Supply risk propagation in international trade networks of the tungsten industry chain

Impact ranges of different economies and identification of the core economies

The avalanche size is an important quantitative indicator in the risk cascade propagation process and can be used to assess the potential impact of a given economy. The distribution of avalanche sizes for all economies depends on the value of α/β. There is a critical value where the distribution of avalanche sizes for all economies follows a power law distribution. First, we attempt to find the core economies with the largest potential impacts according to the avalanche size. At a critical value consistent with a power law distribution, the avalanche sizes in the system can cover the largest range. The avalanche sizes are the most dispersed, which helps to distinguish the potential impact differences among economies. Second, power law distributions exist in various fields as typical distributions (Yu and Deng, 2022; Pinto et al. 2012). Many economic phenomena, such as wealth distribution (Pinto et al. 2012), stock price and trading volume (Gabaix et al. 2003), city size distribution (Hsu, 2012), and firm size distribution (Heinrich and Dai, 2016), obey power law distributions. Like supply risk, the forest fire size distribution (Song et al. 2007), the spread of epidemics (Beare and Toda, 2020), and the size of outages in the power grid (Odor and Hartmann, 2020) obey power law distributions. Finally, many researchers take the power law distribution as an important parameter-taking criterion (Lee et al. 2011; Wang et al. 2018a). Therefore, we choose the critical value of α/β according to the power law distribution.

In the trade network of the tungsten industry chain, assuming that each economy is a risk source, the critical point of each layer is found by adjusting α/β (Fig. 3). From L1 to L5, the critical values of α/β are 8, 5, 4, 4, 5. At the critical point, we traverse the participating economies as risk sources to obtain the impact range. Then, we obtain the top 10 core economies with impact ranges in each layer (Table 2), including the region of risk source (R), impact cycle (T), impact range (A), infection proportion (P), and number of infections in each period (T1–T7).

a Tungsten ore. b Tungstate. c Ferrotungsten. d Tungsten final product. e Tungsten-related product. The horizontal axis represents avalanche size (impact range, A), and the vertical axis represents the number of economies whose avalanche size is ≥A. The horizontal axis has been offset by one to plot the economies with A = 0 on a logarithmic scale.

The influence range of the economies in the tungsten ore trade network is limited by resource endowments. The economy with the largest range is Canada. Among the top 10 economies, Canada, Russia, Bolivia, China, and the United States are all economies with tungsten resource reserves. As the economy with the highest tungsten resource reserves in the world, China’s influence range is ranked seventh. As the strategic position of tungsten continues to grow, China has made a series of policy and strategic adjustments to guide and regulate tungsten mining for its development and national security reasons. For example, the total amount of tungsten exploration and mining has been limited, and a tungsten export quota system has been implemented (Zhu et al. 2019).

The global supply of tungstate is largely dependent on Asia. The top economy in terms of influence range is China, which has long been a dominant player in tungsten ore and primary processing. The second-largest economy is Vietnam. Vietnam has relatively rich tungsten resources. Vietnam ranked second in the world in terms of mineral extraction in 2023 (USGS, 2023). However, Vietnam’s mineral production is still not enough to meet its domestic tungsten smelting capacity, so it also needs to import tungsten ore from other economies. Vietnam primarily processes tungsten ore before it is exported in the form of tungstate. For technical and financial reasons, Masan Group cannot develop the Nui Phao mine completely independently, which is the main source of tungsten ore in Vietnam. American and European investors are rapidly occupying the tungsten ore mining market in Vietnam. In the future, Vietnam’s output of tungsten ore products and tungstate products will continue to grow, and its influence will further expand.

The economy with the largest impact cycle and impact range in the ferrotungsten trade is China. The supply risk from China will propagate six rounds, affecting a total of 102 economies, with an impact ratio of 83.6%. When α/β = 4, if China falls into a supply crisis, basically all economies involved in the trade will also fall into a supply crisis. The influence range of China is nearly three times greater than that of the second-ranked economy (the Netherlands). China exports ferrotungsten mainly to Japan, the Netherlands and Germany. The Netherlands and Germany, with the second and third largest influence range, respectively, play important roles as trade intermediaries.

