==== Front PLoS One PLoS One plos PLOS ONE 1932-6203 Public Library of Science San Francisco, CA USA 10.1371/journal.pone.0286534 PONE-D-22-18165 Research Article Earth Sciences Atmospheric Science Climatology Climate Change Social Sciences Economics Development Economics Economic Development Physical Sciences Chemistry Chemical Compounds Carbon Dioxide Social Sciences Economics Biology and Life Sciences Ecology Nutrient Cycle Carbon Cycle Ecology and Environmental Sciences Ecology Nutrient Cycle Carbon Cycle Earth Sciences Atmospheric Science Climatology Climate Change Anthropogenic Climate Change Biology and Life Sciences Neuroscience Cognitive Science Cognitive Psychology Attention Vigilance Biology and Life Sciences Psychology Cognitive Psychology Attention Vigilance Social Sciences Psychology Cognitive Psychology Attention Vigilance Physical Sciences Chemistry Physical Chemistry Reaction Dynamics Transition State The social cost of carbon driven by green behaviors The social cost of carbon driven by green behaviors Fu Min Formal analysis Funding acquisition Investigation Project administration 1 2 Zhang Yixiang Data curation Methodology Software Writing – original draft 2 3 https://orcid.org/0000-0003-4817-8580 Tian Lixin Conceptualization Methodology Resources Supervision 1 4 * Zhen Zaili Formal analysis Methodology Project administration Supervision 3 4 1 Research Institute of Carbon Neutralization Development, School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, P.R. China 2 Jiangsu Province Engineering Research Center of Spatial Big Data, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, P.R. China 3 Jiangsu Province Engineering Research Center of Industrial Carbon System Analysis, School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, P.R. China 4 Key Laboratory for NSLSCS, Ministry of Education, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, P.R. China Bashir Muhammad Farhan Editor Shenzhen University, CHINA Competing Interests: The authors have declared that no competing interests exist. * E-mail: tianlx@ujs.edu.cn 30 6 2023 2023 18 6 e028653420 7 2022 18 5 2023 © 2023 Fu et al 2023 Fu et al https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. With the change of climate issues and the needs of economic development, the idea of practicing green and low-carbon behaviors sinks deeper and deeper into people’s hearts. This paper based on the social cost of carbon (SCC) model, this paper constructs a new carbon social cost model by adding the impact of green low-carbon behavior. Classify climate states, based on Bayesian statistical knowledge, study the posterior probability distribution of climate state transitions, and discuss the optimal carbon policy for different climate states by balancing emission utility costs and utility weighted carbon marginal products. This article also discusses the damage caused by rising temperatures and explores their impact on carbon price policies. then, the paper calculates SCC under four kinds of climate states, which will be visually displayed with graphs. Finally, we compare SCC obtained in this paper with that in other researches. The results show that: (1) Climate status has a significant impact on carbon policy, and carbon price predictions will dynamically change with climate status. (2) Green low-carbon behavior has a positive impact on climate status. (3) There are differences in the impact of the three types of damage caused by rising temperatures on carbon price policies. (4) Green development is conducive to stabilizing the value of SCC. (5) Close monitoring of the climate state helps to update the probability of damage in time so that we can precisely adjust the corresponding policies on SCC. This study provides theoretical and empirical reference for the government to formulate carbon price policies and promote the development of social green behavior. National Key Research and Development Program of China 2020YFA0608601 https://orcid.org/0000-0003-4817-8580 Tian Lixin http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 72174091 https://orcid.org/0000-0003-4817-8580 Tian Lixin http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 51976085 Fu Min Major Projects of the National Social Science Foundation