The input-output model, developed by Leontief in the 1930s, reflects the quantitative dependence of inputs and outputs among the components of an economic system. It is a useful tool for macroscopic assessment of the amount of resources or pollution contained in goods and services. A single-region input-output model cannot reflect the interrelationships among multiple regions. In practice, the extension of single regional input-output analysis to multiple regional input-output analysis can be used to analyze the interrelationships that exist between sectors in different regions.

The MRIO table can also be divided into competitive input-output tables and non-competitive input-output tables, and the difference between the two lies in the different treatment of imported goods. The competitive input-output table assumes that domestically produced intermediate inputs and imports are fully substitutable, while the non-competitive input-output table is divided into two major parts, domestic intermediate inputs and imported intermediate inputs, reflecting the imperfect substitutability of the two. The non-competitive input-output table used in this paper, excluding exports and other terms can be expressed as: x i r = ∑ s ∑ j x i j r s + ∑ s Y i r s

x i r represents the total output of the regional division I. x i j r s is the intermediate input of region r sector i to region s sector j. y i r s represents the final demand provided by the region r sector i to the region s.

The consumption factor for each department can be expressed as: a i j r s = x i j r s / x j s

The direct consumption factor matrix between the region R and the region S is: A r s = a i j r s

Therefore, the above equation is expressed in the form of a matrix: X = I − A − 1 Y X = X 1 X 2 . . . X m Y = Y 1 Y 2 . . . Y m A = A 11 A 12 . . . A 1 m A 21 A 22 . . . A 2 m . . . . . . . . . . . . A m 1 A m 2 . . . A m n where X= ( X i s ) is the total output matrix. Y= ( Y i s )is the final requirements matrix. I is the identity matrix, and diagonally is 1. The formula can also be written: X = L Y L = I − A 11 A 12 ⋯ A 1 m A 21 A 22 ⋯ A 2 m ⋮ ⋮ ⋱ ⋮ A m 1 A m 2 ⋯ A m m − 1 = L 11 L 12 ⋯ L 1 m L 21 L 22 ⋯ L 2 m ⋮ ⋮ ⋱ ⋮ L m 1 L m 2 ⋯ L m m

The inter-provincial carbon emission coefficient is: E = E 1 0 … 0 0 E 2 … 0 ⋮ ⋮ ⋱ ⋮ 0 0 … E m E r = e 1 r 0 . . . 0 0 e 2 r . . . 0 ⋮ ⋮ ⋱ ⋮ 0 0 . . . e n r

The inter-provincial carbon transfer can be expressed without considering exports (Wang et al., 2018): T = E I − A − 1 Y = E 1 0 … 0 0 E 2 … 0 ⋮ ⋮ ⋱ ⋮ 0 0 … E m L 11 L 12 ⋯ L 1 m L 21 L 22 ⋯ L 2 m ⋮ ⋮ ⋱ ⋮ L m 1 L m 2 ⋯ L m m Y 11 Y 12 ⋯ Y 1 m Y 21 Y 22 ⋯ Y 2 m ⋮ ⋮ ⋱ ⋮ Y m 1 Y m 2 ⋯ Y m m where T is the amount of carbon transfer, I − A − 1 is the Leontiev inverse matrix; Y is the final requirements matrix between regions. I F r = ∑ s , s ≠ r C T s r O F r = ∑ s , s ≠ r C T r s

I F r indicates the total inflow from other provinces to province r, O F r indicates the total amount of outflow from province r to other provinces and cities. Thus, the net carbon outflow of region r can be expressed as: C T r = I F r − O F r

Referring to the formula of embodied carbon, the amount of embodied GDP transfer in interregional trade can be expressed as: V T r = I Z r − O Z r where the positive value of V T r indicates that province r has obtained economic benefits through inter-provincial trade, net transfer of part of GDP from other provinces; A negative value of V T r indicates that province r has transferred part of its GDP to other provinces, which is a negative contribution for province r in terms of economic growth.

Similarly, the employment transfer caused by inter-provincial trade can be expressed as: L = δ I − A − 1 F L T r = I J r − O J r δ is the employment factor, a positive value of L T r means that a large number of employment opportunities are obtained through inter-provincial trade; A negative value indicates that province r has a net transfer of labor to other provinces.

