Co-Beneﬁts of CO 2 Mitigation for NO X Emission Reduction: A Research Based on the DICE Model

: Actions to reduce carbon emissions often entail co-beneﬁts for environmental protection, like air pollutants reduction. Previous studies made contributions to estimate these co-beneﬁts, but few considered the feedbacks from the socioeconomic system and the natural system. This paper extends the Dynamic Integrated model of Climate and the Economy (DICE) model, a classical Integrated Assessment model (IAM), into the Dynamic Integrated model of Climate, Air pollution and the Economy (DICAE) model. Through the hard link between a new air pollution module and the other modules in the original DICE, this paper quantiﬁes the co-beneﬁts of mitigating CO 2 emissions for NO X emission reduction, and compares the predicted climate change, economic output and social utility under seven mixed policy scenarios. In addition, uncertainty analysis based on Monte Carlo simulation is carried out to verify the robustness of the DICAE model. The results indicate that the NO X emissions co-emitted with CO 2 emissions would be over 0.6 Gt/year in a no-policy scenario. In policy scenarios, mitigating CO 2 emissions can simultaneously reduce at least 15% of the NO X emissions, and the more severe the climate mitigation target is, the more obvious co-beneﬁts for NO X emission reduction. Although these co-beneﬁts can offset some mitigation costs, it will not be cost-effective when NO X emission reduction is achieved completely depending on ambitious carbon mitigation, so the end-of-pipe technology for NO X emission is also indispensable. For policymakers, they should recognize the co-beneﬁts of climate policies, actively taking mitigation actions. Moreover, they are encouraged to combine CO 2 mitigation with NO X emission reduction and coordinate their policy intensities to make wise use of the co-beneﬁts.


Introduction
The world today faces the dual challenge of global warming and air pollution, and the two issues are not independent. Major sources of greenhouse gases (GHG) and air pollutants are both the combustion of fossil fuels, so actions to mitigate carbon dioxide often reduce air pollutant emissions at the same time. Previous studies demonstrate that climate mitigation can bring positive impacts for air pollution control and improve human welfare in addition to its initial climate goals, and these indirect benefits are often referred to as "co-benefits" [1][2][3].
The earliest research on co-benefits can be traced back to the work of Davis et al., in which the positive impacts of global climate policies on particulate-matter (PM) exposures and public health were discussed [4]. Since then, more and more scholars from diverse disciplines begun to the optimal pathway to address the climate change and air pollution issues, some model outputs like predicted climate change, economic output and social utility are compared under seven mixed policy scenarios. In this paper, we only select NO X as a case study because of data limitation for other pollutants. More specifically, this paper attempts to solve four sub-questions: (1) How much NO X emissions can be reduced due to CO 2 mitigation, and will these co-benefits change under different policy scenarios? (2) After incorporating co-benefits into the IAM framework, what would happen to the model results of climate change prediction? (3) If both CO 2 mitigation and NO X emission reduction are implemented, how will the joint policy affect the economic output and social utility? (4) How about the model robustness as well as the uncertainty ranges? The rest of this paper is organized as follows. Section 2 describes the methodology. Section 3 presents the model results under different policy scenarios and detailed interpretations. Finally, Section 4 addresses the main conclusions and some policy recommendations.

The DICAE Model
The DICE model consists of three modules: objective function module, global economic module and the climate change module [22]. Through the monetization of climate change damages and mitigation costs, the climate module is linked to the economic module, then the whole model seeks for the optimal economic development and climate mitigation pathway under the goal of social utility maximization.
Our study is based on the DICE-2013R version [23]. The original time step of DICE-2013R is five years, but it takes a long time for the computer to solve the nonlinear optimization problem (NLP), especially when we do Monte Carlo simulations by interfacing General Algebraic Modeling System (GAMS) and MATrix LABoratory (MATLAB) (which will be explained in detail in Section 2.3). As the choice of time step does not affect the model results, this paper sets it to 10-year to improve the computing efficiency. Accordingly, the parameters and initial variables relating to time step need to be adjusted (See Table A1 in Appendix A).
In this paper, the main work about the modeling is designing an air pollution module and realizing the hard-link with the original DICE model (as shown in Figure 1). In the DICAE model, the economy module and the climate module are same as that in the DICE model [23], so we do not introduce them in this paper. Besides, the explanations of the objective function, as well as how to construct the air pollution module and how it connects with other modules are given in the next sections.

