World Input-Output Network

World Input-Output Network

Abstract

Economic systems, traditionally analyzed as almost independent national systems, are increasingly connected on a global scale. Only recently becoming available, the World Input-Output Database (WIOD) is one of the first efforts to construct the multi-regional input-output (MRIO) tables at the global level. By viewing the world input-output system as an interdependent network where the nodes are the individual industries in different economies and the edges are the monetary goods flows between industries, we study the network properties of the so-called world input-output network (WION) and document its evolution over time. We are able to quantify not only some global network properties such as assortativity, clustering coefficient, and degree and strength distributions, but also its subgraph structure and dynamics by using community detection techniques. Over time, we detect a marked increase in cross-country connectivity of the production system, only temporarily interrupted by the 2008-2009 crisis. Moreover, we find a growing input-output regional community in Europe led by Germany and the rise of China in the global production system. Finally, we use the network-based PageRank centrality and community coreness measure to identify the key industries and economies in the WION and the results are different from the one obtained by the traditional final-demand-weighted backward linkage measure.

Complex Networks; Input-Output; PageRank Centrality; Community Detection
pacs:
89.65.Gh; 89.75.-k; 05.10.-a

I Introduction

As the global economy becomes increasingly integrated, an isolated view based on the national input-output table1 is no longer sufficient to assess an individual economy’s strength and weakness, not to mention finding solutions to global challenges such as climate change and financial crises. Hence, a multi-regional input-output (MRIO) framework is needed to draw a high-resolution representation of the global economy wiedmann2011quo (). In practice, however, due to the expensive process of collecting data and the variety of classifications used by different agencies, for a long time, the input-output tables have only been available for a limited number of countries and for discontinuous years. Fortunately, the fully-fledged MRIO databases started to become available in recent years2.

Unlike the national input-output table where exports and imports are aggregated and appended to final demand and country-specific value added respectively, for each individual economy, the MRIO table splits its exports into intermediate use and final use in every foreign economy and also traces its imports back to the industry origins in every foreign economy. As a result, the inter-industrial relationships in the MRIO table are recorded not only within the same economy but also across economies.

The availability of the MRIO databases was soon followed by a wave of empirical studies of topics ranging from global value chains and trade fragmentation in economics baldwin2013supply (); timmer2013fragmentation (); koopman2014tracing () to global environmental accounting in ecology and resources management lenzen2012international (); lenzen2013international (); wiedmann2013material (). However, to the best of our knowledge, our paper is the first attempt to explore the MRIO tables from a networks perspective, even though there have been some networks studies of the input-output tables at the national level and for selected countries blochl2011vertex (); mcnerney2013network (); contreras2014 ().

Complex networks are a modern way to characterize mathematically a series of different systems in the shape of subunits (nodes) connected by their interaction (edges) ABRMP (); SIAM (). Such modeling has been proved to be fruitful for the description of a variety of different phenomena ranging from biology GCbook2 () to economics kitsak2010 (); pammolli2002 (); riccaboni2010 (); riccaboni2013 (); chessa2013 () and finance nature (). Here we move forward by considering the global MRIO system as a world input-output network (WION), where the nodes are the individual industries in different economies and the edges are the monetary goods flows3 between industries, similarly to what have been done recently by Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi for the US economy only acemoglu2012network ().

Different from many network systems observed in reality, the WION has the following features: 1) It is directed and weighted, i.e., an industry can act as both a seller and a buyer at the same time and the monetary goods flows between industries vary a lot; 2) It is much denser within the same economy than across economies, i.e., despite the continuously integrated global economy, most economic transactions still happen within the country border;4 3) It is with strong self-loops, i.e., an industry can acquire a significant amount of inputs from itself5.

Taking into account the features above, we explore the WION by quantifying not only some global network properties such as assortativity but also some local network properties such as PageRank centrality. Furthermore, we apply community detection and community core detection techniques to examine the structure of the WION over time.

This paper makes some significant contributions to the literature of input-output economics. First, it is the first attempt to quantify the network properties of the WION by taking into account its edge weights and directedness6. By doing that, we detect a marked increase in cross-country connectivity, apart from a sharp drop in 2009 due to the financial crisis. Second, the community detection results reveal growing input-output international communities. Among them, we notice in particular the emergence of a large European community led by Germany. Third, we use the network-based PageRank centrality and community coreness measure to identify the key industries and economies in the WION and the results are different from the one obtained by the traditional final-demand-weighted backward linkage measure.

The rest of the paper is structured as follows. Section II describes the database used and the MRIO framework. We also conduct a basic MRIO analysis to identify the key industries at the global level in this section. Section III quantifies some global network properties of the WION and its subgraph structure and dynamics by using community detection techniques. Moreover, we use the network-based PageRank centrality and community coreness measure to identify the key industries in the WION. Finally, Section IV concludes the paper.

Ii The Data Description and the Leontief-Inverse-Based Method of Identifying the Key Industries

ii.1 The WIOD Data and the MRIO Framework

We use the World Input-Output Database (WIOD) timmer2012world () to map out the WION. At the time of writing, the WIOD input-output tables cover 35 industries for each of the 40 economies (27 EU countries and 13 major economies in other regions) plus the rest of the world (RoW) and the years from 1995 to 20117. For each year, there is a harmonized global level input-output table recording the input-output relationships between any pair of industries in any pair of economies8. The numbers in the WIOD are in current basic (producers’) prices and are expressed in millions of US dollars9. Table LABEL:table_1 shows an example of a MRIO table with two economies and two industries. The inter-industry table is called the transactions matrix and is often denoted by . The rows of record the distributions of the industry outputs throughout the two economies while the columns of record the composition of inputs required by each industry. Notice that in this example all the industries buy inputs from themselves, which is often observed in real data. Besides intermediate industry use, the remaining outputs are absorbed by the additional columns of final demand, which includes household consumption, government expenditure, and so forth10. Similarly, production necessitates not only inter-industry transactions but also labor, management, depreciation of capital, and taxes, which are summarized as the additional row of value added. The final demand matrix is often denoted by and the value added vector is often denoted by . Finally, the last row and the last column record the total industry outputs and its vector is denoted by .

ii.2 The Leontief-Inverse-Based Method of Identifying the Key Industries

If we use to denote a summation vector of conformable size, i.e., a vector of all 1’s with the length conformable to the multiplying matrix, and let , we then have . Furthermore, if dividing each column of by its corresponding total output in , we get the so-called technical coefficients matrix 11. Replacing with , we rewrite the above equation as . It can be rearranged as . Finally, we can solve as follows:

(1)

where matrix is often denoted by and is called the Leontief inverse.

