Exploring Potential Pathways toward Energy-Related Carbon Emission Reduction in Heavy Industrial Regions of China: An Input–Output Approach

It is a very urgent issue to reduce energy-related carbon emissions in China. The three northeastern provinces (Heilongjiang (HLJ), Jilin (JL), and Liaoning (LN)) are typical heavy industrial regions in China, playing an important role in the national carbon emission reduction target. In this study, we analyzed the energy consumption, carbon dioxide (CO2) emissions, and CO2 emission intensity of each sector in the three regions, and we compared them with the national level and those of China’s most developed province Guangdong (GD). Then, based on an input–output (I–O) framework, linkage analysis of production and CO2 emission from sector–system and sector–sector dimensions was conducted. The results showed that the three regions accounted for about 1/10 of China’s energy consumption and 1/6 of China’s CO2 emissions in 2012. In addition, the level of energy structure, CO2 emission intensity, and sectoral structure lagged behind China’s average level, much lower than those for GD. According to the sectoral characteristics of each region and unified backward/forward linkages of production and CO2 emissions, we divided sectoral clusters into those whose development was to be encouraged and those whose development was to be restricted. The results of this paper could provide policy–makers with reference to exploring potential pathways toward energy-related carbon emission reduction in heavy industrial regions.


Introduction
Greenhouse gas (GHG) emissions led to a series of environmental problems including the greenhouse effect [1]. As the main component of GHG, energy-related carbon emissions account for more than 80% of the world's anthropogenic emissions [2]. From 1751 to 2012, China accounted for 10.7% of the world's cumulative energy-related carbon dioxide (CO 2 ) emissions. China's carbon emission accounted for a high proportion in the world, which was 26.9% in 2012 [3]. The State Council of China formulated three phases of policies on energy conservation and emission mitigation in the "five-year" cycle and made some achievements [4][5][6]. However, as the largest developing country, China is still facing great challenges in controlling energy consumption and CO 2 emissions on the premise of ensuring stable economic development [7,8].
It was proposed in China's 13th Five-Year Plan (2016-2020) that the energy intensity and carbon intensity should decrease by 15% and 18%, respectively. Considering the heterogeneity of regional social and economic conditions, the targets should be further subdivided [9,10]. As a typical heavy industrial region, northeastern China (Heilongjiang (HLJ), Jilin (JL), and Liaoning (LN), see Figure 1) The input-output (I-O) model was explored to investigate the interdependence among various sectors in an economy [16] and then applied in the environmental fields to quantify pollutant emissions in the consumption of intermediate inputs and final products [17][18][19]. Because of the The input-output (I-O) model was explored to investigate the interdependence among various sectors in an economy [16] and then applied in the environmental fields to quantify pollutant emissions in the consumption of intermediate inputs and final products [17][18][19]. Because of the characteristics of being easily applied to all sectors regardless of the length and complexity of the production chains, the I-O model was widely applied to the analysis of sector-sector linkage on CO 2 and pollutant emissions [20][21][22]. In addition, the I-O model makes it possible to measure both direct CO 2 emissions in production processes and indirect CO 2 emissions embodied in intermediate inputs [23]. Many scholars applied I-O models to analyze energy-related carbon emissions from different perspectives. However, most of them carried out empirical studies at the national level [24][25][26][27]. For a vast country, the industrial structure and economic level of provinces/states are different, which should bring difficulties in seeking an accurate spatial calculation of CO 2 emissions for a country [28]. As far as we know, the studies focusing on regional carbon emissions of large countries were limited to some developed regions or cities such as Beijing [29,30], six large Japanese cities [31], and Guangdong Province [32]. There are few studies focusing on regions where heavy industries dominate the economy. Therefore, this study aims to analyze the characteristics of CO 2 emissions in typical heavy industrial regions in China based on the I-O model and to seek a sustainable development path.
This study intends to make a holistic assessment of sector-sector and sector-system linkages of production and energy-related CO 2 emissions in heavy industrial regions (HLJ, JL, and LN) in 2012 and make a comparison with those of the whole nation and a developed province Guangdong (GD). In detail, regional sectoral energy type and consumption are analyzed. The sectoral CO 2 emissions and CO 2 emission intensity are calculated based on the terminal fossil fuel consumption model proposed by the Intergovernmental Panel on Climate Change (IPCC). Then, the production and energy-related CO 2 emissions linkages are measured within an I-O framework. The sector-sector linkage analysis helps to explore the effects (production and CO 2 emissions) of the changes in final demand or intermediate inputs of one sector on other sectors. The sector-system linkage analysis is Sustainability 2020, 12, 2148 3 of 20 used to investigate how the entire economy or the total CO 2 emissions are affected by the changes in final demand or intermediate inputs of one sector. According to the sectoral characteristics of each region and unified backward/forward linkages of production and CO 2 emissions, encouraged and constrained sectoral clusters are finally proposed.