of China 22&ZD136 https://orcid.org/0000-0003-4817-8580 Tian Lixin Science and technology innovation project of Carbon Peaking and Carbon Neutrality of Jiangsu Province of China BE2022612 https://orcid.org/0000-0003-4817-8580 Tian Lixin Science and technology innovation project of Carbon Peaking and Carbon Neutrality of Jiangsu Province of China BE2022610 Fu Min This work was supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (Grant No.2020YFA0608601); the National Natural Science Foundation of China (Grant Nos. 72174091, 51976085); the Major Projects of the National Social Science Foundation of China (Grant No. 22&ZD136); the Science and technology innovation project of Carbon Peaking and Carbon Neutrality of Jiangsu Province of China (Grant Nos. BE2022612, BE2022610).They play the role of providing paper layout fee in the paper. There was no additional external funding received for this study. Data AvailabilityAll relevant data are within the paper and its Supporting Information files. Data Availability All relevant data are within the paper and its Supporting Information files. ==== Body pmc1. Introduction Climate change is a global issue, and extreme climate events caused by global warming have become a new threat to international peace. The global destiny is shared and no country in the world can stand alone. Only the international community work together, the issue of climate change can better deal with [1]. One of the main sources of climate change is excessive emission of greenhouse gases, which is directly related to carbon emission behaviors. Carbon emissions have externalities, which is difficult to quantify climate changes. Pigou proposed the use of taxes to solve the problem of externalities and the concept of carbon taxes to internalize the external costs of carbon emissions [2]. As people are concerned about the environment, the perception of climate states is constantly updated, a research report issued by the United Nations Intergovernmental Panel on Climate Change (IPCC) pointed out that a temperature rise within 1.5 degrees Celsius will not endanger the habitability of the earth [3]. To assess SCC, we mainly apply to Integrated Assessment Models for Climate, which can be classified into three categories according to the method used: optimization models, computable general equilibrium models (CGE models), and simulation models [4]. A representative model in optimization modeling is the Dynamic Integrated Climate Economy (DICE). Nordhaus W D [5] used the DICE model to calculate SCC by analyzing the economic and environmental impacts of alternative policies using a simple and easy-to-understand approach, and concluded that the losses caused by climate change increase as output decreases. The carbon cycle model in the DICE model is an important prerequisite for estimating SCC and has undergone refinement from an early single-tier carbon pool [6] to a three-tier carbon pool [7]. Bijgaart et al. [8] studied a box carbon cycle system in a continuous state of time and approximated SCC using a marginal cost approach. Michael D G. et al. [9] used a dynamic stochastic general equilibrium model adapted from the DICE model and found that a relaxed “policy slope” mitigation strategy is preferable to a more aggressive mitigation strategy. Botzen W J W. et al. [10] used an alternative approach to calculate the optimal climate policy for the DICE model and showed that the optimal mitigation policy is very sensitive to climate damage. Dayaratna. et al. [11] balanced the climate sensitivity distribution by new estimates in the DICE model and found that appropriate sensitivity parameter values can effectively reduce the uncertainty. The simulation model is primarily used to assess SCC under a variety of possible future emission scenarios. Hope C. [12] applied the PAGE (Policy Analysis of the Greenhouse Effect) model to give the costs of multiple scenarios and optimal pathways. Stanton E A. et al. [13] evaluated SCC in a multi-emissions scenario. Pizer W A. et al. [14] incorporated both potential long-term losses from climate change and the cost of greenhouse gas abatement into a computable general equilibrium model and showed that the price mechanism scheme outperformed the quantity mechanism