Water-Saving Efﬁciency and Inequality of Virtual Water Trade in China

: Virtual water trade is widely considered as a potential method to solve local water shortage and unequal distribution. However, limited research investigated water-saving efﬁciency and water inequality of inter-provincial virtual water trade. In this study, we sought to explore this issue within China based on the 2015 input-output data. A multi-regional input-output model and a modiﬁed input-output model were used to estimate the virtual water trade and its impact on water-saving and water inequality. Our results suggest that: (1) The total virtual water ﬂow across the country is 200.03 × 10 9 m 3 , which accounts for 32.77% of water withdrawal. The agriculture sector contributes the highest proportion (73.99%) to virtual water ﬂow. (2) Virtual water trade could decrease water withdrawal by 446.08 × 10 9 m 3 compared with withdrawal under no-trade situation at a national level, and 22 provinces could gain beneﬁts through inter-provincial trade with a positive water-saving efﬁciency index. (3) Virtual water trade also causes water inequality, which exacerbates water scarcity of exported provinces, especially in northwest provinces. (4) There is a conﬂict between water conservation and water inequality, but different provinces show signiﬁcant heterogeneity.


Introduction
Severe water shortage in China has led to continuous concerns on the strategies of water resources management. With the increasing water demand from human activity, rapidly developing economic and social systems, and accelerated urbanization, water resources in China are under extreme pressure [1,2]. Moreover, uneven distribution of water resources further aggravated the water shortage in China. For example, the yellow river economic belt has 23.78% of the gross domestic product (GDP) and 25.83% of the population in China, yet only shares 12.26% of the national water resources [3]. Additionally, the quantity of freshwater is decreasing under climate change [4]; six large river basins in China have shown a declining trend over the past 60 years, and the declining trend will be faster in the future [5]. This means that the competition for water resources among different industries and regions will become more intensive. Therefore, it is urgent for China to take more initiatives to conserve domestic water resources.
Numerous studies have explored possible ways to alleviate the water shortage. Three possible solutions are considered to make water resources more sustainable, including technological innovation, physical water transfer projects, and virtual water trade [6,7]. However, physical water transfer projects such as "South to North Water Diversion" are costly and might cause negative influences on the local ecosystem [6]. Regional virtual water trade seems to be another alternative way to generate sustainable water management [8][9][10]. Virtual water trade is referred to water flow embodied in the trade of products and goods [11]. According to factor endowment theory, importing water-intensive products from areas with abundant water resources can alleviate the water resources pressure of water-poor areas and improve water-saving efficiency [12][13][14][15][16]. For example, Dalin et al. [17] found that the international food trade led to enhanced savings in global water resources whether inter-provincial virtual water trade decreases national and local water withdrawal by developing MRIO and MIO models, and then estimate the heterogeneity of provinces and sectors. Second, we explored the water inequality of inter-provincial virtual water trade within China by constructing a water plunder index. Then, we tried to find solutions that can improve water-saving efficiency without widening the regional water inequality by analyzing the conflict between water-saving efficiency and water plunder.

Multi-Regional Input-Output Model
Input-output analysis was developed by Leontief [42] in the late 1930s, which is widely applied in the research of trade-related environmental and energy effects. In the multi-regional input-output (MRIO) model, the balance of production activities in province r can be expressed as: where x r i is the total output of sector i in province r, f rs i is the final use of sector i from province r to province s, e r i is the exports of sector i in province r, z rs ij is the intermediate input from the sector i of province r to the sector j of province s.
The direct input coefficient a rs ij can be calculated as a rs ij = z rs ij /x s j , where x s j is the total output of sector j in province s, and Equation (1) can be written as: Solving for the total output and expressed by matrix form, Equation (2) can be written as: The water intensity of province r can be calculated as: where y r i donates the water intensity of sector i in province r, w r i is the water withdrawal of sector i in province r, and x r i is the total output of sector i in province r. Then, the water withdrawal of province r expressed by matrix form is equal to: where W r T is the matrix of water withdrawal in province r under trade, and Y r is the matrix of water intensity in province r.