Energy-Related CO 2 Emissions
The CO 2 emissions are calculated by the terminal energy consumption model proposed by the Intergovernmental Panel on Climate Change (IPCC) [33]. Regional total and sectoral CO 2 emissions are calculated using the following equation: where C, E, and F are the total CO 2 emissions, the terminal fossil fuel (coal equivalent) consumption, and the CO 2 emission coefficients, respectively. Superscript n and m refer to the number of fossil fuel types and the number of sectors, respectively. Subscript i and j denote the i-th fossil fuel and the j-th sector, respectively. The original fossil fuel consumption data are converted into coal equivalent according to the conversion coefficients. Sectoral CO 2 emission intensity (CI j ) is determined by the sectoral output and CO 2 emissions as follows: where X j is the output of the j-th sector.

Non-Competitive Environmentally Extended I-O Framework
The rows in the basic form of the I-O table describe the distribution of producer's output throughout the whole system, while the columns describe the input composition required by a particular sector [34]. In the applied I-O analysis, the distinction between domestically produced and imported inputs cannot be negligible. In order to avoid overestimation of the multiplier effect of a given sector, the linkage calculation should only consider domestically supplied inputs [27]. As an open economic entity, China and regions import and export a great amount of goods/services [35]. Therefore, this study uses a non-competitive I-O table to reorganize the imports used as intermediate inputs (m ij ) and final demand (m f i ). The critical assumption used for eliminating imports is that each final demand category and each sector use the imports with the same proportions [36,37]. The structure of extended I-O table with non-competitive import assumption is shown in Table 1. Domestic supplies and imports are decomposed into two rows as shown in Table 1. Intermediate inputs consist of domestically produced products used as inputs (x d ij ) and imported products used as inputs (m ij ).

Production and CO 2 Emission Linkages Model
Based on the non-competitive environmentally extended I-O framework, we define that the direction of x ij is from sector i to sector j. In order to describe the relationship between two sectors, there are two concepts proposed by Leontief [16] and Ghosh [38], as shown in Equations (3) and (4), respectively.
where A ij denotes the input coefficients, and B ij represents the output coefficients. Equations (3) and (4) can be respectively expressed as follows: where A d denotes the domestic input coefficient matrix (domestically produced goods/services), B d is the domestic output coefficient matrix, and A m and B m are imported input and output coefficient matrices, respectively. A d and B d are used to express the direct linkage between two sectors. However, indirect linkages are generated among sectors in production chains. Therefore, it is necessary to calculate the total linkage among sectors. The matrices of once-indirect Leontief (Ghosh) coefficients among sectors are as follows: The Leontief/Ghosh coefficients matrices (A T /B T ) have the following equilibrium formulas: where (k + 1) represents the k-th indirect Leontief (Ghosh) coefficients among sectors ( k → ∞ , represent the matrices of backward linkage (BL) and forward linkage (FL) between two sectors, also known as the Leontief inverse matrix and Ghosh inverse matrix, respectively.
(I) Sector-sector linkages of production and CO 2 emissions: The sum of each column of the Leontief (row of Ghosh) inverse matrix is calculated to obtain the BL j (FL i ), which indicates the output of all sectors generated from the unit final demand of sector j (the effect on output of all sectors of unit change in primary inputs for sector i). BL and FL between two sectors are not simple reciprocal relations. Figure A1 (Appendix A) illustrates these two indicators with a simple example.
where n i=1 α d ij and n j=1 β d ij are the i-th row and j-th column elements of the matrix I − A d −1 and , respectively. Equations (11) and (12) show the sector-sector backward and forward linkages from an economic point of view, respectively. Then, CO 2 emission intensity (CI) is introduced into Equations (11) and (12) to formulate sector-sector backward (BLC j ) and forward (FLC i ) linkages of CO 2 emissions.
(II) Sector-system linkages of production and CO 2 emissions: In order to better compare the degree of the linkages between sector and system (the entire economy), BL j and FL i are standardized to obtain the unified backward linkage (UBL) and unified forward linkage (UFL) in terms of production.
UBL j and UFL i are capable of reflecting the effect of unitary change in final demand for sector j and primary inputs to sector i on the entire economy, respectively. If UBL j > 1, a unitary increase in final demand for sector j generates an above-average increase in the entire economy. If UFL i > 1, a unitary increase in primary inputs to sector i leads to an above-average increase in the entire economy. Accordingly, if UBL j > 1 and UFL i > 1, this sector can be recognized as a key sector in terms of economy. Therefore, it influences the whole economy to a great extent. In contrast, if UBL j < 1 and UFL i < 1, this sector can be recognized as a non-significant sector. Equations (15) and (16) show sector-system production linkages from an economic point of view. Sector-system linkages of CO 2 emissions are formed as follows: A similar interpretation can be adopted to CO 2 emission linkages. UBLC j > 1 indicates that a unitary increase in the final demand for sector j draws an above-average increase in CO 2 emissions, and UFLC i > 1 represents that a unitary increase in the primary inputs to sector i leads to an above-average increase in CO 2 emissions. The relatively small changes in the sectors (UBLC j > 1 and UFLC i > 1) which are defined as the key sectors in terms of CO 2 emissions could greatly affect the total CO 2 emissions in an economy. Therefore, industrial restructuring provides a potential pathway to reduce CO 2 emissions with relatively less negative effects on the economy through establishing two sectoral groups: constrained group (UBL j < 1, UFL i < 1, UBLC j > 1, and UFLC i > 1) and encouraged group (UBL j > 1, UFL i > 1, UBLC j < 1, and UFLC i < 1).