The Objective Function
The DICAE model assumes that economic and climate policies should be designed to optimize the flow of consumption over time. It is important to emphasize that consumption should be interpreted as "generalized consumption," which includes not only traditional market goods and services like food and shelter but also non-market items such as leisure, health status, and environmental services [23,24].
The mathematical representation of this assumption is that policies are chosen to maximize a social utility function. The following equation is the mathematical statement of the objective function: where U is the present value of total social utility; L * (t) is the effective labors/population; c(t) is the per capita consumption; α and ρ represent the marginal utility elasticity of consumption and pure social time preference, respectively.

The Air Pollution Module
The air pollution module includes the quantitative description of air pollutant emissions co-emitted with CO 2 emissions, their damages to the socioeconomic system and the costs of abatement. It should be noted that we only analyze one type of air pollutant, NO X , in this study because of data limitation, and we hope to incorporate more air pollutants, expanding the scope of model applications in future work.

NO X emissions
Nitrogen oxides co-emitted with carbon dioxides mainly come from the combustion of coal, oil and natural gas [25], and carbon emissions from energy consumption are also mainly derived from these three major fossil fuels. In this context, we can build the relationship between CO 2 and NO X based on the homology of emissions.
Assuming that the total energy consumption of the economy is EC(t), and the proportions of coal, oil and natural gas are Coal(t), Oil(t), Gas(t); The proportion of CO 2 emissions produced by energy consumption is w; CO 2 emission factors (emissions from per unit of fuel) of coal, oil and natural gas are EF C coal , EF C oil , EF C gas , and NO X emission factors are EF N coal , EF N oil , EF N gas ; CO 2 emissions and NO X emissions are E C (t) and E N (t), respectively. Thus, we can use two equations below to represent the emissions.
Please note that the NO X emissions calculated in Equation (2) are only the emissions from fossil fuel combustion, under the assumption that all the NO X co-emitted with CO 2 comes from the combustion of coal, oil and natural gas. According to Equations (2) and (3), we can get another equation to express NO X emissions: Then we use α CN to indicate the amount of NO X emissions co-emitted by a unit of CO 2 emission, calling it co-emit coefficient.
Based on the above equations, it is possible to calculate the NO X emissions based on the CO 2 emissions and the energy consumption structure. In addition, if there are actions to reduce CO 2 and NO X , Equation (6) needs to be modified. Here we use µ C (t) and µ N (t) to indicate the emission reduction rates of CO 2 and NO X , respectively, so now their relation satisfies the following equation.
The emission factors in this paper are collected from IPCC EFDB (Emission Factor Database) [26], and their values are shown in Table 1. According to the IPCC AR4 report, CO 2 emissions produced by fossil fuels account for more than 80% of the total anthropogenic CO 2 emissions. Therefore, we set the parameter w as 0.8.
This study assumes that the changes of the energy consumption structure are exogenous. Considering the time span and fitting effect of the energy structure data, we choose the data from the baseline scenario of the Emissions Prediction and Policy Analysis (EPPA) model developed by Massachusetts Institute of Technology (MIT) [27], and get the proportion trends of fossil fuels in the energy consumption structure through the Curve Fitting Toolbox in MATLAB [28] (the coefficient of determination R-square is over 95%). The precise expressions are shown below: Oil(t) = c 1 t c 2 (9) The coefficients in the above equations are obtained from data fitting, and their values are shown in Table 2. Inspired by the DICE model, which divides the impacts of carbon dioxide on the socio-economic system into two parts-environmental damages caused by emissions and control costs of mitigation measures, we divide the impacts of NO X into damages and costs in the DICAE model. As for damages of air pollutants, many studies have approximated them as human health losses. For example, Yang et al. represented the environmental damages of SO 2 , NO X and PM 10 by the value of premature deaths [29]. Thus, in this paper, we also indirectly quantify the environmental damages of NO X emissions through health impairment. Meanwhile, in terms of abatement costs, this paper fits a cost curve of NO X abatement, which will be described in detail in the next sub-section.
To evaluate the health impacts caused by NO X , the inhalation factor method inferred by Li was adopted [30]. Inhalation factor refers to the proportion of total pollutants absorbed by the human body, so it is a dimensionless parameter and can also be called exposure efficiency [31]. This method calculates the inhaled dose in human body firstly, then calculates the health impacts through a dose-response coefficient, and it can be used to evaluate the economic losses further.
The formula for calculating the health damages of NO X is as follows: where HE is the health losses (incidence and mortality); γ is the coefficient of dose-response, which represents the health impacts caused by per unit of inhaled NO X ; The inhalation factor is IF, and the value is 2.47 × 10 −6 [32]; E N (t) indicates the NO X emissions which we have discussed in the previous section.