Modified Input-Output Model
The modified input-output (MIO) model can calculate the water withdrawal for each province under no-trade. According to Yang et al. [19], we derived the single regional input-output table in each region from the multiregional input-output table to guarantee the equality of the final consumption under both trade and under no-trade conditions. The traditional MRIO model can be expressed as: (6) where x r is the total output of province r, z rr is the intermediate input from province r to province r, f rr is the final use from province r to province r, z sr is the intermediate input from province s to province r, f sr is the final use from province s to province r, z wr is the intermediate input from foreign country w to province r, f wr is the final use from foreign country w to province r, ex rs is export from province r to province s, ex rw is export from province r to foreign country w, im sr is import from province s to province r, im wr is import from foreign country w to province r.
Due to ∑ w im wr = ∑ w z wr + ∑ w f wr , Equation (6) can be written as: Using matrix notation, Equation (8) can be shown as: Under no-trade conditions, we assume that province r has no exports, and the product that needs to be imported is produced locally. Therefore, Equation (9) can be expressed as: X r = X r + I M sr (10) where X r is the total output of province r under no-trade, just including output driven by local demand and import from other provinces. Therefore, the direct input coefficient α r in the MIO model can be calculated as: Then, Equation (12) can be written as: where A r is the matrix of the direct input coefficients. Solving for variable X r : Since our study aimed at examining the impact of no-trade-induced regional economic input-output structure changes on water withdrawal, we assumed that the water intensity of each province under no-trade was equal to that under trade. Then, the water withdrawal of province r can be calculated by: where W r NT is the matrix of water withdrawal in province r under no-trade conditions, and Y r is the matrix of water intensity in province r.

Water-Saving Efficiency Index
Water-saving efficiency index (WEI) of inter-provincial virtual water trade represents whether trade can save water, which can be constructed as follows: where WEI r is water-saving efficiency index of province r, W r NT represents the water withdrawal of province r under no-trade, and W r T represents the water withdrawal of province r under trade. A positive WEI r means that water withdrawal under no-trade is greater than that under trade in province r and province r will achieve water conservation through inter-provincial virtual water trade; otherwise, there will be a loss of water resources through inter-provincial virtual water trade for province r.

Water Plunder Index and Water Scarcity Index
As we all know, the spatial distribution of water resources is uneven. Water resources in one region may be plundered by others through inter-provincial trade, and this may exacerbate the water inequality among provinces. According to the environmental plunder index proposed by Yang et al. [41], water plunder index (WPI) is applied to determine water inequality induced by trade. The water plunder index (WPI) of inter-provincial virtual water trade can be calculated as follows: where WPI r is water plunder efficiency index of province r, CW r T is consumption-based water withdrawal under trade of province r, and PW r T is production-based water withdrawal under trade of province r. If WPI r is positive, province r will plunder water resources from others to meet its own water demand; otherwise, the water resources of province r will be plundered.
The water scarcity index (WSI) can be used to assess the local water scarcity of each province, and it can be calculated as follows: where WSI r is the water scarcity index of province r, W r is the total water withdrawal of province r, and W r total is the total available water resources of province r. If the value of WSI r is 20-40%, 40-100%, and over 100%, respectively, the province r will be under moderate, severe, and extreme water scarcity [6,43,44]. This study referred to the WSI result estimated by Cai et al. [6] and modified it based on the growth rate of total water resources.

Data Sources
Our study is based on two types of data: The first is multi-regional input-output data in China, which can be collected from an inter-regional input-output table in 2015. We obtained this table from China Emission Accounts and Datasets (CEADs) (https://www.ceads.net/data/input_output_tables/, accessed on 25 February 2021). This table quantifies the economic transactions across 31 mainland provinces amongst 42 sectors.
The second is water withdrawal data by different sectors in China. There are no official water withdrawal data for each economic sector. Following Cai et al. [6], Zhang et al. [40], and Sun et al. [45], we collected aggregate water withdrawal data of agriculture, industry, and service sectors for each province from the Chinese Water Resources Bulletin. It is noted that water withdrawal of service sectors was included in domestic water use, and domestic water use was not linked to economic activities. Referring to provinciallevel Water Resources Bulletin for each province, we estimated the separate amounts of water withdrawal of service sector. Then, we disaggregated the water withdrawal data of industry and services sector by sectors according to the proportion of sectoral water withdrawal data from the Chinese Economic Census Yearbook (2008).

