Empirical Diffusion

-Just by Looking at Pictures
-Considering the Possible Transitions Between Products

Just by looking at pictures

Once the product space has been created and visualized, it becomes relatively easy to visualize the structural transformations of countries and how they are conditioned by the space itself. This study begins by visualizing where countries are located at different times, an amazing visual experience able to summarize the productive structure of a nation that preserves a significant level of detail. Figure 12s shows the products for which Malaysia has developed RCA with black squares. Figure 13s shows the same for Colombia. The versions presented here come from the beginning of our research, in which the layout was a slightly different, but still conserves the same color code and overall position. Node sizes are still proportional to world trade. We can appreciate that Malaysia had an impressive spread over the electronics and forest products cluster while during these same time period Colombia was able to spread through the garments sector.

Figure 1. Evolution of Malaysia (High Resolution Image) The products for which Malaysia has developed RCA are shown with black squares. Vector Image .ai.

Figure 2. Evolution of Colombia (High Resolution Image) The products for which Colombia has developed RCA are shown with black squares. Vector Image. ai.

Possible transitions between products

The visual examples presented above help develop our intuition and explain in a simple way how countries undergo structural transformations. They show that there is a tendency for countries to develop RCA close to products for which RCA was already developed, but are not a proof of this. For simplicity, we call a product for which a country has developed RCA, an occupied product (O), and one for which it has not an unoccupied product (U). When we compare two time points there are 4 possible transitions (U->U,U->O,O->U,O->O), and in our case, we are concerned with the second one which takes unoccupied products to occupied ones. Additionally, we call a product undergoing this particular transition: transition products. We now ask: are transition products closer to occupied products than to unoccupied ones? If this is significantly the case, it would be evidence supporting that countries perform structural transformations by jumping from occupied products to nearby ones.

To proof this we need to define some quantities. First we define density as the weighted fraction of the space which appears to be occupied from the point of view of a product in a particular country. Mathematically density wcan be written as:

,

where f ij is the proximity between the i'th and j'th product and x i is 1 when the i'th product is occupied and zero otherwise. To measure this quantity empirically we consider as undeveloped products all those that had an RCA<0.5 on 1990. Starting from this definition, transition products are the ones that had an RCA >1 on 1995 and undeveloped products are the ones that remain with an RCA<0.5 on 1995. The ones that had an RCA between 0.5 and 1 in 1995 were regarded as inconclusive.

Figure 2. Density distribution for products that underwent a transition and those that remain undeveloped.

Figure 14s shows that the density distribution for transition products takes significantly larger values than for products that remained undeveloped, suggesting that density predicts a transition. To further characterize this we can take the ratio between the average density of products on countries were they underwent a transition and compare it to the average density for countries were they remain undeveloped. We call this the discovery factor (H) which can be written as

where the top summation goes over the T countries where the j'th product underwent a transition and the bottom one over the N-T countries were the product remain undeveloped. Figure 15s shows that in fact for more ~80% of the goods this ratio is larger than one, illustrating again that density tends to be higher for transition products.

Figure 3. Distribution of the discovery factor H.

Yet another way to show this is to consider the probability for a product to develop given that the closest developed product is at proximity f. Figure 16s shows that this is a monotonically increasing function of f. In fact further inspection shows that P has a quadratic dependence on f. Thus the chances for a country to develop a product increase enormously when that product is close to an already developed one.

Figure 4. Probability of undergoing a transition given that the closest occupied product is at proximity f.