Data
This study focuses on sector-sector and sector-system linkages of production and energy-related CO 2 emissions in three heavy industrial regions (HLJ, JL, and LN). Simultaneously, linkage measurements for China and GD (a developed region) are also conducted for a comparative analysis. Two databases need to be established: an economic database and an energy-related CO 2 emission database. The economic database includes sectoral output and I-O relationships of China and four regions. Sectoral output data are used to calculate CO 2 emission intensity (see Equation (2)). The original I-O tables are used to produce extended I-O tables with non-competitive import assumption (see Table 1). These data are directly obtained from the I-O tables published by the Chinese Input-Output Association in 2016 and the three provinces' Statistical Yearbooks in 2015 (the latest published I-O tables) [39][40][41][42]. The establishment of the sectoral energy-related CO 2 emission database requires the sectoral terminal energy consumption (physical unit) and CO 2 emission coefficient of each fossil fuel (proposed by the IPCC) as the original data (see Equation (1)). These original data are obtained from the China Energy Statistical Yearbook and the Statistical Yearbooks of three provinces in 2012 [14,[43][44][45]. Sectoral energy-related CO 2 emissions are used to quantify sectoral CO 2 emission intensity. The extended I-O tables and sectoral CO 2 emission intensity are applied to calculate input and output coefficients (see Equations (3) and (4)), the basic equilibrium relationships (see Equations (5) and (6)), Leontief/Ghosh coefficient matrixes (see Equations (7)-(10)), sector-sector linkages (see Equations (11)-(14)), and sector-system linkages (see Equations (15)-(18)).
The classifications of sectors among these original data are different. According to the research purpose and data availability, the sectors are aggregated into 29 sectors (see Table 2). It must be pointed out that, when discussing environmental issues, the splitting and restructuring of sectors would lead to deviations in results [46]. Su and Ang [21] also found that regrouping of sectors would increase the uncertainty in I-O analysis. Table 2. Classification of aggregate sectors.

S1
Agriculture, forestry, animal husbandry, and fishery products and services S2 Mining and washing of coal S3 Extraction of petroleum and natural gas S4 Mining and processing of metal ores S5 Mining and processing of non-metal ores S6 Manufacture of food and tobacco S7 Manufacture of textile S8 Manufacture of textile, wearing apparel, shoes, hats, leather, feather, and related products S9 Processing of wood, bamboo, rattan, palm, and straw products and manufacture of furniture S10 Manufacture of paper and paper products; education and sport activities S11 Petroleum processing and coking S12 Manufacture of chemical products S13 Manufacture of non-metallic mineral products S14 Smelting and calendaring of metals S15 Manufacture of metal products S16 Manufacture of general and special purpose machinery S17 Manufacture of transport equipment S18 Manufacture of electrical machinery and equipment S19 Manufacture of communication equipment, computer and other electronic equipment S20 Other manufacturing industries S21 Waste material S22 Repair services for metal products, machinery, and equipment S23 Production and supply of heat and electricity S24 Production and supply of gas S25 Production and supply of water S26 Construction S27 Transport, storage, and post S28 Wholesale, retail trades, hotels, and catering services S29 Other service sectors a a "Information and communication", "financial and insurance activities", "real estate activities", "professional, scientific and technical activities", "administrative and support service activities", "public administration and defense; compulsory social security", "education", "human health and social work activities" and "arts, entertainment and recreation".