Inter-Provincial Virtual Water Trade Pattern
In this sector, we first characterize the flow of inter-provincial virtual water trade and differences between provinces and sectors ( Figure 1). From the national level, the total flow of virtual water trade was 200.03 × 10 9 m 3 , which accounts for 32.77% of China's total  [6,9]. Among sectors, Agriculture sector and Production and Supply of Electric Power and Heat Power sector are the two dominant sectors in the inter-provincial virtual water trade. The total water flow in Agriculture sector is 148.01 × 10 9 m 3 , accounting for 73.99% of the total water flow. The main reason is that the Agriculture sector has a higher water footprint and larger trade volume. Agricultural production needs to consume a large amount of freshwater due to a higher water-use coefficient and production scale, which leads to a higher water footprint [40]. In addition, the water flow in the Production and Supply of Electric Power and Heat Power sector is 26.53 × 10 9 m 3 , accounting for 13.27% of the total water flow.
Water 2021, 13, x FOR PEER REVIEW 6 of 15 water withdrawal. It is consistent with previous studies for 2007 and 2012 [6,9]. Among sectors, Agriculture sector and Production and Supply of Electric Power and Heat Power sector are the two dominant sectors in the inter-provincial virtual water trade. The total water flow in Agriculture sector is 148.01 × 10 9 m 3 , accounting for 73.99% of the total water flow. The main reason is that the Agriculture sector has a higher water footprint and larger trade volume. Agricultural production needs to consume a large amount of freshwater due to a higher water-use coefficient and production scale, which leads to a higher water footprint [40]. In addition, the water flow in the Production and Supply of Electric Power and Heat Power sector is 26.53 × 10 9 m 3 , accounting for 13.27% of the total water flow. The flow direction of virtual water is mainly from west to east and from north to south. Specific to the provinces, the main inflow provinces include Guangdong, Shandong, Zhejiang, Henan, Shanghai, Anhui, Chongqing, and Jiangsu, which accounts for 51.77% of the national total water inflow. Guangdong is the largest virtual water inflow province, which imports 24.97 × 10 9 m 3 of virtual water, followed by Shandong (16.63 × 10 9 m 3 ) and Zhejiang (13.14 × 10 9 m 3 ). The main virtual water outflow provinces are Xinjiang, Jiangsu, Heilongjiang, Anhui, Hunan, and Guangxi, accounting for 51.18% of the national total virtual water outflow. Among these provinces, Xinjiang has the largest virtual water outflow (28.91 × 10 9 m 3 ), followed by Heilongjiang, which exports 21.21 × 10 9 m 3 of virtual water, and Jiangsu ranks third with 16.47 × 10 9 m 3 of water outflow.
The inter-provincial virtual water trade pattern was further mapped in Figure 2. As the province with the largest water inflow, virtual water of Guangdong mainly comes from Xinjiang, Heilongjiang, Jiangsu, Anhui, Guangxi, and Hunan. The largest water outflow province, Xinjiang, mainly exports virtual water to Guangdong, Shandong, and the provinces in the Yangtze River Delta. In addition, the virtual water trade in the North China Plain was relatively frequent, especially in Jiangsu, Hebei, Henan, and Anhui. In southern China, with abundant water resources, Guangxi, Hunan, and Jiangxi are the main virtual water export provinces, providing water resources to the eastern developed areas such as Guangdong and Shanghai. Figure  The flow direction of virtual water is mainly from west to east and from north to south. Specific to the provinces, the main inflow provinces include Guangdong, Shandong, Zhejiang, Henan, Shanghai, Anhui, Chongqing, and Jiangsu, which accounts for 51.77% of the national total water inflow. Guangdong is the largest virtual water inflow province, which imports 24.97 × 10 9 m 3 of virtual water, followed by Shandong (16.63 × 10 9 m 3 ) and Zhejiang (13.14 × 10 9 m 3 ). The main virtual water outflow provinces are Xinjiang, Jiangsu, Heilongjiang, Anhui, Hunan, and Guangxi, accounting for 51.18% of the national total virtual water outflow. Among these provinces, Xinjiang has the largest virtual water outflow (28.91 × 10 9 m 3 ), followed by Heilongjiang, which exports 21.21 × 10 9 m 3 of virtual water, and Jiangsu ranks third with 16.47 × 10 9 m 3 of water outflow.
The inter-provincial virtual water trade pattern was further mapped in Figure 2. As the province with the largest water inflow, virtual water of Guangdong mainly comes from Xinjiang, Heilongjiang, Jiangsu, Anhui, Guangxi, and Hunan. The largest water outflow province, Xinjiang, mainly exports virtual water to Guangdong, Shandong, and the provinces in the Yangtze River Delta. In addition, the virtual water trade in the North China Plain was relatively frequent, especially in Jiangsu, Hebei, Henan, and Anhui. In southern China, with abundant water resources, Guangxi, Hunan, and Jiangxi are the main virtual water export provinces, providing water resources to the eastern developed areas such as Guangdong and Shanghai.

