This paper estimates the macroeconomic costs of CO_{2} emission reduction in China employing the inputoutput analysis with the multiobjective programming approach. The results show that the effect of reducing CO_{2} emissions on China’s economy is significant. Under the present conditions, the estimated macroeconomic costs of CO_{2} emission reduction in 2010 for China are approximately 3,100–4,024 RMB t ^{ 1} . The stronger the abatement actions, the higher the macroeconomic costs of per unit emission reduction would be. Excavation industry, oil industry, chemical industry, and metal smelting industry have high potential to abate their CO_{2} emissions.
CO2 emission reduction ; macroeconomic cost ; multiobjective programming ; inputoutput analysis
Global warming has been posed widespread concern on international level. In order to mitigate climate change, some developed countries have begun to promote emission reduction of greenhouse gases in terms of agreements. However, the emission reduction can sacrifice economic costs which may be different in various countries for their diversity in many aspects such as stage of development, economic industry structure and energy consumption structure. China is currently in the process of industrialization and urbanization. The proportion of heavy and chemical industry is rather high, resulting in rapid increasing in energy consumption. Thus mandatory emission reduction will have serious impacts on China’s economy. Given these situations, it is important to estimate the macroeconomic costs of emission reduction in China through objective and reasonable assessment of the impact on its economy. This may provide a scientific foundation for countries at different development levels to participate actively in international climate change negotiations and to take actions to reduce CO_{2} emissions in a reasonable way.
In order to quantitatively model the effects of CO_{2} emission reduction on a country’s economy, many researchers have employed various methodologies to study the complex system of economyresourceenvironment and the relevant issues of CO_{2} emission reduction. Manne and Richels [1991] presented the Global 2100 model, a nonlinear programming model for evaluating the costs and benefits of controlling CO_{2} emission. They analyze the impacts of CO_{2} emission reduction on the economy of the U. S., and believe that under the scenario of limiting emissions by OECD (Organization for Economic Cooperation and Development), the annual GDP loss for CO_{2} emission reduction will rise from 2% in the year 2000 to above 4% in 2020. Rose and Steven [1993] established a nonlinear programming model to simulate and estimate the net welfare loss due to CO_{2} emission reduction strategies. The results indicate that the strategy of integrated emission reduction would be better than the strategy of nonelastic emission reduction in each country by 20%. Hafkamp and Nijkamp [1982] discussed the effects of resource allocation policies and showed the disadvantages of singleobjective models in the assessment of changes in social welfare. Hsu and Chou [2000] analyzed the integrated planning for CO_{2} emission reduction of Taiwan and estimated the macroeconomic costs based on multiobjective programming. The macroeconomic costs of CO_{2} emission reduction were estimated about 345–404 US$ t^{ 1} . Yang [2000] also used the multiobjective programming method to estimate macroeconomic costs of CO_{2} emission reduction in Taiwan, which were 7,512–8,202 TWD t^{ 1} (about 263–287 US$ t ^{ 1} ). Chen [2001] presents an integrated analysis on the effects of emission reduction on Taiwan’s economic growth through multiobjective programming. The results show that if Taiwan’s emissions in 2000 were limited to 128% of the level in 1990, the average annual economic growth rate would reduce to 5.4%, compared with the targeted GDP growth rate. These studies provide useful references for the estimation of macroeconomic costs of China’s CO_{2} emission reduction in this paper.
Similar to the studies of Hsu and Chou [2000] and Yang [2000], in this paper the macroeconomic costs of mandatory CO_{2} emission reduction are defined in short as the GDP losses due to the adjustment of industrial structures or limiting the development of highemission sectors to achieve emission reduction at the current economic development stage and without taking into account the changes in technology advancement, energy consumption level, and emission factors. This is different from the common definition of CO_{2} emission reduction costs, which usually considers the technology or capital investment that is needed to reduce CO_{2} emissions (through improving energy efficiency or utilizing new technologies to cut emissions) and is generally a measure of direct costs to enterprises.
In this paper, a model based on multiobjective programming is established to balance and simulate the two objectives of optimizing economic growth and reducing CO_{2} emissions. An inputoutput model is employed to reflect the relations in economy. Thus the macroeconomic losses of CO_{2} emission reduction (i.e., the macroeconomic costs of mitigation) are studied in this paper.
Reducing CO_{2} emissions through adjusting the industrial structure or limiting the development of highemission sectors will constrain the development of some industries, which to some extent will result in the country’s macroeconomic losses. The conflict between economic development and reducing CO_{2} emissions is in need of being balanced by policymakers. In this paper, a multiobjective programming model based on inputoutput analysis is developed to study the relationship between the development of China’s economy and the CO_{2} emission reductions in different scenarios. Through comparing these results, the macroeconomic costs of CO_{2} emission reduction in China are estimated.
Considering the availability of data on energy consumption, water utilization coefficients, inputoutput tables, etc., we combined 42 sectors in the inputoutput table to 24 sectors for the sake of avoiding nonconsistency in sector classification. The developed model has 24 decision variables (the output of each sector), 2 objective functions, and 97 constraints.
Two objective functions in the model represent the maximized GDP ( Z_{GDP} , the sum of added value over sectors) and the minimized CO_{2} emission ( , the sum of CO_{2} emission over sectors) respectively.