scheme and that the efficiency of the hybrid mechanism scheme would be improved. Adao B. et al. [15] studied the impact of technological progress on the optimal transition to a renewable energy driven world economy. In addition, studies exploring the future SCC, which combine elements of technological progress, green behaviors, and probability, have received increasing attention in recent years. Dietz [16] considered damages from sea level rise in the probabilistic comprehensive assessment model to empirically test the key theories in the study and expressed the key parameters of economic costs and climate sensitivity with the help of the thick-tailed distribution. Golosov et al. [17] innovated the neo-classical model and divided the carbon tax into a fixed tax and a time-varying tax for oil, indicating that the optimal strategy is robust to uncertainty. Gerlagh R., Liski M. [18] provide a detailed description of learning dynamics and the emission-temperature response under the description of the global carbon cycle in a climate economic model. Pycroft J. et al. [19] estimated SCC and assessed the probability of losses from climate change by using a comprehensive evaluation model based on economic and climate systems. This paper helps to show the uncertain climate impacts and related estimates of SCC in the integrated system model. Cai Y. et al. [20] established a nine-dimensional dynamic optimization question which was presented by Bellman equation to discuss SCC under a variety of abrupt climate change scenarios, concluding that SCC would fluctuate greatly due to economic or climate risks. Bourgeon J M. and Hovsepian [21] analyzed the use of green technology in a dynamic economy affected by stochastic impact. Gerlagh R., Liski M. [22] studied the optimal future pricing of SCC when the effects of climate change are uncertain, and a quantitative assessment suggests that the price of carbon will grow roughly at the economic growth rate over the next 100 years. Wan B. et al. [23] expressed the diffusion of green low-carbon behaviors in terms of the amount of knowledge diffusion and proposed and compared three regimes of green low-carbon behaviors. Besides, some scholars used the meta-analysis method to explore the factors affecting the green behavior of enterprises, government and rural areas, exploring their behavioral mechanisms [24–26]. Sujahangir K S et al. [27] analyzed the future SCC under two emission scenarios and derived the optimal policy by using Malaysia as a starting point to achieve the emission reduction target by 2050. Zhen Z, Tian L. [28] compared the effects of different climate damage functions and different values of temperature increase on SCC. Zeng Hui fang and Xiong [29] explored the effect of prior information on SCC in a Bayesian statistical approach, and the correction can make SCC less affected by the prior information. Stern N, Stiglitz J E. [30] argued that the flaws in the IAMs model would overestimate SCC. While Khanna M et al. [31] studied the impact of repealing the Clean Power Plan on SCC. Larry S. K et al. [32] constructed a new type of cap-and-trade system to pool information through market prices in order to eliminate the uncertainty caused by asymmetric information. It can be seen that the researches above mainly study SCC through comprehensive climate assessment models, including temperature rise risk, different carbon emission scenarios, discount rates, and extreme disasters. There are few studies on the structure of SCC with green behaviors, and not many of them combine the knowledge related to Bayesian statistics to study the climate states. In addition, a major reason for the elevated SCC estimates is the elevated damage function [20, 33], but there is few researches that analyze the damage of temperature rise utility. The differences between the paper and existing studies are shown in Table 1. 