Water Withdrawal without Trade and with Trade
We then simulated the water withdrawal without trade using the MIO model and compared it with water withdrawal with trade ( Figure 3). The total water withdrawal without trade in all provinces is 914.33 × 10 9 m 3 , while that with trade in all provinces is 468.25 × 10 9 m 3 . It shows that inter-provincial virtual water trade decreased the national water withdrawal by 446.08 × 10 9 m 3 , which indicates that inter-provincial virtual water trade saved water resources nationwide. A possible reason is that current virtual water importer regions would be inefficient at carrying out the production they are importing. Our result is also different from the findings of Liu et al. [9], who argued that interprovincial trade leads to an increase in national water use. An explanation is that Liu et al. [9] directly imposed homogeneity on the water-use coefficient between different provinces, that is, imported water would be equal to the water withdrawal. However, this is not completely consistent with the factor endowment theory. Therefore, we further considered differences in the water use coefficient using the MIO model.
On regional scale, water withdrawal without trade is larger than that with trade in most provinces (22/31), suggesting inter-provincial virtual water trade has decreased water withdrawal in most provinces. Zhejiang has the highest water withdrawal, amounting to 234.92 × 10 9 m³ (25.69%) under no-trade, while it has 11.71 × 10 9 m³ (2.5%) of water withdrawal under trade. It reflects that Zhejiang would consume a larger amount of its water to meet regional development and consumption demand when there is no external water supply. In addition, Guangdong has the highest GDP and Jiangsu ranked second in 2015, which indicates its vigorous economic development demand and huge population consumption demand that both require a large amount of water resources. With the larger water demand, water withdrawal of Guangdong and Jiangsu are among the top under both situations. Under no-trade conditions, Guangdong has the second largest water withdrawal amounting to 202.50 × 10 9 m 3 (22.15%), followed by Jiangsu with 47.60 × 10 9 m³ (5.21%). In terms of the trade situation, Jiangsu has the second-largest water withdrawal, amounting to 34.67 × 10 9 m³ (7.41%), and Guangdong ranks in third with 27.80 × 10 9 m³ (5.94%).  .92 × 10 9 m³ and 202.5 × 10 9 m 3 , respectively; water withdrawal without trade in S1, S2 and S25 is 354.74 × 10 9 m 3 , 380.53 × 10 9 m 3 , 75.59 × 10 9 m 3 , respectively; water withdrawal with trade in S1 and S25 is 343.76 × 10 9 m 3 and 56.18 × 10 9 m 3 , respectively.
From the sectoral perspective, water withdrawal without trade is larger than that with trade in most sectors (39/42). The highest water withdrawal amounting to 380.53 × 10 9 m 3 was from the Coal Mining Products sector (S2) without trade. However, it only has 1.92 × 10 9 m 3 water withdrawal under trade situation, indicating the Coal Mining Products sector (S2) conserves water through trade. In addition, Agriculture (S1) and Production and Supply of Electric Power and Heat Power (S25) sectors have the largest water withdrawal in both no-trade and trade conditions. Without trade, Agriculture sector (S1) holds the second largest water withdrawal with 354.74 × 10 9 m 3 (38.80%), and Production and Supply of Electric Power and Heat Power sector (S25) ranks third with 75.59 × 10 9 m³  region and (b) by sector. Note: water withdrawal without trade in Zhejiang and Guangdong is 234.92 × 10 9 m 3 and 202.5 × 10 9 m 3 , respectively; water withdrawal without trade in S1, S2 and S25 is 354.74 × 10 9 m 3 , 380.53 × 10 9 m 3 , 75.59 × 10 9 m 3 , respectively; water withdrawal with trade in S1 and S25 is 343.76 × 10 9 m 3 and 56.18 × 10 9 m 3 , respectively.
On regional scale, water withdrawal without trade is larger than that with trade in most provinces (22/31), suggesting inter-provincial virtual water trade has decreased water withdrawal in most provinces. Zhejiang has the highest water withdrawal, amounting to 234.92 × 10 9 m 3 (25.69%) under no-trade, while it has 11.71 × 10 9 m 3 (2.5%) of water withdrawal under trade. It reflects that Zhejiang would consume a larger amount of its water to meet regional development and consumption demand when there is no external water supply. In addition, Guangdong has the highest GDP and Jiangsu ranked second in 2015, which indicates its vigorous economic development demand and huge population consumption demand that both require a large amount of water resources. With the larger water demand, water withdrawal of Guangdong and Jiangsu are among the top under both situations. Under no-trade conditions, Guangdong has the second largest water withdrawal amounting to 202.50 × 10 9 m 3 (22.15%), followed by Jiangsu with 47.60 × 10 9 m 3 (5.21%). In terms of the trade situation, Jiangsu has the second-largest water withdrawal, amounting to 34.67 × 10 9 m 3 (7.41%), and Guangdong ranks in third with 27.80 × 10 9 m 3 (5.94%).
From the sectoral perspective, water withdrawal without trade is larger than that with trade in most sectors (39/42). The highest water withdrawal amounting to 380.53 × 10 9 m 3 was from the Coal Mining Products sector (S2) without trade. However, it only has 1.92 × 10 9 m 3 water withdrawal under trade situation, indicating the Coal Mining Products sector (S2) conserves water through trade. In addition, Agriculture (S1) and Production and Supply of Electric Power and Heat Power (S25) sectors have the largest water withdrawal in both no-trade and trade conditions. Without trade, Agriculture sector (S1) holds the second largest water withdrawal with 354.74 × 10 9 m 3 (38.80%), and Production and Supply of Electric Power and Heat Power sector (S25) ranks third with 75.59 × 10 9 m 3 (8.27%) of water withdrawal. With trade, Agriculture (S1) has the largest water withdrawal amounting to 343.76 × 10 9 m 3 (73.41%), followed by Production and Supply of Electric Power and Heat Power sector (S25) with 56.18 × 10 9 m 3 (12%) of water withdrawal. This suggests that both sectors did not decrease water withdrawal by virtual water trade. The water use efficiencies of these two sectors are relatively low, which makes them become the largest users of water under trade and no-trade conditions [6].