The multi-regional input-output tables for China and total carbon emissions data for each province in 2012 and 2017 were both accessed from the China Emission Accounts and Datasets (CEADs) (Mi et al., 2018; Zheng et al., 2020a). This paper considers only the impact of domestic inter-provincial trade. In order to avoid data interference, other items and exports are deducted from total output. Due to data unavailability, the study excludes Tibet, Hong Kong, Macau and Taiwan. The provincial GDP in 2012 and 2017 is reported in the China Statistical Yearbook, and the employment data is collected from the 2013 and 2018 Provincial Statistical Yearbook. In order to better analyze the results of the study, we divided the Chinese mainland provinces into eight regions according to the economic, resource and environmental differences, as shown in Table 1.

Based on the MRIO tables in 2012 and 2017, this study indicates that the net transfer out of embodied carbon was concentrated in the Beijing-Tianjin region, the eastern coastal region and the southern coastal region, which was basically overlap with the three major economic regions in China (i.e. the Beijing-Tianjin-Hebei, Yangtze River Delta and Pearl River Delta economic regions) (Figure 1). For example, the eastern coastal region (e.g., Shanghai, Jiangsu, and Zhejiang) had consistently maintained high embodied carbon net transfer out, 546.31 Mt and 406.64 Mt in 2012 and 2017, respectively. In contrast, the net transfer of embodied carbon was concentrated in the central and northwestern regions. This inter-provincial trade pattern was the embodiment of coal transportation from the north to the south and energy from the west to the east, and reflects the pattern of economic resources after the China’s reform and opening up. China’s eastern coastal region had a developed economy and a large demand for resources and energy, which needs to be transferred from western China. Complementarily, the industrial level of western China is relatively low, and it relies on the outflows of traditional high carbon, low-value-added products.

Notably, the Southwest has changed from a net transfer-in region in 2012 to a net transfer-out region in 2017 due to the long-term support of the Western Development Strategy launched at the end of the last century (see Figure 1). In 2012, the net transfer in from the Southwest was 12.96 Mt, and in 2017, the net transfer out was 321.99 Mt, which is the opposite of the performance in 2007–2012 (Mi et al., 2017). In addition, since 2007, China has adopted a series of energy transition and emission reduction policies. For example, in 2007 China’s National Leading Committee on Climate Change and The National Climate Change Program were established, introducing goals to reduce energy intensity and increase the share of non-fossil energy (Liu et al., 2022). The Nationally Appropriate Mitigation Actions (NAMAs) followed, as did China’s Intended Nationally Determined Contributions (INDCs) in 2015, the latter of which aimed to achieve 60%–65% carbon intensity reductions by 2030 (from 2005 levels) and to reach peak emissions around 2030 (Liu et al., 2022). However, these national energy efficiency campaigns and broad industrial low-carbon transitions have not been met with immediate results in the short term. The scale of net transfer-in of embodied carbon in northeastern China, where the proportion of traditional heavy chemical industries was relatively high, had further increased, from 148.98 Mt in 2012 to 312.55 Mt in 2017, and the low-carbon transition still remained slow.

The inter-provincial carbon emission transfer between 2012 and 2017 is characterized by neighboring spatial transfer, energy economy complementarity, and transfer-in and -out asymmetry, as shown in Figure 2.

1) It is obvious that carbon transfers from geographically close provinces. A typical example is the Beijing-Tianjin-Hebei economic region, where close economic and trade ties promote the transportation of products or fuels in close proximity. The embodied carbon emissions borne by Hebei for Beijing and Tianjin in 2012 were 4,726.16 Mt and 2,269.07 Mt. Similar characteristics are also found between Hebei, Shanxi and Inner Mongolia, between Jiangsu and Shanghai, and between Shandong and Henan. 2) Provinces with strong complementary industrial and economic structures have obvious carbon transfer. For example, Guangdong Province is a modern manufacturing-oriented province with strong energy dependency, while Hebei Province is a large producer of traditional energy and has a large energy trade volume between the two provinces. This causes Hebei to bear a large amount of carbon emissions for Guangdong Province. In 2012 and 2017, the embodied carbon emissions borne by Hebei Province for Guangdong Province were 10588.09 Mt and 5,667.74 Mt. Other provinces with similar characteristics include Beijing and Hebei, Guangdong and Liaoning, and Shanxi and Henan. 3) The scale of carbon emission transfer in and out among provinces is found to be asymmetric. The thickness of the lines of the chord diagram indicates the size of the embodied carbon transfer to and from each province, and the asymmetry of the embodied carbon transfer to and from each province can be seen from the thickness of the lines. For example, the embodied carbon transferred to Guangdong Province mainly comes from Beijing, Shanghai, Jiangsu and Zhejiang, with the transferred amounts of 1,013.27 Mt, 1,847.17 Mt, 938.93 Mt and 970.07 Mt, respectively, accounting for 27.3% of the total amount transferred to Guangdong Province. Meanwhile, the embodied carbon transfer out provinces in Guangdong Province mainly include Hebei, Inner Mongolia, Jiangsu and Shandong, with the transferred amounts of 10,588.09 Mt, 8653.96 Mt, 9,255.48 Mt and 7,370.95 Mt, respectively, accounting for 35.25% of the total transferred out amount in Guangdong Province.

