Structural Properties Evolution and Influencing Factors of Global Virtual Water Scarcity Risk Transfer Network

Abstract

Loss of production due to local water scarcity, i.e., Local Water Scarcity Risk (LWSR), is transferred downstream through international supply chains to distant economies, causing potential economic losses to countries and sectors that do not directly experience actual water scarcity, which is defined as Virtual Water Scarcity Risk (VWSR). Much research has focused on assessing VWSR and characterizing the structure of VWSR transfer networks, without explaining the formation and dynamics of VWSR transfer network patterns. In this study, the global VWSR transfer networks for 2001–2016 are then constructed based on a multi-regional input-output model and complex network theory. The determinants influencing the formation of VWSR transfer networks are further explored using the time-exponential random graph model. The results demonstrate that: (1) The VWSR transfer networks exhibit a distinctly small-world and heterogeneous nature; (2) Asia and Europe are the main targets of VWSR transfers, and Asia is also the main source of risks; (3) China and the USA play a leading role on the import side of VWSR, and India is the largest exporter of VWSR; (4) The evolution of VWSR transfer networks is significantly influenced by transitivity and stability. Countries located on the same continent, sharing geographical borders and having a higher level of economic development, have a facilitating effect on the formation and evolution of VWSR transfer networks. Countries with a higher share of merchandise trade are more inclined to receive VWSR inflows, while the urbanization rate has a restraining effect on VWSR outflows. The study provides a network-based insight that explores the structural evolution of VWSR transfer networks and the determinants of their formation, informing policy makers in developing strategies to mitigate the cascading spread of VWSR.

1. Introduction

1.1. Background

According to the 2022 report of the World Meteorological Organization (WMO) at the 2022 United Nations Climate Change Conference, climate change is exacerbating water scarcity, and the water scarcity crisis is expected to become worse in the future [1]. Over the past decade, overexploitation, pollution, and climate change have led to severe water stress on a global scale. The new concept of virtual water, introduced by Tony Allen in the 1990s, offers a unique perspective to alleviate the pressure of water scarcity and maintain the sustainability of global water resources. By transferring goods to other countries through trade, water resources are actually exported in virtual form, resulting in virtual water trade [2,3]. The virtual water trade is penetrating into the global economic development process.

Economic globalization has facilitated virtual water flows between economies, and water consumption in one region can have a significant impact on water demand in distant countries and sectors. Virtual water trade exacerbates water stress in regions where water resources are scarce. In other words, the water scarcity risk in one country or sector can spread to countries or sectors downstream through trade networks and cause economic losses. In essence, the water scarcity risk is a global supply chain risk to the economy [4,5]. Exploring water scarcity risks through trade networks is more relevant to alleviating global water stress, as inter-local coordination is easier to achieve than global coordination. Thus, quantifying and analyzing the determinants of water scarcity risks that spread across regions (sectors) is important and challenging.

1.2. Literature Review

Regions are interconnected by increasingly close trade relations and because of regional and sectoral heterogeneity, multi-regional input–output (MRIO) analysis is often applied to track the transfer flows of water, energy, etc., embodied in trade [6,7,8,9,10]. MRIO models are a useful tool for reflecting the technological linkages of production between sectors within a region, as well as the integrated balance between supply and demand. Some researchers have used MRIO analysis to track the flow of resources embodied in complex economic systems, from their source to where they are utilized [11,12,13,14,15]. For example, Wiedmann accounted for the energy footprint embodied in trade from and into the UK based on the MRIO model to quantify the impacts associated with consumption and trade in other countries [14]. White et al. assessed virtual water flows in inter-regional trade in the Haihe river basin and their impact on the hydraulic system based on the MRIO model to avoid greater water stress to other regions [15]. These findings not only provide a good basis for studying the impact of individual economic activities on regional water consumption, but also offer valuable suggestions for reducing water consumption.

Further, to reveal the impact of regional and sectoral structural roles in supply chains on embodied resource transfers, some researchers have combined MRIO analysis [16,17,18] with complex network approaches [19,20,21,22]. For example, Chen applied complex network analysis tools to study the structure of embodied energy flow networks at global, regional, and national levels based on environmentally extended MRIO [16]. These studies demonstrate that economic activities in one region may be influenced by the consumption of resources in another region or sector. Thus, although the pressure on water-scarce regions can be mitigated by virtual water trade, it also poses indirect risks to non-water-scarce regions [23,24]. Limited water resources can pose a significant risk to economic development, and it is necessary to describe the pattern of scarcity risk that emerges in the international trading system [4,25,26].

In recent years, VWSR has attracted a lot of attention from scholars. Studies have generally concluded that water scarcity risk has a ripple effect due to increased trade relations between regions and countries [5,27,28,29]. Yao et al. found that VWSR can spread along the energy supply chain and pose a threat to the stability of national energy systems [30]. Qu et al. discussed the role of the LWSR in influencing the international trading system between 1995 and 2009, highlighting the increasing geographical segregation between actual water scarcity and production losses due to water scarcity [4]. Zhao et al. quantified the LWSR using a multi-regional input-output table for China and analyzed its impact on the inter-provincial trading system in China [29].

However, network analysis has been used in some studies to reveal the spatial structural characteristics and network evolutionary trends of global VWSR transfer networks, rather than reflecting network formation. In fact, previous references seldom reveal the determinants of the dynamic evolution of VWSR transfer networks. In recent years, as research on complex networks has intensified, many empirical studies on network drivers at the regional level have emerged, particularly using an exponential random graph model (ERGM). ERGM is a unique and effective network statistics tool for understanding whether the formation of an observed network arises from certain attribute characteristics of nodes or from a model of relationships during network formation. The ERGM is essential for modelling global virtual water scarcity risk transfer networks, elucidating the structural characteristics of the network and the determinants, but not explaining the formation and dynamic evolution of network patterns. Longitudinal analysis can better reveal the dynamic evolution of the network [31,32]. The most widely used longitudinal models include the stochastic actor-oriented model (SAOM) [33] and the temporal exponential random graph model (TERGM) [34]. The SAOM requires higher level dependencies between relationships and is not suitable for evaluating actual networks [31]. TERGMs can effectively solve the time-dependent problem of longitudinal data and break through the limitations of the traditional static network analysis [34]. By integrating the endogenous structure and exogenous factors of the system, the model can be better used to analyse the formation and dynamic evolution of the network [35,36,37,38]. This property can be used to explore the structural evolution and influencing factors of global VWSR transfer networks. With the rapid development of world economic integration, risk transfer is not unilateral and unchanging, but interactive and changing. Therefore, it is necessary to study the structural dynamic changes of the global VWSR transfer network and its determinants, and identify key countries and risk transfer paths, which are conducive to reducing the spatial correlation effect of VWSR flows, and thereby alleviating the cascading spread of VWSR in the international supply chain.