The intuition behind the Leontief inverse is that an increase in the final demand of an industry’s output will induce not only more production from the industry itself but also more from other related industries because more inputs are required. Therefore, the Leontief inverse takes into account both the direct and indirect effects of a demand increase. For instance, measures the total output produced in Industry given a one-unit increase in Industry ’s final demand12. As a result, sums up each column of and each sum measures the total output of all the industries given a one-unit increase in the corresponding industry’s final demand. The vector is called the backward linkage measure13 and can be used to rank the industries and identify the key ones in the economy yotopoulos1973balanced (). However, as pointed out by Laumas laumas1976weighting (), the key assumption embedded in the backward linkage measure is that every industry is assigned with the same weight (or unweighted), which is far from the reality. The problem with the unweighted backward linkage measure can be demonstrated by using the hypothetical data from Table LABEL:table_1. The calculated is , which considers the industries in Economy 1 more important than the ones in Economy 2, despite the fact that Economy 2 is a lot larger than Economy 1 in terms of total outputs.

The industries of the 40 economies covered in the WIOD are very heterogeneous in terms of both total outputs and technical structure, which certainly makes the unweighted backward linkage measure not a good choice to identify the most central industries on a global scale. In order to identify the key industries in the WIOD, we hence follow Laumas laumas1976weighting () and use the final-demand-weighted backward linkage measure, which is denoted by and is defined here as the Hadamard (element-wise) product of the vector of the unweighted backward linkage measure and the vector of the percentage shares of the total final demand across industries, i.e.,

(2)

where is the element-wise multiplication operator.

Table 1 shows the top 20 industries for the years 1995, 2003, and 2011, respectively. The first column of each year is produced by the final-demand-weighted backward linkage measure, i.e., . For the selected years, only four large economies, China, Germany, Japan, and USA, ever qualified for the top 20. Another noticeable change over time is the rise of China, which topped the list in 2011 with its industry of construction.

Tables A3 and A4 in the appendix provide an alternative way of viewing the key industries and economies over time identified by the final-demand-weighted backward linkage measure. In particular, Table A3 lists the most important economies by industry while Table A4 lists the most important industries by economy.

Iii The Network Properties of the WION and the Network-Based Methods of Identifying the Key Industries

As mentioned in Section I, the complex networks approach has been widely used in economics and finance in recent years kitsak2010 (); pammolli2002 (); riccaboni2010 (); riccaboni2013 (); chessa2013 (); nature (). Designed to keep track of the inter-industrial relationships, the input-output system is an ideal test bed for network science. Particularly the MRIO system can be viewed as an interdependent complex network, i.e., the WION, where the nodes are the individual industries in different economies and the edges are the flows between industries.

Figure LABEL:table1Net provides a topological view of Table LABEL:table_1. The blue nodes are the individual industries. 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 edges are with arrows indicating the directions of the monetary goods flows14 and with varying widths indicating the magnitudes of the flows. The color of the edge is set the same as the source node’s. 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.

1995 2003 2011
Rank
1 USA-Pub USA-Pub USA-Pub USA-Pub USA-Hth USA-Obs CHN-Cst GBR-Hth CHN-Cst
2 JPN-Cst USA-Tpt JPN-Cst USA-Hth DEU-Tpt USA-Est USA-Pub DEU-Tpt USA-Obs
3 USA-Cst DEU-Tpt USA-Obs USA-Cst USA-Pub USA-Fin USA-Hth USA-Pub CHN-Met
4 USA-Hth USA-Hth USA-Cst USA-Est USA-Tpt USA-Pub USA-Est CHN-Elc USA-Pub
5 USA-Est DEU-Cst USA-Est USA-Rtl GBR-Hth USA-Hth CHN-Elc USA-Hth USA-Est
6 USA-Rtl RUS-Hth USA-Hth CHN-Cst ESP-Cst CHN-Cst USA-Rtl CHN-Cst CHN-Agr
7 USA-Fod DEU-Fod JPN-Htl JPN-Cst DEU-Hth JPN-Cst USA-Cst CHN-Met CHN-Fod
8 JPN-Pub GBR-Cst JPN-Met USA-Fin GBR-Cst USA-Ocm USA-Fin USA-Tpt USA-Fin
9 USA-Tpt USA-Cst USA-Met USA-Tpt USA-Cst CHN-Met CHN-Fod ESP-Cst CHN-Min
10 JPN-Est FRA-Tpt JPN-Obs USA-Fod USA-Obs USA-Met CHN-Mch AUS-Cst USA-Cok
11 JPN-Hth USA-Fod DEU-Cst USA-Htl FRA-Tpt JPN-Obs JPN-Cst ITA-Hth CHN-Elc
12 USA-Fin GBR-Hth JPN-Pub USA-Ocm TUR-Tex JPN-Htl USA-Fod DEU-Hth USA-Hth
13 USA-Htl USA-Obs JPN-Hth JPN-Pub USA-Est CHN-Agr USA-Htl USA-Obs CHN-Omn
14 JPN-Fod JPN-Cst JPN-Ocm USA-Obs AUS-Cst USA-Cst CHN-Tpt RUS-Hth CHN-Cok
15 JPN-Rtl DEU-Mch JPN-Fod JPN-Est USA-Fod JPN-Pub JPN-Pub CHN-Tpt CHN-Mch
16 DEU-Cst ESP-Cst JPN-Fin JPN-Hth ITA-Hth USA-Agr USA-Tpt DEU-Mch USA-Cst
17 JPN-Elc JPN-Tpt USA-Agr USA-Whl DEU-Cst USA-Tpt USA-Ocm FRA-Cst CHN-Chm
18 JPN-Whl DEU-Met USA-Fod JPN-Tpt DEU-Fod JPN-Met CHN-Pub CHN-Tex JPN-Obs
19 JPN-Tpt USA-Elc JPN-Whl CHN-Elc DEU-Mch JPN-Hth USA-Obs GBR-Cst USA-Ocm
20 JPN-Mch USA-Est USA-Pup DEU-Tpt CHN-Elc CHN-Elc USA-Whl DEU-Met JPN-Cst
Table 1: Top 20 industries identified by the three methods for selected years. The first method is the final-demand-weighted backward linkage measure, . The second is the PageRank centrality, . The third is the community coreness measure .

The visualization of the WION in 1995 (Figure 1(a)) and 2011 (Figure 1(b)) are shown in Figure 1. Each node represents a certain industry in a certain economy. The size of the node is proportional to its total degree. The edges are directed and only those with strength greater than one billion US dollars are present. Finally, different colors represent different economies. Clearly the WION has become denser over time and some countries like China have moved to the core of the network, thus confirming the results in Table 1.

