The rise and fall of countries in the global value chains

Countries become global leaders by controlling international and domestic transactions connecting geographically dispersed production stages. We model global trade as a multi-layer network and study its power structure by investigating the tendency of eigenvector centrality to concentrate on a small fraction of countries, a phenomenon called localization transition. We show that the market underwent a significant drop in power concentration precisely in 2007 just before the global financial crisis. That year marked an inflection point at which new winners and losers emerged and a remarkable reversal of leading role took place between the two major economies, the US and China. We uncover the hierarchical structure of global trade and the contribution of individual industries to variations in countries’ economic dominance. We also examine the crucial role that domestic trade played in leading China to overtake the US as the world’s dominant trading nation. There is an important lesson that countries can draw on how to turn early signals of upcoming downturns into opportunities for growth. Our study shows that, despite the hardships they inflict, shocks to the economy can also be seen as strategic windows countries can seize to become leading nations and leapfrog other economies in a changing geopolitical landscape.


NACE Rev. 2 Division
Description of economic activities A01 Crop and animal production, hunting and related service activities A02 Forestry and logging A03 Fishing and aquaculture B Mining and quarrying C10-C12 Manufacture of food products, beverages and tobacco products C13-C15 Manufacture of textiles, wearing apparel and leather products C16 Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials C17 Manufacture of paper and paper products C18 Printing and reproduction of recorded media C19 Manufacture of coke and refined petroleum products C20 Manufacture of chemicals and chemical products C21 Manufacture of basic pharmaceutical products and pharmaceutical preparations C22 Manufacture of rubber and plastic products C23 Manufacture of other non-metallic mineral products C24 Manufacture of basic metals C25 Manufacture of fabricated metal products, except machinery and equipment C26 Manufacture of computer, electronic and optical products C27 Manufacture of electrical equipment C28 Manufacture of machinery and equipment n.e.c. C29 Manufacture of motor vehicles, trailers and semi-trailers C30 Manufacture of other transport equipment C31 C32 Manufacture of furniture; other manufacturing C33 Repair and installation of machinery and equipment D35 Electricity, gas, steam and air conditioning supply E36 Water collection, treatment and supply E37-E39 Sewerage; waste collection, treatment and disposal activities; materials recovery; remediation activities and other waste management services F Construction G45 Wholesale and retail trade and repair of motor vehicles and motorcycles G46 Wholesale trade, except of motor vehicles and motorcycles G47 Retail trade, except of motor vehicles and motorcycles H49 Land transport and transport via pipelines H50 Water transport H51 Air transport H52 Warehousing and support activities for transportation H53 Postal and courier activities I Accommodation and food service activities J58 Publishing activities J59 J60 Motion picture, video and television program production, sound recording and music publishing activities; programming and broadcasting activities J61 Telecommunications Continued on next page Supplementary Hierarchical structure of the multi-layer network

A) B)
Supplementary Fig. 1. Hierarchical structure of the multi-layer network. Matrix plot of the correlation distance among all pairs of time series of eigenvector centrality for buyers (A) and sellers (B). The color of each cell is proportional to the correlation distance between the corresponding time series. The dendrograms associated with this matrix show the hierarchical clustering based on Ward's minimum variance method. The colored squares located below the dendrogram branches indicate the clusters obtained by cutting the dendrogram at the threshold distance that maximizes the silhouette score. The buyers' distance matrix has 6 clusters, whereas the sellers' distance matrix only 4 clusters.