1.3. Research Contribution

This study first quantifies the LWSR for 159 countries. Then, the multi-regional input–output (MRIO) model and complex network method are combined to construct the global VWSR transfer network for 2001–2016, and its structural characteristics and spatial patterns are investigated. TERGMs are used to explore the mechanisms of endogenous structural effects and exogenous factors that influence the evolution of VWSR transfer networks. The study provides a theoretical basis and policy implications for promoting a virtuous cycle of international trade and sustainable use of water resources.

The paper is organized as follows. Section 2 shows the data sources, the quantification of LWSR, the construction of the VWSR transfer network and the complex network approach. Section 3 analyzes the structural characteristics of the global VWSR transfer network and investigates the determinants of its evolution using TERGM. The main conclusions are given in Section 4.

2. Data and Methodology

2.1. Data Sources

The sources of data used for the VWSR calculations are: global MRIO tables and sectoral water consumption from the Eora database [39] and national freshwater withdrawals and renewable water resources collected from the Food and Agriculture Organization of the United Nations FAO, AQUASTAT [40].

For the selection of TERGM variables, GDP is used to measure national economic development; the urbanization rate (URB % of total population) is a measure of regional socioeconomic development; Merchandise trade (% of GDP) reflects the extent of a country or region’s externally oriented economy, these three data are from the World Bank database [41]. The common official language (COL) network and the common geographical boundary (CGB) network are used to reflect cultural similarity and geographical proximity between countries, respectively, and are derived from the CEPII database [42]. The elements of the adjacency matrix of the corresponding network take the value of 1 if the two countries share a common language or a common geographical boundary, and 0 otherwise. The regional free trade agreement (RTA) network shows the trade liberalisation of countries. The corresponding element of the adjacency matrix is 1 if a free trade agreement has been signed between two countries, otherwise it is 0. The data is taken from the WTO database [43].

2.2. Quantification of the Water Scarcity Risk Embodied in International Trade

2.2.1. Local Water Scarcity Risk (LWSR)

Economic activities in water-intensive sectors are vulnerable in areas with high water consumption. The economic losses incurred are related to the output of the sector and its dependence on water. On this basis, the LWSR can be defined, as follows [4]:

$$LWS{R}_{k,c}=WS{P}_c\times W{D}_k\times x_{k,c},$$

(1)

where $LWS{R}_{k,c}$ denotes the potential economic loss of sector k in country c due to local water scarcity, $x_{k,c}$ is the economic output of sector k in country c under the condition of sufficient water resources. $WS{P}_c$ denotes the probability of water scarcity in country c and thus assesses the potential reduction in water use in the country. $WS{P}_c$ denotes the probability of water scarcity in country c and thus assesses the potential reduction in water use in the country. The normal distribution has a wide practical background. However, for many practical problems, particularly reliability problems, the actual data do not always follow a normal distribution. It is clear from the probability distribution of the log-normal distribution that it has a long tail that reflects the fact that the probability of extreme events is much higher than in the normal distribution. Considering that global economies are intertwined through international trade and that the transfer of VWSR along the supply chain exhibits complex characteristics, it is practical to apply a log-normal distribution to describe the water scarcity probabilities of countries [28,44]. Thus, $WS{P}_c$ is evaluated by a log-normal distribution function $f_{WSP}({\mu }_c,{\sigma }^2)$, where the standard deviation $\sigma =1$, the median value ${\mu }_c=log\frac{1}{WS{I}_c}$, the water stress index $WS{I}_c$ is measured by the ratio of total freshwater withdrawal to total renewable water resources [4,28]. The sectoral water dependence $W{D}_k$ demonstrates the proportion of sectoral output reduced as a result of a 1% reduction in water use. It is measured by the logistic function $W{D}_k=\frac{1}{1+e^{-\alpha W{I}_k}(\frac{1}{0.001}-1)}$, where $W{I}_k$ is the water intensity of sector k and is computed by dividing the sector’s water consumption by its economic output, $\alpha$ is set as 0.5 [4].

2.2.2. Virtual Water Scarcity Risk (VWSR)

The multi-regional input-output (MRIO) model captures the interdependence of inputs and outputs across sectors in the economic system [45]. It has column equilibrium, i.e., the total input of each sector is equal to the sum of its intermediate inputs and value added, as shown in Equation (2).

$$X=eZ+V,$$

(2)

where the $1\times n$ vectors X and V represent the total input and value added for each sector, respectively, the $n\times n$ matrix Z reflects the amount of economic transactions between sectors, and the elements in the $1\times n$ vector e are all 1. Define the direct output coefficient matrix B, which expresses the ratio of the allocation of products from one sector to another, satisfying Equation (3). Substituting Equation (3) into Equation (2) yields Equation (4).

$$XB=Z,$$

(3)

$$X=V{(I-B)}^{-1},$$

(4)

where ${(I-B)}^{-1}$ is called the Ghosh inverse matrix, whose elements in one row reflect the total output (both direct and indirect) of each sector resulting from the unit of value added in the sector represented by the row [46].

The matrix VWSR is obtained by diagonalising the vector LWSR and multiplying it by the Ghosh inverse matrix according to Equation (4) [44]:

$$VWSR=diag\left(LWSR\right)\times {(I-B)}^{-1},$$

(5)

where the elements in its columns reflect the loss of output in the sector shown in that column, caused by the LWSR of the sector represented by the row. Further, combining all sectors in a country yields an inter-country VWSR transfer matrix.

2.3. Construction of VWSR Transfer Network

A sequence of directed and weighted VWSR transfer networks with countries as nodes and risk transfer relationships as connecting edges is constructed based on the global VWSR transfer matrix from 2001 to 2016. For the sake of brevity, specific codes are used to abbreviate the names of different countries, as shown in

Table A1. List of economies covered in this paper.