(a) 1995
(b) 2011
Figure 1: The WION in 1995 and 2011. 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.

In this section, we first examine some global network properties of the WION such as assortativity, clustering coefficient, and degree and strength distributions. We also study the subgraph structure and dynamics of the WION by using community detection techniques. Finally, we use the network-based PageRank centrality and community coreness measure to identify the key industries and economies in the WION and the results are different from the one obtained by the above Leontief-inverse-based method.

iii.1 The Global Network Properties of the WION

Because the WION is directed, we can calculate the assortativity coefficient in three ways, namely, in-degree assortativity, out-degree assortativity, and total-degree assortativity. As shown in Figure 2, they all behave similarly over time. First, they have all been negative throughout the whole period. Since assortativity measures the tendencies of nodes to connect with other nodes that have similar (or dissimilar) degrees as themselves, a negative coefficient means that dissimilar nodes are (slightly15) more likely to be connected.16 One possible explanation of the negativity is that high-degree industries such as construction often take inputs (or supply outputs) from (or to) low-degree industries such as transport services. Moreover, the spatial constraints (each node has only few neighboring nodes in the same country) introduce degree-degree anticorrelations (disassortativity) since high degree sectors are in different countries and the probability to connect decays with distance havlin2014 (). Second, all the coefficients show an increasing trend before 2007 and a significant decline after 2007. The behavior of the assortativity measures seems to be correlated with the trend of the foreign share in the inter-industrial transactions over time (Figure 3(a)). That is, we can calculate a globalization indicator as the percentage of inputs from foreign origins (or equivalently, the percentage of outputs to foreign destinations) of the transactions matrix of the 40 WIOD economies. Same as observed in assortativity, the foreign share of had a steady growth (from 9.9% in 1995 to 12.8% in 2007) before 2007 and a sharp decrease after 200717. The increase in the foreign share implies more interactions across economies and hence tends to make the WION less dissortative. The opposite happens when the foreign share goes down as a result of the global financial crisis. Third, we notice that the in-degree assortativity tends to be lower than the out-degree assortativity, but there is a tendency to close the gap between the two measures. We interpret this evidence as a clear signal of the globalization of production chains, that is to say, both global buying and selling hubs have now a higher chance to be connected across borders.

Figure 2: Assortativity of the WION over time. From top to bottom, we show the over time out-degree assortativity, in-degree assortativity, and total-degree assortativity, respectively.
(a) All 40 Economies
(b) Selected Regions
Figure 3: Globalized WION. Figure 3(a) shows the foreign share of the transactions matrix over time. We calculate the percentage of inputs from foreign origins (or equivalently, the percentage of outputs to foreign destinations) of the transactions matrix of the 40 WIOD economies. It can be viewed as a globalization indicator becasue it measures how much inter-industrial transactions are made through international trade. Figure 3(b) considers the intra-region foreign share out of the total foreign share for some regions classified in Table A1 in the appendix. For the three regions, Euro Zone 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 fluctuates over time, it almost always declines in Euro Zone. Finally, all the three regions became less dependent on the intra-region foreign trade before the 2008 crisis. After the crisis, East Asia increased the intra-region foreign trade immediately, which is followed by NAFTA, and then by Euro Zone.

The hump-shaped behavior is also observed in the clustering coefficient. Figure 4(a) shows that the average weighted clustering coefficient of the WION has been steadily increasing but was followed by a decline since 2007. Again, a possible explanation is that the booming economy before 2007 introduced more interactions between industries, hence higher clustering coefficient, and the financial crisis after 2007 stifled the excess relationships.

(a) Clustering Coefficient
(b) Domestic and Foreign
Figure 4: Clustering coefficient of the WION over time. Figure 4(a) shows the average weighted clustering coefficient of the WION over time. Figure 4(b) further decomposes the clustering coefficient into domestic clustering coefficient and foreign clustering coefficient. Clearly the behavior in Figure 4(a) is more explained by the foreign clustering coefficient.

We can also examine the global network properties of the WION by plotting its degree and strength distributions. Recall that the transactions matrix is essentially a weighted adjacency matrix, which records the edge weights between any pair of nodes in the WION. If we denote the regular binary adjacency matrix as , where if either or , then we have the following definitions for a given node : 1) In-degree: ; 2) Out-degree: ; 3) Total-degree: ; 4) In-strength: ; 5) Out-strength: ; 6) Total-strength: .

As shown in Figure 5, unlike other network systems such as the internet, where the degree distributions follow the power law, the WION is characterized by the highly left-skewed degree distributions. Most nodes enjoy high-degree connections in the WION because the industries are highly aggregated. That is, it is hard to find two completely disconnected industries given the high level of aggregation. Furthermore, the WION is almost complete, i.e., every node is connected with almost every node, if represented by unweighted edges18.

Figure 5: 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.

We can also take into account the edge weights and examine the strength distributions of the WION. Figure 6 shows the in-strength, out-strength, and total-strength distributions for the years 1995, 2003, and 2011. We perform Gabaix-Ibragimov test gabaix2009power (); gabaix2011rank () to see if the tails of the distributions are Pareto but find no significant power-law tails. Moreover, like the previous studies at the national level mcnerney2013network (), the strength distributions can be well approximated by the log-normal distributions. As reasoned by Acemoglu et al. acemoglu2012network (), this asymmetric and heavy-tailed distribution of strength in the WION may serve as the origin of economic fluctuations.

Figure 6: 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.

iii.2 The Community Detection in the WION

Another main property of networks is the community structure, i.e. the partition of a network into clusters, with many edges connecting nodes in the same cluster and few connecting nodes between different ones fortunato2010 (). In the following we use the modularity optimization method introduced by Newman and Girvan newman2004finding (). It is based on the idea that a random graph is not expected to have a community structure. Therefore, the possible existence of clusters is revealed by the comparison between the actual density of edges in a subgraph and the expected density if the nodes are attached randomly. The expected edge density depends on the chosen null model, i.e., a copy of the original graph keeping some of its structural properties but without community structure fortunato2010 ().

The most popular null model, introduced by Newman and Girvan newman2004finding (), keeps the degree sequence and consists of a randomized version of the original graph, where edges are rewired at random, under the constraint that the expected degree of each node matches the degree of the node in the original graph.

The modularity function to be optimized is, then, defined as:

(3)

where the summation operator runs over all the node pairs. is the adjacency matrix, and is the total number of edges. The function equals 1 if the two nodes and are in the same community and 0 otherwise. Finally, is the probability of the presence of an edge between the two nodes and in the randomized null model.

