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Simulated Diffusion

One diffusion step

Empirically, we showed using examples and statistics that products in which countries develop RCA tend to lie close to other products for which these countries have already developed RCA.

Using these we try to anticipate how a country will diffuse across the product space. As an example, we show figure 17s, in which we highlighted with black squares all products at a given proximity of the ones already developed by Chile and Korea. We refer to this example as one diffusion step.

In this case we tuned the proximity of the jump and show that for high proximities the set of options available is small while for low proximities is large, however different.

The available options are strongly conditioned by current exports. Korea is a country that has developed RCA in several branches of machinery and therefore can diffuse from the center of the space. At proximity of 0.5 its options include the entire core of the network plus the entire electronics and garments clusters, among other things. Chile diffuses from the periphery and to achieve a similar set of options needs to diffuse as far as proximities of 0.3.

In summary we find that the set of options available for a country are strongly conditioned by its position in the product space and its ability to diffuse into products up to given proximities.

Figure 1. One step diffusion process for Korea and Chile. The black squares denote all products closer than a given proximity considering their exports baskets in the year 2000.

Iterated diffusion

We can refine the diffusion process presented above by choosing a particular proximity and iterate the one step diffusion process. This represents a set of products potentially available to countries after diffusing to close products iteratively. At this point we ask ourselves: Is there a critical value of proximity at which countries will be able to diffuse across the product space? To explore this question we simulate a diffusion process in which a country "jumps" to all goods reachable from its current export basket, such that the proximity to them is larger or equal than a given value. Figure 18s illustrates through a color code the products available to Chile and Korea after diffusing iteratively at different proximities for 4 time steps. We observe that at relatively low proximities ( f = 0.55) both countries are able to diffuse, however Chile does so much slower and reaches the core in the second and third rounds, compared to Korea which does so on the first and second. At larger proximities the diffusion process halts. At f = 0.65 Chile is unable to diffuse at all, while Korea slowly does so close to the core of the product space.

Figure 2. Iterated diffusion process for Chile and Korea.

Economic Convergence

We characterize the value of a certain configuration by considering the value of its top products. We can assign value to a good by following the work of Hausmann, Hwang and Rodrick in which the value or sophistication of a good is equal to the average GDP per capita associated with that good. This quantity is called PRODY and in our particular example we consider the average PRODY of the top N products of a countries export basket after M diffusion steps with proximity f. We denote this quantity by .

Figure 3. Distribution for the average PRODY of the top 50 products reached after 20 diffusion steps at three different proximities.

Figure 19s shows that the original distribution of is bimodal. Indicating a world in which countries are divided into those producing sophisticated goods and unsophisticated ones. If we allow countries to diffuse in this space to acquire only goods that are really close by ( f=0.65). This distribution remains practically unchanged evidencing the structural constrains imposed by the product space. Whereas, if we allow countries to diffuse into products at relatively large proximities ( f=0.55) we find that after a large number of rounds most countries are able to reach the most attractive parts of the space, except for a few of them that remain stuck in the lowest bracket of this distribution