Results
The sectoral terminal energy consumption of three heavy industrial regions and China is firstly analyzed to provide critical information on energy consumption distribution among sectors. Subsequently, energy structure and energy-related CO 2 emissions of three heavy industrial regions and China are compared. Sectoral CO 2 emission intensity is also shown to clarify the sectoral and spatial differences in CO 2 emission by unit output. Based on the CO 2 emission intensity results and extended I-O tables, sector-sector and sector-system linkages of production and CO 2 emissions are finally derived and analyzed.

Terminal Energy Consumption
The total terminal energy consumption of China, HLJ, JL, and LN was 3220.66 million tons of coal equivalent (Mtce), 42.50 Mtec, 39.32 Mtec, and 222.67 Mtec, respectively, in 2012. The terminal energy consumption of HLJ, JL, and LN accounted for 1.32%, 1.22%, and 6.91% of that of China, respectively ( Figure 2). From the sectoral perspective, smelting and calendaring of metals (S14) contributed the most to energy consumption in China, accounting for 23.13%, followed by manufacture of chemical products (S12) and transport, storage, and post (S27). However, the distribution characteristics of sectoral energy consumption of the three regions were different from that of China. The top three energy consumers were S14, petroleum processing and coking (S11), and S27 in HLJ (accounting for 52.18% of total energy consumption), S14, manufacture of non-metallic mineral products (S13), and manufacture of food and tobacco (S6) in JL (accounting for 41.14%), and S11, S14, and production and supply of heat and electricity (S23) in LN (accounting for 66.34%). The total energy consumption in LN was larger than the sum for HLJ and JL in 2012. Specifically, energy consumption of mining and washing of coal (S2), S11, S12, S13, S14, and S23 in LN was much larger than that of these sectors in HLJ and JL. According to the top panel in Figure 2, the sum of energy consumption of three regions in some sectors exceeded 1/10 of China's corresponding sectors', including high-energy-consumption sectors (mining and washing of coal (S2), manufacture of food and tobacco (S6), S11, and S23) and low-energy-consumption sectors (mining and processing of non-metal ores (S5), waste material (S21), repair services for metal products, machinery, and equipment (S22), and production and supply of gas (S24)). The above results show that the three heavy industrial regions were more energy-intensive, especially LN. production and supply of heat and electricity (S23) in LN (accounting for 66.34%). The total energy consumption in LN was larger than the sum for HLJ and JL in 2012. Specifically, energy consumption of mining and washing of coal (S2), S11, S12, S13, S14, and S23 in LN was much larger than that of these sectors in HLJ and JL. According to the top panel in Figure 2, the sum of energy consumption of three regions in some sectors exceeded 1/10 of China's corresponding sectors', including high-energyconsumption sectors (mining and washing of coal (S2), manufacture of food and tobacco (S6), S11, and S23) and low-energy-consumption sectors (mining and processing of non-metal ores (S5), waste material (S21), repair services for metal products, machinery, and equipment (S22), and production and supply of gas (S24)).
The above results show that the three heavy industrial regions were more energy-intensive, especially LN.

CO2 Emissions
CO2 emissions of HLJ, JL, and LN accounted for 3.58%, 2.94%, and 9.91% of that of China in 2012, respectively ( Figure 3). Heat used by LN was not listed separately in the terminal energy consumption table published by the Statistics Bureau of Liaoning. Therefore, the category structure of energy sources was different from that in the other two regions and China. CO2 emissions from

CO 2 Emissions
CO 2 emissions of HLJ, JL, and LN accounted for 3.58%, 2.94%, and 9.91% of that of China in 2012, respectively ( Figure 3). Heat used by LN was not listed separately in the terminal energy consumption table published by the Statistics Bureau of Liaoning. Therefore, the category structure of energy sources was different from that in the other two regions and China. CO 2 emissions from heat and electric consumption accounted for more than 50% of total energy-related CO 2 emissions in HLJ, LN, and China. The shares of CO 2 emissions from different types of energy sources in HLJ and JL were similar. However, the proportion of CO 2 emissions from consumption of "petroleum and its products + natural gas" in HLJ (20%) was higher than that in JL (10%). In particular, CO 2 emissions from using "petroleum and its products + natural gas" and "coal and its products" both contributed over 45% of the total CO 2 emissions in LN. It can be concluded that LN is a region highly dependent on fossil fuel to support industrial production activities. At the national level, the proportion of CO 2 emissions from fossil fuel used to produce electricity was much larger than that of the three regions. Therefore, there is great potential to optimize the terminal energy consumption structure.