NO X reduction costs
In this paper, the reduction costs are calculated based on the NO X emission data in the RAINS model developed by IIASA [33]. Figure 2 shows the NO X reduction cost curve, and the corresponding function of the curve is: where θ 3 = 1.280, θ 4 = 1643.047, θ 5 = 2.584; µ N (t) refers to the reduction rate of NO X , and TC N (t) refers to the reduction costs.

Linking with the DICE Model
After creating the air pollution module, we can extend the DICE model into the DICAE model. As shown in Figure 1, carbon emissions in the climate module connect with NO X emissions in the air pollution module, which has already been realized through Equation (7). And environmental damages and reduction costs of air pollutants would influence the final output in the economic module through the following Equations (13)- (18).
In the original economic module, the production function is based on a Cobb-Douglas function which is fixed-scale returns, and then we introduce a climate-feedback coefficient to form an expression of the aggregate output: where Y(t) is the total economic output at time t; A(t), K(t) and L(t) represent the total factor productivity, capital stock and labors (population) at time t; δ represents the capital elasticity; ϕ(t) is the climate-feedback coefficient which is calculated by environmental damages DA(t) and mitigation costs TC(t) of CO 2 , and its specific expression is: After introducing the air pollution module, we update the above equations: By adding NO X reduction costs TC N (t), Equation (16) adjusts the climate-feedback coefficient into a climate & environment-feedback coefficient ϕ * (t). Then this paper reflects the health damages of NO X on the population and productivity. Concretely, the mortality rate ω(t) would affect the effective labors L * (t), while the incidence rate v(t)) could reduce the actual productivity A * (t).
Consequently, the two-way feedback between the air pollution module and the original DICE model is realized in the DICAE model. The DICAE model totally includes 45 parameters and 29 variables, since the number of equations is greater than the number of variables, the optimal solution for each variable can be obtained. We solve this NLP problem using the GAMS software [34].

Scenarios
To discuss the influence of adding NO X on the model results and compare the implementation effects of CO 2 reduction policies, as well as NO X control policies with different intensity levels, setting different scenarios for future emission target is extremely necessary. Therefore, seven mixed emission scenarios are developed in this paper to compare the effects of different emission reduction policies for CO 2 and NO X . These scenarios are made up of three CO 2 emission scenarios: reference scenario (REF), mitigation scenarios (MIT550 and MIT450), and three NO X emission scenarios: no policy (NP), relaxed policy (RP), and stringent policy (SP). The specific meanings of each scenario are listed in Table 3.