China still occupies an important position in the tungsten final product trade. If China had a supply problem, 90% of the economies involved in the trade would be in a supply crisis. Three of the top five economies are located in Europe. This indicates that the European and American markets are more competitive. Since 2016, the US stopped producing primary processed products of tungsten (Case et al. 2022). Germany, France and the UK do not have advantages in terms of raw materials. However, they still have a high influence, mainly due to a strong level of technology and processing capabilities. These economies import upstream raw materials and midstream primary products and then export high-value-added final products after refining. As China’s tungsten trade unit price is high in imports and low in exports (Li et al. 2020), China needs to identify the sources of raw materials or intermediate products for processing final products in the other core economies to avoid exporting raw materials at a low price and importing final products at a high price.

The results in tungsten-related products are similar to those for final products. The economies with the greatest influence range are China, Germany and the United States. Half of the top ten economies are located in Europe, which is an important processing and manufacturing location for tungsten products. Among the top ten economies, only China and the United States have some resource advantages, and the United States does not mine tungsten. This shows that for economies to have high influence, they not only rely on their resource endowment but also need to have advanced processing technology. There is a need to develop key technologies and products that are compatible with the characteristics of the resources and capable of meeting the demands of the international market.

The model involves mainly the parameter α/β, which may affect the propagation process. Although the rankings may be slightly different, the top 10 economies are similar (Table S1) under different parameters (Hu et al. 2023). Therefore, the parameter settings do not affect the main findings.

Correlation analysis of the factors affecting the impact range

To further reveal the factors influencing the impact range, the correlations between the impact range (A) and impact cycle (T), export value (EV), number of trade export partners (NEP), GDP, closeness centrality (CC), betweenness centrality (BC), PageRank (PR), and technological development level (TECH) are explored in different product trade networks (Fig. 4).

a Tungsten ore. b Tungstate. c Ferrotungsten. d Tungsten final product. e Tungsten-related product. *p < 0.05, **p < 0.01, ***p < 0.001. The horizontal and vertical coordinates represent different influencing factors, which are reflected in the diagonal positions. The value below the diagonal corresponds to the size and color of the circle above the diagonal.

Only three factors have a significant impact on upstream products, and the number of factors with a significant impact gradually increases for mid- and downstream products. For all products, there is a significant positive correlation between the import range and the export value, the impact cycle, and the number of export partners. The number of export trading partners, the export value, and the period of impact correspond to the channel of propagation, the intensity of propagation, and the time of propagation, respectively, and an increase in all three factors contribute to a wider impact. From the industry chain perspective, the impact range in the midstream products is also closely related to the betweenness centrality. Increasing the mediating capacity in the trade of midstream products helps to increase the influence of trade. The influence range in the final product is related to the level of economic development and closeness centrality. Increasing trade relationships with different economies helps to increase the influence. The influence factors in tungsten-related products and the final products are basically the same. In the downstream, economies with higher levels of economic development invest more in product processing and manufacturing, which helps improve the competitiveness of export products. The greater the competitiveness of the product is, the higher the export value and the greater the impact on the global supply. In addition, tungsten final products are widely embedded in strategic emerging industries such as photovoltaics, lithium batteries, and semiconductors. With economic development, the competition for tungsten final products will continue to intensify, which may accelerate the restructuring of the trade pattern of tungsten products.

The findings of Sohail and Din (2024) and Ruan et al. (2024) validate our findings that economic development can positively promote mineral resource trade and increase the influence of economies. Shao et al. (2021) showed that betweenness centrality significantly contributes to the intensity of competition in the lithium trade. The greater the betweenness centrality is, the better the ability to control resources and the greater the potential influence on trade. Wang et al. (2018a) found that the avalanche size in the upstream natural graphite trade is related to GDP and export value. In this study, the significant effect of GDP on the avalanche size occurred mainly in the downstream. The downstream products are more technologically sensitive. Economic development drives the increase in research and development investment for industrial upgrading and technological innovation. Economies produce higher-quality final products that are more competitive. The influence of the economy will also be greater.