( 1) 

( 2) 
Here, X_{i} is the output of sector i ; V_{i} is the added value coefficient of sector i ; P_{i} is the emission coefficient of sector i ; n = 24, which is the number of sectors.
Mainly 97 constraints can be included into four groups in the model, the general equilibrium constraints, water resource constraints, sector expansion constraints and nonnegative constraints. The general equilibrium constraints mean that the sum of output and import for each sector must equal to the sum of its final consumption demand and intermediate demand from other sectors, while the final demand for the planning year should not be lower than that in 2005. This is consistent with other researches [ Hsu and Chou, 2000 ; Chen, 2001 ]. Water resource constraints require that the sum of water utilization in all sectors can not be larger than the maximum supply of water resource. Constraints on the industry sector expansion put limits on industry adjustment. And nonnegative constraints are required for the practical significance of the decision variables.
General equilibrium constraints

( 3) 
Water resource constraints

( 4) 
Sector expansion constraints

( 5) 
Nonnegative constraints

( 6) 
In the constrains above, F is the final demand for all sectors (n×1 matrix); I is an identity matrix; A is a n × n matrix of intermediate consumption coefficients; M is the n × n import coefficient diagonal matrix; X is the output vector for the n sectors (n × 1 matrix); F_{2005} is the final consumption demand for all sectors in year 2005 (n × 1 matrix); r_{i} is the water utilization coefficient for sector i ; W_{max} is the upper bound for water resource supply; X_{i}^{L} and X_{i}^{U} are the lower and upper bounds for the output expansion of sector i .
The data used in the model include the data from inputoutput table and the balance tables of energy consumption in 2005 [ NBSC and NEA, 2008 ], CO_{2} emission factors estimated on basis of IPCC [ Gomez et al., 2006 ], water utilization coefficients from the Researching Group of Chinese InputOutput Association [ RGCIOA, 2007 ], the water supply data from the Macroeconomic Research Institute of National Development and Reform Commission [ MRINDRC, 2004 ], CO_{2} emissions data from the International Energy Agency (IEA) [ IEA , 2008 ], and GDP data from National Bureau of Statistics of China [ NBSC , 2008 ]. The planning year in the model is set to 2010.
We estimate the CO_{2} emission in the production process by each sector through multiplying its consumption of various energy sources by the emission factors. From the China energy statistical yearbook, we obtained the consumption of each energy source, including coal, coke, crude oil, gasoline, kerosene, diesel, fuel oil, natural gas and electricity. Afterwards the CO_{2} emissions of each sector are calculated based on the carbon emission factors provided by IPCC.
As electricity produced by power sector is mainly consumed by other sectors, the large amount of CO_{2} emissions produced in the process of generating electricity from fossil fuels should not be put on power sector alone. Referring to various studies, for example Hsu and Chou [2000], we allocated the CO_{2} emission from power sector among all sectors according to their electricity consumption. Then the CO_{2} emission coefficient of each sector is obtained based on CO_{2} emissions and outputs for each sector.
The two objective functions represent the maximized GDP and the minimized CO_{2} emission, respectively, and compose a twodimensional space ( S objective) ( Fig. 1 ). The constrains in the model form the constrainsset R. This paper aims to roughly estimate the macroeconomic costs of emission reduction in China through examining the tradeoff relationship between GDP growth and CO_{2} emissions, i.e. the potential GDP loss when reducing a certain amount of CO_{2} emissions. Therefore we employ the “compromise method” [ Zeleny, 1982 ] which is described stepwise in the following to obtain the noninferior solutions of the multiobjective programming model.