Figures 7, 8, and 9 report the community detection results for the selected years 1995, 2003, and 2011, respectively19. The 40 countries in the WIOD are arranged by rows while the 35 industries are arranged by columns. Different colors indicate different communities detected. There are two interesting findings in our results. First, most communities were based on a single economy, i.e., the same color often goes through a single row. This echoes one of the features of the WION mentioned in Section I, i.e., most of the inter-industrial activities are still restricted in the country border. Second, for all the three years selected, we always color the community involving Germany in red and put it on the top. As a result, our algorithm captures a growing Germany-centered20 input-output community.

Figure 7: 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.
Figure 8: 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.
Figure 9: 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.

Since the WIOD monetary goods flows are based on undeflated current prices, one possible reason for the emergence of the German community is that the community members may have experienced significantly more inflation and/or exchange rate volatility than other regions in the world. Referring to the World Bank inflation data and the exchange rate data used in the WIOD, we show that this is hardly the case. Panel (a) of Figure A1 in the appendix compares the average inflation rate, i.e., the annual GDP deflator, across all the WIOD economies21 with the average annual GDP deflator across the 9 major member economies in the German community detected in 2011, i.e., Germany, Austria, Belgium, Luxembourg, Hungary, Czech Republic, Slovakia, Slovenia, and Poland. During 1995-2011, the average inflation of the German community was almost always below that of all the WIOD economies. Panel (b) of Figure A1 in the appendix compares the average exchange rate, i.e., US dollars per unit of local currency, across all the WIOD economies22 with the average exchange rate across the above 9 major economies in the German community detected in 2011. The average exchange rate of the German community was basically below that of all the WIOD economies before 2000. Only from 2001, the community average became slightly (no more than 16%) higher than the overall average. Therefore, the emergence of the German community cannot be attributed to inflation or exchange rate dynamics. Since most of the 40 economies in the WIOD are in Europe, we cannot rule out the possibility that similar regional input-output communities are emerging in other continents. Indeed, we find also an integrated NAFTA community in North America. However, since many Asian economies are not included in the WIOD, we cannot argue if a similar trend is ongoing in the Far East.

Within each community, we also carry out the community core detection (see below for more technical details). In Figures 7-9, we identify the top 3 core economy-industry pairs for each community. 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. In general, the cores are mostly concentrated in the industries of agriculture (1), mining (2), food (3), metals (12), construction (18), and financial, business, and public services (28-31). Over time, while the services industries (28-31) have become the cores in more and more developed economies, the primary industries (1-3) have become less central in the developed economies and have only remained as the cores in a few emerging economies, which is consistent with the Kuznets facts kuznets1957quantitative (); kuznets1973modern (). Furthermore, for the growing community centered on Germany, the cores are always identified in Germany (that is why we simply call it the German community) for the three selected years. It is also worth noting that, the German industry of transport equipment (15) is identified as a core in 2011 and the car industry is the most integrated in the German community, which spans over 17 economies.

iii.3 The Network-Based Methods of Identifying the Key Industries

Since on a global scale the traditional assumption of stable input-output technical coefficients is violated due to the dynamics of international trade, the traditional final-demand-weighted backward linkage measure alone is insufficient to evaluate the importance of any given industry on the global economy. However, the networks approach provides us a holistic view of the global production system and we can compute various centrality measures to compare the nodes in the network. Here we focus on two network-based methods of identifying the key industries in the WION, PageRank centrality23 and community coreness measure.

PageRank Centrality

Given a network, it is a problem of capital importance to bring order to its structure by ranking nodes according to their relevance. Among the many proposed, a successful and widely used centrality measure is PageRank page1999pagerank (), a Google patented method. The idea is that the nodes are considered important if they are connected by other important nodes.

Since the WION is weighted, we use a weighted version of PageRank, which is computed iteratively as follows:

  1. At , an initial probability distribution is assumed, usually where is the total number of nodes;

  2. At each time step, the PageRank of node is computed as:

    (4)

    where are the in-neighbors of , is the weight of the link between the nodes and , is the sum of the weights of the outgoing edges from , and the damping factor is set to its default value, 0.85.

In Table 1, the second column of each year is produced by the PageRank centrality, which is denoted by .24 Unlike the final-demand-weighted backward linkage measure, where only 4 economies are among the top 20, the PageRank centrality recognizes 10 economies in the top 20 list for the three selected years.

Tables A5 and A6 in the appendix provide an alternative way of viewing the key industries and economies over time identified by the PageRank centrality. In particular, Table A5 lists the most important economies by industry while Table A6 lists the most important industries by economy.

Community Coreness Measure

The other network-based method of identifying the key industries is the community coreness measure. Nodes of a community do not have the same importance for the community stability: the removal of a node in the core of the community affects the partition much more than the deletion of a node that stays on the periphery of the community deleo2013 (). Therefore, in the following we define a novel way of detecting cores inside communities by using the properties of the modularity function III.2.

By definition, if the modularity associated with a network has been optimized, every perturbation in the partition leads to a negative variation in the modularity, . If we move a node from its community, we have possible choices, with as the number of communities, as the node’s new host community. It is possible to define the associated with each node as the smallest variation in absolute value (or the closest to 0 since is always a negative number) of all the possible choices. We call the community coreness measure.

In the WION, once we have the for each industry, we can consider the one with the biggest the most important. We can also normalize the to identify the most important nodes within each community. The results are shown in Figures 7, 8, and 9, where the first place in each community is with thick and solid border, the second place is with thick dashed border, and the third place is with both border and texture.

In Table 1, the third column of each year is produced by the community coreness measure, which is denoted again by . Interestingly, like the final-demand-weighted backward linkage measure, the community coreness measure also only includes China, Germany, Japan, and USA in the top 20 list for the selected years.

Tables A7 and A8 in the appendix provide an alternative way of viewing the key industries and economies over time identified by the community coreness measure. In particular, Table A7 lists the most important economies by industry while Table A8 lists the most important industries by economy.

Now we have totally three methods to identify the key industries in the WION, the traditional final-demand-weighted backward linkage measure, the PageRank centrality measure, and the community coreness measure. They have different results from each other. For instance, the industry of transport equipment in Germany is captured by the PageRank but not by the other two while the industry of other business activities in USA is more important by than by the other two (see Table 1). Table 2 reports the correlation coefficient matrix among the three methods for the selected years 1995, 2003, and 2011. We find that all the three methods are positively correlated, while and are correlated even more. Therefore, the network-based and especially can be used to complement, if not to substitute, to identify the key industries in the WION.