Code	Name	Code	Name	Code	Name
ALB	Albania	DZA	Algeria	AGO	Angola
ATG	Antigua and Barbuda	ARG	Argentina	ARM	Armenia
AUS	Australia	AUT	Austria	AZE	Azerbaijan
BHR	Bahrain	BGD	Bangladesh	BRB	Barbados
BRL	Belarus	BEL	Belgium	BLZ	Belize
BEN	Benin	BTN	Bhutan	BOL	Bolivia
BIH	Bosnia and Herzegovina	BWA	Botswana	BRA	Brazil
BRN	Brunei Darussalam	BGR	Bulgaria	BFA	Burkina Faso
BDI	Burundi	KHM	Cambodia	CMR	Cameroon
CAN	Canada	CPV	Cape Verde	CAF	Central African Republic
TCD	Chad	CHL	Chile	CHN	China
COL	Colombia	COG	Congo	CRC	Costa Rica
HRV	Croatia	CUB	Cuba	CYP	Cyprus
CZE	Czech Republic	CIV	Cote d’Ivoire	COD	Democratic Republic of the Congo
DNK	Denmark	DJI	The Republic of Djibouti	DOM	Dominican Republic
ECU	Ecuador	EGY	Egypt	SLV	El Salvador
ERI	Eritrea	EST	Estonia	ETH	Ethiopia
FJI	Fiji	FIN	Finland	FRA	France
GAB	Gabon	GMB	Gambia	GEO	Georgia
DEU	Germany	GHA	Ghana	GRC	Greece
GTM	Guatemala	GIN	Guinea	GUY	Guyana
HTI	Haiti	HND	Honduras	HUN	Hungary
ISL	Iceland	IND	India	IDN	Indonesia
IRN	Iran	IRQ	Iraq	IRL	Ireland
ISR	Israel	ITA	Italy	JAM	Jamaica
JPN	Japan	KAZ	Kazakhstan	JOR	Jordan
KEN	Kenya	KWT	Kuwait	KGZ	Kyrgyzstan
LAO	Lao People’s Democratic Republic	LVA	Latvia	LBN	Lebanon
LSO	Lesotho	LBR	Liberia	LBY	Libyan Arab Jamahiriya
LTU	Lithuania	LUX	Luxembourg	MDG	Madagascar
MWI	Malawi	MYS	Malaysia	MDV	Maldives
MLI	Mali	MLT	Malta	MRT	Mauritania
MUS	Mauritius	MEX	Mexico	MNG	Mongolia
MAR	Morocco	MOZ	Mozambique	MMR	Myanmar Burma
OMN	Oman	NAM	Namibia	NPL	Nepal
NLD	Netherlands	NZL	New Zealand	NIC	Nicaragua
NER	Niger	NGA	Nigeria	NOR	Norway
PAK	Pakistan	PAN	Panama	PNG	Papua New Guinea
PRY	Paraguay	PER	Peru	PHL	Philippines
POL	Poland	PRT	Portugal	QAT	Qatar
KOR	Republic of Korea	MDA	Republica Moldova	ROM	Romania
RUS	Russian Federation	RWA	Rwanda	SAU	Saudi Arabia
LKA	Sri Lanka	SEN	Senegal	SER	Serbia
SLE	Sierra Leone	SGP	Singapore	SVK	Slovakia
VNM	Viet Nam	SVN	Slovenia	ZAF	South Africa
ESP	Spain	SUR	Suriname	SWE	Sweden
CHE	Switzerland	SYR	Syrian Arab Republic	TJK	Tajikistan
THA	Thailand	TGO	Togo	TTO	Trinidad and Tobago
ARE	United Arab Emirates	TUN	Tunisia	TUR	Turkey
TKM	Turkmenistan	UGA	Uganda	UKR	Ukraine
GBR	United Kingdom	TZA	United Republic of Tanzania	UZB	Uzbekistan
URY	Uruguay	USA	United States of America	VEN	Venezuela
YEM	Yemen	ZMB	Zambia	ZWE	Zimbabwe

in the Appendix A.

Table A2. Abbreviation list with definition.

Abbreviation	Full Name	Definition in the Main Text
LWSR	Local water scarcity risk	The potential economic loss of water-using sector due to local water scarcity.
VWSR	Virtual water scarcity risk	Production loss due to water shortages abroad, transferred through global supply chains.
WSP	Probability of water scarcity	The potential reduction in water use due to lack of water resources in a region.
WSI	Water stress index	The ratio of total freshwater withdrawal to total renewable water resources.
WI	Water intensity	The ratio of a sector’s water consumption to its unitary economic output.
WD	Water dependence	The proportion of sectoral output reduced as a result of 1% reduction in water use.
MRIO	Multi-regional input-output	Methodology used to analyze economic interdependence between countries and sectors.
ERGM	Exponential random graph model	The model used to describe the network formation mechanism observed at a certain time point.
TERGM	Temporal exponential random graph model	An extension of the ERGM designed to accommodate inter-temporal dependence in longitudinally observed networks.

in the Appendix A shows the list of abbreviations with definitions.

2.3.1. Macro-Level Indicators

The macro-level indicators of the network include number of nodes, number of edges, density, average path length, average clustering coefficient, small-world nature, reciprocity and assortativity. The number of nodes ($N_v$) and the number of edges ($N_e$) indicate the number of countries and VWSR transfer relations, respectively. Density $\rho =N_e/N_v(N_v-1)$ quantifies the tightness of the connections in the network. The distance $d_{ij}$ denotes the number of edges on the shortest path connecting country pairs i and j. The average path length (L) represents the average distance between all country/region pairs in the network, which is computed by [47]:

$$L=\frac{1}{N_v(N_v-1)}\sum _{i\ge j}{d}_{ij},$$

(6)

where L reflects the efficiency of VWSR transfers in the international supply chain.

The clustering coefficient of country i, $C_i=\frac{1}{s_i(k_i-1)}{\sum }_{j,h}\frac{(w_{ij}+w_{ih})}{2}{a}_{ij}{a}_{ih}{a}_{jh}$ [48] quantifies the extent to which the neighbouring nodes of i are clustered together to form a cluster (complete graph), where $k_i$ and $s_i$ are, respectively, the degree and strength of country i, $w_{ij}$ represents the weight of the edge connecting i to j, and $a_{ij}$ is an element of the adjacency matrix of the VWSR transfer network. The average clustering coefficient (C) is defined as the average of the clustering coefficients for all countries [48]. Reciprocity (R) measures the extent to which pairs of countries in a network form interconnections [49]. The expressions for these two indicators are:

$$C=\frac{1}{N_v}\sum _{i=1}^{N_v}{C}_i,$$

(7)

$$R=\frac{{\sum }_{i\ne j}(w_{ij}-\overline{w})(w_{ji}-\overline{w})}{{\sum }_{i\ne j}{(w_{ij}-\overline{w})}^2},$$

(8)

where $\overline{w}={\sum }_{i\ne j}{w}_{ij}/N_e(N_e-1)$. If $R>0$, reciprocity exists in the network; otherwise, the network is anti-reciprocal.