Uncertainty Analysis
In the DICAE model, in addition to the deviation of the model assumptions from the scientific facts, some parameters are collected from expert evaluation or data fitting, which also contains a certain degree of subjectivity and bias. In this case, it is worth doing uncertainty analysis of free parameters.
The framework of uncertainty analysis is shown in Figure 3. Since the DICAE model consists of the DICE model and an air pollution module, so we filter sensitive parameters from these two parts, respectively. First, we filter the sensitive parameters of the air pollution module by single-value sensitivity analysis, and then identify the parameters which have relatively great impacts on model outputs in the climate module and the economy module based on the previous literature [35][36][37][38]. After defining the probability density functions (PDFs) of these selected free parameters, Monte Carlo simulation is applied to spread the joint uncertainties of all the sensitive parameters through interfacing GAMS and MATLAB software [39]. Finally, we compare the new outputs with the original results. Figure 3 shows the framework of uncertainty analysis.

Results
This section reports the model results under different emission scenarios to answer the four sub-questions proposed in the introduction section. Hence, the results are presented in four sections: (1) co-benefits for NO X emission reduction across scenarios; (2) predicted climate change across scenarios; (3) effects of joint policies for CO 2 and NO X emission reduction, and; (4) results of the uncertainty analysis.

Co-Benefits for NO X Emission Reduction
In this section, we quantify the co-benefits of climate mitigation for NO X abatement and compare the co-benefits under different policy scenarios. We unify NO X emissions into the no policy scenario (NP) and divide CO 2 emissions into three scenarios of different policy intensity (REF, MIT550 and MIT450), so that we can discuss the co-benefits under three combined scenarios (REF-NP, MIT550-NP and MIT450-NP). Figures 4 and 5 illustrate that climate mitigation can effectively reduce carbon dioxide emissions and significantly reduce nitrogen dioxides emissions, realizing coordinated emission reduction of both greenhouse gases and air pollutants. In Figure 6, if we do not take any mitigation actions, the CO 2 emission shows an increase tendency, reaching 157.48 Gt in 2050 and nearly 250 Gt in 2150. If the mitigation target is set at 550 × 10 −6 CO 2 e, the CO 2 emissions will still increase slightly at the initial stage but decline thereafter, and finally become stable after realizing the mitigation target.
When the target is set to be more ambitious, at 450 × 10 −6 CO 2 e, the emissions decline rapidly in the early periods, and gradually be stabilized at around 10 Gt. As for NO X (Figure 5), the changes of NO X emissions are largely the same as CO 2 . In the absence of carbon mitigation, a great amount of CO 2 emissions will co-emit lots of NO X , and the quantity can be 0.6 Gt/year. Fortunately, reducing CO 2 emissions can at least cut down 15% of the NO X emissions in the first two periods. Comparing MIT550-NP and MIT450-NP, it is not difficult to find that the more severe the climate mitigation target, the more obvious co-benefits for NO X abatement. However, finally, NO X emissions can be stabilized at a low level in both cases.

Climate Change Prediction
To answer question 2 raised in the introduction section, we compare the CO 2 concentration and global temperature increase of the reference scenario in DICE model (not listed in Table 3, this scenario means no climate mitigation in DICE model) and the REF-NP scenario in DICAE model.
From Figure 6, we can find that in the first three periods, the atmospheric CO 2 concentration after considering NO X (DICAE-REF-NP scenario) is basically the same as it does when NO X is not considered (DICE-REF scenario). But later, the concentration in the DICAE model is lower than that in the DICE, and the gap is gradually increasing. Correspondingly, the global temperature rise in the DICAE-REF-NP scenario is also progressively lower than that in the DICE-REF scenario over time (indicated in Figure 7). By 2150, the difference reaches approximately 0.103 • C. After considering the co-emitted NO X from CO 2 , per unit CO 2 emissions will bring greater losses to the whole economy, as it includes damages from both carbon dioxide and nitrogen dioxides. With the increase of CO 2 emissions from human activities, it can produce more co-emitted air pollutants, then, the negative impacts on the economic output becomes increasingly severe. Therefore, under the goal of maximizing the discounted sum of the utilities of per capita consumption in the DICAE model, less anthropogenic CO 2 would be emitted as considering the co-benefits of CO 2 mitigation, even in the no mitigation policy scenario (DICAE-REF-NP). As a result, less CO 2 is emitted in DICAE-REF-NP, which leads to lower concentration and lower temperature rise in the middle and later periods.