The correlation between the influence range and the technical factors is not significant. However, the indirect correlation gradually increases as the chain extends downward. There is no relationship between these two factors in the upstream. For midstream products, the technology factor is significantly correlated with the number of export trading partners, which is significantly correlated with the influence range. For downstream products, the technology factor is significantly correlated with the number of export trading partners, PageRank, betweenness centrality, and closeness centrality. All four are significantly correlated with the influence range. Technological progress can promote industrial restructuring, enhance product total factor productivity (Liang et al. 2023), and increase product output. In the tungsten industry chain, there is strong technological dependence on upstream ore dressing, midstream smelting and purification, and downstream processing and manufacturing. Ruan et al. (2024) found that technological factors significantly affect the trade of basic lithium products in economies along the Belt and Road. As the production of midstream lithium products needs processing and refining technology, the level of technology will greatly affect the production, which in turn affects the influence of economies. Therefore, technological progress helps to improve the influence range of economies in the midstream and downstream.

Spatial aggregation and indirectness of supply risk propagation

Risk propagation is a gradual process. We start by finding three economies with the largest avalanches in different regions. Then, the proportions of the directly affected economies located in the same region as the risk sources are calculated to assess the degree of spatial clustering of risk propagation (Table 3).

As shown in Table 3 and Fig. 5, when the economy with the largest influence range serves as the risk, the proportions of the directly affected economies located in the same region as the risk sources are relatively low. However, when the remaining economies act as sources of risk, the proportions are relatively high, suggesting spatial aggregation in the propagation of supply risk. From the perspective of economies, South Africa has the strongest spatial aggregation of propagation when it is the risk source of tungsten ferroalloy, and Canada has the weakest when it is the risk source of tungsten ore. From a product perspective, the spatial aggregation of risk propagation is strongest for trade in ferrotungsten and weakest for trade in tungsten ore. The degree of spatial aggregation of supply risks indirectly indicates whether there are regional effects on product production. Tungsten mineral products are limited by resource endowment, and economies in different regions all need to import minerals from core economies, so the spatial aggregation is weak. As the industrial chain extends downward, the restriction of resources on product production gradually decreases, and the regional effects of product production and exports gradually strengthen. Considering transport costs and safety, economies prefer to import products from economies closer to them. Therefore, the spread of supply risk shows spatial aggregation. Economies that rely on tungsten imports need to pay close attention to the supply status of core economies located in the same region to make timely adjustments when risks occur.

a–c Tungsten ore. d–f Tungstate. g–i Ferrotungsten. j–l Tungsten final product. m–o Tungsten-related product.

A comparison of the trade relationships and risk propagation pathways reveals that the failed economies are not exclusively those that have trade relationships with risk sources. Even if they do not directly import products from the risk source, they are still affected. To analyze the role of indirect contagion in risk propagation, the three economies with the largest avalanches from each tungsten product are selected as the objects of study. There are three types of avalanches: one-step direct avalanches, multistep direct avalanches, and indirect avalanches (Fig. 6). In the upstream and midstream, the proportions of indirect avalanches from most economies are above 56%. In contrast, in downstream products and overall tungsten product trade, direct avalanches predominate. The main reason is that the selected core economies have trade relationships with most of the economies involved in trade, so direct avalanches are mainly dominant. Compared with previous studies (Sun et al. 2022; Lee et al. 2011), there is a difference in the results, mainly because the study by Sun et al. (2022) focused mainly on upstream cobalt mining products, whereas this study focuses on products at all stages. The risk transmission in tungsten ores is also mainly based on indirect propagation. However, the results for downstream products and tungsten-related products are the opposite, reflecting the heterogeneity of products at different stages (Lee et al., 2011). In addition, the avalanche size is still relatively small in the first propagation cycle, and the range gradually increases mainly in the subsequent propagation process. Therefore, it is important to pay close attention to the supply situation in the core economies so that timely measures can be taken to minimize the losses.

Profiles of failed economies.

Influence of core economies

Canada has the largest impact on L1, whereas China has the largest impact on the other layers. The influence range depends largely on α/β (Wang et al. 2018a). To further analyze the influence of Canada and China, we simulate the change in avalanche size when there are different decreases in tungsten product trade exports from Canada and China by adjusting α/β (Fig. 7).

a The risk propagation range of Canada as a risk source for different α/β values in the tungsten ore trade network. b–e The risk propagation range of China as a risk source for different α/β values in the corresponding tungsten trading network. γ = α/β. The variation in avalanche size is reflected in the line charts.