Assortativity (A) measures the tendency for nodes with similar numbers of partners in a network to be more likely to be connected and is calculated as follows [50]:

$$A=\frac{1}{{\sigma }_q^2}\sum _{jk}jk(e_{jk}-q_j{q}_k),$$

(9)

where $e_{jk}$ is the fraction of edges connecting nodes j and k, ${\sum }_{jk}{e}_{jk}=1$, ${\sum }_j{e}_{jk}=q_k$, and ${\sigma }_q^2={\sum }_k{k}^2{q}_k-{\left[{\sum }_{k}k{q}_k\right]}^2$.

The small world quotient ($\delta$) can be obtained by comparing the average clustering coefficient and average path length of the network with an equivalent random network having the same average degree. It is calculated as follows [44]:

$$\delta =\frac{\frac{C}{C_r}}{\frac{L}{L_r}},$$

(10)

where $C_r$ and $L_r$, respectively, represent the average clustering coefficient and average path length of the equivalent random network. If $\delta$ is far greater than 1, it indicates that the network is the small world [51].

2.3.2. Micro-Level Indicators

Degree and strength are the most intuitive micro-level indicators to measure the importance of nodes in complex networks. The degree $k_i$ of a node i represents the number of neighbouring nodes of i. In a directed network, the degree includes in-degree and out-degree, where the in-degree of a node is the number of edges ending at that node and the out-degree of a node is the number of edges starting at that node [47]. In a global VWSR transfer network, the in-degree $k_i^{in}$ and out-degree $k_i^{out}$ of node i denote the number of source and destination countries of VWSR risk in country i, respectively, and can be expressed as:

$$k_i^{in}=\sum _{j=i,j\ne i}^{N_v}{a}_{ji},$$

(11)

$$k_i^{out}=\sum _{j=i,j\ne i}^{N_v}{a}_{ij},$$

(12)

where $k_i=k_i^{in}+k_i^{out}$, $a_{ij}\left(a_{ji}\right)$ is an element of the adjacency matrix of the VWSR transfer network. If there is an edge connecting from node $i\left(j\right)$ to node $j\left(i\right)$, $a_{ij}\left(a_{ji}\right)$ = 1, otherwise $a_{ij}\left(a_{ji}\right)$ = 0.

The strength of node i, $s_i$ is the total weight of the connected edges of node i [47]. In a directed network, the strength $s_i$ includes in-strength $s_i^{in}$ and out-strength $s_i^{out}$. In the global VWSR transfer network, $s_i$ is used to measure the ability of country i to control the VWSR transfer, and $s_i^{in}$ and $s_i^{out}$ denote the inflow and outflow of VWSR for i, respectively, and the expressions are as follows [52]:

$$s_i^{in}=\sum _{j=i,j\ne i}^{N_v}{w}_{ji},$$

(13)

$$s_i^{out}=\sum _{j=i,j\ne i}^{N_v}{w}_{ij},$$

(14)

where $s_i=s_i^{in}+s_i^{out}$.

2.4. Temporal Exponential Random Graph Model

The temporal exponential random graph model (TERGM) is developed from the exponential random graph model (ERGM). ERGM is used to study the network formation mechanism observed at a certain time point. TERGM can take multi-period networks as a whole to study the impact of network patterns in different periods [53]. Its unique advantage lies in that the time dependence of network data is fully considered, which is suitable for the study of dynamic observation networks [54]. This study explores endogenous mechanism effects, economic attribute effects and relations embedding effects to quantify the probability of relationship formation in the global VWSR transfer network, and the TERGM model is constructed, as follows [55]:

$$P\left(y^t\right|y^{t-K},\dots ,y^{t-1},\theta )=\frac{exp\{{\theta }_{\alpha }^T{g}_{\alpha }(y^t,y^{t-1},\dots ,y^{t-K})+{\theta }_{\beta }^T{g}_{\beta }(y^t,y^{t-1},\dots ,y^{t-K})+{\theta }_{\gamma }^T{g}_{\gamma }(y^t,y^{t-1},\dots ,y^{t-K})\}}{c(\theta ,y^{t-K},\dots ,y^{t-1})},$$

(15)

where $K\in [0,1,\dots T-1]$ presents the lag order, $c(\theta ,y^{t-K},\dots ,y^{t-1})$ is the normalized constant. $g_{\alpha }(y^t,y^{t-1},\dots ,y^{t-K})$, $g_{\beta }(y^t,y^{t-1},\dots ,y^{t-K})$ and $g_{\gamma }(y^t,y^{t-1},\dots ,y^{t-K})$ are network statistics of endogenous mechanism effects, economic attribute effects, and the relations embedding effects over time. ${\theta }_{\alpha }^T$, ${\theta }_{\beta }^T$ and ${\theta }_{\gamma }^T$ are the corresponding parameter vectors to be estimated. If these estimated parameters can satisfy the statistical significance test, this indicates that these variables have a significant role in the evolution of the global VWSR network.

To further explore the determinants of the dynamic evolution of network y during $K+1$ and T, a joint probability model is developed by multiplying the conditional probabilities of individual networks with each other [48]:

$$P(y^{K+1},\dots ,y^T|y^1,\dots ,y^K,\theta )={\Pi }_{t=K+1}^{T}P\left(y^t\right|y^{t-K},\dots ,y^{t-1},\theta ).$$

(16)

2.4.1. Endogenous Mechanism Effect

Endogenous network structure variables are used to test and control for endogenous self-organising features. The following endogenous network structure variables: edges, reciprocity, transitivity, connectivity and stability are introduced into the model. Reciprocity measures the tendency for pairs of countries to form interconnections and describes the feedback effects in the formation and evolution of networks [49]. Transitivity elaborates that triads with two connections are more likely to form a third connection, reflecting the clustering characteristics of the network [48]. To reduce the uncertainty caused by information asymmetry, a country usually tends to establish new dependencies with partners in the country it depends on. Connectivity reflects the fact that intermediate nodes both send relations to some nodes and receive relations from others [54]. In a global VWSR transfer network, indirect transfers of VWSR between countries are achieved through multiple pathways, creating a connectivity effect. Therefore, the following hypothesis is proposed:

Hypothesis 1.

The formation and evolution of global VWSR transfer networks are affected by reciprocity, transitivity and connectivity.

Dependencies between economies are characterized by vulnerability. If existing dependencies are broken, countries will suffer certain economic losses. That is, the formation and evolution of the global VWSR transfer network is path-specific dependent. Therefore, the global VWSR transfer network discussed in this paper has a time-dependent effect. On this basis, the following hypothesis is proposed:

Hypothesis 2.