10.1371/journal.pone.0286534.t001 Table 1 Research progress on the social cost of carbon. Literature Green low -carbon behaviors Temperature rise damage Climate models Classification of climate states Carbon cycle Combined with Bayesian statistics Dietz [16] No Yes No No Linear No Golosov et al. [17] No Yes No No Linear No Gerlagh R. et al. [18] No Yes No No Linear No Pycroft J. et al. [19] No No No No No Yes Cai Y et al. [20] No Continuous Yes 2 kinds Linear No Bijgaart et al. [8] No Yes No No Linear No Gerlagh R. et al. [18] No Discrete Yes 3 kinds Linear Yes Zhen Z. et al. [28] No Discrete No 2 kinds No No This paper Yes Discrete Yes 4 kinds Nonlinear Yes Therefore, considering the realistic research context and theoretical research development, this paper presents the core research question: From the perspective of people’s green behavior, how to calculate SCC? This paper explores and construct a SCC model driven by green behaviors from three modules. On the level of economic module, the value of green behaviors is represented by the amount of green behaviors output, and the accounting of gross product takes into account consumption, investment, and production losses due to temperature rise. The utility module takes into account consumption, environmental quality, and the loss of utility due to temperature rise. On the level of climate module, a stochastic probability model of climate based on the carbon cycle and climate damage function is established to classify climate states into four types and to study the corresponding SCC under different climate states. The research framework of this paper is shown in Fig 1: 10.1371/journal.pone.0286534.g001 Fig 1 The research framework of this paper. This study constructs a new carbon social cost model from three modules of economy, utility, and climate to study the best carbon social cost under different climate conditions. The output of green behavior is constructed in the economic module to describe the value generated by green behavior, and the setting of other functions and the interaction between functions are considered more comprehensively. In the utility module, in addition to considering the two indicators of consumption and the loss of utility caused by temperature rise, this article also considers the impact of environmental quality on people’s happiness. In the climate module, the detected temperature rise is used to measure whether the temperature rise has an impact on economic development. Compared with previous studies, the innovation of this paper is mainly shown in the following four aspects: From research perspective: this paper constructs the output of green behaviors based on the climate change information dissemination model as a way to characterize the positive effects of green behaviors on economic development and environmental quality and to consider the multifaceted effects of green behaviors on economy, utility and climate. From research design: in the assessment of SCC, this paper also considers the marginal utility cost in addition to the economic marginal cost. The marginal loss of carbon emissions to economy and utility is considered in SCC. Besides, this paper increases the utility damage of current carbon emissions to three aspects, and discusses the impact of these three aspects of utility damage on the estimated damage to SCC. Based on previous studies, we reasonably assume different forms of distribution to discuss in the form of mathematical expectations in the undamaged climate state. From analysis methods: based on the carbon cycle system with nonlinear structure and climate damage function, this paper considers the uncertainty of climate states and obtains the updated value of probability of temperature rise damage through Bayesian statistical method. This method makes up for the deficiency that SCC is difficult to change with the climate states, and provides a more accurate and flexible analysis method for the estimation of SCC. From research conclusions: We found that SCCS change smoothly with four climate states, SCC increases most moderately in the undamaged state, followed by the interception phase of temperature rise. The increase of SCC in the verge of damage state is slightly larger, but it is much smaller than that in the damaged state. This paper provides more theoretical explanations for the carbon price in the environment of green behavior. This study provides theoretical and empirical reference for the government to better set carbon price. In addition, this article uses a new perspective of thinking to promote the green development of society. 