International Trade Network: Fractal Properties and Globalization Puzzle

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

Figure 1

The effect of distance on trade. Main stage: scattered plot of $v_{ij}=T_{ij}/(Q_i{Q}_j)$ versus $r_{ij}$, cf. Eq. (1), for the year 1980. Inset: cumulative measure $V(r)={\int }_r^{\pi R}{v}_{ij}d{r}_{ij}$, where $R$ is Earth’s radius. (The noise inherent to the data makes it difficult to clearly appreciate the power-law scaling of trade with distance. To overcome this problem and to estimate the value of $\alpha$, we have defined the quantity $V(r)$, which is integrated with respect to distance and corresponds to the area under the scattered plot shown in the main stage in the figure. The distance coefficient $\alpha$ has been calculated from the slope of the linear part of the plot $\ln V(r)$ versus $\ln r$, as shown in the inset. This procedure has been used to calculate distance coefficients for all the years in the period 1950–2000; see Fig. 2).

Figure 2

The year-by-year values of the distance coefficient $\alpha$ (black squares) in comparison with (i) the fractal dimension $d$ obtained from the box counting method (open triangles), and (ii) the parameter $\gamma$ obtained from the spatial choice model (open circles). Inset: the number of independent states in the world.

Figure 3

The object (i.e., set of circles of different radius) that reflects the topography of the real-world spatial economy in the year 1995. Description of the figure is given in the text.

Figure 4

The number of nonempty boxes $N$ needed to cover the object which is shown in Fig. 3 as a function of the size $ϵ$ of boxes. The scale is expressed in steradians. The gray area represents the sizes from about 100 to about 2000 km.

Figure 5

Histograms of the number of existing trade channels for three years: 1960 (bottom), 1980 (middle), and 2000 (top). Solid lines represent the best fits of Eq. (4) to real data.

Figure 6

(a) Basic spatial choice model in which agents are homogeneously distributed in the two-dimensional flat plane. (b) Model with agents homogeneously distributed on the sphere. (c) Model with agents heterogeneously distributed on the sphere. The corresponding diagrams below the schematic drawings show, how the number of available (black line) and realized (gray line with shaded area under it) connections depend on their length.

Figure 7

Time dependence of (i) the average length $⟨r⟩$ of the trade connection (black circles), (ii) the mean of the distribution given by Eq. (2) (gray stars), and (iii) the mean of the distribution given by Eq. (4) (open squares).