Figure 1. Several noninferior solutions for the multiobjective programming model and their curve fitting in twodimensional objective space

In the first step, the optimal values for the two objectives under the constrainsset are derived. The value for the maximized GDP is trillion RMB, while the value for the minimized CO_{2} emission is . The two optimal values can not be reached simultaneously, i.e., there is not such a solution that can satisfy the maximized GDP and minimized CO_{2} emission at the same time. The main attempt is to approach the two optimal values as close as possible.
For the second step, with the optimal values of the objectives being defined as the ideal values for GDP and CO_{2} emissions, respectively, we try to minimize the Euclidean distance (d ) from the two objectives to their ideal values under the constrainsset (R ) of the model. Following this, the noninferior solutions for the original multiobjective programming model can be obtained by solving the nonlinear programming problem.

( 7) 
With W_{1} and W_{2} being defined as the weights for two objectives, and can represent the relative weights of two objectives — GDP (w_{1} ) and CO_{2} emissions (w_{2} ) respectively, and w_{1} + w_{2} = 1 . By changing the relative values of w_{1} and w_{2} , several groups of noninferior solutions for the multiobjective programming model can be estimated.
If w_{1} = 1, it means that the policy makers consider only the single objective of maximizing GDP and do not consider CO_{2} emissions reduction, which results in a maximum GDP of 35.3 trillion RMB, which is the same to the ideal value of GDP obtained above. The corresponding CO_{2} emissions will be 9.7 Bt. If the value of w_{1} is changed to 0.875, 0.75, 0.625, 0.5, 0.375, 0.25 and 0.125, respectively, it implies that the policy makers gradually relax the objective of maximizing GDP, and pay more attention to reducing the CO_{2} emissions. We obtain the following noninferior solutions of : (30.67, 6.9), (28.09, 6.4), (25.85, 6.1), (24.16, 5.8), (23.19, 5.7), (21.60, 5.5), and (20.18, 5.3). Here, the unit is trillion RMB for GDP and billion tons for CO_{2} emission. If w_{1} = 0 (i.e., w_{2} = 1), it is implying that at this time the policy makers only consider the CO_{2} emission reduction and have no concern on the GDP growth. The minimized CO_{2} emissions are 5.1 Bt, while the corresponding GDP is 18.69 trillion RMB. The relative positions of the groups of noninferior solutions in the objective space are shown in Figure 1 . We used a polynomial curve, which was chosen as it fit the calculated points relatively well, so as to obtain the estimated relation between GDP and CO_{2} emissions.

( 8) 
The fitting degree of the function above for the nine planning points is 0.9968, and when Z_{GDP} > 23.66, this function is convex. So it can be seen as an estimation of the tradeoff relationship between macroeconomic growth and CO_{2} emissions.
We consider 4 scenarios of the average annual GDP growth rate for China from the base year (2005) to the planning year (2010) (denoted as S1, S2, S3, and S4): 8%, 9%, 10% and 11% respectively. The GDP of 2010 would be 27.02, 28.29, 29.61, and 30.98 trillion RMB, respectively. According to the curve in Figure 1 , the corresponding CO_{2} emissions are 6.1, 6.3, 6.6, and 7.1 Bt, respectively.
It can be seen that different CO_{2} emission levels correspond to different GDP growth rates, in other words, the restrictions on CO_{2} emissions may lead to decrease in the rate of GDP growth. Considering the actual growth rates in recent years and the national economic plan, the scenario S4 is set to be the base case. When the GDP growth rate is reduced from 11% (S4) to 10% (S3), CO_{2} emission will be reduced by 442 million tons, implying that the macroeconomic loss would be 1.37 trillion RMB, that is, an average macroeconomic cost of 3,100 RMB per ton CO_{2} . With reducing the GDP growth rate to 9% (S2), the CO_{2} emission reduction will reach 759 million tons, implying that the macroeconomic losses would be 2.69 trillion RMB, i.e., an average macroeconomic cost of 3,544 RMB per ton CO_{2} . When the GDP growth rate is decreased to 8% (S1), CO_{2} emissions will be reduced by 984 million tons, and the macroeconomic costs would be 3.96 trillion RMB, implying an average macroeconomic cost of 4,024 RMB per ton CO_{2} .
In Table 1 it is obvious that the stronger the abatement actions, the greater the macroeconomic losses due to emission reduction will be, and the higher the corresponding macroeconomic costs for per unit CO_{2} emission reduction will be. When the emission reduction changes from 442 million to 759 million tons (increase by 72%), the corresponding macroeconomic cost rises by 14% (from 3,100 RMB t ^{ 1} to 3,544 RMB t ^{ 1} CO_{2} ), implying that in average a 1% increase in emission reduction will lead to about 0.2% increment of macroeconomic cost. When the emission reduction increases from 759 million to 984 million tons (increase by 29.6%), the corresponding macroeconomic cost would go up from 3,544 RMB t ^{ 1} to 4,024 RMB t ^{ 1} ( increase by 13.5%), implying that a 1% increase in reductions would result in about 0.46% increment of macroeconomic cost in average in this interval. It can be observed that the magnitude of the rise in macroeconomic costs will increase with the magnitude of emission reduction efforts.
CO_{2} emission reduction^{a} (million tons)  Macroeconomic loss (trillion RMB)  GDP growth rate (%)  Macroeconomic cost for per unit emission reduction (RMB per ton CO_{2} )  The decrease of carbon intensity^{b} (take 2005 as the base year) (%) 

