A microscopic study of the fitness-dependent topology of the world trade network
Introduction
The world trade network (WTN) has received a considerable amount of attention in the last decade. A detailed understanding of the network structure of international trade facilitates a better comprehension of crises that spread across a country’s frontiers. It is generally agreed that a static hidden variable model [1], [2] best describes the topology of the WTN. The static model is most suitable because there are only a finite number of distinct countries in the world. Depending on the scope of the analysis, previous contributions understand the network as growing since the number of vertices increased from 86 in the year 1950 to 190 in the year 2000 [3]. However, since there are–depending on the definition–approximately 195 countries in the world to date, the growth of the network cannot be sustained. A dynamic perspective on the world trade network, by investigating the duration and strength of individual connections and also the relationship between the development status of a country and its ability to establish long-lasting trade relationships has been discussed in Refs. [4], [5]. It has been shown in Refs. [6], [7], that the static fitness model is an adequate model to describe the structure of the world trade network for several years, not just on the level of node degree distributions, but up to higher order statistics, such as the average nearest neighbour degree. In this article, we look into the microscopic structure of the WTN. The main quantity of interest is the edge density, that is the probability matrix for any two nodes of fitness and to share an edge. The fitness model is found to be an excellent fit for the WTN. However, the previously found multiplicative attachment kernel varies significantly from the kernel that we find by investigating the edge density.
A review of the literature on the network of international trade reveals that many results are not without controversy. Even first order results, such as the form of the degree distribution, differ between various publications. One reason for these discrepancies is the choice of data source. Every trade relationship between two countries should be reported twice, once as an export and once as an import. However, this is not always the case [8]. As a result, different data providers report different trading data. Another issue is the way these disparities are corrected. Some [9], [10] simply use only import data, which is deemed more reliable than export data, others [11], [12], [13] interpolate between reports of exports and imports.
The data set we use for the present article is provided by the National Bureau of Economic Research (NBER) [8] and forms an excellent starting point for this investigation. The special feature of this data set is that one part of it has been adjusted for errors, while another part has not. The adjustments have been made by specialised macroeconomists and can therefore be deemed reliable.
The world trade network is treated as directed and binary in this article. That means that directionality of trade is taken into account, but the traded amounts are ignored. Others [7], [14], [12], [15] have argued that directionality could be ignored because of the high reciprocity, i.e. export links are usually reciprocated with import links. However, since the world trade network is directed by nature, the analysis in the present article is laid out in terms of a directed network. A weighted representation of the WTN has been investigated for example in Refs. [12], [16], [13]. Curiously, the additional information of edge weight is not always of greater explanatory power than binary network analysis [10], [17]. In Refs. [10], [17] a network randomisation technique was used to show that by knowing the degree sequence of the binary WTN, higher order statistics like the average neighbour degree and the clustering coefficient can be obtained. However, using a weighted network approach and fixing the sequence of interaction strengths, these higher order statistics cannot be found anymore. This suggests that binary network analysis used in economics is a powerful tool, because all the necessary information is contained in the first order statistics.
In principle, the WTN is a spatially embedded network. However it has been illustrated that distances between countries do not add a significant amount of information to a binary analysis of international trade [18]. Similarly, also in the weighted regime, the importance of geographic distance for understanding international trade is declining over time [19]. The results of Ref. [19] are in contrast to the standard notion in economics, that the intensity of trade between pairs of countries is strongly related to their distance, see for instance [20]. Another aspect that will not feed into the analysis in this article is the multi-layered architecture of international trade. Every reported trade flow is an aggregation over different product categories. Refs. [10], [17], [9], [21] investigate these different layers separately.
The investigation of the topology of the world trade is not conducted as an end in itself. Its aim is to understand how trade can affect economic welfare. Many aspects are yet to be understood. The theory of complex systems is just one of the building blocks towards a good understanding of those effects [22], [23]. Network-theoretic measures have been shown to explain parts of nation’s income. In Ref. [24] it is shown that an improvement of the degree centrality ranking by ten units increases the average GDP per capita by 0.27%. Others [11], [6], [25], [3] investigate correlation structures of income, connectivity and interaction strength in weighted networks and illustrate that an involvement in international trade has a direct impact on income and vice versa. Additionally, it has been shown that network properties have good explanatory power to detect vulnerable economies in the WTN [26], [27].
This paper is organised as follows. In Section 2, the static fitness model is reviewed and the central quantities for this study are derived. In Section 3, the data set is introduced and reasons for its choice are discussed. In Section 4, the definition of fitness is elucidated. In Section 5, the inter-temporal structure of the WTN is clarified and in Section 6, the static structure is investigated. Section 7 closes the article with concluding remarks.
Section snippets
The static fitness model
The empirical analysis in this article is based on the static fitness model, as it was introduced in Refs. [1], [28], [2]. The investigation that is presented later in the text relies on results that are reviewed in the following.
The static fitness model is a network model with nodes and directed edges. Each node inside the network is endowed with a fitness value , that is drawn from a probability density function . The probability that a node with fitness originates a link towards
The choice of a data source
The choice of the data set is crucial for the validity of the derived results. Data for the WTN can be found in various publications [29], [30], [8]. The concern of data validity is raised in various places [13], [12], [10], [9], [8]. Data on world trade should always be reported in two statements. Every flow of goods or services occurs in one country as an export and in another country as import. However, it occurs that a significant amount of trade is only reported on one side. This leads
Definition of fitness
It is undisputed that the world trade network falls into the class of hidden variable models [6], [7], [3]. However, it is not clear how to define fitness. There is general agreement that fitness is defined over some constraint interval, usually . Two different definitions of fitness are investigated in the following.
One possibility is to impose a ranking on the node’s GDP and normalise this ranking to the unit interval. Formally, denote the income of country as . Then the
Intertemporal structure of the WTN
The structure of the world trade network is permanently changing, new trade relations are established and existing ones are terminated. Fig. 4 illustrates the macroscopic behaviour of the WTN over time. The number of nodes is almost static apart from the sudden increase of trading countries when the Soviet Union collapsed. Since this event is not system inherent, the network can be regarded as static with respect to the number of nodes. The number of edges is almost constantly increasing. In
Static structure of the WTN
In order to get a more complete picture of the internal mechanism of the WTN, it is useful to look also at the mere existence of links, rather than at their emergence. We will restrict ourselves here to the years 1984 and 2000. Fig. 7 pictures the fitness and in-degrees of nodes that are adjacent to edges in the years 1984 and 2000. The results are similar to the findings in the previous section. Most of the trade flows between dissimilar countries, low connected countries trade with highly
Conclusion
In this article, we have discussed empirical aspects of international trade. The microscopic structure of the world trade network, that we have illustrated by computing the edge density matrix, exhibits a pattern which is significantly different from previously assumed ones. We have found that the income dependency of trade between two countries is not purely multiplicative, but also at least partially additive with a preference for trade between dissimilar countries. It has also been shown
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