The formation and evolution of global VWSR transfer networks is stable, and the risk transfer relationship has a tendency to remain unchanged in a certain period.

2.4.2. Economic Attribute Effect

In the formation and evolution of the global VWSR transfer network, this study considers homophily, sender effects and receiver effects as economic attribute effects. Homophily reflects the tendency to establish relationships between countries with similar characteristics (expressed in terms of geographical proximity). Sender effects and receiver effects are used to examine trends in VWSR sending and receiving for countries with specific attributes (expressed in terms of merchandise trade as a share of GDP (MT), GDP and urbanization rate (URB)). Countries located at the same continent are more likely to establish trade relations and thus VWSR transfers will be more frequent than countries located on different continents. The higher the MT, the greater the contribution of foreign trade to the domestic economy. Countries with higher MT and GDP tend to be oriented towards international market demand, import needed resources and materials from abroad and then export products to drive their own economy. These countries are more likely to facilitate the transmission of VWSR. Urbanization rate (URB) is a metric of urbanization. Countries or regions with higher urbanization rates have a a relatively high level of technological progress, which contributes to the improvement of water use efficiency. These countries have a disincentive effect on the transfer of VWSR. Therefore, Hypotheses 3 and 4 are proposed, as follows:

Hypothesis 3.

VWSR is more likely to be transmitted within the same continent.

Hypothesis 4.

Countries with higher MT and GDP are more likely to promote VWSR imports and exports, while countries with higher URB are more likely to inhibit VWSR transmission.

2.4.3. Relations Embedding Effect

The formation and evolution of VWSR transfer networks is influenced by external binary relationships, including geographical boundaries, official language and regional free trade agreements, which are called relation embedding effects. Geographical distance plays a crucial role in international trade. Studies have shown that trade volume is inversely related to geographical distance [56,57]. Countries with common geographical borders are more likely to establish trade relations that promote the spread of VWSR. Official language is a key factor affecting trade flows between economies [58,59]. Countries with a common official language are more likely to establish dependencies due to lower information or transaction costs, which facilitates the spread of VWSR in international supply chains. The signing of regional trade agreements, while achieving the internal liberalization of the region, still retains the trade barriers to countries outside the region and exhibits exclusionary characteristics. In particular, it is difficult for products from developing countries outside the region to access markets within the region, blocking trade flows between economies. This has a negative effect on the transfer of VWSR to some extent. Based on the above, the following hypothesis is proposed:

Hypothesis 5.

Common geographical borders or official language have a positive effect on the transmission of VWSR in global supply chains, while the signing of regional trade agreements has a negative effect on the transfer of VWSR.

The variables used in this study are demonstrated in

Table 1. Variables of TERGM.

Classification	Variable Name	Meaning	Statistic	Hypotheses
Constant Term	Edges	Network density	${\sum }_{i,j}{y}_{ij}$	Constant
Endogenous Mechanism Effect	Mutual	Reciprocity	${\sum }_{i,j}{y}_{ij}{y}_{ji}$	Hypothesis 1
	Gwesp	Transitivity effect	${\sum }_{i,j,k}{y}_{ij}{y}_{jk}{y}_{ik}$
	Gwdsp	Connectivity effect	${\sum }_{i,j,k}{y}_{ij}{y}_{jk}$
	Stability	Stability effect	${\sum }_{i,j}{y}_{ij}^t{y}_{ij}^{t-1}+(1-y_{ij}^t)(1-y_{ij}^{t-1})$	Hypothesis 2
Economic Attribute Effect	Homophily (Continent)	Continent homophily	${\sum }_{i,j}{y}_{ij}Continen{t}_{i}Continen{t}_j$	Hypothesis 3
	Receiver (MT)	MT receiver effect	${\sum }_{i,j}M{T}_j{y}_{ij}$	Hypothesis 4
	Receiver (URB)	URB receiver effect	${\sum }_{i,j}UR{B}_j{y}_{ij}$
	Receiver (GDP)	GDP receiver effect	${\sum }_{i,j}GD{P}_j{y}_{ij}$
	Sender (MT)	MT sender effect	${\sum }_{i,j}M{T}_i{y}_{ij}$
	Sender (URB)	URB sender effect	${\sum }_{i,j}UR{B}_i{y}_{ij}$
	Sender (GDP)	GDP sender effect	${\sum }_{i,j}GD{P}_i{y}_{ij}$
Relations Embedding Effect	Edgecov (CGB)	CGB embedding effect	${\sum }_{i,j}CG{B}_{ij}$	Hypothesis 5
	Edgecov (COL)	COL embedding effect	${\sum }_{i,j}CO{L}_{ij}$
	Edgecov (RTA)	RTA embedding effect	${\sum }_{i,j}RT{A}_{ij}$

. Mutual, Gwesp and Gwdsp are used to test Hypothesis 1. Stability is selected to test Hypothesis 2. Homophily, Nodiecov, Nodoecov and Edgecov are used to test homogeneity effects, receiver effects, sender effects, and external relations embedding effects with respect to Hypotheses 3, 4 and 5. The analysis framework of this study is shown in Figure 1.

2.4.4. Goodness of Fit Test

To further test the ability of the TERGM model to explain the formation of VWSR transfer networks, the goodness-of-fit (GOF) method was used to compare the differences between the structural features of the model-based simulations and the observed networks. Four key network structure statistics, namely Edge-wise Shared Partners, Dyad-wise Shared Partners, Geodesic distance and Degree, are used for comparison and analysis. Edge-wise Shared Partners expresses the tendency in the observed network for tied nodes to have multiple shared partners. Dyad-wise Shared Partners reflects the tendency in the observed network for dyads (whether tied or not) to have multiple shared partners. Geodesic distance is the distance of the shortest path between two nodes. Degree is the number of edges directly connected to the node in the network.

3. Results and Discussion

3.1. Evolution of Structural Features of VWSR Transfer Networks

3.1.1. Macro-Level Analysis

The macro-level structural characteristics of the global VWSR transfer network for the period 2001–2016 are shown in

Table 2. Macro-level analysis of the VWSR transfer networks during 2001–2016.