Sectoral CO2 Emission Intensity
CO2 emission intensity is defined as the amount of CO2 emission of unit sectoral output. The sectoral CO2 emission intensities of three regions and China in 2012 are shown in Figure 4. In order to investigate the differences in CO2 emission intensity between heavy industrial and developed regions, we added Guangdong (GD) Province's CO2 emission intensity into Figure 4. The CO2 emission intensities of HLJ, JL, LN, and GD were 1.85, 1.43, 2.00, and 0.68 times that of China, respectively. From the sectoral perspective, CO2 emission intensities of S2, S11, and S23 in LN, S5 and S19 in JL, and S11, S14, and S24 in LN were much larger than that of China and GD. However, it is unreasonable to restrict the production of some sectors with relatively higher CO2 emission intensity. This is because the sectors with high CO2 emission intensity are usually recognized as critical sectors which provide raw material and energy to downstream sectors or supply products to final consumption sectors. Therefore, it is necessary to explore methods to balance the economic growth and CO2 emission reduction.   Figure 4. In order to investigate the differences in CO 2 emission intensity between heavy industrial and developed regions, we added Guangdong (GD) Province's CO 2 emission intensity into Figure 4. The CO 2 emission intensities of HLJ, JL, LN, and GD were 1.85, 1.43, 2.00, and 0.68 times that of China, respectively. From the sectoral perspective, CO 2 emission intensities of S2, S11, and S23 in LN, S5 and S19 in JL, and S11, S14, and S24 in LN were much larger than that of China and GD. However, it is unreasonable to restrict the production of some sectors with relatively higher CO 2 emission intensity. This is because the sectors with high CO 2 emission intensity are usually recognized as critical sectors which provide raw material and energy to downstream sectors or supply products to final consumption sectors. Therefore, it is necessary to explore methods to balance the economic growth and CO 2 emission reduction.

Sector-System Production and CO2 Emission Linkages
The main goal of this study is to reduce carbon emissions while not affecting the economic growth obviously. It is clear that allocating the CO2 emission reduction task by sector is unfair and unfeasible because all sectors are correlated in supply-and-demand relationships. Therefore, production limits should focus on industrial groups defined by linkage characteristics, rather than separate key emission sectors. Unified forward linkage of production (UFL), unified backward linkage of production (UBL), unified forward linkage of CO2 (UFLC) emissions, and unified backward linkage of CO2 (UBLC) emissions were quantified (see Equations (15)-(18)) to explore the effect of the unit change of one sector's final demand or intermediate inputs on the entire economy and total CO2 emissions. All panels are organized showing unified backward linkages on the vertical axis and unified forward linkages on the horizontal axis in Figure 5. Comparing the left and right panels, it can be clearly revealed that a unified linkage concept from economy into CO2 emission terms increases the range of linkage values; this finding is consistent with Chang [27] and Lenzen [47].  19 in LN, respectively). From the perspective of the sectoral level, some specific sectors (i.e., S14 and S24 in HLJ, S14, S5, and S21 in JL, and S2 and S23 in LN) induce the wide distribution of linkage values in the three heavy industrial regions.
The definition of key sectors in terms of production and CO2 emissions was explained in Section 2.3. For comparison, key productive sectors (left panels) and key CO2 emission sectors (right panels) are identified in the upper right corner in each panel (see Figure 5). As an alternative way to reduce CO2 emissions, industrial restructuring should be undertaken with sectoral groups as objectives, which corresponds to the values of unified forward and backward linkages of production and emission, simultaneously. If the sectors are non-significant sectors for production and key sectors for CO2 emissions, they can be set as the constrained group ( < 1, < 1, > 1, and > 1). If the sectors are key sectors for production and non-significant sectors for CO2 emissions, they can be set as the encouraged group ( > 1, > 1, < 1, and < 1). The productive change of encouraged sectors could affect the whole economy to a great extent and total CO2 emission