1995 2003 2011
1 0.664224 0.819625 1 0.688819 0.724121 1 0.64281 0.754442
0.664224 1 0.650459 0.688819 1 0.596233 0.64281 1 0.592057
0.819625 0.650459 1 0.724121 0.596233 1 0.754442 0.592057 1
Table 2: Correlation coefficient matrix among the three key-industry-identification methods for selected years. The first method is the final-demand-weighted backward linkage measure, . The second is the PageRank centrality, . The third is the community coreness measure .

Iv Concluding Remarks

This paper investigates a MRIO system characterized by the recently available WIOD database. By viewing the world input-output system as an interdependent network where the nodes are the individual industries in different economies and the edges are the monetary goods flows between industries, we study the network properties of the so-called world input-output network (WION) and document its evolution over time. We are able to quantify not only some global network properties such as assortativity, clustering coefficient, and degree and strength distributions, but also its subgraph structure and dynamics by using community detection techniques. Over time, we trace the effects of globalization and the 2008-2009 financial crisis. We notice that national economies are increasingly interconnected in global production chains. Moreover, we detect the emergence of regional input-output community. In particular we see the formation of a large European community led by Germany. Finally, because on a global scale the traditional assumption of stable input-output technical coefficients is violated due to the dynamics of international trade, we also use the network-based PageRank centrality and community coreness measure to identify the key industries in the WION and the results are different from the one obtained by the traditional final-demand-weighted backward linkage measure.

As mentioned above, due to the limited coverage of the WIOD, we cannot argue if the input-output integration is also observed in other continents. Therefore, in our future work, we will utilize another MRIO database, EORA lenzen2012mapping (); lenzen2013building (), which covers about 187 countries in the world and the years from 1990 to 2011. Moreover, since each of the three methods of identifying the key industries captures a different aspect of the importance of any given industry, future work is also needed to compare the methods so as to identify the systematically important industries for the global economy.

V Acknowledgments

Authors thank Michelangelo Puliga for insightful discussions. All authors acknowledge support from the FET projects MULTIPLEX 317532 and SIMPOL 610704 and the PNR project CRISIS Lab. MR and ZZ acknowledge funding from the MIUR (FIRB project RBFR12BA3Y). FC gratefully acknowledges Sardinia Regional Government for the financial support of her PhD scholarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2007–2013 - Axis IV Human Resources, Objective l.3, Line of Activity l.3.1.).