Year	${\mathit{N}}_{\mathit{v}}$	${\mathit{N}}_{\mathit{e}}$	$\mathit{\rho }$	L	C	$\mathit{\delta }$	R	A
2001	118	1338	0.053	1.946	0.753	6.565	0.268	−0.467
2002	121	1308	0.052	1.959	0.757	6.757	0.266	−0.474
2003	124	1269	0.051	1.969	0.754	6.978	0.247	−0.469
2004	123	1199	0.048	1.970	0.742	7.418	0.232	−0.476
2005	125	1132	0.045	1.970	0.745	8.056	0.214	−0.491
2006	127	1104	0.044	1.981	0.736	8.196	0.214	−0.503
2007	127	1215	0.048	1.954	0.749	7.414	0.221	−0.505
2008	127	1333	0.053	1.917	0.743	6.611	0.210	−0.500
2009	126	1347	0.054	1.934	0.743	6.457	0.223	−0.475
2010	128	1321	0.053	1.918	0.733	6.597	0.209	−0.491
2011	128	1234	0.049	1.943	0.729	7.104	0.211	−0.502
2012	127	1226	0.049	1.932	0.721	7.127	0.207	−0.504
2013	129	1206	0.048	1.936	0.720	7.265	0.196	−0.506
2014	129	1191	0.047	1.941	0.716	7.337	0.202	−0.503
2015	127	1192	0.047	1.936	0.722	7.398	0.205	−0.500
2016	137	1331	0.053	1.921	0.776	6.898	0.204	−0.496

Note: $N_v$ and $N_e$ denote the number of nodes and edges in the VWSR transfer network, respectively. $\rho$ is density, L is average path length, C is average clustering coefficient, $\delta$ is the small world quotient, R is reciprocity, and A represents assortativity.

. It can be observed that the number of edges and network density tends to decrease over time, bottoming out in 2006 and slowly rising thereafter. This may be related to the global supply chain crisis triggered by the outbreak of the US subprime mortgage crisis in 2006, resulting in the sparse VWSR transfer network. Figure 2a shows the trend of the number of edges and density in the VWSR transfer network over time.

On the other hand, global VWSR transfer networks exhibit small-world characteristics. Small-world networks generally have higher average clustering coefficients (C) and smaller average path lengths (L) [60]. For VWSR transfer networks between 2001 and 2016, the average clustering coefficients ranged from 0.72–0.78, while the average path length ranged from 1.91–1.99. This is further validated by the fact that the small world quotients all lie above 6.45. This result suggests that most of the partners of one country are likely to be partners of other countries as well, and that VWSR can spread from one country to another in just two steps. Due to the sensitivity of small world networks, VWSR generated in highly connected countries or regions can be quickly transmitted to countries or regions that are far away, potentially triggering economic losses in the global supply chain.

In addition, the global VWSR transfer networks exhibit low reciprocity and disassortativity. As shown in Table 2 and Figure 2b, the reciprocity (R) ranges between 0.19 and 0.27, indicating that two-way VWSR transfer relationships exist between countries but are not common. The assortativity (A) of the VWSR transfer networks is negative, revealing disassortativity characteristics. This reflects the preference of the economy in choosing the VWSR transfer relationship. Countries with fewer partners tend to connect with countries with more partners, thus making countries with higher degree values the core of VWSR transfer networks, while countries with low degree values become peripheral economies.

3.1.2. Micro-Level Analysis

To track the main sources and destinations of VWSR flows, Figure 3 shows the evolution of the top five economies in terms of $k^{in}$, $k^{out}$, $s^{in}$ and $s^{out}$ from 2001 to 2016.

From the inflow side of the VWSR, as shown in Figure 3a,c, the top five countries are mainly located in Asia, Europe and North America. Countries with higher in-degree values also have larger in-strength values. In particular, the number of China’s VWSR import partners and VWSR imports both show a significant increasing trend from 2001 to 2016, while the US shows a sharp decreasing trend. In other words, more countries are changing the destination of VWSR transfers from the USA to China. This suggests that some sectors of the Chinese economy are heavily dependent on imports from water-scarce countries, making them the most affected when upstream countries face water scarcity.

From the outflow side of the VWSR, as shown in Figure 3b,d, economic losses due to water shortages are mainly from Asia, including countries such as India, Iran and Thailand. Losses in these countries can lead to potential economic losses in other economies through trade. India and Iran are the top two countries in terms of the out-degree and out-strength from 2001–2016, and show a strong increasing trend. This indicates that they are the main source of VWSR for many downstream economies in the international supply chain and contribute the most to VWSR outflows. Therefore, downstream countries should reduce imports from these countries to improve their robustness against water scarcity risks abroad.

3.2. Determinants of the VWSR Transfer Networks Evolution

3.2.1. Analysis of TERGM Results

In order to reveal the factors influencing the global VWSR transfer network, the coefficients of TERGM (Equation (16)) are estimated by the Markov Chain Monte Carlo for the maximum likelihood estimation (MCMC-MLE) method [61]. In addition, MCMC-MLE obtains values for Akaike Informative Criterion (AIC) and Bayesian Information Criterion (BIC) [62], which can be applied to the selection of the most parsimonious VWSR network model. The empirical results obtained by estimating and fitting the TERGM to the longitudinal international VWSR transfer network from 2001–2016 are shown in

Table 3. Estimation results of TERGM for VWSR transfer networks for the period of 2001–2016.

	Model 1	Model 2	Model 3
Endogenous Mechanism Effect
Edges	−3.19 (0.01) ***	−19.83 (0.52) ***	−17.00 (0.54) ***
Mutual			0.20 (0.08) **
Gwesp			1.55 (0.05) ***
Gwdsp			−0.03 (0.00) ***
Stability			3.64 (0.03) ***
Economic Attribute Effect
Homophily (Continent)		0.40 (0.06) ***	0.21 (0.06) ***
Receiver (MT)		0.62 (0.02) ***	0.53 (0.06) ***
Receiver (URB)		−0.12 (0.00) *	−0.31 (0.00) *
Receiver (GDP)		1.51 (0.01) ***	0.77 (0.03) ***
Sender (MT)		0.25 (0.03) **	0.04 (0.07) *
Sender (URB)		−3.54 (0.05) ***	−2.28 (0.13) ***
Sender (GDP)		1.64 (0.01) ***	0.62 (0.03) ***
Relations Embedding Effect
Edgecov (CGB)	1.44 (0.03) ***	1.36 (0.04) ***	0.88 (0.10) ***
Edgecov (COL)	0.14 (0.02) ***	0.23 (0.02) **	0.06 (0.07)
Edgecov (RTA)	0.74 (0.02) ***	−0.19 (0.06) ***	−0.14 (0.06) **
AIC	154,290.91	108,508.54	18,648.23
BIC	154,334.52	108,628.48	18,851.53

Note: * significant at 5%; ** significant at 1%; *** significant at 0.1%. The values in parentheses are stable standard errors.

