Table 1.
A hypothetical two-economy-two-industry GMRIO 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. The numbers are made up in such a way that Economy 2 is much larger than Economy 1 in terms of industry outputs. However, as shown below, the Rasmussen method of backward linkages will consider industries in Economy 1 more important than the ones in Economy 2. Hence, we use the Laumas method of backward linkages instead to identify the key industries in the WIOD.
Fig 1.
A hypothetical two-economy-two-industry WION.
This is a topological view of Table 1. The blue nodes are the individual industries. The label “ExIy” should read “Industry y in Econoomy x”. The red nodes are the value added sources from the two economies, whereas the green nodes are the final demand destinations in the two economies. The label “Vx” should read “Value Added from Economy x”, whereas the label “Fx” should read “Final Demand in Economy x”. The edges are with arrows indicating the directions of the monetary goods flows and with varying widths indicating the magnitudes of the flows. Finally, because we are only concerned with the inter-industrial input-output relationships, when formulating the WION, we focus our attention on the network among the blue nodes.
Fig 2.
Each node represents a certain industry in a certain economy. The size of the node is proportional to its total degree (number of edges). The edges are directed and only those with strength greater than 1000 millions of US dollars are present. Finally, different colors represent different economies.
Fig 3.
Assortativity of the WION over time.
In Panel (A), from top to bottom, we show the over time out-degree assortativity, in-degree assortativity, and total-degree assortativity, respectively. Panel (B) compares the total-degree assortativity calculated from the original WION with that calculated from its random counterpart which preserves the degree distribution of the original network. For each year the random counterpart is simulated for 50 times and the 95% confidence interval is shown. Therefore, even with small magnitude, the assortativity coefficients are nevertheless statistically significant.
Fig 4.
Foreign Share of the Intermediate Transactions.
We calculate the foreign share of the transactions matrix Z over time. We calculate the percentage of inputs from foreign origins (or equivalently, the percentage of outputs to foreign destinations) of the transactions matrix Z of the 40 WIOD economies. The same hump-shaped behavior over time is observed here as in assortativity and clustering coefficient.
Fig 5.
Clustering coefficient of the WION over time.
Panel (A) shows the average weighted clustering coefficient of the WION over time. Panel (B) further decomposes the clustering coefficient into domestic clustering coefficient and foreign clustering coefficient. Clearly the behavior in Panel (A) is more explained by the foreign clustering coefficient.
Fig 6.
Histogram of in-degree, out-degree, and total-degree distributions for selected years.
For the selected years 1995, 2003, and 2011, the first row has the in-degree distributions while the second row and the third row have the out-degree and total-degree distributions respectively. The WION is characterized by the highly left-skewed degree distributions. Most nodes enjoy high-degree connections in the WION due to the aggregated industry classification.
Fig 7.
Empirical counter-cumulative distribution functions of in-strength, out-strength, and total-strength for selected years.
For the selected years 1995, 2003, and 2011, the first row has the in-strength distributions while the second row and the third row have the out-strength and total-strength distributions respectively. The observed data are in black circles while the green curve is the fitted log-normal distribution.
Fig 8.
Community detection and community core detection results in 1995.
The economies are arranged by rows and the industries are arranged by columns. Each color represents a community detected, except that the black color indicates the isolated nodes with only self-loop. Within each community, the top 3 core economy-industry pairs are identified. The first place is with thick and solid border. The second place is with thick and dashed border. The third place is with border and texture.
Fig 9.
Community detection and community core detection results in 2003.
The economies are arranged by rows and the industries are arranged by columns. Each color represents a community detected, except that the black color indicates the isolated nodes with only self-loop. Within each community, the top 3 core economy-industry pairs are identified. The first place is with thick and solid border. The second place is with thick and dashed border. The third place is with border and texture.
Fig 10.
Community detection and community core detection results in 2011.
The economies are arranged by rows and the industries are arranged by columns. Each color represents a community detected, except that the black color indicates the isolated nodes with only self-loop. Within each community, the top 3 core economy-industry pairs are identified. The first place is with thick and solid border. The second place is with thick and dashed border. The third place is with border and texture.
Fig 11.
Regional clustering coefficient and intra-region foreign share of the foreign intermediate transactions over time.
Panel (A) shows the average weighted clustering coefficient over time for three regions, EU27 (i.e., “Euro-Zone” and “Non-Euro EU” in S1 Table), NAFTA (see S1 Table), and East Asia (see S1 Table). EU27 and NAFTA have higher coefficients than East Asia and EU27 has an increasing trend over time, which coincides with the detection of the growing European community led by Germany. Panel (B) considers the intra-region foreign share out of the total foreign intermediate transactions for the same three regions. EU27 relies on the intra-region foreign trade the most and East Asia the least. Moreover, while the intra-region share in the other two regions is roughly stable, it has a clear decreasing trend in EU27.
Table 2.
Top 20 industries identified by the four methods for selected years.
The first is the Laumas method of backward linkages, w. The second is the eigenvector method of backward linkages, e. The third is PageRank centrality, PR. The fourth is community coreness measure ∣dQ∣.
Table 3.
Correlation coefficient matrix among the four key-industry-identification methods for selected years.
The first is the Laumas method of backward linkages, w. The second is the eigenvector method of backward linkages, e. The third is PageRank centrality, PR. The fourth is community coreness measure ∣dQ∣. ** and * mean that the coefficient is significant at 1% level and at 5% level respectively.