Countries’ positions in the international global value networks: Centrality and economic performance

Centrality has long been a fundamental concept in the study of various types of networks. Most measures of centrality so far advocated aim to capture a node’s structural importance by computing its involvement in the walk structure of a network (Borgatti and Everett 2006; Freeman 1978). Among various empirical applications, centrality has been used to investigate power (Brass 1984; Burt 1982), social influence in inter-organisational networks (Laumann and Pappi 1973; Galaskiewicz 1979), adoption and diffusion of innovation (Coleman et al. 1966), and employment opportunities (Granovetter 1974).

While centrality measures have mostly been developed for one-mode, binary, and time-invariant networks, there have been a number of attempts to extend such measures to two-mode networks (Faust 1997), or more generally K-partite graphs, as well as weighted (Barrat et al. 2004), multiplex (Boccaletti et al. 2014; Menichetti et al. 2014; Rahmede et al. 2017) and time-varying networks (Nicosia et al. 2013). Attempts have also been made to cross-classify centrality measures in terms of various criteria, including their underlying assumptions on how processes unfold in a network (e.g., the trajectories followed and the method of spread) (Borgatti 2005), and the type of nodal involvement and property of walk assessed (Borgatti and Everett 2006).

Recently, a number of studies have drawn upon the network literature to develop suitable sets of metrics to capture the role that countries play in the international GVCs. For instance, it has been suggested that measures for identifying hubs and spokes at the sectoral level can help uncover the connection between global trade patterns and global supply chains (Lejour et al. 2014). Yet, what is still largely missing is an analytical framework in which the centrality of a country is explicitly formalised as a multi-faceted measure that captures the country’s position at the various production stages into which the international GVNs are organised.

The international GVN in a given industry can be regarded as a special case of K-partite weighted and time-varying networks in which goods and services flow from one country to another following complex trajectories along the production process, typically ending in final consumption. These trajectories can be seen as organised into K distinct stages that can be traversed by goods and services along one distinct direction – i.e., from upstream toward downstream – yet through transactions in which the same country can occupy multiple roles. For example, country n _i may export an intermediate product to country n _j to be transformed, and then import from the same country n _j the output of such transformation that, in turn, will be further transformed. Thus, the flow process of production may involve the same country multiple times. Moreover, links between countries are weighted as, by construction, they are associated with the volume or value of the goods and services exchanged. Finally, as the production process unfolds over time, each transaction is time-stamped and the underlying network is therefore time-varying.

where A _i,j is the sub-matrix of the adjacency matrix A representing the links from nodes in set k _i to nodes in set k _j , for 1≤i<j≤K. Thus, adjacency matrix A is a block matrix, with blocks A _i,j . As an illustrative example, Fig. 1 shows an input-output tripartite graph in which the three sets correspond to distinct production stages and contain four, three, and four countries, respectively.

Unlike affiliation networks, in which each link relates an actor to a subset of events and each event to a subset of actors, the international GVN is dyadic since links relate countries with one another, albeit in different roles (Faust 1997). Correspondingly, the duality property of affiliation networks does not apply to the GVN as countries are not linked to one another through shared memberships of collectives, and collectives are not linked through shared countries. Rather, countries sharing connections to or from the same country may be seen as competing for the same customer or for the same supplier, respectively.

As in affiliation networks, however, in the GVN there should be centrality scores for each country belonging to each of the K sets. Furthermore, there should be some analytical relationships between these scores. That is, it is reasonable to assume that the centrality of a country n _i in set k _i is proportional to: (i) the centralities of the countries that are members of the set k _i−1 from which n _i receives a connection, and (ii) the centralities of the countries in set k _i+1 to which n _i directs a connection. Thus, as in the case of affiliation networks, focusing only on single sets of nodes (e.g., on a single stage of the production) would imply neglecting the fundamental relationships among sets of nodes across the whole network. Rather, the centrality of a country at a given production stage within a given industry should quantify the salience of that country for the entire GVN, and thus explicitly depend on the centrality of the other countries located at other production stages and with which the focal country is connected.

Our study draws upon the bilateral trade data set extracted from the BACI-CEPII database. The data set refers to the years 2007 and 2014, and includes 221 countries. Trade flows are recorded as 6-digit codes according to the Harmonized System (HS) classification (Revision 2002). We restricted our analysis to the trade flows in three industrial sectors: Electronics (HS02 Codes 85XXXX), Motor Vehicles (HS02 Codes 87XXXX), and Textiles and Apparel (HS02 Codes from 50XXXX to 63XXXX).

As indicated by Tables 1 and 2, between 2007 and 2014 the traded value of Motor Vehicles increased by 15%, which is less than the increase in the traded value in Electronics (25%) and in Textiles and Apparel (26%). Over the same period, the value of merchandise trade (including commodities) at world level increased by approximately 35%. Our period of observation includes the years in which trade was deeply affected by the international financial crisis, displaying large economic fluctuations, especially in sectors with a strong presence of GVCs, such as the ones considered here. In spite of this, no substantial change in trade composition can be observed between the two years analysed. Nevertheless, it is worth noting that in the Textiles and Apparel industry the finished products represent two thirds of the total trade in the same industry, with only a small difference between 2007 and 2014. The same can be observed in the Motor Vehicles sector. In particular, in Motor Vehicles, finished products toward final consumption represent more than 50% of the total trade in that industry in both years, with only a negligible decline in 2014. At the same time, trade of intermediate inputs increased between 2007 and 2014 while trade of finished products decreased, and trade of consumer goods remained lower than trade of capital goods in both years. By contrast, in Electronics trade remained concentrated more on intermediate inputs than finished products, and trade of capital goods was higher than trade of consumer goods in both 2007 and 2014, though between the two years the former increased while the latter decreased.