. The relations embedding effect is included in Model 1. All attribute variables are significant at the 0.1% level. The introduction of economic attribute variables and endogenous structural variables to Model 1 leads to Models 2 and 3. Model 3 has the smallest AIC and BIC reflecting the best fit. The results of Model 3 are analyzed below.

First, in terms of endogenous mechanism effects, the coefficients for Gwesp and Gwdsp are 1.55 and −0.03, respectively, and both are significant at the 0.1% level. This suggests that the transitivity effect is important for the formation and evolution of VWSR transfer networks, while local connectivity is weaker than expected, which supports Hypothesis 1. The coefficient for Mutual is positive and significant at the 5% level. This indicates that there is no strong feedback effect in the formation of the VWSR transfer network. This does not support Hypothesis 1. The coefficient on Stability is 3.64 and is significantly positive, reflecting the stability of the global VWSR transfer network structure. In other words, there is a tendency for existing VWSR transfer relationships to remain stable over time, supporting Hypothesis 2. Overall, the formation and evolution of VWSR transmission networks are affected by endogenous mechanism effects and exhibit certain path-dependent characteristics.

In terms of the economy attribute effects, Homophily (Continent) is significantly positive at the level of 0.1% from 2001–2016, which indicates that countries located in the same continent are more likely to form VWSR transfer flows due to geographical proximity and lower transport costs. This result supports Hypothesis 3. Table 3 also shows that there is a difference between the Receiver effect and the Sender effect on the formation of VWSR transmission networks. In particular, the Receiver effect for GDP and MT is positive and significant, revealing that countries with larger economies or commodity trade shares have a higher probability of receiving more VWSR, which is consistent with Hypothesis 4. The Receiver effect for URB does not pass the significance test, meaning that there is no evidence that countries with higher levels of urbanization have a tendency to receive more VWSR flows, which is inconsistent with Hypothesis 4. On the other hand, the Sender effect for GDP is positive and significant, indicating that the GDP variable is an important factor influencing VWSR outflows. The negative Sender effect for URB may be due to the fact that countries or regions with higher levels of urbanization are more concerned with improving water use efficiency, which acts as a disincentive for VWSR outflows, and Hypothesis 4 is tested. The positive but insignificant coefficient for Sender (MT) suggests that there is no evidence that countries with a larger share of merchandise trade are more inclined to send more VWSR flows. This finding does not support Hypothesis 4.

Finally, in terms of relations embedding effects, the coefficient on Edgecov (CGB) is positive and significant at the 0.1% level. This reflects the fact that geographical distance has a significant impact on the VWSR transfer and that VWSR transfer relationships are more likely to be formed between neighbouring economies, a result that is consistent with Hypothesis 5. The negative and significant coefficient of Edgecov (RTA) supports Hypothesis 5. That is, RTA has a binding effect on the formation of VWSR transfer networks. This may be due to the fact that RTA, while facilitating trade cooperation among member countries, limits trade liberalisation with non-member countries. In particular, the difficulty for developing countries outside the region to join the intra-regional market acts as a disincentive for VWSR flows between economies to a certain extent. Hypothesis 5 is tested. the Edgecov (COL) variable does not pass the significance test, i.e., there is no evidence that economies sharing the same official language contribute significantly to the formation mechanism of the VWSR transfer network, and therefore Hypothesis 5 is not supported.

In summary, the formation and evolution of VWSR transfer networks are influenced by the relations embedding effect, the endogenous mechanism effect and the economic attribute effect. It is also found that with the addition of economic attribute variables and endogenous mechanism variables to the VWSR transfer network, the effect of relational embedding effect on VWSR transfer network formation was reduced.

3.2.2. Robustness Test

To test the robustness of Model 3, an empirical analysis of TERGM was conducted by adjusting the time interval, time step and changing the estimation method, and the results are presented in

Table 4. Robustness test results of TERGM.

	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9
Endogenous Mechanism Effect
Edges	−18.71 (0.79) ***	−17.68 (0.90) ***	−15.41 (0.68) ***	−15.77 (0.62) ***	−15.81 (0.67) ***	−16.29 [−16.14;−18.10] *
Mutual	0.05 (0.11) *	0.24 (0.13) *	0.20 (0.10) *	0.12 (0.09) *	0.07 (0.11) *	0.42 [0.42;0.20] *
Gwesp	1.57 (0.08) ***	1.44 (0.08) ***	1.66 (0.08) ***	2.06 (0.08) ***	2.25 (0.10) ***	1.18 [1.17;1.08] *
Gwdsp	−0.03 (0.00) ***	−0.03 (0.00) ***	−0.03 (0.00) ***	−0.05 (0.00) ***	−0.06 (0.00) ***	−0.02 [−0.02;−0.03] *
Stability	3.60 (0.04) ***	3.73 (0.04) ***	3.28 (0.03) ***	2.70 (0.03) ***	2.25 (0.03) ***	3.70 [3.74;3.37] *
Economic Attribute Effect
Homophily (Continent)	0.16 (0.08) **	0.31 (0.08) ***	0.16 (0.07) **	0.21 (0.06) ***	0.23 (0.07) ***	0.26 [0.25;0.07] *
Receiver (MT)	0.58 (0.08) ***	0.55 (0.09) ***	0.53 (0.07) ***	0.54 (0.06) ***	0.49 (0.07) ***	0.64 [0.64;0.53] *
Receiver (URB)	−0.60 (0.20) **	−0.10 (0.21) *	−0.54 (0.18) **	−0.40 (0.16) *	−0.45 (0.18) **	−0.41 [−0.42;−0.70] *
Receiver (GDP)	0.88 (0.05) ***	0.75 (0.06) ***	0.74 (0.04) ***	0.67 (0.04) ***	0.64 (0.04) ***	0.83 [0.83;0.69] *
Sender (MT)	0.24 (0.10) *	0.05 (0.11) *	0.15 (0.09) *	0.02 (0.08) *	0.06 (0.08) *	0.25 [0.27;0.60] *
Sender (URB)	−3.00 (0.19) ***	−2.17 (0.19) ***	−2.31 (0.15) ***	−2.27 (0.14) ***	−2.27 (0.15) ***	−2.40 [−2.40;−2.96] *
Sender (GDP)	0.73 (0.05) ***	0.68 (0.05) ***	0.53 (0.04) ***	0.58 (0.04) ***	0.60 (0.04) ***	0.57 [0.57;0.42] *
Relations Embedding Effect
Edgecov (CGB)	1.15 (0.15) ***	0.59 (0.17) ***	0.97 (0.14) ***	0.88 (0.13) ***	0.89 (0.14) ***	0.88 [0.88;0.61] *
Edgecov (COL)	0.04 (0.10)	0.02 (0.11)	0.02 (0.08)	0.04 (0.08)	0.04 (0.08)	0.04 [0.00;0.18] *
Edgecov (RTA)	−0.28 (0.08) ***	−0.16 (0.09) **	−0.28 (0.07) ***	−0.20 (0.07) **	−0.24 (0.07) **	−0.15 [−0.16;−0.42] *
AIC	8812.75	8256.84	11,021.53	11,362.30	8848.88
BIC	8993.18	8437.27	11,201.96	11,532.64	9003.88

Note: * significant at 5%; ** significant at 1%; *** significant at 0.1%. Values in parentheses are stable standard errors and values in square brackets are 95% confidence intervals.