Water-Saving Efficiency of Virtual Water Trade
The water-saving efficiency index (WEI) in each province is shown in Figure 4a. Most provinces (22/31) could gain benefits through inter-provincial virtual water trade with a positive WEI. Among the 22 benefited provinces, Zhejiang, Guangdong, Shanghai, and Tianjin are the biggest beneficiaries of virtual water trade in terms of water conservation, with higher WEI above 50% (95.02%, 86.27%, 67.75%, and 61.34%, respectively). Furthermore, Zhejiang, Guangdong, Shanghai, and Jiangsu make the greater contributions to national water conservation as they have the largest amount of decreased water withdrawal under trade. However, there are still nine provinces with negative WEI, indicating that they have not gained the water benefit from inter-provincial virtual water trade. Xinjiang, Heilongjiang, and Gansu hold low WEI (−40.24%, −32.79%, and −27.32%), suggesting that they are victims in inter-provincial virtual water trade. Although virtual water trade could achieve water-saving for most provinces, it could not completely increase the sustainability of water use. Because virtual water in China mainly flows from the water-deficient north to the water-rich south, the water shortage in water-scarcity regions increases.
We found that most sectors (39/42) have positive WEI, which reflects that they gained water benefits from inter-provincial virtual water trade. Five sectors, including Coal Mining Products (S2), Petroleum and Natural Gas Extraction Products (S3), and Telecommunications and Electronic Equipment (S20) hold the highest WEI with 99.50%, 90.74%, and 82.09%, respectively, which suggests that these sectors play an important role in water conservation through trade. However, Agriculture (S1) and Production and Supply of Electric Power and Heat Power (S25), with a large amount of decreased water, hold lower WEI. This shows that the improvement of water resources conservation efficiency in these two sectors will have an important impact on national water conservation and should attract sufficient attention from policymakers.  We found that most sectors (39/42) have positive WEI, which reflects that they gained water benefits from inter-provincial virtual water trade. Five sectors, including Coal Mining Products (S2), Petroleum and Natural Gas Extraction Products (S3), and Telecommunications and Electronic Equipment (S20) hold the highest WEI with 99.50%, 90.74%, and 82.09%, respectively, which suggests that these sectors play an important role in water conservation through trade. However, Agriculture (S1) and Production and Supply of Electric Power and Heat Power (S25), with a large amount of decreased water, hold lower WEI. This shows that the improvement of water resources conservation efficiency in these two sectors will have an important impact on national water conservation and should attract sufficient attention from policymakers.

