Table 1.
A hypothetical two-economy-two-industry MRIO table.
The 4 × 4 inter-industry transactions matrix records outputs selling in its rows and inputs buying in its columns. The additional columns are the final demand and the additional row is the value added. Finally, the last column and the last row record the total industry outputs.
Fig 1.
The impact of α on the GVTs obtained.
Panel (a) shows the relationship between the tree size variation and the value of α while panel (b) shows the relationship between the number of available GVTs and the value of α. The 95% confidence intervals are based on the time variation during 1995-2011. The maximum variation of tree size is obtained when α = 0.019. The number of available GVTs according to this value of α is still very large (around 1300) given that the total number of industries in the WIOD is 1400.
Fig 2.
The GVT rooted at Germany’s transport equipment industry (DEU_15) in 2011.
The edge weight threshold is set to 0.019. Different colors of the nodes indicate different countries. The red edges indicate cross-country relationships while the gray edges indicate domestic relationships. The edge width is proportional to the edge weight, i.e., the share of the value-added contribution. The codes of countries and industries can be found in S1 and S2 Tables.
Fig 3.
Examples of the allometric scaling relationship.
The numbers inside the node circles are Xi’s whereas those next to the circles are Yi’s. The node with the thick circle is the root. From left to right, they are a chain (a), a star (b), and a tree (c), respectively.
Fig 4.
Estimation of the allometric scaling exponent η.
Panel (a) shows the log-log plot of the root-node Yi-Xi pairs in 2011, where the horizontal axis is the Xi of the root node, i.e., the total number of nodes in a given GVT (the tree size), and the vertical axis is the Yi of the root node, which we call the accumulative tree size. The gray crosses are the observed data points. The thick blue dashed line is fitted with the observed data and with the slope of η. The fitting lines for star and chain based on the same set of Xi’s are the green dashed line and the red dashed line respectively. Panel (b) plots the estimated η’s over time.
Fig 5.
The domestic and foreign GVTs where Japan’s transport equipment industry (JPN_15) has the highest importance score in 2011.
Panel (a) shows the domestic GVT where Japan’s transport equipment industry (JPN_15) has the highest importance score while panel (b) shows the foreign GVT where Japan’s transport equipment industry (JPN_15) has the highest importance score. The edge weight threshold is set to 0.019. Different colors of the nodes indicate different countries. The red edges indicate cross-country relationships while the gray edges indicate domestic relationships. The edge width is proportional to the edge weight, i.e., the share of the value-added contribution. High-resolution plots for both panels can be found in S1 and S2 Figs. The codes of countries and industries can be found in S1 and S2 Tables.
Table 2.
The Pearson correlation coefficient matrix between the tree-based importance measure and other network centrality measures (in logarithm) for the selected years.
The size of the sample is in the parentheses next to the corresponding years. TI is the tree-based importance measure, CC is the closeness centrality, PR is the PageRank centrality, BC is the betweenness centrality, and VT is the industry total value-added. ** means that the coefficient is significant at 1% level. ** means that the coefficient is significant at 1% level.
Fig 6.
The evolution of the GVTs rooted at South Korea’s electrical equipment industry (KOR_14).
Panels (a), (b), and (c) show the GVTs for 1995, 2003, and 2011 respectively. The edge weight threshold is set to 0.019. Different colors of the nodes indicate different countries. The red edges indicate cross-country relationships while the gray edges indicate domestic relationships. The edge width is proportional to the edge weight, i.e., the share of the value-added contribution. China’s cluster is with light green color. High-resolution plots for all the panels can be found in S3, S4 and S5 Figs. The codes of countries and industries can be found in S1 and S2 Tables.
Fig 7.
The TI scores of China’s indutries in the GVTs rooted at South Korea’s electrical equipment industry (KOR_14).
The TI scores of three China’s industries in the GVTs rooted at South Korea’s electrical equipment industry are compared over the years. China’s textiles industry (CHN_2; blue bars) has the highest TI score among the three in 1995 and disappears in the GVTs in 2003 and 2011. China’s metals industry (CHN_12; red bars) has the highest TI score among the three in 2003 but decreases again in 2011. China’s electrical equipment industry (CHN_14; green bars) has increased its TI score over time and has the highest TI score among the three in 2011.
Fig 8.
The comparison of the transport equipment industry between Indonesia (IDN_15) and Japan (JPN_15) in 1995.
In panel (a) and panel (b), the GVTs are rooted at the tranport equipment industry in Indonesia (IDN_15) and Japan (JPN_15) respectively in 1995. The edge weight threshold is set to 0.019. Different colors of the nodes indicate different countries. The red edges indicate cross-country relationships while the gray edges indicate domestic relationships. The edge width is proportional to the edge weight, i.e., the share of the value-added contribution. High-resolution plots for both panels can be found in S6 and S7 Figs. The codes of countries and industries can be found in S1 and S2 Tables.