Sector-System Production and CO 2 Emission Linkages
The main goal of this study is to reduce carbon emissions while not affecting the economic growth obviously. It is clear that allocating the CO 2 emission reduction task by sector is unfair and unfeasible because all sectors are correlated in supply-and-demand relationships. Therefore, production limits should focus on industrial groups defined by linkage characteristics, rather than separate key emission sectors. Unified forward linkage of production (UFL), unified backward linkage of production (UBL), unified forward linkage of CO 2 (UFLC) emissions, and unified backward linkage of CO 2 (UBLC) emissions were quantified (see Equations (15)-(18)) to explore the effect of the unit change of one sector's final demand or intermediate inputs on the entire economy and total CO 2 emissions. All panels are organized showing unified backward linkages on the vertical axis and unified forward linkages on the horizontal axis in Figure 5. Comparing the left and right panels, it can be clearly revealed that a unified linkage concept from economy into CO 2 emission terms increases the range of linkage values; this finding is consistent with Chang [27] and Lenzen [47]. The values of UFLC and UBLC (0.06-2.  19 in LN, respectively). From the perspective of the sectoral level, some specific sectors (i.e., S14 and S24 in HLJ, S14, S5, and S21 in JL, and S2 and S23 in LN) induce the wide distribution of linkage values in the three heavy industrial regions.
The definition of key sectors in terms of production and CO 2 emissions was explained in Section 2.3. For comparison, key productive sectors (left panels) and key CO 2 emission sectors (right panels) are identified in the upper right corner in each panel (see Figure 5). As an alternative way to reduce CO 2 emissions, industrial restructuring should be undertaken with sectoral groups as objectives, which corresponds to the values of unified forward and backward linkages of production and emission, simultaneously. If the sectors are non-significant sectors for production and key sectors for CO 2 emissions, they can be set as the constrained group (UBL j < 1, UFL i < 1, UBLC j > 1, and UFLC i > 1). If the sectors are key sectors for production and non-significant sectors for CO 2 emissions, they can be set as the encouraged group (UBL j > 1, UFL i > 1, UBLC j < 1, and UFLC i < 1). The productive change of encouraged sectors could affect the whole economy to a great extent and total CO 2 emission to a small extent. The productive change of constrained sectors would have the opposite effects. As shown in Figure 5, the encouraged sectors are S13 and other manufacturing industries (S20) for HLJ, S11 and manufacture of metal products (S15) for JL, and manufacture of paper and paper products; education and sport activities (S10), manufacture of textile (S7), and S20 for LN. When selecting the constrained sectors, we find that there were few sectors meeting the criteria. Thus, we lowered the production linkage criteria (values of UBL and UFL smaller than 1.2). The constrained sectors are S24 and S10 for HLJ, communication equipment, computer, and other electronic equipment (S19), S13, S25, S27, and S10 for JL, and S11 and S27 for LN.

Sector-Sector Production and CO 2 Emissions Linkages
Section 3.4 helped to identify the encouraged and constrained sectoral groups. However, it is not sufficient to explore potential pathways toward energy-related carbon emission reduction. The pulling and pushing effects among sectors also should be well clarified, which can be accomplished by using sector-sector linkages. Backward linkage can quantify the extent to which a sector relies on other sectors for its inputs. Forward linkage can quantify the extent to which a sector supplies inputs to other sectors throughout the entire economy. The results of sector-sector linkages of production and CO 2 emissions are illustrated by Figures A2 and A3 (see Appendix A), respectively. The sector-sector linkage results of GD (a developed region in China) (see Figure A4 in Appendix A) were also measured to clarify the gap between developed region and three heavy industrial regions.
HLJ's sector-sector production linkages were weaker than those of GD or even JL and LN, with unobvious gaps among three heavy industrial regions. The structure features of sector-sector CO 2 emission linkages of the three heavy industrial regions were similar; however, they were far more complicated than that of GD. Specifically, the highest values of production and CO 2 emission linkages both occurred between one sector and itself (the main diagonal in each panel in Figures A2 and A3, Appendix A). The reason for this phenomenon is that this study reorganized the sectors, and the aggregate sectors could be further divided into more detailed and closely related sectors in actual production activities. However, there were some exceptions; the largest values of FL/FLC occurred between mining and processing of metal ores (S4) and S14/waste material (S21) and S14 in China and JL; the highest values of FL and FLC occurred between extraction of petroleum and natural gas (S3) and S11 in HLJ and LN. The highest values of FL/FLC in the above three pairs of sectors represent the great pushing effect of the former sector on the latter sector. These special cases can be explained using actual production process; metal mining and manufacturing, waste and metal manufacturing, petroleum mining and processing are the adjacent sectors in the production chain with high energy consumption/carbon emission, respectively.
According to the FLC plots in Figure A3 (see Appendix A), some sectors in heavy industrial regions (S11, S14, S23, and transport, storage, and post (S27) in HLJ, manufacture of food and tobacco (S6), manufacture of chemical products (S12), manufacture of non-metallic mineral products (S13), S14, and manufacture of transport equipment (S17) in JL, and S2, S11, S12, S13, S14, S23, and S27 in LN) were intensively pushed by their upstream sectoral clusters to emit CO 2 . According to the results, the high-energy-consumption sectors of HLJ and LN (e.g., metal mining and manufacturing, energy mining, and heavy industry) had a strong pushing effect on other sectors in terms of CO 2 emissions. JL is a major agricultural and vehicle manufacturing region, whose food-related industries and automobile industry have a great pushing effect on others in terms of CO 2 emissions. On the other hand, in the BLC plots, some sectors in heavy industrial regions (S2, S11, S12, S14, S23, and S27 in HLJ and LN, and S12, S14, S23, and S27 in JL) would pull upstream sectoral clusters to emit CO 2 to a great extent.
In HLJ and JL, for coal mining and chemical manufacturing, the BLC was larger than FLC. The reason is that the upstream sectors of these two sectors feature high energy consumption/carbon emissions. Thus, a unit increase in final demand of these two sectors' products would drive more CO 2 emission from upstream sectors than that emitted by the downstream sectors pushed by a unit increase in intermediate inputs of these two sectors. On the contrary, in JL, food manufacturing and non-metallic mineral manufacturing industries had a great pushing effect on downstream sectors in terms of CO 2 emissions, whereas their pulling effect on upstream sectors (with relatively low CO 2 emission intensity) was lower in terms of CO 2 emissions. Attention should be paid to the differences between the above two situations. These sectors were all downstream sectors in the supply chain. The first case emphasizes the effect of other sectors on objective sector in terms of CO 2 emissions. However, the conditions for the second case are converse. For FL and BL, similar situations can be observed in the corresponding plots of each panel. We infer that this situation is mainly determined by the characteristics of the I-O structure of the three regions.