Effects of Joint Policies
Since climate mitigation can bring co-benefits for air pollutant management, in turn, will air pollution policies affect CO 2 emissions? Figure 8 states the answer. Since NO X emissions associated with CO 2 emissions from combusting fossil fuels can be reduced through end-of-pipe technology, some of them will not emit into the atmosphere, so the environmental damages can be decreased, which means the negative impact of per unit CO 2 emission can be weakened. Hence, the amount of CO 2 emissions in the early periods is larger than that under the no NO X policy scenario. When we compare MIT550-SP with MIT550-RP or MIT450-SP with MIT450-RP, it reveals that stricter NO X reduction policies will allow for more CO 2 emissions. Nevertheless, this situation will change later (after about 2070), because for the aim of achieving the climate goal, CO 2 emissions must be drastically reduced at that time, which can compensate for the previous over-emissions. Now the more severe NO X reduction policy corresponds to a lower level of CO 2 emissions, although the gaps among different scenarios are not obvious. In this case, in terms of CO 2 emissions, there is no evidence to prove that the end-of-pipe technology for NO X will have absolute positive or negative synergies on CO 2 mitigation, because the short-term impacts are different from that in the long term. Now we explore the impacts of joint policies on world economic output and social utility From Figure 9, we can see that the total outputs in different scenarios all have an increase trend, and the gaps are totally negligible in the early periods but become bigger in the later periods. For ease of comparison, the total output in 2150 is enlarged to the upper left corner of Figure 9, so it is easy to find that the outputs from high to low are: MIT550-RP > MIT450-RP > MIT550-SP > MIT450-SP > REF-NP. It suggests that no emission reduction actions or radical reduction measures cannot bring the highest economic output, while the relatively moderate emission reduction policies for CO 2 and NO X can produce the greatest economic benefits. The reason behind this phenomenon is clear. Without mitigation, the environmental damages of CO 2 and NO X will affect the economic growth, but if people make ambitious efforts to reduce CO 2 emissions, they need to invest a lot, which may reduce the net economic output and affect economic growth when the co-benefits cannot cover the mitigation costs. For instance, in the MIT450-RP scenario, people need to invest 8 trillion USD/year more for mitigation than that in the MIT550-RP scenario, which can produce more co-benefits for NO X emission reduction. However, the overall economic output would reduce by 0.43% in MIT450-RP even if the co-benefits of mitigation have been added. In contrast, modest joint policies can balance the environmental damages caused by emissions and the fiscal costs of emission reductions, and ultimately maximize the total output. Comparing the social utilities (the mathematical statement is shown in Equation (1)) in each scenario, as shown in Table 4, the quantities from high to low are: MIT550-SP > MIT450-SP > MIT550-RP > MIT450-RP > REF-NP > MIT550-NP > MIT450-NP. It illustrates that the combination of a modest CO 2 policy and a stringent NO X policy yields the greatest utility and other joint policies can also make higher social utilities than the no policy scenario (REF-NP). It is worth noting that the social utility in the case of only reducing CO 2 emissions but without NO X abatement (MIT550-NP) would be even lower than the REF-NP scenario. On the one hand, the costs of carbon mitigation cause a burden on the economy which does harm to the utility growth. On the other hand, it shows that the co-benefits of CO 2 reduction on NO X abatement is not enough to cover the negative externalities caused by air pollutants. Therefore, the end-of-pipe technology for NO X is still quite necessary.