A necessary step toward the assessment of the centrality of countries in GVCs is represented by the extraction of the GVNs – i.e., the networks in which connections between countries are qualified as a function of the type of product traded – from the underlying international trade networks – i.e., the networks in which countries are connected to one another irrespective of the stage of production they occupy.

To this end, we define the tripartite valued graph whose nodes are partitioned into three different independent sets, U, M, and D, such that no two endpoints of a link belong to the same set, nor one to set U and the other to set D. The first set U refers to the population of exporters of intermediate inputs. The second set M refers to the population of countries that are importers of intermediate products or exporters of finished products or both importers of intermediate products and exporters of finished products. Finally, the third set D includes the importers of finished products.

So conceived of, only directed links connecting nodes in set U to nodes in set M and directed links connecting nodes in set M to nodes in set D are allowed. In particular, a directed link is established from a node in set U to a node in set M if the former node supplies intermediate inputs to the latter. Similarly, a directed link is established from a node in set M set to a node in set D if the former node supplies a finished product to the latter. Moreover, the weight of each link is given by the value in US dollars of the goods traded by the two connected countries.

In each set, each country can play an “active” or a “non-active” role. A country is active in a given set when it is involved in at least a trade flow of the nature defined by the set. For example, if a node is connected to the other nodes by only import trade flows of finished products, then it will be classified as “active” in set D and ”non-active” in the remaining two sets. The total number of countries N thus corresponds to the maximum number of “active” nodes each set can include. Moreover, in a given industry and a given year, each node in set U can have at most N−1 outgoing links pointing to nodes in set M. Each node in set M can have at most N−1 incoming links emanating from nodes in set U and N−1 outgoing links pointing to nodes in set D. Finally, each node in set D can receive at most N−1 incoming links from nodes in set M. That is, while a given country n _i can be member of all three sets, and therefore exert different roles at the same time in the GVN, it cannot point a link to itself in a different set.

Formally, we indicate with \(w_{um}^{I}\) the outgoing weighted link representing the trade of intermediate inputs from node u belonging to set U to node m belonging to set M. Moreover, we indicate with \(w_{md}^{F}\) the outgoing weighted link representing the trade of finished products from node m belonging to set M toward node d belonging to set D.

Notice that in the international GVNs each country can play multiple roles simultaneously. For instance, within the same industry a country may import both intermediate and finished products, and at the same time also export both intermediate and finished products. So conceived of, the international GVNs thus capture the nuances of the GVCs, such as the exchange of the same intermediate or final products among different countries. In the case of intermediate products, when multiple transactions of intermediate products take place before the final products are exported, each country involved in such transactions would play the dual roles as exporter and importer of intermediate products, and thus would belong to both set U and set M. Similarly, in the case of multiple transactions of the same final products among countries, each country involved would play the roles as exporter and importer of such products, and would thus belong to both set M and set D.

The international GVN in a given industry can also be formalised as a two-layer multiplex network, in which the nodes are the countries, and each layer corresponds to one of two types of product traded between countries: intermediate and finished (De Domenico et al. 2015; Rahmede et al. 2017). Countries that belong to all three sets would also be part of both the intermediate-product layer and the finished-product layer. Countries that only belong to set U or only to set D would be nodes, respectively, in the intermediate-product layer or the finished-product layer. Countries belonging to set M that both import intermediate products and export finished ones would be nodes in both layers. Finally, countries in set M that only export finished products or only import intermediate products would be nodes only in the finished-product layer or in the intermediate-product layer, respectively.

Given an industry, these three measures will be applied to the directed and weighted international global value tripartite network defined above, in which nodes are suitably labelled according to the roles they play as exporters or importers of intermediate or finished products.

We now proceed to formalise the three recursive measures of centrality. We begin by formalising the first-order midstreamness centrality, and we then formalise the first-order upstreamness and first-order downstreamness centralities as a function of first-order midstreamness centrality. In a similar way, we show how a h-order midstreamness centrality can be defined in terms of the h−1-order upstreamness and h−1-order downstreamness centralities. The three centralities then converge to higher-order values that are the solutions of a linear system of equations.

where \(\mu ^{*}=\underset {m}{max}\,(\mu _{m}^{1})\).

where \(\upsilon ^{*}=\underset {u}{max}\,(\upsilon _{u}^{1})\).

where \(\delta ^{*}=\underset {d}{max}\,(\delta _{d}^{1})\).

where \(\mu ^{*}=\underset {m}{max}\,(\mu _{m}^{2})\).

All countries that are involved in at least one transaction (exports or imports) of (intermediate or finished) products will be assigned at least one value of the centralities defined above. In the previous section we mentioned that the international GVNs capture the nuances of international trade, such as chains of multiple transactions of intermediate or finished products. In particular, two cases can be identified. First, a country may well control the whole production of a given product, and contribute to the exports without importing any input. Second, a country may play a prominent role in many stages of the transformation process without necessarily exporting the final product. In the former case, the country that exports finished products but does not import intermediate ones would still occupy the midstream stage of the GVN and thus be classified as part of set M. However, since there would be no incoming links pointing to the country, its midstreamness centrality would not be defined in terms of the upstreamness of other countries. Similarly, in the latter case, the country that exports and imports only intermediate products would occupy both an upstream and a midstream stage in the GVN, and would thus be classified as a member of both set U and set M. However, since there are no outgoing flows of finished products from that country toward other countries, its midstreamness centrality would not be defined in terms of the downsteamness centralities of the other countries.