Carbon Reduction Potential of Heavy Industrial Regions
The regional and national I-O tables are compiled every five years in China. The latest published I-O tables (2012) of the three heavy industrial regions and 2012 terminal energy consumption data were used in this study. In 2012, the use of terminal energy in heavy industrial regions (HLJ, JL, and LN) still mainly depended on fossil fuel. The proportion of renewable energy was lower than that of national level. Considering the sectoral production and energy-related CO 2 emissions, the backwardness of production technologies and the unsustainable energy structure in heavy industrial regions were more obvious, especially in HLJ and LN. From a sectoral perspective, most sectors in HLJ and LN have a large potential to reduce CO 2 emissions compared with the national level. Emphatically, MINING and washing of coal (S2), petroleum processing and coking (S11), and production and supply of heat and electricity (S23) should be focused on firstly due to their great potential for CO 2 emission reduction. Compared with HLJ and LN, the CO 2 emission intensity gap between JL and China was not so large. However, there was still a large gap between JL and a developed province (GD) in terms of CO 2 emission intensity.

Dividing Sectoral Clusters
For the three heavy industrial regions, the top three clusters in terms of CO 2 emission were S2 and S3 (mining and washing of coal; extraction of petroleum and natural gas), which provide the original resources and energy for downstream sectoral production; S11-S14 (petroleum processing and coking; manufacture of chemical products; manufacture of non-metallic mineral products; smelting and calendaring of metals), which provide critical materials to downstream manufacture sectors; and S27-S29 (wholesale and retail trades, hotels; catering services; other service sectors), which provide living goods/services to residents. However, it is difficult to obtain some clusters in terms of energy-related CO 2 emission intensity. In general, CO 2 emission intensities of production and supply of energy and resources industries (production and supply of heat and electricity (S23), mining and washing of coal (S2), and petroleum processing and coking (S11)) and heavy industries (S13, S14, and S5) are much higher than other sectors in the three regions studied.
However, if the industrial restructuring is conducted only based on sectoral terminal energy and sectoral CO 2 emission intensity, the macroeconomic benefit is lost to some extent. It must also be pointed out that allocating the emission reduction task by sector is unfair and unfeasible because all sectors are correlated in backward and forward partnerships. Therefore, to balance the conflict between CO 2 emission reduction and economic growth, production and CO 2 emission linkages should be jointly considered when discussing the role of sectors in an economy. Encouraged and constrained sectoral groups were established based on the sector-system linkages. The development of encouraged sectors can affect the whole economy to a great extent and slightly influence the total CO 2 emissions. Restricting constrained sector production can reduce total carbon emissions significantly with less impact on the whole economy. However, several sectors were classified into encouraged and constrained groups. Thus, based on the results of unified linkages of production and CO 2 emissions, we made a table as a key output ranking the sectors. In addition to encouraged and constrained sectors, slightly encouraged and constrained sectors were defined (see Table A1, Appendix A). These results will help researchers and policy-makers to clarify the carbon reduction potential of each sector when formulating industrial restructuring.