*

APPENDIX

Euro-Zone Non-Euro EU NAFTA East Asia BRIIAT
Economy 3L Code Economy 3L Code Economy 3L Code Economy 3L Code Economy 3L Code
Austria AUT Bulgaria BGR Canada CAN China CHN Australia AUS
Belgium BEL Czech Rep. CZE Mexico MEX Japan JPN Brazil BRA
Cyprus CYP Denmark DNK USA USA South Korea KOR India IND
Estonia EST Hungary HUN Taiwan TWN Indonesia IDN
Finland FIN Latvia LVA Russia RUS
France FRA Lithuania LTU Turkey TUR
Germany DEU Poland POL
Greece GRC Romania ROM
Ireland IRL Sweden SWE
Italy ITA UK GBR
Luxembourg LUX
Malta MLT
Netherlands NLD
Portugal PRT
Slovakia SVK
Slovenia SVN
Spain ESP
Table A1: List of WIOD economies.
Full Name ISIC Rev. 3 Code WIOD Code 3-Letter Code
Agriculture, Hunting, Forestry and Fishing AtB c1 Agr
Mining and Quarrying C c2 Min
Food, Beverages and Tobacco 15t16 c3 Fod
Textiles and Textile Products 17t18 c4 Tex
Leather, Leather and Footwear 19 c5 Lth
Wood and Products of Wood and Cork 20 c6 Wod
Pulp, Paper, Paper , Printing and Publishing 21t22 c7 Pup
Coke, Refined Petroleum and Nuclear Fuel 23 c8 Cok
Chemicals and Chemical Products 24 c9 Chm
Rubber and Plastics 25 c10 Rub
Other Non-Metallic Mineral 26 c11 Omn
Basic Metals and Fabricated Metal 27t28 c12 Met
Machinery, Nec 29 c13 Mch
Electrical and Optical Equipment 30t33 c14 Elc
Transport Equipment 34t35 c15 Tpt
Manufacturing, Nec; Recycling 36t37 c16 Mnf
Electricity, Gas and Water Supply E c17 Ele
Construction F c18 Cst
Sale, Maintenance and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuel 50 c19 Sal
Wholesale Trade and Commission Trade, Except of Motor Vehicles and Motorcycles 51 c20 Whl
Retail Trade, Except of Motor Vehicles and Motorcycles; Repair of Household Goods 52 c21 Rtl
Hotels and Restaurants H c22 Htl
Inland Transport 60 c23 Ldt
Water Transport 61 c24 Wtt
Air Transport 62 c25 Ait
Other Supporting and Auxiliary Transport Activities; Activities of Travel Agencies 63 c26 Otr
Post and Telecommunications 64 c27 Pst
Financial Intermediation J c28 Fin
Real Estate Activities 70 c29 Est
Renting of M&Eq and Other Business Activities 71t74 c30 Obs
Public Admin and Defence; Compulsory Social Security L c31 Pub
Education M c32 Edu
Health and Social Work N c33 Hth
Other Community, Social and Personal Services O c34 Ocm
Private Households with Employed Persons P c35 Pvt
Table A2: List of WIOD industries.
(a) Inflation
(b) Exchange Rate
Figure A1: Average inflation rate and exchange rate. (a) shows the average inflation rate of all the 40 WIOD economies (except Taiwan and Bulgaria) versus the average inflation rate of the German community. We compare the average inflation rate, i.e., the annual GDP deflator, across all the WIOD economies (except Taiwan and Bulgaria) with the average annual GDP deflator across the 9 major member economies in the German community detected in 2011, i.e., Germany, Austria, Belgium, Luxembourg, Hungary, Czech Republic, Slovakia, Slovenia, and Poland. During 1995-2011, the average inflation of the German community was almost always below that of all the WIOD economies. The data source is the World Development Indicators, the World Bank, http://data.worldbank.org/indicator/NY.GDP.DEFL.KD.ZG. (b) shows the average exchange rate of all the 40 WIOD economies versus the average exchange rate of the German community. We compare the average exchange rate, i.e., US dollars per unit of local currency, across all the WIOD economies with the average exchange rate across the 9 major economies in the German community detected in 2011, i.e., Germany, Austria, Belgium, Luxembourg, Hungary, Czech Republic, Slovakia, Slovenia, and Poland. The average exchange rate of the German community was basically below that of all the WIOD economies before 2000. Only from 2001, the community average became slightly (no more than 16%) higher than the overall average. The data source is the exchange rate data used in the WIOD, http://www.wiod.org/protected3/data/update_sep12/EXR_WIOD_Sep12.xlsx.
Industry/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Agr CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Min USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Fod USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA CHN
Tex USA CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Lth CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Wod JPN USA USA USA USA USA USA USA USA USA USA USA USA CHN CHN CHN CHN
Pup USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Cok USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Chm USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Rub USA USA USA USA USA USA USA USA USA USA USA USA CHN CHN CHN CHN CHN
Omn CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN USA USA DEU CHN CHN CHN CHN
Met JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN CHN CHN CHN
Mch JPN JPN USA USA USA USA USA USA USA USA CHN CHN CHN CHN CHN CHN CHN
Elc JPN USA USA USA USA USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN CHN
Tpt USA USA USA USA USA USA USA USA USA USA USA USA USA USA CHN CHN CHN
Mnf USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ele USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Cst JPN JPN USA USA USA USA USA USA USA USA USA USA CHN CHN CHN CHN CHN
Sal USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Whl JPN JPN USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Rtl USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Htl USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ldt JPN JPN JPN USA USA USA USA USA USA USA USA USA USA USA USA USA IND
Wtt USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ait USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Otr DEU DEU DEU DEU DEU USA USA ITA ITA ITA ITA ITA ITA ITA ITA CHN CHN
Pst USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Fin USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Est USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Obs USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pub USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Edu JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN USA CHN CHN CHN CHN CHN
Hth USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ocm USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pvt ITA ITA ITA USA USA USA USA USA ITA ITA ITA ITA ITA ITA ITA ITA ITA
Table A3: The most important economies by industry over time: using the final-demand-weighted backward linkage measure.
Economy/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
AUS Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
AUT Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
BEL Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
BGR Fod Fod Fod Fod Agr Agr Fod Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst
BRA Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub
CAN Pub Pub Cst Pub Tpt Tpt Pub Pub Cst Cst Cst Cst Cst Cst Cst Cst Cst
CHN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
CYP Htl Cst Htl Htl Htl Htl Htl Pub Pub Cst Cst Cst Cst Cst Cst Cst Cst
CZE Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Tpt Tpt
DEU Cst Cst Cst Cst Cst Cst Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt
DNK Fod Fod Cst Cst Cst Cst Cst Hth Hth Hth Cst Cst Cst Hth Hth Hth Hth
ESP Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
EST Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
FIN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
FRA Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
GBR Pub Cst Cst Cst Cst Cst Cst Cst Cst Cst Hth Hth Hth Hth Hth Hth Hth
GRC Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Pub Pub Pub
HUN Fod Fod Fod Fod Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc
IDN Cst Cst Cst Cst Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
IND Agr Agr Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
IRL Fod Fod Fod Elc Elc Elc Elc Elc Cst Cst Cst Cst Cst Cst Cst Chm Chm
ITA Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
JPN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
KOR Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
LTU Fod Fod Pub Cst Cst Fod Fod Cst Cst Cst Cst Cst Cst Cst Fod Fod Fod
LUX Cst Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin
LVA Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
MEX Fod Fod Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
MLT Elc Elc Elc Elc Elc Elc Elc Cst Cst Elc Cst Ocm Ocm Ocm Ocm Ocm Ocm
NLD Fod Fod Fod Fod Cst Cst Cst Cst Pub Pub Pub Pub Cst Cst Pub Pub Pub
POL Fod Fod Fod Cst Cst Cst Cst Fod Fod Fod Fod Fod Cst Cst Cst Cst Cst
PRT Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
ROM Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst
RUS Fod Cst Cst Cst Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
SVK Cst Cst Cst Cst Cst Cst Tpt Tpt Tpt Tpt Cst Tpt Tpt Tpt Cst Cst Cst
SVN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
SWE Est Est Est Est Est Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth
TUR Cst Cst Cst Cst Fod Fod Fod Tex Tex Tex Fod Fod Tex Fod Fod Fod Fod
TWN Cst Cst Pub Pub Elc Elc Elc Elc Elc Cst Cst Cst Cst Cst Cst Cst Cst
USA Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub
Table A4: The most important industries by economy over time: using the final-demand-weighted backward linkage measure.
Industry/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Agr RUS RUS RUS RUS DEU BGR BGR CHN CHN CHN CHN CHN CHN RUS CHN CHN CHN
Min RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS RUS
Fod DEU DEU DEU USA DEU USA USA USA USA USA USA USA USA USA USA USA USA
Tex ITA ITA ITA ITA ITA TUR ITA TUR TUR TUR TUR TUR TUR TUR TUR TUR CHN
Lth ITA ITA ITA ITA ITA ITA ITA CHN CHN CHN ITA ITA ITA ITA CHN CHN CHN
Wod DEU DEU USA USA USA USA USA USA LVA USA USA USA LVA CHN CHN CHN CHN
Pup USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Cok BRA USA BRA BRA BRA USA USA USA DEU DEU USA USA USA RUS RUS USA FRA
Chm DEU USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA CHN
Rub DEU DEU USA DEU USA USA USA USA USA DEU DEU DEU DEU CHN CHN CHN CHN
Omn CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Met DEU DEU DEU DEU USA DEU DEU DEU DEU DEU DEU CHN CHN CHN CHN CHN CHN
Mch DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU
Elc USA USA USA USA USA USA DEU DEU CHN CHN CHN CHN CHN CHN CHN CHN CHN