Uncertainties
The single-value sensitivity analysis is carried out by floating ±5% on the free parameters in air pollution module. According to the fluctuation of model outputs, we select three sensitive parameters: coal consumption coefficient 2, NO X reduction cost coefficient 1, and the proportion of CO 2 emissions from energy consumption. What's more, their induced fluctuations of the model outputs are all in the range of 1%~2%, which means the newly extended air pollution module doesn't introduce much uncertainty. As for the other three modules, we select nine sensitive parameters and define their probability distribution functions (PDFs) based on some previous studies pertaining to uncertainty analysis of the DICE model [35,36], including some researches discussing fat-tailed probability distributions and unbounded climate risks [37,38]. Therefore, we filter 12 sensitive parameters in the DICAE model, and their PDFs are listed in Table 5. Capital depreciation rate Beta distribution up = 0.12, lo = 0.08, µ = ν = 4.5 03 Initial productivity growth rate Beta distribution up = 0.19, lo = 0.11, µ = ν = 4.5 04 Decline rate of population growth Beta distribution up = 0.4, lo = 0.2, µ = ν = 6 05 Pure rate of social time preference Beta distribution up = 0.06, lo = 0, µ = 7,ν = 4 06 Growth rate of carbon intensity Beta distribution up = −0.05, lo = −0.2, µ = 4, ν = 6 07 Carbon reduction cost coefficient 1 Beta distribution up = 0.04, lo = 0.02, µ = ν = 5.5 08 Climate sensitivity Logarithmic normal distribution avg = 1.071, sd = 0.527 09 Damage function exponent Triangular distribution max = 5, min = 1, avg = 2 10 Coal consumption coefficient 2 Normal distribution avg = 0.012, sd = 1 11 NO X reduction cost coefficient 1 Normal distribution avg = 1643.048, sd = 0.527 12 Proportion of CO 2 emissions from energy consumption Normal distribution avg = 0.8, sd = 1 Note: µ and ν are two parameters of the beta distribution function, which can control the distribution shape; up = upper limit, lo = lower limit, avg = average value, sd = standard deviation, max = maximum, min = minimum. Probability distribution functions (PDFs).
Then, according to the PDFs, we adopt the Monte Carlo simulation to spread the uncertainties of 12 free parameters and focus on three indicate endogenous variables (temperature increase, co-emitted NO X and total output) from different modules to check the changes of model results. After perturbing these free parameters randomly by ±5% through 1000 simulations, the distributions of the indicator variables in the MIT550-RP scenario in year 2050 are shown in Figure 10. Their values can pass the normal distribution test. Based on the 3σ principle, the 95% confidence intervals for each indicator variable can be calculated using the mean value and standard deviation. Choosing 2050 as an example, the confidence interval of temperature increase is (1.432, 1.628) • C, and the interval for NO X emissions is (0.082, 0.120) Gt, as for total output, it is (182.898, 194.439) trillion USD. Similarly, the confidence intervals in each year can be estimated. Figure 11 depicts the original results of the indicator variables from 2010 to 2150, as well as their 95% confidence intervals from Monte Carlo simulation. It can be found that after introducing the randomness of free parameters, the model results would have a great deal of uncertainties. First, for temperature increase, uncertainties in the later periods are obvious, since the uncertainties gradually accumulate, leading to great deviations from the original output. Moreover, the blue line is a bit below the center of the light blue shade, indicating that the mean value of temperature increase in the uncertain condition is higher than that of the original model. It may relate to our definition about the PDF of the climate sensitivity parameter based on the fat-tailed distribution. Second, in view of NO X emissions co-emitted with CO 2 emissions, the values fluctuate within the ±20% range of the original result, which means when all the 12 sensitive parameters in the DICAE model are perturbed randomly by ±5%, it may be difficult to get an accurate estimation of NO X emissions. Finally, as for economic output, the initial confidence interval is (65.47, 67.58) trillion USD, with a fluctuation range of 3.15%, but the interval becomes larger afterwards. In 2150, the interval is (828.54, 1011.54) trillion USD, and the fluctuation range is 20.18%. Likewise, it demonstrates that the uncertainty in subsequent periods of the model is larger than that in the early years. Although there are lots of uncertainties, if we understand the sources and scope of the uncertainty, the model results can still have reasonable applications.