The net transfer of embodied GDP from 2012 to 2017 show that the scale of net transfer in the Beijing-Tianjin region and the southern coastal region had been increasing, with an increase rate of 138.03% and 153.71%, respectively (Figure 3). Meanwhile, the scale of embodied GDP net transfer out of the southwestern, northwestern and central regions was gradually increasing, with 991.31 billion yuan, 789.33 billion yuan and 1,501.87 billion yuan, respectively. The net transfer scale in the northern coastal region has decreased significantly by 66.1% within 5 years. It should be pointed out that the most economically developed and densely populated eastern coastal region and southern coastal region were observed the largest changes in the net transfer of embodied GDP.

The embodied GDP transfer matrix from 2012 to 2017 shows that the impact of inter-provincial trade on the economy of each province varied significantly (see Figure 4). The impact of inter-provincial trade on the embodied GDP in the developing western provinces, e.g., Sichuan and Ningxia, had changed from a positive boost in 2012 to a negative deprivation in 2017. The reason for this may be the rapid economic growth in the western region with the continued support of the targeted poverty alleviation strategy since 2015, and the large amount of energy needs to be transferred and compensated accordingly. On the contrary, the impact on the developed eastern provinces, such as Beijing, Tianjin, Shanghai, and Guangdong, has changed from a negative weakening to a positive pulling, which may be related to the local advantages of high-tech, high-value-added industries.

Inter-provincial trade has led to regional economic differences and complementary development, which is closely related to China’s environmental and economic policy adjustments over the past decade. For example, the obligatory energy and carbon intensity targets stipulated were included in the Five-Year Plans (FYPs), since 12th FYP (2011–2015) (Liu et al., 2022). Moreover, the Action Plan for the Prevention and Control of Air Pollution promulgated in 2013 required that, compared with 2012, the concentration of inhalable particulate matter in cities at the prefecture level and above should be reduced by more than 10% by 2017. These targets strictly restricted the development of “two highs and one low (i.e. high energy consumption, high pollution, and low-output level)” industries, shutting down and transferring thousands of small and medium-sized enterprises. Traditionally energy-rich central and western regions (e.g., Hebei, Shanxi, Inner Mongolia, Henan, and Guizhou provinces) have thus been subjected to significant environmental and economic pressures, leading to slower economic growth.

Changes of embodied employment capacity caused by inter-provincial trade reflect the vitality of regional economy. Unfortunately, this has rarely been mentioned in previous studies. From 2012 to 2017, the provinces with the net transfer out of embodied employment were mainly concentrated in the Beijing-Tianjin region, the eastern coastal region and the southern coastal region, of which the latter two changed the most (see Figure 5). For example, Guangdong Province transferred out 29.27 million workers and 3.97 million workers in 2012 and 2017, respectively, mainly because these provinces consume large amounts of energy transferred from other provinces. Meanwhile, subject to socio-economic factors, the size of the net transfer of embodied labors in northwestern China continued to increase by 82.2% from 2012 to 2017. This suggests that the divergence between labor-intensive industries and technology-intensive and capital-intensive industries was accelerating in eastern and western China. It is worth pointing out that the provinces with the net transfer in of labor were mainly concentrated in the northern coastal region, the central region and the southwest region. Among them, the overall change in the central region was relatively large. From 2012 to 2017, the net employment transfer volume decreased from 45.23 million to 24.42 million, with a reduction rate of 46.0%.