The results when Canada is the risk source of tungsten ore trade are shown in Fig. 7a. When α/β ≤ 2, no economy is affected. When 2 < α/β ≤ 5, up to three economies are affected, namely, the Netherlands, Curaçao and Egypt. These three economies are heavily dependent on Canada for tungsten ore. When 5 < α/β < 7.5, the affected economies are mainly Asian and European economies, including Vietnam, China, Indonesia, Laos, Italy, Serbia, and Croatia. From 2020, with the implementation of a quota system for tungsten ore exports, the export value of China declined. Moreover, because of the gradual expansion of China’s capacity for intermediate products, China is also producing intermediate products for other economies in the form of processing raw materials (Tang et al. 2022). Vietnam also needs to import minerals from other economies, as tungsten ore production within the economy cannot meet demand because of the expansion of midstream product capacity. Canada is the main source of mineral products for China and Vietnam. When 7.5 ≤ α/β < 16, Canada begins to impact African and American economies. When 16 ≤ α/β ≤ 40, a crisis in Canada has the greatest impact on Asia and Europe, followed by the Americas, where Canada is located. Fifty-three percent of African economies are affected. When α/β > 40, essentially all economies involved would be affected.

The results of the risk propagation simulation when China is the risk source in tungstate trade are shown in Fig. 7b. When α/β = 1, only Timor–Leste will be affected. Because Timor–Leste imports tungstate only from China. When 1 < α/β < 1.5, the affected economies are mainly Asian and European. In addition to Timor–Leste, there are four Asian economies, namely, Brunei, Iran, Japan and Korea. Resource-poor economies such as Japan and South Korea compete to import from China. Japan has advanced technology and exceptional production and processing capacity. Japan imports midstream products from China and transforms them into high-value-added final products. China relies on Japan for tungsten metal products. A tungstate crisis from China may affect the final product supply in China by affecting the tungstate supply in Japan. When 1.5 ≤ α/β ≤ 5, African and American economies start to be affected. When 5 < α/β ≤ 9, the other affected economies are located mainly in Asia, Africa, and Europe. When α/β > 9, essentially all of the economies are affected.

The variation and distribution of the impact range when China is the risk source in the trade of ferrotungsten are shown in Fig. 7c. When α/β < 1.25, no economy is affected. When 1.25 ≤ α/β ≤ 2.5, all four economies involved in the trade in Oceania would be affected. Other affected economies are located in Asia and the Americas. These include Japan, Iran, Singapore, the US, Peru and Bolivia. Developed economies, such as the United States and Japan have a high demand for tungsten products and, therefore, need to import large quantities of intermediate products from China. Similar to the case of tungstates, developed economies import intermediate products and then export highly profitable final products after they are finished. When 2.5 < α/β < 3.75, economies in Europe and Africa begin to be affected. No European or African economies were affected before. Europe is an important producer of intermediate products, and the European economies tend to choose their import sources from Europe because of transport costs. Therefore, European economies will not be affected by a small export restructuring in China. The economic development in Africa is slower, and the demand for tungsten products is lower, so it is not easily affected. When α/β ≥ 3.75, basically all participating economies will be affected. When α/β is ~3.57, the avalanche size is only 35, but when α/β is 3.75, the avalanche size increases directly to 102, indicating that the ferrotungsten trade is less robust.

The results for the final products are shown in Fig. 7d. When α/β ≤ 1, no economy is affected. When 1 < α/β < 3.5, if a tungsten final product supply crisis occurs in China, the affected economies are mainly Asian and African. These economies are relatively weak in tungsten product finishing and rely only on imports to meet their development needs. A small decline in exports from core economies will cause these economies to fall into a supply crisis. When 3.5 ≤ α/β ≤ 3.75, the economies of Europe, the Americas, and Oceania begin to suffer, including Canada and the United States. Canada’s raw material advantage slows the rate at which Canada is affected. The United States, with higher tungsten exports, was affected later because it can produce and process tungsten products. When α/β > 3.75, essentially all of the economies involved will be affected. This reflects China’s important role in the final product trade.