Water Inequality Embodied Invirtual Water Trade
Based on water plunder index (WPI) and water scarcity index (WSI) under trade conditions ( Figure 5), we found that inter-provincial virtual water trade has exacerbated regional water inequality. Fifteen provinces have positive WPI, which suggests that they plunder water resources from other provinces to meet their local water demand. Among these 15 provinces, 11 provinces with WSI above 20% are in a state of water shortage. They  Table S1 presented in Supplementary Material. The decreased water under trade in Zhejiang and Guangdong is 223.21 × 10 9 m 3 and 174.70 × 10 9 m 3 , respectively; the decreased water under trade in S2 and S25 is 378.61 × 10 9 m 3 and 19.40 × 10 9 m 3 , respectively.

Water Inequality Embodied Invirtual Water Trade
Based on water plunder index (WPI) and water scarcity index (WSI) under trade conditions ( Figure 5), we found that inter-provincial virtual water trade has exacerbated regional water inequality. Fifteen provinces have positive WPI, which suggests that they plunder water resources from other provinces to meet their local water demand. Among these 15 provinces, 11 provinces with WSI above 20% are in a state of water shortage. They relieve local water shortages by importing virtual water from others. As China's economic and political center, Tianjin and Beijing, with high WSI above 100%, both hold the highest WPI, suggesting that they plunder water over 50% of their water consumption from others to alleviate local water scarcity. However, there are four provinces without water shortage (i.e., Zhejiang, Qinghai, Yunnan, and Sichuan) that still plunder water resources from others. This has exacerbated regional water inequality.
Sixteen provinces show a negative WPI, indicating that they lost water resources as a result of inter-provincial virtual water trade. Among these 16 provinces, ten of them have high WSI above 20%, which suggests that trade leads to more severe water scarcity in these provinces. Heilongjiang and Xinjiang had the lowest WPI (−110.30%, −100.32%), which indicates that they export more than 100% of local water consumption to other provinces. Furthermore, Hebei, Ningxia, Gansu, and Jiangsu with WSI above 70% are virtual water net outflow provinces, implying that virtual water trade has exacerbated water shortages in these provinces. The plunder patterns we estimated were similar to the findings of other studies [25,27].
WPI, suggesting that they plunder water over 50% of their water consumption from others to alleviate local water scarcity. However, there are four provinces without water shortage (i.e., Zhejiang, Qinghai, Yunnan, and Sichuan) that still plunder water resources from others. This has exacerbated regional water inequality.
Sixteen provinces show a negative WPI, indicating that they lost water resources as a result of inter-provincial virtual water trade. Among these 16 provinces, ten of them have high WSI above 20%, which suggests that trade leads to more severe water scarcity in these provinces. Heilongjiang and Xinjiang had the lowest WPI (−110.30%, −100.32%), which indicates that they export more than 100% of local water consumption to other provinces. Furthermore, Hebei, Ningxia, Gansu, and Jiangsu with WSI above 70% are virtual water net outflow provinces, implying that virtual water trade has exacerbated water shortages in these provinces. The plunder patterns we estimated were similar to the findings of other studies [25,27]. Figure 5. The water plunder index and water scarcity index of each province. Note: The columns marked in red, orange and yellow indicate that provinces are under extreme, severe, moderate water shortage, respectively; and the points marked in blue indicate that there is no water shortage.