442  1.37  10  3 100  18 
759  2.69  9  3 544  20 
984  3.96  8  4 024  20 
Notes:
a. Calculated with setting 11% as the base case of GDP annual growth rate
b. CO_{2} emission is based on the estimation by IEA
Looking at different sectors, the effects of increasing magnitudes of emission reductions show that mining industry, oil industry, chemical industry, and metal smelting industry are high CO_{2} emission industries, and have more potential to abate their CO_{2} emissions. For example, the possible reduction in the chemical industry’s emission with increasing the magnitude of emission reduction can theoretically reach 43%, while for other highemission sectors, such as mining and metal smelting, the possible reduction magnitude in CO_{2} emissions can reach more than 50%. In contrast, the construction industry has much less CO_{2} emissions (about 50 million tons in average), and has not much potential for reducing emissions.
The results in this paper indicate that CO_{2} emission reduction has a significant effect on China’s economy. It is estimated that the macroeconomic cost of China’s CO_{2} emission reduction in 2010 will be 3,100–4,024 RMB per ton CO_{2} (about 456–592 US$ per ton), which is higher than estimated for Taiwan through multiobjective programming [ Hsu and Chou, 2000 ; Yang, 2000 ]. Therefore, the impact of CO_{2} emission reduction on China’s economy may be higher compared with that on the economy of Taiwan.
In this study, the macroeconomic costs of emission reduction include not only the direct costs of emission reduction through investing in green or advanced technologies, but also the national macroeconomic losses due to limiting the development of highemission sectors. Mandatory emission reduction may have more significant effects on the economy of developing countries and regions, i.e. their macroeconomic costs may be higher due to their economic development stage and energyeconomy characteristics. As has been pointed out by Yang [2000], high dependency of economy on mass energy inputs and highcarbon energy consumption may result in higher macroeconomic costs of emission reduction. Currently, China’s economy has high dependency on fossil fuels and highemission sectors. Mandatory emission reduction in China would have a significant macroeconomic impact, i.e., relatively high macroeconomic costs of CO_{2} emissions. Therefore, the commitment to reduce CO_{2} emissions is very cost intensive in China, but is an important contribution to global climate change mitigation.
Mining industry, oil industry, chemical industry, and metal smelting industry have high potential to abate their CO_{2} emissions. China should increase the investment to improve the technology in the energyintensive industries, such as oil and chemical industries, and accelerate the technology and equipment reconstruction to decrease energy consumption and improve the energy usage efficiency, and thus to reduce their CO_{2} emissions.
With an increasing magnitude of emission reduction effort, the corresponding macroeconomic costs of reducing CO_{2} emissions increase too. Therefore, when setting the targets of controlling CO_{2} emissions, the effects of CO_{2} emission reduction on economy must be taken into account. Reasonable targets should be set based on the principles of “common but differentiated responsibilities” established by the Kyoto Protocol [ UN, 1997 ] and the real potential or endurance. Emission reduction should depend on technological advances in the long term.
Estimating the macroeconomic costs of CO_{2} emission reduction in countries at different economic development stages can give insights to the macroeconomic impact of mandatory CO_{2} emissions on different countries. This is also of significance regarding the allocation of responsibility at international level. This study on China’s macroeconomic costs of CO_{2} emission reduction will help to increase the understanding of impacts of emission reduction on China’s economy. To create a uniform modeling framework and uniform data specifications, so as to estimate and compare macroeconomic costs of CO_{2} emission reductions in different countries and regions, is an interesting task for further research.
This paper is supported by the National Natural Science Foundation of China under Grant Nos. 70825001 and 70941039.
Published on 15/05/17
Submitted on 15/05/17
Licence: Other
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