2. Model construction Based on the perspective of people practicing green behaviors, this paper establishes a novel model of SCC through the study of economic module, utility module and climate module. Compared with previous studies, this paper has three aspects of improvement: constructing the output of green behaviors to represent the economic value of green behaviors, and nesting it into the utility module and climate module; obtaining the updated value of the probability of temperature rise damage by using Bayesian methods; and considering SCC based on a combination of the marginal economic cost and the marginal utility cost. Based on the Cobb-Douglas production function and incorporating the production loss due to temperature rise into the production structure [22], the equation for the gross product is obtained as yt=ktα[At(ly,t,et)]βw(st), (1) where kt represents capital, At(ly,t,et) represents the labor-energy compound function and α, β are coefficients of elasticity. For the convenience of general analysis, we set α+β = 1. The gross production value can be written as: yt=ct+kt+1. (2) Based on the research of Gerlagh R and Liski [18], assuming a constant share of investment in GDP of g, 0μt-1 until the damage occurs. When the damage occurs in period t, the climate state is Mt = 1 and is also updated to the damage stage, and the probability of damage occurrence is μt = 1. According to the setting of the probability of climate state transfer, the following conditions can be deduced: (1) The probability of climate state Mt = 0 is shown as follows: Pr(Mt=0)=Pr(Mt=0|p=λ)+Pr(Mt=0|p=0)=μ0(1‐λ)t+(1‐μ0)(1‐0)t=μ0(1‐λ)t+(1‐μ0), (11) p = λ or p = 0 at Mt = 0, so the above formula indicates that the climate state has not caused damage to the economy at t (time). (2) The probability of period t in the interception state of temperature rise is: Pr(p=λ∩Mt=0)=μ0(1‐λ)t, (12) It means that the climate state did not cause damage to the economy in period t (time), but the temperature detection value T exceeded the set temperature alert value T•, so people controlled or reversed the trend of temperature rise through a series of measures such as increasing green behaviors. (3) The damage probability of period t is: Pr(p=λ|Mt=0)=μ0(1‐λ)tμ0(1‐λ)t+1‐μ0, (13) Eq (13) indicates there is a probability of damage, although the climate state does not cause damage to the economy in the period of t. 3. Social cost of carbon Marginal economic cost was usually considered in the previous studies on SCC. This paper also considers marginal loss of utility, that is, to find the optimal SCC by balancing the marginal cost of carbon between economy and utility. The expressions of optimal SCC at Mt = 1 and Mt = 0 are given below, and the estimated damage changes under two climate transition states are explained. 3.1. The social cost of carbon in the state of damage When the damage state Mt = 1, we first work out L, the present value of utility marginal cost of current carbon emission, and the economic marginal cost and utility marginal cost of current carbon emission are balanced. We find the corresponding SCC through ∂y∂E∂μ∂C=L. For convenience, set Δ as the total degree of utility marginal cost (utility loss), that is, set Δ as the discount value of the derivative of utility μt to climate damage Dt. Therefore, the utility loss of carbon emission in period t is: Δ=−∑τ=0∞δτdμt+τdDt, (14) where μt+τ is the utility in the t+τ period, Dt is the carbon emission in the t period, and δ is the discount factor. The Eq (14) is obtained by discounting τ periods. When the temperature rise damage occurs, the temperature rise also leads to the direct utility loss, so we have the Eq (10) Δ=∑τ=0∞δτd(Δu,t+τDt+τ)dDt−∑τ=0∞δτd[ω1lnct+τ]dDt−∑τ=0∞δτd[ω2lnGt+τ]dDt, And when Mt = 1, there are Δu,t+τ = Δu. According to Eq (3), we can get: Δ=Δu−∑τ=0∞δτd[ω1ln((1−g)yt+τ)]dDt−∑τ=0∞δτd[ω2lnGt+τ]dDt, According to the Eq (1), yt+τ is expanded: Δ=Δu−∑τ=0∞δτω1kt+ταBt+τβ[At+τ(ly,t+τ,et+τ)]γe−ΔyDt+τ(−Δy)(1−g)yt+τ+ω2∑τ=0∞δτGt+τlnΔGυGt+τ, The result is shown as follows: Δ=Δu+11−δω1Δy1−g+11−δω2υlnΔG. (15) Therefore, the utility loss of carbon emissions consists of direct utility loss, output loss and green behavior loss. The third green behavior loss is included because the amount