Hierarchical (nested) stochastic block model
In addition to the hierarchical clustering analysis of the time series, we considered the hierarchical (nested) stochastic block model (nested SBM) to find the economic blocs 1 . We computed the modular/block structure of the network obtained from the correlation distance matrix of the time series θ i (t) of eigenvector centralities. In this network, each node is a country and the weights of links are the correlation distances d i j between the time series of countries i and j. To run the nested SBM algorithm, we considered normal priors for the weight distribution and collected the partitions for 10, 000 sweeps of a Metropolis-Hastings acceptance-rejection Markov Chain Monte Carlo 2 with multiple moves to sample hierarchical network partitions, at intervals of 10 sweeps. The block structure obtained with the hierarchical (nested) SBM for buyers and sellers are shown in Supplementary  Figure 2A and Supplementary Figure 2B, respectively. The different colors represent the economic blocs and the adjacency edges are bundled together for a better visualization of the network hierarchical structure. We further estimated the marginal probabilities of node membership using the fraction of times a node is found in a given partition on our sampled partitions data. In Supplementary Figure 2, the pie charts illustrate the marginal probabilities (fractions of occurrence on the sampled data) that a given node belongs to a partition.
We next compared the results of the nested SBM with the results obtained with the hierarchical clustering analysis of the time series. To do so, we use the normalized mutual information (NMI) to quantify the overlap between the clusters found with the two approaches. Results suggest a great overlap between the results found with the two approaches. The NMI is ≈ 0.7 for the buyers, and ≈ 0.6 for sellers, thus highlighting the robustness of our findings.

A) B) Buyers Sellers
Supplementary Fig. 2. Hierarchical modular structure of the correlation network and marginal probabilities of node membership. In this representation, nodes represent countries, and the pie divisions represent the marginal posterior probability that a node belongs to a given group (the different colors). The probabilities were obtained by collecting the node membership for 10, 000 sweeps of a Metropolis-Hastings acceptance-rejection Markov Chain Monte Carlo with multiple moves to sample hierarchical network partitions, at intervals of 10 sweeps. The edges and their weights are proportional to the correlation distance of the eigenvalue time series θ i (t) and θ j (t) associated with country i and j. A) Modular structure of buyers' correlation network shows a great overlap with the hierarchical cluster analysis (NMI≈ 0.7). B) Similarly, the modular structure of sellers' correlation network shows a great overlap with the hierarchical cluster analysis (NMI≈ 0.6).

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Fraction of purchases and sales by economic bloc

Mean geodesic distance within and between blocs
Economic bloc Within-bloc mean distance Between-bloc mean distance Mean geodesic distance between buyers. The first column indicates the economic blocs of buyers. The second column shows the mean geodesic distance (computed using the geographical centroid of countries) between countries within the same economic bloc. The third column shows the mean distance between each country within a given bloc and all the other countries not in the bloc. Notice that since bloc no. 6 includes only one country, the mean distance is 0. Except for the largest cluster (i.e., economic bloc no. 1), for all the other clusters of buyers within-bloc distances are smaller than between-bloc distances.
Economic bloc Within-bloc mean distance Between-bloc mean distance Mean geodesic distance between sellers. The first column indicates the economic bloc of sellers. The second column shows the mean geodesic distance (computed using the geographical centroid of countries) between countries within the same economic bloc. The third column shows the mean distance between each country within a given bloc and all the other countries not in the bloc. For all clusters of sellers, within-bloc distances are smaller than between-bloc distances.

C) D)
Supplementary Fig. 13. IPR computed on real multi-layer networks compared with the IPR obtained from synthetic random multi-layer network realizations. A) Ratio IPR/ IPR random for buyers (red circles). B) Ratio IPR/ IPR random for sellers (red circles). If localization observed in the real network can be replicated using random synthetic multi-layer networks, the ratio is close to one (black dashed lines). Panels A and B suggest that the values of IPR, respectively for buyers and sellers, are almost three times as large as the average values found on the ensembles of random synthetic multi-layer networks. Panels C and D report the confidence intervals for IPR random , based on 1, 000 realizations, respectively for buyers and sellers. All values of the observed IPR are statistically significantly different from IPR random at the 5% significance level. The box-plot panels show the values from the ensembles of random network realizations for buyers (C) and sellers (D), and also include the values of the IPR observed in the real networks (red circles). Each blue box represents the two innermost quartiles. The whiskers represent the 95% confidence intervals, the red horizontal lines are the medians, and the small black dots are outliers of the ensembles of synthetic random multi-layer networks.

A) B) C)
Supplementary Fig. 15. Evolution of countries' international trade and domestic trade. The US has always secured the largest share of imports (A) and exports (B), while Germany ranked second, and in 2007 China overtook other countries reaching the third position. While Japan was characterized by a significant share of global domestic trade, its share of international trade did not rank as high as the other major countries' share. C) Domestic trade significantly increased in China during the observation period, whereas countries such the US, Germany, and Japan witnessed a much smaller growth.