and H 4 have been verified, showing that the empirical results can support the theoretical conclusions. In other words, green fiscal policies can indeed trigger the willingness of enterprises for green innovation, but their practical green innovation activities are the real key factor to catalyze carbon mitigation and corporate performance, and only in this way can the collaborative goal of government carbon mitigation and the increase of enterprise efficiency be achieved.

Discussion
The impact of green fiscal policies on carbon emission and EV is first reduced and then increased. It is a strange phenomenon at first sight, but a reasonable conclusion in theory. Carbon emission declines with the increase of carbon tax, but when the tax crosses a certain threshold, the carbon tax will be   reduced to mitigate carbon emission. The trigger effect of green fiscal policies on green efficiency and enterprise profits is reflected in the catalyst effect on green investment, the acceleration effect on carbon mitigation, and the compensation effect on performance. More emphasis is placed on the pressure resistance ability of enterprises facing green fiscal policies. The evolutionary process of carbon mitigation mechanisms, and the sustainability of carbon mitigation measures have been analyzed. The theoretical and numerical analysis has proved that the carbon tax will not increase continuously, but will gradually reduce or withdraw from carbon regulations with the increase of green innovation. So, the empirical analysis is consistent with our theoretical and numerical analysis.
Although H 2 has been proved in mathematical analysis, this is an interesting hypothesis that needs to be proved by practice, and will be given enough attention in future research. Maybe the relationship between them is non-linear, and shows a marginal decline law of green innovation on carbon emission. We believe that it is only a matter of time to prove H 2 with empirical data.
As for carbon emission variables, we convert the regional emission data according to the enterprise output into matching data. Therefore, carbon emissions belong to regional data. At present, China has not released the carbon emissions data of enterprises. This calculation method of carbon emission data will have an impact on the green investment behavior of heterogeneous under the financial policy incentive, but it will hardly affect the exploration of the evolution game of carbon emission reduction policies and the general rules of the double effect model. We will continue to pay attention to this research and believe that there will be more complete data in the near future.

Conclusion
The mechanism of green fiscal policies and green investment in carbon mitigation was analyzed. The combination of theoretical and empirical analysis clarifies the impact of green fiscal policies and green investment on carbon mitigation and corporate performance. The mechanism of green fiscal policies and green investment is explained by the following conclusions: x The carbon tax directly encourages green investment, rather than carbon mitigation. y Carbon tax is the trigger effect, and green investment is the catalyst effect for enterprises to reduce carbon emissions with economic efficiency enhancement; these two factors jointly promote green development and EV. z Carbon tax is a short-term measure that may eventually withdraw from the green fiscal policies. { Green investment is a long-term strategy that directly encourages carbon mitigation, but enterprises value the support of green subsidy in the short term.
The following four suggestions on the effectiveness of green fiscal policies are put forward: Firstly, carbon tax and green subsidy should be strengthened to realize their operation. Enterprises should be encouraged to improve green investment from the establishment of an incentive and restraint mechanism. By the trigger mechanisms, they should be orderly and guided to realize the transformation of carbon mitigation from government compulsion to enterprise autonomy.
Secondly, the government's carbon reduction measures and enterprises' green innovation behavior should be adjusted appropriately. The government should pay more attention to the strength of carbon reduction measures at different stages, introduce carbon taxes and green subsidies into the market in an orderly manner, formulate the strength of mandatory and incentive measures reasonably according to the response of enterprises, and choose the replacement and parallel of different measures when necessary to ensure that enterprises can reduce carbon, survive and develop, and reasonably guide enterprises to achieve carbon reduction while improving performance.
Thirdly, pilot policies of the stepped carbon tax and green subsidy should be considered to increase the enterprises' sensitivity in energy conservation and carbon mitigation, stimulate green investment and enhance enterprises' resilience to cope with the pressure of green fiscal policies. The utility of green investment can be encouraged by supporting enterprises to realize Innovation Compensation and sustainable development.
Fourthly, encourage the government to implement classified management and targeted carbon reduction measures for different enterprises. Different carbon taxes will be levied on enterprises without green innovation, different green subsidies will be given to enterprises with green innovation, and different carbon reduction means will be given depending on the degree of innovation. Necessary compensation for green innovation loans, diversification of green innovation methods, and diversification of collaborative innovation methods are needed to help enterprises build the confidence of carbon reduction through innovation, and help enterprises clarify the double dividend of long-term development of carbon reduction through green innovation.
Finally, the conclusions of the mathematical analysis are useful, and although some of them are difficult to be supported by empirical data: the regulation of the carbon trading market should be continuously improved. As the demand law of carbon quotas in the two trading markets should be adequately intervened, the minimum price limit of the carbon quota should be adopted to hold the demand of carbon emissions to increase the EV. At the same time, enterprises need be encouraged to participate in the Secondary Trading Market of carbon quota.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.