Tpt USA DEU USA DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU DEU
Mnf DEU DEU ITA DEU ITA DEU DEU ITA ITA DEU DEU DEU DEU DEU DEU DEU DEU
Ele FRA FRA RUS FRA DEU USA USA DEU DEU DEU DEU DEU DEU DEU DEU RUS RUS
Cst DEU DEU DEU USA USA USA USA ESP ESP ESP ESP ESP ESP ESP ESP CHN CHN
Sal ROM ROM ROM ROM ROM ROM ROM ROM ITA ITA ITA ITA ITA ITA ITA ITA ITA
Whl ITA ITA ITA ITA ITA ITA ITA ITA ITA ITA ITA ITA RUS RUS RUS RUS RUS
Rtl USA USA USA USA USA USA GBR GBR GBR GBR USA USA GBR USA GBR USA USA
Htl USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ldt IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND
Wtt JPN JPN JPN JPN JPN JPN JPN DNK JPN JPN JPN JPN JPN JPN JPN JPN JPN
Ait CYP CYP CYP CYP CYP CYP CYP CYP CYP CYP CYP DEU DEU DEU DEU DEU DEU
Otr DEU DEU DEU DEU DEU DEU DEU DEU SWE DEU DEU DEU DEU DEU DEU SWE SWE
Pst USA USA USA USA USA KOR USA USA USA USA USA USA USA USA USA USA USA
Fin USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Est USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Obs USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pub USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Edu RUS RUS RUS RUS GBR GBR GBR GBR CHN GBR CHN CHN CHN CHN DEU CHN CHN
Hth USA USA USA USA USA USA USA USA USA USA GBR GBR GBR GBR GBR GBR GBR
Ocm USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pvt IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND IND
Table A5: The most important economies by industry over time: using the PageRank centrality measure.
Economy/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
AUS Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
AUT Cst Cst Cst Cst Cst Cst Cst Cst Hth Cst Cst Cst Cst Cst Cst Cst Cst
BEL Hth Hth Hth Hth Cst Hth Cst Hth Hth Hth Cst Cst Cst Cst Cst Cst Cst
BGR Fod Fod Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Fod Cst Cst Cst Cst
BRA Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Tpt Tpt Fod Tpt Tpt
CAN Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Pub Tpt Tpt
CHN Tex Tex Met Tex Tex Elc Tex Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc
CYP Fod Fod Fod Pub Fod Fod Pub Fod Fod Fod Pub Pub Pub Cst Pub Pub Pub
CZE Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Tpt Tpt
DEU Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt
DNK Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Obs Obs Obs Obs Obs Obs
ESP Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
EST Fod Fod Fod Fod Otr Otr Otr Otr Otr Otr Otr Cst Cst Cst Otr Otr Otr
FIN Pup Pup Pup Cst Cst Elc Cst Cst Cst Cst Cst Hth Hth Hth Hth Hth Hth
FRA Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Cst
GBR Cst Cst Cst Cst Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth
GRC Pub Fod Fod Fod Pub Pub Pub Fod Cst Fod Fod Cst Ocm Fod Ocm Ocm Ocm
HUN Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Agr
IDN Cst Cst Tex Fod Fod Fod Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst
IND Fod Ldt Ldt Ldt Ldt Fod Ldt Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst
IRL Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Hth Hth Hth
ITA Cst Cst Cst Tex Tex Tex Tex Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth
JPN Cst Cst Tpt Cst Cst Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt
KOR Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt Tpt
LTU Cst Cst Pub Cst Cst Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Fod Fod
LUX Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin
LVA Agr Otr Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
MEX Fod Fod Cst Cst Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
MLT Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Ocm Ocm Ocm Ocm Ocm Ocm Ocm
NLD Fod Cst Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Fod Fod
POL Fod Fod Fod Fod Fod Cst Fod Fod Fod Fod Fod Fod Fod Cst Cst Cst Cst
PRT Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Hth Hth Hth
ROM Sal Fod Sal Sal Sal Sal Sal Sal Fod Cst Fod Cst Cst Cst Cst Cst Cst
RUS Hth Hth Hth Hth Fod Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth Hth
SVK Pub Pub Cst Pub Pub Cst Ele Ele Ele Cst Cst Cst Cst Cst Cst Cst Cst
SVN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
SWE Hth Obs Obs Hth Obs Obs Obs Tpt Tpt Tpt Tpt Tpt Tpt Tpt Obs Tpt Tpt
TUR Tex Tex Fod Fod Tex Tex Tex Tex Tex Tex Tex Tex Tex Tex Tex Tex Tex
TWN Fod Pub Pub Pub Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc Elc
USA Pub Pub Pub Pub Pub Pub Pub Hth Hth Hth Hth Hth Pub Pub Pub Pub Pub
Table A6: The most important industries by economy over time: using the PageRank centrality measure.
Industry/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Agr USA USA USA USA CHN USA CHN CHN CHN CHN USA CHN CHN CHN CHN CHN CHN
Min USA USA USA CHN CHN USA USA USA CHN CHN USA CHN CHN CHN CHN CHN CHN
Fod JPN USA USA USA JPN USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN CHN
Tex CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN BRA CHN CHN CHN CHN CHN CHN
Lth CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN BRA CHN CHN CHN CHN CHN CHN
Wod JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN CHN CHN CHN CHN CHN CHN CHN
Pup USA USA USA JPN JPN JPN JPN JPN JPN JPN USA USA USA USA USA USA USA
Cok USA USA USA JPN USA USA USA CHN USA CHN USA USA USA USA CHN USA USA
Chm JPN JPN JPN JPN JPN JPN JPN JPN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Rub USA USA USA USA USA USA USA USA USA USA USA USA CHN CHN CHN CHN CHN
Omn CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Met JPN JPN JPN USA USA USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN CHN
Mch USA USA USA USA USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Elc USA USA USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN CHN
Tpt USA USA USA USA USA USA USA USA USA USA USA USA USA CHN CHN CHN CHN
Mnf USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ele JPN USA USA USA USA USA USA USA JPN USA USA USA USA USA JPN JPN JPN
Cst JPN JPN JPN JPN JPN JPN JPN CHN CHN CHN USA USA CHN CHN CHN CHN CHN
Sal JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN
Whl JPN USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Rtl USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Htl JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN
Ldt JPN JPN JPN JPN JPN JPN JPN JPN JPN JPN USA USA USA USA IND IND IND
Wtt USA USA CHN CHN CHN CHN CHN CHN CHN CHN BGR CHN CHN CHN CHN CHN CHN
Ait USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Otr USA USA USA USA USA USA USA USA USA USA BEL USA USA USA USA USA USA
Pst USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Fin JPN JPN JPN USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Est USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Obs USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pub USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Edu JPN JPN JPN JPN JPN USA USA USA USA CHN CHN CHN CHN CHN CHN CHN CHN
Hth USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Ocm JPN USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA USA
Pvt USA USA USA USA USA USA USA USA USA USA BGR USA USA USA USA USA USA
Table A7: The most important economies by industry over time: using the community coreness measure.
Economy/Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
AUS Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Fod Obs Obs Obs Obs Obs Obs
AUT Fin Fin Fin Fin Cst Whl Obs Est Est Met Pub Cst Obs Obs Met Met Met
BEL Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Otr Obs Obs Obs Obs Obs Chm
BGR Fod Fod Ele Ele Agr Ele Agr Agr Agr Cst Ocm Cok Cst Cst Cst Cst Cst
BRA Fod Fod Obs Fod Fod Fod Fod Fod Fod Fod Tex Cok Fod Fod Fod Fod Min
CAN Cst Cst Cst Cst Whl Obs Obs Whl Whl Obs Ldt Whl Obs Obs Cst Cst Cst
CHN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Met Met Met Cst Cst Cst
CYP Cst Cst Cst Htl Htl Htl Htl Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
CZE Cst Cst Cst Cst Met Met Met Met Met Met Met Met Met Met Obs Est Met
DEU Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Met Cst Cst Cst Met
DNK Cst Cst Cst Cst Obs Obs Obs Obs Cst Obs Obs Obs Obs Obs Obs Obs Obs
ESP Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
EST Agr Agr Agr Agr Otr Elc Elc Elc Elc Elc Agr Cst Cst Obs Obs Obs Obs
FIN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
FRA Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs
GBR Fin Fin Fin Fin Fin Fin Fin Fin Fin Obs Obs Obs Obs Fin Obs Obs Obs
GRC Fod Fod Fod Fod Fod Cst Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
HUN Agr Agr Agr Agr Elc Elc Fod Fod Fod Elc Elc Tpt Tpt Tpt Elc Elc Mch
IDN Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr Agr
IND Agr Agr Agr Agr Agr Agr Agr Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
IRL Fod Fod Fod Fod Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Chm Chm
ITA Met Met Met Met Met Cst Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs
JPN Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Obs Obs Obs
KOR Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Met Met Met Met Met Met Met
LTU Agr Agr Agr Agr Fod Agr Agr Ele Ele Ele Ele Ele Est Whl Ele Ele Ele
LUX Cst Cst Rub Cst Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin Fin
LVA Fod Agr Agr Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst
MEX Min Min Min Min Min Min Min Min Min Cok Cok Cok Cok Cok Cok Cok Min
MLT Elc Ele Elc Elc Elc Elc Ele Elc Elc Ele Ele Ele Ele Ele Ocm Ele Ele
NLD Obs Obs Obs Obs Obs Obs Obs Obs Cst Obs Obs Obs Obs Obs Cst Cst Est
POL Agr Agr Agr Agr Cst Fod Cst Cst Ele Cst Cst Cst Cst Cst Cst Cst Cst
PRT Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Cst Obs Obs Obs Obs
ROM Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod Fod
RUS Ele Ele Ele Ele Ele Ele Ele Ele Ele Ele Cok Cok Cok Cok Cok Cok Cok
SVK Ele Ele Cst Ele Ele Cok Cok Tpt Tpt Tpt Tpt Tpt Tpt Ele Cst Cst Elc
SVN Cst Cst Cst Cst Cst Cst Cst Obs Cst Cst Cst Cst Cst Cst Cst Cst Cst
SWE Est Est Est Est Est Est Est Est Est Est Est Est Est Est Est Est Est
TUR Cst Cst Cst Fod Agr Agr Fod Agr Agr Agr Agr Fod Fod Fod Agr Agr Agr
TWN Cst Cst Cst Cst Cst Cst Cst Cst Cst Met Met Met Met Met Chm Met Met
USA Pub Pub Pub Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs Obs
Table A8: The most important industries by economy over time: using the community coreness measure.