. TERGM results for the periods 2001–2008 (Model 4) and 2009–2016 (Model 5) are presented. Models 6, 7 and 8 show the empirical results for adjusting the time step of the longitudinal VWSR transfer network to 2, 3 and 5, respectively. By replacing the estimation method of TERGM with MCMC-MLE, the empirical results of TERGM are presented in Model 10. As can be found from Table 4, Model 4–Model 9 present empirical results consistent with Model 3, indicating the robustness of Model 3.

3.2.3. Goodness-of-Fit Test

To test the ability of Model 3 to explain the mechanism by which VWSR transfer networks are formed, goodness of fit (GOF) is evaluated by comparing the structural statistics of the model-based simulations with those of the observed networks. Figure 4 illustrates the model-based simulations, including Edge-wise shared partners, Dyad-wise shared partners, Geodesic distance and Degree values, and the observed VWSR transfer networks based on Model 3. It can be found that the model-based simulation results are very close to the distribution of the observed structural statistics of the VWSR transfer networks. This indicates that the combination of variables in TERGM is well fitted and can reveal well the underlying characteristics and key mechanisms of the VWSR transfer network formation.

4. Conclusions and Future Research

4.1. Conclusions

The water resource crisis has become a major environmental issue facing human society, and is aggravated by economic development, climate change and environmental pollution. International trade can transfer the risk of local water scarcity to remote economies through the global supply chain. This suggests that water scarcity in one country can trigger the risk of subsequent production losses in another country. To reveal the vulnerability of the global economy to water scarcity its evolution pattern, this study quantifies the virtual water scarcity risk and constructs global VWSR transfer networks for 2001 to 2016. Then, the structural evolution of VWSR transfer networks is analyzed from macro and micro perspectives. Further, TERGM is used to explore the determinants of the formation of longitudinal VWSR transfer networks, which helps to reduce the spatial correlation effects of VWSR and thus mitigate the cascading propagation of virtual water scarcity risks along global supply chains. In contrast to previous studies, revealing the determinants of the formation and dynamic evolution of VWSR transfer networks fills a research gap in the longitudinal analysis of virtual water scarcity risk. The main conclusions are as follows.

(1) Analysis of structural characteristics reveals that VWSR transfer networks have small-world characteristics. The VWSR in any key country can spread rapidly through the supply chain to other countries, leading to large-scale spillovers.

(2) VWSR transfer networks show the characteristics of disassortativity and low reciprocity. The core-periphery features of global VWSR transfer networks are significant, and there is no obvious bidirectional flow.

(3) On the VWSR import side, VWSR targets are mainly located in Asia, Europe and North America. Countries with more import partners import more VWSRs. In particular, the United States was the largest importer of VWSRs until 2008. China’s VWSR imports showed an increasing trend. After 2008, China surpassed the United States to become the largest destination for global VWSRs transfers. This suggests the vulnerability of some economic sectors in China when upstream countries face water scarcity. Policymakers should diversify their suppliers in the upstream supply chain to reduce potential risks. On the VWSR export side, the number of trading partners and VWSR export volume of India and Iran remained the top two during 2001–2016 and showed a continuous increasing trend, becoming the main source of VWSRs for many downstream countries. As long as the economic sectors of these countries remain strongly dependent on water resources, the VWSRs transferred by them will continue to rise. Therefore, these countries should develop long-term strategies to reduce water consumption. In conclusion, these key countries are critical to increasing the resilience of international supply chains to VWSRs, and should be focused on to reduce the cascading spread of VWSRs.

(4) With regard to the endogenous structural effects, the formation and evolution of VWSR transfer networks are influenced by transitivity and stability. In other words, in the process of network formation, VWSR transfer relationships will show certain path-dependent characteristics along with trade dependency relationships. It is more likely that partners of transfer partners will become partners again, forming a network cluster structure.

(5) In terms of the economic attribute effect, VWSR transfer flows are more likely to form between countries located on the same continent. Countries with higher economic development level can promote the formation of the VWSR transfer relationship. Countries with a higher share of merchandise trade are more inclined to receive VWSR inflows, while the urbanization rate has a restraining effect on VWSR outflows. Therefore, dialogue and cooperation between trading partners, especially between the same continent and neighboring countries, should be strengthened to effectively mitigate the indirect impact of VWSRs on other economies. Countries with high levels of economic development and merchandise trade shares should improve import standards and establish regulatory mechanisms to reduce dependence on commodities from countries with high water scarcity pressures. At the same time, domestic enterprises should be encouraged to improve water use efficiency and urbanization to reduce the impact of local water scarcity risks on the international trading system.

(6) The results of relations embedding effects suggest that VWSR transfer relationships are more likely to be established between economies sharing geographical boundaries. In contrast, the signing of regional trade agreements did not play a positive role in the formation of VWSR transfer relations. Therefore, on the basis of regional trade agreements, a unified and orderly international VWSR coordination mechanism should be established to adjust trade patterns and realize synergistic water resources management by taking into account the water resources endowments of each economy.

4.2. Future Research

This paper explores the evolutionary characteristics of the VWSR transfer networks and uses TERGM to empirically analyze the factors that influence their formation and evolution. Several challenges for VWSR transfer networks still exist: (1) This work considers research at the national level, rather than the sectoral level; (2) Risk is defined in terms of economic loss, without consideration of the environmental hazards caused by water scarcity.

Therefore, improvements can be made in future research in two ways: (1) Explore the determinants of the formation of VWSR transfer relationships at the sectoral level, which can provide valuable information for rationalizing industrial structures and improving water efficiency; (2) Examine the combined impact of the two risks of economic loss and environmental harm caused by water scarcity, which can help to more rationally reshape the virtual water trade structure and thus develop strategies to mitigate possible economic and environmental risks.