Grand canonical validation of the bipartite international trade network

Devising strategies for economic development in a globally competitive landscape requires a solid and unbiased understanding of countries' technological advancements and similarities among export products. Both can be addressed through the bipartite representation of the International Trade Network. In this paper, we apply the recently proposed grand canonical projection algorithm to uncover country and product communities. Contrary to past endeavors, our methodology, based on information theory, creates monopartite projections in an unbiased and analytically tractable way. Single links between countries or products represent statistically significant signals, which are not accounted for by null models such as the bipartite configuration model. We find stable country communities reflecting the socioeconomic distinction in developed, newly industrialized, and developing countries. Furthermore, we observe product clusters based on the aforementioned country groups. Our analysis reveals the existence of a complicated structure in the bipartite International Trade Network: apart from the diversification of export baskets from the most basic to the most exclusive products, we observe a statistically significant signal of an export specialization mechanism towards more sophisticated products.

Figure 1

The $V_{\alpha }^{ij}$ motif is illustrated by the bold black edges between node couples $(i,\alpha )$ and $(j,\alpha )$. Analogously, the edges between $(j,\alpha )$ and $(j,\beta )$ describe the ${\mathrm{\Lambda }}_{\alpha \beta }^j$ motif. The top layer contains the “Latin” nodes, the bottom the “Greek” nodes. Other edges are indicated by dotted gray lines.

Figure 2

Communities of countries based on the BiCM projection for the years 1995, 2001, 2010. Even though the division in communities shows some noise, the partition in the following communities is stable: developed countries [blue (dark gray), see central Europe], newly industrialized and developing countries [light purple (lighter gray), see China], developing countries [green (darker gray), see central Africa], and countries whose exports rely on raw materials, e.g. oil [orange (light gray), see Russia].

Figure 3

Country communities based on the ${\mathrm{BiPCM}}_c$ projection for the years 1995, 2001, 2010. Compared to the BiCM communities of Fig. 2, the partition here is more stable.

Figure 4

Structure of the projected country network obtained with the BiCM and the ${\mathrm{BiPCM}}_{\text{c}}$ for the year 2001. Note that in weakening the constraints, i.e., passing from BiCM to ${\mathrm{BiPCM}}_{\text{c}}$, the connectance increases. The node colors correspond to those in Figs. 2 and 3.

Figure 5

Comparison of the product networks for the years 1995–2010. The Jaccard index measures the similarity between their edge sets $E$ and is defined as $|E_{{\mathrm{year}}_i}\cap E_{{\mathrm{year}}_j}|/|E_{{\mathrm{year}}_i}\cup E_{{\mathrm{year}}_j}|$. The values fall very quickly below 0.5 for $|{\mathrm{year}}_i-{\mathrm{year}}_j|>2$.

Figure 6

${\mathrm{BiPCM}}_{\text{p}}$ product network spanned by FDR validated edges for $\alpha ={10}^{-2}$ in the year 2000. The communities have been obtained using the enhanced Louvain algorithm and include, among others, the following products, starting on the top and going clockwise: fabrics and yarn; clothes and shoes; sugar and yeast; wooden materials; animal products; heavy machines; basic electronics; heavy-duty vehicles, pipes, dairy products; wood pulp; chemical products; machines, motors, tools; flat iron products; metal products, tramway locomotives, tires, and turbines.

Figure 7

The images show the relative focus of the country communities' exportation on different product cluster of the ${\mathrm{BiPCM}}_p$ product network for the year 2000. Top: developed countries occupy the central communities of highly technological and chemical products. Middle: developing countries focus on peripheral communities with relatively low complexity [13, 14]. Bottom: raw material exporters are comparatively less focused, as shown in the link densities.

Figure 8

Representation of the biadjacency matrix for the year 2000 with countries along the rows and products along the columns. Fitness and complexity increase from top to bottom and left to right, respectively [13, 14]. Links are shown as white dots. The superimposed colors (gray shading) correspond to the $z$ scores of the connectivity with respect to the BiCM. The $z$ scores are calculated for boxes containing 21 countries and 81 products which are centered on the respective matrix entry. Lighter colors indicate a higher presence of links than in the random null model, darker shades a lower one. As can be seen in the lower right corner, the most developed countries (i.e., the bottom rows in the figure with the largest export baskets) have higher densities that exceed the expectations from the null model for the most sophisticated products, i.e., those with the fewest exporters ($z\sim 25$). On the other hand, the least developed countries with the smallest export baskets focus their exports on basic products ($z\sim 30$), as shown in the upper left corner. In addition, the lower left part of the matrix shows that high fitness countries export low complexity products much less than would be expected from the BiCM. This indicates that countries export as many products as they are capable of while focusing their efforts on the most sophisticated commodities at the same time.

Figure 9

BiRG (top) and ${\mathrm{BiPCM}}_{\text{c}}$ (bottom) product networks for the year 2000. The networks are dominated by the largest connected components whose cores are composed of high degree nodes. The degree values refer to the original country-product bipartite network.

Figure 10

Properties of the product networks spanned by the statistically significant edges according to the respective null models. The ${\mathrm{BiPCM}}_{\text{p}}$ network is highly fragmented, as shown by the comparatively large number of connected components (top) and the low connectance (bottom). On the other hand, both BiRG and ${\mathrm{BiPCM}}_{\text{c}}$ are composed of comparatively densely connected clusters. Isolated nodes are ignored in both figures.