Footnotes

  1. Ever since Leontief leontief1936quantitative () formalized its structure, the input-output table has been used extensively by economists, environmentalists, and policy makers alike. By keeping track of the inter-industrial relationships, the input-output table offers a reasonably accurate measurement of the response of any given economy in the face of external shocks or policy interventions.
  2. Tukker and Dietzenbacher tukker2013global () summarize the recent development of the MRIO databases.
  3. More precisely, the edges are the monetary goods and services flows. The direction of the flows go from the seller industry to the buyer industry. They are monetary because they are denoted in current US dollars.
  4. In contrast, due to the low-digit industry classification, the input-output networks at the national level are almost complete blochl2011vertex ().
  5. This is also due to the aggregated industry classification.
  6. Carvalho carvalho2013survey () also use a networks approach to study the WIOD data. But he only uses a single year (2006) and considers it as an unweighted network.
  7. Tables A1 and A2 in the appendix have the lists of countries and industries covered in the WIOD.
  8. Again, the relationship can also be an industry to itself and within the same economy.
  9. The basic prices are also called the producers’ prices, which represent the amount receivable by the producers. An alternative is the purchases’ prices, which represent the amount paid by the purchases and often include trade and transport margins. The former is preferred by the WIOD because it better reflects the cost structures underlying the industries timmer2012world ().
  10. Here we only show the aggregated final demand for the two economies
  11. The ratios are called technical coefficients because they represent the technologies employed by the industries to transform inputs into outputs.
  12. The Leontief inverse is demand-driven, i.e., a repercussion effect triggered by an increase in final demand. Another strand of the input-output economics literature is based on the supply-driven model, where a repercussion effect is triggered by an increase in value added (primary inputs) ghosh1958input (); miller2009input ().
  13. It is backward because the linkage is identified by tracing back to the upstream industries.
  14. Strictly speaking, the flows from the red nodes to the blue nodes are not goods but primary inputs in nature.
  15. In the case of WION, all the coefficients are of very small magnitude less than 0.06.
  16. Notice that when calculating the assortativity for in-degree, out-degree, and total-degree, respectively, we consider the nodes as the neighbors of a given node if they are connected with the given node by only incoming edges, by only outgoing edges, and by either incoming or outgoing edges, respectively. In contrast, Carvalho carvalho2013survey () defines the neighborhood solely on the basis of the incoming edges and finds a positive assortative relationship.
  17. While the most severely depressed domestic edges during 2008-2009 in terms of the magnitude of the reduced flows are mostly within USA, the top 3 most impacted foreign edges are all from the mining industry to the coke and fuel industry and are from Canada to USA, from Netherlands to Belgium, and from Mexico to USA, respectively.
  18. The same feature is also found in the input-output networks at the national level mcnerney2013network (). Using a single-year (2006) data of the WIOD, Carvalho carvalho2013survey () also reports the heavy-tailed but non-power-law degree distributions.
  19. We perform the community detection for all available years (1995-2011). Results are available upon request.
  20. It is centered on Germany because the community core detection results below show that the cores of this red community are all within Germany.
  21. The data is unavailable for Taiwan. We also exclude Bulgaria because it had a hyperinflation in 1997, which will bias the average if included. The data source is the World Development Indicators, the World Bank, http://data.worldbank.org/indicator/NY.GDP.DEFL.KD.ZG.
  22. The data source is the exchange rate data used in the WIOD, http://www.wiod.org/protected3/data/update_sep12/EXR_WIOD_Sep12.xlsx.
  23. We choose PageRank over other centrality measures such as closeness and betweenness because the former systematically measures the influence of a given node and has been widely used in the previous literature to identify the key nodes acemoglu2012network (); carvalho2013survey ().
  24. Our PageRank result differs from the one reported by Carvalho carvalho2013survey (), where he uses an unweighted version of PageRank.

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