Water-Saving Efficiency and Water Inequality
To explore the conflict of water-saving effect and water inequality, we compared the water-saving efficiency index (WEI) and water plunder index (WPI) by dividing 31 provinces into four quadrants ( Figure 6).
Provinces in the first quadrant, including Zhejiang, Guangdong, and Shandong, etc., have both positive WEI and WPI. It means that virtual water trade could help these provinces efficiently save water resources through importing virtual water. Among 13 provinces, 12 provinces (except Qinghai) have a huge demand for water resources due to the large population/economic scale. Therefore, they highly depend on external water resources. It should be also noted that even though Guangdong, Zhejiang, and Hubei have abundant water resources, they still import virtual water from some water-scarce provinces. This might increase the regional water resource inequality.
Shaanxi and Liaoning are in the second quadrant (negative WEI, positive WPI), which means that they plunder water resources from other regions through virtual water trade, but they do not achieve local water conservation from a national perspective. However, as the main imported sources, including Heilongjiang, Jiangsu, and Anhui, which are water-rich provinces, the current trade patterns are beneficial for the two provinces.

Water-Saving Efficiency and Water Inequality
To explore the conflict of water-saving effect and water inequality, we compared the water-saving efficiency index (WEI) and water plunder index (WPI) by dividing 31 provinces into four quadrants ( Figure 6).

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The provinces in the third quadrant including Hunan, Guangxi, Gansu, Xinjiang, and Heilongjiang have negative WEI and negative WPI, indicating that they are water-plundered provinces, and the trade patterns are not conducive to water conservation. Moreover, Gansu, Xinjiang, and Heilongjiang are under severe water shortage and need to adjust their trade structure to change the unsustainable trade pattern. Guangxi, with sufficient water resources, can further moderately expand the utilization of water resources and exports.
Twelve provinces (Anhui etc.) are in the fourth quadrant with positive WEI and negative WPI, indicating that they have saved local water resources through virtual water import, and do not plunder water resources for other provinces. From a national perspective, this seems to be beneficial to the sustainable use of water resources, but from a regional perspective, it is not beneficial to provinces with a high WSI. Therefore, water shortage provinces such as Ningxia, Hebei, Jiangsu, Jilin, Anhui, and Inner Mongolia still need to pay attention to the structural adjustment of virtual water trade to prevent the deterioration of regional water shortages, while provinces with lower WPI but abundant water resources such as Sichuan, Guizhou, Fujian, and Jiangxi can moderately expand virtual water exports.
Based on the difference between the four quadrants, we found the provinces show a strong heterogeneity in the association between water conservation and water plunder. Therefore, it is difficult to consistently answer the question of "whether virtual water trade saves water resources?". Additionally, the endowment of water resources should be taken into consideration when formulating individualized virtual water trading strategies for each province.