Conclusions
Integrated Assessment Models (IAM) that do not consider co-benefits would inevitably underestimate the real benefits of climate mitigation actions and may hamper policy makers from selecting the optimal mitigation pathways. In this paper, we extend the Dynamic Integrated model of Climate and the Economy (DICE) model into the Dynamic Integrated model of Climate, Air pollution and the Economy (DICAE) model by linking an air pollution module, and taking NO X as an example, the co-benefits of CO 2 mitigation for air pollutants reduction are analyzed. Furthermore, the predicted climate change, the economic output and social utility of joint policies are also explored. At last, we do an uncertainty analysis to test the robustness of the DICAE model and give the uncertainty ranges of model results. The following implications can be drawn from this study.
Firstly, CO 2 mitigation has significant co-benefits for NO X emission reduction, which can reduce at least 15% of the NO X emissions, and the emission reduction rate would be greater if we increase the climate mitigation intensity. These benefits can invariably occur in the short-term and lower the net costs of climate mitigation. However, the end-of-pipe technology for NO X emissions is also necessary, as it will not be cost-effective when NO X emission reduction is achieved completely depending on ambitious CO 2 mitigation. The predominant joint policy is the one that can coordinate the environmental damages and mitigation costs, maximizing the total output or social utility in a sustainable pathway. The single-value sensitivity analysis identifies three sensitive parameters from the air pollution module. After disturbing them by ±5%, respectively, the changes of main output variables are negligible, which means that the new module doesn't introduce many uncertainties. Further, the results of Monte Carlo simulation of 12 selected sensitive parameters manifest that the uncertainties in the later period of the model are larger than that in the early years. Ignoring these uncertainties may cause great risks.
Secondly, there are some implications for policy decision. Comparing the climate change predictions in the DICE model and the DICAE model, the global warming would be relieved to some extent in DICAE, because humans tend to take active mitigation actions due to the incentives from co-benefits for NO X emission reduction. Thus, policy makers should recognize the co-benefits of climate mitigation policies and join in climate actions actively. Especially for developing countries, the government should be aware that, when compared to the long-term and global features of climate mitigation, co-benefits for air pollutants can happen quickly and locally, which would offset some costs of climate policies and strike a balance between short-term interests and long-term development. Furthermore, in the joint policy scenarios, the economic output and social utility are both higher than that in single policy scenarios, which indicate the significance of combining climate policies with air pollution policies and coordinating their intensities to make full use of the co-benefits between them.
Finally, as for modeling work, our study shows the attempt to incorporate co-benefits of climate mitigation into the IAM framework which can capture the feedbacks between the socioeconomic system and the natural system, as well as provide cost-benefit analysis for various policy scenarios. Based on the DICAE model, this paper gives more accurate estimations of these co-benefits for NO X emission reduction and predicted future climate change after considering the response from human-beings and the natural system in an integrated policy assessment framework. However, it has some limitations and more future work needs to be done. For instance, we can apply the framework of the DICAE model to other air pollutants, getting a more comprehensive analysis about co-benefits for air pollutants. Another promising area of future research is realizing the partitioning of the model, to focus on specific mitigation policies within a country or a region, which could lay a more concrete foundation for informed decision-making. Author Contributions: Yuwei Weng and Wenjia Cai conceived and designed the research; Xi Xie contributed to data collection; Xi Xie and Yuwei Weng performed research and analyzed the data. All authors participated in writing this paper. They all read and approved the final manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.