Improvement Measures for Sectors
The non-competitive I-O model was used in this study; thus, the inflows from foreign countries and other regions in China (out-of-region) were removed. The four panels on the left in Figure A2 (Appendix A) show the intra-regional sectoral production linkage. The degree of the linkage is mainly affected by two factors: supply chain and the proportion of imports in output. Decreasing the value of the second factor decreases the value of UBL. For example, the proportions of imports in total output of manufacture of electrical machinery and equipment (S18) were 0.07, 0.73, 0.36, and 0.21 in China, HLJ, JL, and LN, respectively, and the S18 UBL values of China and three regions were 1.22, 0.90, 1.00, and 1.19, respectively. Of course, the impact of the second factor is much smaller than that of the first factor.
In Section 3.4, we pointed out the encouraged and constrained sectoral groups. For the encouraged sectors, the proportion in total output should be promoted [48]. We can take some measures to constrained sectors: optimizing the energy structure, increasing the share of renewable energy, improving energy efficiency through technological innovations, and reducing the proportion of constrained sectors' output in total output [49,50]. However, according to the actual situation, the above approaches may not be all applicable. For example, the production of manufacture of non-metallic mineral products (S13) and transport, storage, and post (S27) in JL and S27 in LN should be restricted. However, according to Figure A2 (Appendix A), these three sectors have strong sector-sector linkage relationships with many sectors. Changing their production will induce unexpected turbulence in the economy. Therefore, for such sectors, some measures should be implemented for improving energy efficiency or changing the energy source. More specifically, as a heavy industry, S13 heavily relies on raw coal. Thus, it would be easier to improve energy efficiency than change the energy structure. However, S27 has a complicated energy structure. It would be easier to reduce carbon emissions by changing the energy structure [51].

Conclusions
Reducing CO 2 emissions by adjusting the industrial structure constrains the development of some sectors, which results in macroeconomic losses to some extent. In addition, allocation of emission reduction task by sector is unfeasible because all sectors are correlated in supply and demand relationships. For avoiding the above situations, we applied linkage analysis within the input-output framework to explore potential pathways toward energy-related carbon emission reduction in heavy industrial regions in China (Heilongjiang (HLJ), Jilin (JL), and Liaoning(LN)), considering the backward and forward partnerships among sectors. Sector-sector and sector-system linkages (forward and backward) of production and CO 2 emissions were quantified at regional (HLJ, JL, LN, and Guangdong (GD), a developed region) and national (China) levels. The encouraged and constrained sectoral groups in terms of CO 2 emissions were established. The significant findings are as follows: A: The CO 2 emissions in HLJ, JL, and LN account for 3.58%, 2.94%, and 9.91% of that of China, respectively. The dependence on fossil fuel energy in the above three heavy industrial regions is higher than that in China.
B: Sector-system linkage analysis helped to identify the encouraged or constrained sectoral groups. Manufacture of non-metallic mineral products (S13) and other manufacturing industries (S20) in HLJ, other manufacturing industries (S11) and manufacture of metal products (S15) in JL, and manufacture of paper and paper products; education and sport activities (S10), manufacture of textile (S7), and S20 in LN were identified as encouraged sectors. Production and supply of gas (S24) and S10 in HLJ, manufacture of communication equipment, computer, and other electronic equipment (S19), S13, production and supply of water (S25), transport, storage and post (S27), and S10 in JL, and S11 and S27 in LN were suggested as constrained sectors. Based on the results obtained, four categories of sectors in terms of potential of CO 2 emission reduction were classified.
C: Some sectors set to be constrained have strong sector-sector linkage relationships with other sectors. Therefore, changing production of these sectors will induce unexpected turbulence in the economy. Improving energy efficiency, optimizing energy structure, and production technology innovations for these sectors should be considered with priority. In addition, the actual social situation and the sectoral practical significance should be included when formulating policies.
This study provides a potential pathway in heavy industrial regions toward energy-related carbon emission reduction. In the future, if more detailed data are available, we will carry out an optimization simulation to explore more details and practical results, which will help decision-makers to better formulate policies and measures.      S1  S01  S01  01S  S2  S02  S02  S02  S3  S03  S03  S03  S4  S04  S04  S04  S5  S05  S05  S05  S6  S06  S06  S06  S7  S07  S07  S07  S8  S08  S08  S08  S9 S09 S09 S09 S10 S10 S10 S10 S11 S11 S11 S11 S12 S12 S12 S12 S13 S13 S13 S13 S14 S14 S14 S14 S15 S15 S15 S15 S16 S16 S16 S16 Figure A4. Sector-sector linkages of production and CO 2 emission in Guangdong. In each panel, rows and columns represent upstream sectors and downstream sectors, respectively. Each point represents the pushing effect/pulling effect of row/column sector on the column/row sector (FL: forward linkage of production; BL: backward linkage of production; FLC: forward linkage of CO 2 emission; BLC: backward linkage of CO 2 emission). Table A1. Classification of sectors in terms of potential of CO 2 emission reduction (UBL: unified backward linkage of production; UFL: unified forward linkage of production; UFLC: unified forward linkage of CO 2 emissions; UBLC: unified backward linkage of CO 2 emissions).