of green behavior is considered in the utility. While the temperature rise decreases people’s enthusiasm to practice green behaviors, and then abandons green behaviors because they think their behaviors have no or small significance, so that the temperature rise restrains the output of green behaviors. In addition, when considering the marginal utility loss of current carbon emissions, we can get −dμtdDt=d(Δu,tDt)dDt−d[ω1lnct]dDt−d[ω2lnGt]dDt, From Eq (3), it is concluded that: −dμtdDt=Δu,t−d[ω1ln((1−g)yt)]dDt−d[ω2lnGt]dDt, According to Eq (1), we can obtain that: −dμtdDt=Δu,t−ω1ktαBtβ[At(ly,t,et)]γe−ΔyDt(−Δy)(1−g)yt+ω2GtlnΔGυGt, The result is shown as follows: −dμtdDt=Δu,t+ω1Δy1−g+ω2υlnΔG, We consider the present value of utility cost L of current carbon emissions, which can be easily obtained from the definition: L=−∑τ=1∞δτdμt+τdEt, (16) From Eq (3), it can be concluded that: L=−∑τ=0∞δτdμt+τdDt+τdDt+τdEt=Δ∑τ=0∞δτdDt+τdEt, From Eq (7), it can be concluded that: L=Δ∑τ=0∞δτπε∑i∈Lai(1−ηi)τ−(1−ε)τε−ηi(1−2Etnke), The result is shown as follows: L=δΔπε1−δ(1−ε)∑i∈Lai1−δ(1−ηi)(1−2Etnke). (17) The utility loss per unit of emissions Et during the time period t is decomposed into two components: the effect of temperature rises on utility and the effect of emissions on temperature rise. For the optimal SCC, we consider the weighted utility. τt=∂yt∂Et=L∂ct∂μt can be obtained through ∂yt∂Et∂μt∂ct=L and ∂μt∂ct=1ct=1(1‐g)yt, and the optimal SCC is obtained when the climate state is Mt = 1. τt=L(1‐g)yt, (18) The above equation is expanded to τt(1‐g)ytδΔπε1−δ(1−ε)∑i∈Lai1−δ(1−ηi)(1−2Etnke), which shows that the optimal SCC is directly proportional to the income, indicating that SCC will increase with the increase of income. 3.2. Carbon social cost without damage When the climate state is Mt = 0, it means that the temperature rise has no impact on the economy, or the damage information of the temperature rise to the economy has not been observed. At this time, it is necessary to investigate the parameter distribution of the occurrence time of the temperature rise damage. We set random variable Q to represent the utility cost of the current increase in emissions in the future. We make Lt=Et(Q) to denote the expected present value of future utility losses related to the current unit of emissions. The value of Q is Q1,Q2,…,Qτ means SCC emitted in the period t in which the damage information was first observed and calculated in the period t+τ. Therefore, we assume that climate state Mt remains 0 in all periods before the period t+τ and then changes to 1 in period t+τ, so Qτ represents the present value of marginal loss caused by carbon emissions in t periods and qt accumulated in τ periods. Therefore, under the condition of Mt = 0, the distribution of Q is: P(Q=Qτ|Mt=0)=P(Mτ=1∩Mτ−1=0|Mt=0). The premise of the above equation is that the subjective belief of the occurrence of temperature rise damage in period t is μt, and the temperature rise damage is observed in v periods just after period τ. In order to find the lost corresponding cumulative distribution function Ft(Q), we first discuss the probability of the occurrence of the damage in t periods when the initial subjective belief is μ0 (whether or not it appears for the first time in the period t). First, we find out the probability of Mt = 1: P(Mt=1)=P(Mτ=0∩Mτ−1=0|Mt=0), From Table 2, the probability of climate state transfer p is two-point distribution, and the above equation can be converted into: P(Mt=1)=(1−μ0)P(Mt=1|p=0)+μ0P(Mt=1|p=λ), Since Mt = 1 and Mt = 0 are mutually opposite events, we have P(Mt=1)=1−(1−μ0)P(Mt=0|p=0)−μ0P(Mt=0|p=λ), According to the knowledge of Bayesian statistics, we have P(Mt=1)=1−(1−μ0)P(Mt=0∩p=0)P(p=0)−μ0P(Mt=0∩p=λ)P(p=λ), From Eq (11), the above equation can be simplified as: P(Mt=1)=1−(1−μ0)−μ0(1−λ)t, The result is shown as follows: P(Mt=1)=μ0[1−(1−λ)t], When the subjective belief is μt, the probability of damage in the period t+τ is: P(Mt+τ=1|Mt=0)=μt[1−(1−λ)τ], (19) The cumulative distribution function of Q is obtained: Ft(Qτ)=P(Q≤Qτ|Mt=0)=1−μt+μt(1−λ)τ‐1. Considering the expected utility loss of current carbon emissions Lt, we can know from the definition that Lt=Et∑τ=1∞δτdμt+τdEt, After introducing the temperature rise damage