Date Published: January 26, 2017
Publisher: Public Library of Science
Author(s): Rita María del Río-Chanona, Jelena Grujić, Henrik Jeldtoft Jensen, Irene Sendiña-Nadal.
The international trade naturally maps onto a complex networks. Theoretical analysis of this network gives valuable insights about the global economic system. Although different economic data sets have been investigated from the network perspective, little attention has been paid to its dynamical behaviour. Here we take the World Input Output Data set, which has values of the annual transactions between 40 different countries of 35 different sectors for the period of 15 years, and infer the time interdependence between countries and sectors. As a measure of interdependence we use correlations between various time series of the network characteristics. First we form 15 primary networks for each year of the data we have, where nodes are countries and links are annual exports from one country to the other. Then we calculate the strengths (weighted degree) and PageRank of each country in each of the 15 networks for 15 different years. This leads to sets of time series and by calculating the correlations between these we form a secondary network where the links are the positive correlations between different countries or sectors. Furthermore, we also form a secondary network where the links are negative correlations in order to study the competition between countries and sectors. By analysing this secondary network we obtain a clearer picture of the mutual influences between countries. As one might expect, we find that political and geographical circumstances play an important role. However, the derived correlation network reveals surprising aspects which are hidden in the primary network. Sometimes countries which belong to the same community in the original network are found to be competitors in the secondary networks. E.g. Spain and Portugal are always in the same trade flow community, nevertheless secondary network analysis reveal that they exhibit contrary time evolution.
International trade is a key part of the global economy. A common approach to study international trade is to analyse input-output tables, which was developed in 1941 by Wassily Leontief  when he divided the economy in a number of sectors which would trade with each other. In order to rank the sectors he developed a procedure which is considered to be an early example of the PageRank measure , which would later obtain fame as being a crucial part of the Google’s algorithm . This work brought him a Nobel Prize in Economics in 1973. With the growth of economic data availability, input-output networks have been increasingly analysed using network theory. Sectors or countries are usually considered as the nodes of the networks and links represents the transaction between them. One of the first datasets to become available was the International Trade Data  which contains information about the trade flow for different products for a large number of countries. The properties of the resulting network – the International Trade Network (ITN)—has been extensively investigated [5–7], observing fat-tail distributions. The data has also been used to form a so called product space, where products are linked with a proximity measure [8, 9]. The data set can also be used to construct bipartite networks of countries and their export products. This network has formed the basis of attempts to predict future economic development of specific countries [10, 11] and to define new metrics which in the case of  has yielded new and very important insights.
The World Input Output Database (WIOD)  has been developed to enable analyse of the effects of globalisation on trade patterns, stress on the environment and the socio-economic development across a wide set of countries. The database covers 27 EU countries and 13 other major economies (Canada, United States, Brazil, Mexico, China, India, Japan, South Korea, Australia, Taiwan, Turkey, Indonesia, Russia) in the world. Trade with countries not among those listed is aggregated into one post labelled “trades with the rest of the world” or RoW, for the period from 1995 to 2009. Although the RoW is an artificial economy and not a country we include it in the analysis as it allows countries which major trade is not in Europe to maintain their trade information. The entire data set covers more than 85% of world GDP in 2008.
In this section we present our results in three parts. First we analyse the PageRank and normalised strength time series of the six leading countries, although we are able to obtain interesting insights this analysis is very is time consuming. Second we find communities of the Country-WION which obey geographic and political relations. In the third part we propose a method to analyse the dynamics in a more efficient manner than in the first part. Here we find that by comparing both PageRank and normalised strength networks we can observe common clusters, which we interpret as countries/sectors that are subject to similar economic dynamics in contrast to countries/sectors with essentially independent dynamics. For sectors, the correlation networks reveal clusters which are related to the specifics of the resource (renewable and non-renewable) the sectors depend on. With these finding we show that the correlation networks provide significant additional insights. Although in this work we portray simple examples to outline the methodology and its advantages, in the supporting information we show that this methodology can be applied to larger and disaggregated data sets. Its application highlight interesting features and encourage further work on the analysis of correlation networks. Furthermore in this section we also present the results of a randomized test which shows the significance of the correlations found.
We analysed the World Input Output Network with a focus on the dynamics of the importance of nodes (countries or sectors) as measured by either PageRank or economical strength. We find the PageRank and strength allows for complimentary insights. First we analyse the primary networks of countries or sectors where the weight of the links are given by the annual trade flow. The correlations over time between nodes are used to construct secondary networks which contains information about the similarity of the development of the two given countries or sectors. Furthermore, we construct networks based on the negative correlations, which pin-points the countries or sectors that are in competition with each other. We find that these secondary networks gives us a new valuable information. For example Portugal and Spain are always in the same module when we analyse the primary network, which is understandable given their geographical proximity and historical connections. However, when we analyse the secondary network we find that they are actually negatively correlated with each other, suggesting that these country are in competition with each other. Furthermore, we identify a similarity of behaviour of Latvia, Luxembourg and China and to some extend Spain, however this behaviour is unlikely a consequence of a real connection of these countries. This shows that we, obviously, have to be careful when interpreting correlations. However the investigation of the correlation network can be a very powerful tool, which help to identify possible interesting dynamics and can suggest where additional analysis is needed in order to test potential interrelationships. Furthermore, our approach may help clarify possible connections between different economies or even reveal anticorrelation as in the case of Spain and Portugal. The rise of China is very well documented by now, however our analysis is able to suggest the markets China is overtaking; namely the markets of Germany, Japan as well as Taiwan, Portugal and Sweden. We find evidence of three large “local” leaders, which are Germany, USA and China whose development is strongly correlated with the surrounding countries. This is another aspect which can not see from the primary network. We find that sectors separate into two different groups, sector based on renewable resource and the once based on non-renewable resources. However in general the sectors are found to anti-correlate which may suggest highly competitive relationships. Obviously correlations do not necessarily imply causation, it will therefore be of great interest in the future when sufficient data becomes available to do the above network analysis using information theoretic causality measures. Our work encourages further research regarding the topology of the correlation and anticorrelation networks, which could contribute to the analysis of these networks. Finally, this method can be expanded to be used on any case where we have temporal networks.