The results when China is the risk source in the trade of tungsten-related products are shown in Fig. 7e. When α/β ≤ 1, no economy is affected. When 1 < α/β ≤ 2.5, the affected economies are mainly Asian economies. These economies are highly dependent on China. When 2.5 < α/β ≤ 3, European economies, in addition to Asian economies, begin to be affected. The affected economies include the Netherlands, South Korea, Malaysia, and Ukraine. Among them, the Netherlands is an important intermediate economy, and the risk will spread further through it. When 3 < α/β ≤ 3.57, the risk spreads widely within this range and may be affected by the intermediate economies falling into supply risk in the previous period. These include the United States and India, which play important roles in the trade. The impact range in the next period is further extended through these economies. When 3.57 < α/β < 5, the additional economies are mainly in Africa and Europe. When α/β ≥ 5, essentially all economies are affected.

The critical values in tungsten ore products are much larger than those in the trade of other products. All economies import minerals in one direction from a few resource-advantaged economies; thus, the trade relationship is relatively sparse, and the supply system is relatively stable. The critical value of tungsten ferroalloys and final products is the smallest. Trade in the final tungsten products and ferrotungsten is highly globalized, with close relationships between economies. Small export restructuring in the core economies will affect most of the economies involved in trade.

We further analyze the evolution of the infection proportion of core economies, and extend the core economies from those with the largest avalanche size to those ranked in the top three in avalanche size (Fig. 8). The evolution of the core economies can be classified into three categories. For the first category, the dominant position was reflected mainly in the previous period, including tungsten ore. The main influence of Canada is reflected in the pre-2016 period. In 2016, the infection proportion in Canada declined significantly. In 2015, the tungsten ore market was oversupplied, tungsten prices were low (USGS, 2016), and many economies reduced production. One of the major tungsten mines in Canada, the Cantung mine, was shut down for maintenance in 2015 (USGS, 2016), severely affecting the production and export of Canadian tungsten. The impact proportions of Russia and Bolivia were relatively stable, and by 2020, the impact proportions of both economies were essentially the same.

a Tungsten ore. b Tungstate. c Ferrotungsten. d Tungsten final product. e Tungsten-related product.

The second category, in which the infection proportion of the core economies fluctuates in ranking, consists of tungstate and ferrotungsten. The influence of China was lower than that of Vietnam only in 2016 and 2020. The influence of Vietnam was lower than that of China and Germany until 2014 when it exceeded that of Germany. The influence of Vietnam exceeded that of China in 2020, making Vietnam the economy with the largest infection proportion. The growth in global demand for high-quality tungstates led to an overall strengthening of the global tungstate trade in 2014, with the core economies all increasing their infection proportions, with Vietnam experiencing the largest increase. The largest tungsten mine in Vietnam, which is the second-largest mine in the world, the Nui Phao mine (Ha et al. 2019), was officially put into full production (Bradshaw, 2023), leading to a significant increase in tungsten exports in 2014. Masang Resources, the operating company of the Nui Phao mine, has further upgraded its processing capacity to start producing tungstate with high added value. Compared to 2019, the production of midstream products in 2020 increased by 67.5% (Masan High-Tech Materials, 2021).

The impact of China on the trade of ferrotungsten was greater than that of the Netherlands and Germany until 2012. In 2013 and 2014, the impact of China was lower than that of the Netherlands and Germany. China reduced its export quota in 2013 to protect resources and the environment and to better promote a sustainable supply of tungsten products. In 2015, the proportion of China significantly increased again, and it has remained the absolute leader since then. The World Trade Organization ruled that the restrictive export measures taken were inconsistent with WTO obligations in 2014. China canceled the export quota system and export tariffs on tungsten products in 2015 (USGS, 2016). This significantly increased Chinese tungsten exports, further expanding China’s influence on the tungsten trade.

The third category, in which the core economies have largely maintained their absolute leadership, consists of tungsten final products and tungsten-related products. The influence of China and the United States on the tungsten final product trade was essentially the same in the first two years. The infection proportion of China increased significantly in 2011 and has remained the absolute leader since then. The global economy gradually recovered from the financial crisis, leading to an increase in the global demand for tungsten final products in 2011. Chinese products are more competitively priced because of their lower labor and raw material costs. The infection proportions of the United States and Germany are relatively stable. For tungsten-related products, the infection proportion of China is maintained at 0.8, which is significantly greater than that of Germany and the United States.