Limitation
Our study estimated water withdrawal under trade and no-trade conditions by developing a modified input-output model. To the best of our knowledge, this is the first attempt in virtual water research. However, there are still some limitations that need to Provinces in the first quadrant, including Zhejiang, Guangdong, and Shandong, etc., have both positive WEI and WPI. It means that virtual water trade could help these provinces efficiently save water resources through importing virtual water. Among 13 provinces, 12 provinces (except Qinghai) have a huge demand for water resources due to the large population/economic scale. Therefore, they highly depend on external water resources. It should be also noted that even though Guangdong, Zhejiang, and Hubei have abundant water resources, they still import virtual water from some water-scarce provinces. This might increase the regional water resource inequality.
Shaanxi and Liaoning are in the second quadrant (negative WEI, positive WPI), which means that they plunder water resources from other regions through virtual water trade, but they do not achieve local water conservation from a national perspective. However, as the main imported sources, including Heilongjiang, Jiangsu, and Anhui, which are water-rich provinces, the current trade patterns are beneficial for the two provinces.
The provinces in the third quadrant including Hunan, Guangxi, Gansu, Xinjiang, and Heilongjiang have negative WEI and negative WPI, indicating that they are waterplundered provinces, and the trade patterns are not conducive to water conservation. Moreover, Gansu, Xinjiang, and Heilongjiang are under severe water shortage and need to adjust their trade structure to change the unsustainable trade pattern. Guangxi, with sufficient water resources, can further moderately expand the utilization of water resources and exports.
Twelve provinces (Anhui etc.) are in the fourth quadrant with positive WEI and negative WPI, indicating that they have saved local water resources through virtual water import, and do not plunder water resources for other provinces. From a national perspective, this seems to be beneficial to the sustainable use of water resources, but from a regional perspective, it is not beneficial to provinces with a high WSI. Therefore, water shortage provinces such as Ningxia, Hebei, Jiangsu, Jilin, Anhui, and Inner Mongolia still need to pay attention to the structural adjustment of virtual water trade to prevent the deterioration of regional water shortages, while provinces with lower WPI but abundant water resources such as Sichuan, Guizhou, Fujian, and Jiangxi can moderately expand virtual water exports.
Based on the difference between the four quadrants, we found the provinces show a strong heterogeneity in the association between water conservation and water plunder. Therefore, it is difficult to consistently answer the question of "whether virtual water trade saves water resources?". Additionally, the endowment of water resources should be taken into consideration when formulating individualized virtual water trading strategies for each province.

Limitation
Our study estimated water withdrawal under trade and no-trade conditions by developing a modified input-output model. To the best of our knowledge, this is the first attempt in virtual water research. However, there are still some limitations that need to be stated.
First, our study is based on the data from the multi-regional input-output table in 2015, but it is still complicated to obtain the most recent table. Limited by the availability of the multi-regional input-output table, the data used for analysis in this study have an obvious time lag.
Second, water intensity of each province under no-trade was assumed to be similar to that under trade conditions. However, the water intensity of each province might be changed if there is no trade, and estimated water resources under no-trade conditions may be larger than the actual value. Therefore, the variations of water intensity under no-trade conditions need to be further studied.

Conclusions
Severe water shortage in China has led to continuous concerns on the strategies of water resources management. Virtual water trade has been considered as an alternative way to generate sustainable water management. However, limited studies have estimated the difference between water withdrawal under inter-provincial trade and no-trade, and they did not investigate the water-saving effects and water inequality caused by virtual water trade. In this study, a multi-regional input-output table in 2015 was used to investigate this issue, and the main findings are summarized as follows: The total water flow within China is 200.03 × 10 9 m 3 , accounting for 32.77% of water withdrawal nationwide. Moreover, the Agriculture sector contributes to the highest proportion (73.99%) of virtual water flow. The main virtual water flow is from the northeast and northwest regions with the Agriculture sector as the leading industry to the more economically developed southern regions and eastern coastal regions.
Inter-provincial virtual water trade could achieve water conservation at the national scale, which decreased water withdrawal by 446.08 × 10 9 m 3 compared with the notrade conditions. Furthermore, 22 provinces could decrease the local water withdrawal through trade, indicating inter-provincial virtual water trade is also conducive to local water conservation in most provinces within China. However, inter-provincial virtual water trade also leads to water inequality, which would exacerbate water scarcity of exported provinces (i.e., Xinjiang, Heilongjiang, Jiangsu, Gansu, Hebei, and Anhui). In addition, the conflict between water conservation and water plunder actually exists because of the difference in water resources endowments of each province, but different provinces show significant heterogeneity.
Based on these findings, our implication is that the province's water resources policies and trade strategies should be adjusted according to local water resource endowment. This may be an effective way to resolve the conflict between water conservation and water inequality caused by trade. In the water-scarce northwest and northeast regions, the water productivity of the agricultural sector needs to be improved and the virtual water export from the Agriculture sector needs to be controlled to ensure water balance while reducing water consumption. For the provinces with a developed economy and a high degree of external dependence on water resources, such as Beijing, Tianjin, Guangdong, Chongqing, and provinces in eastern regions, water resources marketization, including water pricing and water rights, can further improve water conservation and reduce the water plunder. As for regions with rich water resources, such as Yunnan, Jiangxi, Guangxi, and Hunan, the water resources utilization and export can be moderately strengthened to alleviate the water pressure of water-poor regions.