Dt, it can be transformed into: Lt=Et∑τ=1∞δτdμt+τdDt+τdDt+τdEt, According to Eq (7) and Eq (10), we have Lt=Et∑τ=1∞δτΔu,t+τRD,τMt+τ, By replacing Mt+τ equivalently, we can get the following result: Lt=Δu,t+τ∑τ=1∞δτRD,τP(Mt+τ=1|Mt=0), By using the Eq (19), it can be obtained that: Lt=Δu,t+τ∑τ=1∞δτRD,τμt[1−(1−λ)τ], The equivalent transformation is shown as follows: Lt=Δu,t+τμt∑τ=1∞[δτRD,τ−δτRD,τ(1−λ)τ], According to Eq (7), we get the following result: Lt=μt[πΔu,t+τδ(1−2Etnke)ε1−δ(1−ε)∑i∈Lai1−δ(1−ηi)−πΔu,t+τ(1−2Etnke)δ(1−λ)ε1−δ(1−λ)(1−ε)∑i∈Lai1−δ(1−λ)(1−ηi)]. For convenience, it can be equivalent to: Lt=μtLl (20) It can be seen from the final result Lt = μtLl that when the climate state is Mt = 0, that is, when the temperature rise is in the stage of no damage to economic development, the expected utility loss Lt of current carbon emissions is directly proportional to the posterior probability μt of temperature rise damage. People will have an optimistic prediction of the future according to the current situation. For the undamaged stage, μt will decrease with the passage of time, so SCC described by the present value of expected utility loss Lt=Et(E) will decrease with the passage of time. Therefore, when the climate state Mt = 0, the optimal SCC is shown as follows: τt=μtLl(1−g)yt. (21) The expected utility loss of carbon emission is expressed as Lt = μtLl, which shows that the probability of post-test of temperature rise damage μt has an indicative effect on the prediction of SCC. If climate change has no damage to economic development, the posterior probability of temperature rise damage is μt→0, and the predicted value of SCC will decrease. If the posterior probability of temperature rise damage is μt→1, the damage of temperature rise to economic development is on the verge. When Ll→Lt→L, the predicted value of SCC is close to Eq (18), that is, the optimal SCC when climate state Mt = 1. 3.3. Change of estimated damage in transition state The change of SCC in the transition state is explained below. When the temperature detection value T exceeds the set temperature alert value T•, it enters the transition state. From the results, the transition state can be divided into the stage of temperature rise interception and the stage of damage approaching. This section discusses the damage changes of SCC estimation under these two states. 3.3.1. Estimated damage in the interception phase of temperature rise The stage of temperature rise interception refers to that people make greater efforts to practice green behaviors to reverse the rising trend of temperature and reduce the temperature to a safe range after entering the transition state. For The stage of temperature rise interception, people increase the intensity of green behaviors after observing the temperature alert value, so that we assume that μt>μt+11−λ in this stage. Considering people’s caution, the climate change in this stage is adjusted to the following form: Pr(p=λ∩Mt=0)=μ0(1−λ)t. After a certain period of time, the accumulated value of temperature rise drops below the set sensitive value of temperature rise T¯. In the stage of damage approaching, the present value of the expected utility cost of current carbon emissions decreases gradually. Lt>Lt+1,t•Δu,t+1μt+1(1−λ)i−1∑s=1iδs+1dDt+1+sdEt+1=Δu,t+1Pr(p=λ∩Mt+1=0∩⋯∩Mt+i=0)∑s=1iδs+1dDt+1+sdEt+1=EtΔu,t+1∑s=1iδs+1Mt+1+sdDt+1+sdEt+1=Lt+1 The conclusion is proved. People adopt a vigilant policy and increasingly practice green behaviors after rising to the temperature rise alert value. During the period, it did not rise to the temperature sensitive value, and the temperature rise trend was suppressed, gradually returning to below the temperature safety line. 3.3.2. Estimated damage in the near damage stage When the green behaviors failed to reverse the rising trend of temperature in the interception stage of temperature rise, the temperature rise damage occurred with a certain probability after it entered the stage of damage approaching. However, we study the stage of imminent damage from Mt = 0 to Mt = 1. We assume that the temperature Tt^ corresponding to the period t^ is the first period which satisfies Tt^>T˜ and t^<∞. The expected utility loss increases gradually in the near damage stage, so Lt