The embodied employment transfer matrix shows that the inter-provincial transfer of embodied employment presented three main characteristics from 2012 to 2017 (see Figure 6). First, the asymmetry of the embodied employment transfer in and out was observed in each province. For example, in 2012, the embodied employment transfer in Hebei Province was relatively large, mainly in Guangdong, Zhejiang, Jiangsu, Shanghai, Shandong and Henan. Meanwhile, the scale of embodied employment transfer out was relatively small, mainly to Jiangsu, Anhui and Henan. In comparison, the scale of embodied employment transfer in Guangdong Province is small, but the scale of transfer out is large. Second, due to the close economic ties and convenient transportation, the embodied employment transfer was observed remarkably between neighboring provinces, for example, between Beijing, Hebei and Tianjin, between Hebei, Shanxi and Inner Mongolia, between Jiangsu and Shanghai, and between Shandong and between Henan. Finally, stimulated by national environmental and climate policies, some provinces presents a reversal between net transfer in and out of the employment. For example, Jiangsu, Shandong, Hubei, Chongqing, Yunnan, and Ningxia changed from net inflows to net outflows of embodied employment, while Jilin, Shanghai, Zhejiang, Fujian, and Hainan performed the opposite.

As of 2017, China’s GDP has increased more than 30 times compared to the beginning of reform and opening up (National Bureau of Statistics of China, 2018). Meanwhile, China has been actively exploring compatible models of economic transformation and environmental protection in the context of fierce economic competition in international trade (National Bureau of Statistics of China, 2020). These changes in climate economic policy have resulted in making trade-offs between carbon emissions reduction and economic development in each province. Since 2011, China’s economic transition has accelerated with slow growth. Especially, from 2013 to 2016, the growth rate of CO₂ emissions has continued to decline (Green & Stern, 2017; Guan et al., 2018; Zheng et al., 2019).

From 2012 to 2017, the quadrant diagram shows a clear provincial divergence between net transfer of embodied carbon and net transfer of embodied GDP (see Figure 7). First, most provinces were located in the second and fourth quadrants, indicating relatively equitable carbon-economy model in inter-provincial trade. This equitable model of the carbon economy implies that when a province provides energy-intensive or carbon-intensive products to other provinces and bears the pressure of carbon emission reduction for other provinces, it will also receive a net transfer in of embodied GDP from other provinces as compensation, and vice versa. Second, some provinces were fixed in a certain quadrant, such as the northern coastal region (Hebei and Shandong) and the central region (Shanxi and Anhui) were always located in the second quadrant; the northwestern region was concentrated in the third quadrant. This suggests that China’s climate economy policies will hardly change the trend of carbon economy in these provinces in the short run. Finally, Carbon inequity was observed in inter-provincial trade. For example, from 2012 to 2017, developing provinces in the western region, such as Gansu and Ningxia, moved from the second quadrant to the third quadrant. In inter-provincial trade, these remotely located provinces relied mainly on exporting low-value-added primary products and importing high-value-added products and services from other provinces for their development. The lock-in effect of low-end energy industries made these provinces slow to make the low-carbon transition and at a significant disadvantage in the competition for a low-carbon economy. Inter-provincial equity and central and western support policies of carbon economy has been fully considered in future development plans, e.g., the 13th (2016–2020) and 14th (2021–2025) FYPs.

After the Copenhagen Climate Conference in 2009, China started three batches (in 2010, 2014 and 2017) of low-carbon provinces and cities successively, and wrote the goal of energy conservation and carbon reduction into the 12th (2011–2015) and 13th (2016–2020) FYPs. These energy-related policies have driven low-carbon actions in the provinces, leading to employment changes following the broad transformation of energy-saving and carbon-reduction industry.

From 2012 to 2017, the net transfer of embodied carbon and employment revealed obvious intrinsic correlation (see Figure 8). First, Most provinces are located in Quadrants 2 and 4, indicating that the net transfer of embodied carbon was accompanied by an equitable compensation for the net transfer of embodied employment. Second, the relationship between the net transfer of embodied carbon and embodied employment in some provinces did not change significantly. For example, the northern coastal region (Hebei and Shandong) were always in the second quadrant, and the northwestern provinces were mainly concentrated in the third quadrant. This indicates that while providing high-carbon products to other provinces and bearing the pressure of carbon emissions, it brings an inflow of employment. Likewise, the central region provinces were largely fixed in the second and fourth quadrants. Finally, the net transfer of embodied carbon is not accompanied by a reasonable compensation for embodied employment in some provinces. For example, provinces in the third quadrant, such as Inner Mongolia and Xinjiang, exhibited a net transfer in of embodied carbon and a net transfer out of embodied employment, and were at a competitive disadvantage; provinces in the first quadrant, on the contrary, including Hunan and Henan, gained a competitive advantage in the carbon economy. The above irrational performances tend to be in the energy-rich provinces of the western region and are the focus of future low-carbon economic equity decision-makings.