Graph Theory and — lost— Economic Development: Argentina in the 90s
Economic development was investigated by Hidalgo, Klinger, Barabási, and Hausmann(2007)[1] in a novel way. They analysed the exports for every country and created a graph relating exported products. This technique offers new visual and analytical tools to study economic development. When reading this paper, I wanted to replicate the analysis to get a deeper understanding on the decade of 1990 in my country, Argentina. The economic policy of this decade is blamed for the infamous crisis of 2001. In this post I’ll explain how I replicated the paper — which was a straightforward task — and I’ll do some comments comparing the year 1990 and the year 2000 in Argentina. You can find the Python code for this article is here.
The Model
This model uses data from international trade[2]. To create the objects of the model, we have to follow three steps:
- For each country compute its Revealed Comparative Advantage (RCA). This will give a value for each pair country-product. If for a country c and a product i, the RCA is bigger than 1, this shows that this country c significantly exports the product i—has revealed comparative Advantages.
- Using the RCA computed for all countries and products, we compute a distance between products: phi(r,s). This distance selects all the countries exporting product s, and compute the proportion of them which also export product r. Those countries export product r and product s in tandem. Probabilistically, we said that conditioned to a country exporting product s (RCA(s) >1), which is the probability for this country to export product r? These probabilities forms a square matrix, phi, which relates every product with all the others products. To compute this matrix the authors made it symmetric, computing the minimum value between the probability of export r conditioned to export s, and the probability of export s conditioned to export r. Additionally, this operation avoids technical issues that arise when a acountry is the only exporter of a given product.
- Finally, they needed a way to analyse this (sparse) matrix. We can view this matrix as a graph, where every product is a node and every cell represents a weighted edge. Now, we need a subgraph of this graph with all the nodes. To do so, we start with a set with some node (any node). Then, we add a neighbor not presented in the set using the edge with the highest weight. If we perform the described algorithm until all the nodes are in the set, the result will be a tree. In particular, this tree will be the maximum spanning tree.
The previous tree is the most important object of the work described. It has very interesting economics meaning. From its definition, we know that products that are close in the tree are more likely to be developed together — in the same country — .
Also, the authors found that
“industrialised countries occupy the core, composed of machinery, metal products, and chemicals[…]. Whereas Latin America and the Caribbean are further out in the periphery in mining, agriculture, and the garments sector.”
Having read that I want to see how my country looks like in this tree. As expected, the tree was populated in the periphery, having some clusters in a few branches (literally)
Argentina 1990–2000
To analyse this decade, we can plot in our tree the products that were exported in 2000 and weren’t exported back in 1990 — following the paper, I use RCA < 0.5 to define a non exported item — and the product exported in 1990 that weren’t exported in the year 2000.
As can be seen, the number of products exported in 2000 is higher (163 products) than the number of products exported in 1990 (156 products). But, does it means economic development? This question can be answered with a method proposed by the authors of the paper: a diffusion process. In its simple way, the diffusion process is an iterative process and in each iteration we add to the set of exported goods all the products that are neighbours of products currently exported. The metric of relevance is the number of iterations required to complete the tree. Surprisingly, if we use the export data from Argentina in 1990, it takes 16 iterations to complete. On the other hand, it requires 17 iterations using data from the year 2000! This is unsound given that the initial set is bigger in the year 2000! Moreover, using the number phi — the previously computed distance between products— as a probability of transition we can limit the diffusion process to products connected to exported products with an edge having a phi value greater than a threshold. In the definition of the phi value above, we relate it to the probability of export a product conditioned to being exporting a given product. Now, the diffusion process is simulating this contagious effect, with a minimum required probability.
As can be seen, the simulation using data from 1990 (the earlier state) took less iterations to run. Also, when the diffusion process stoped before reaching all the nodes, the set of developed products was consistently higher for the year 1990 than the year 2000 — for all phi values — . This result is very important and it is related to the quality of development: in Argentina, in the year 2000, we were in a bad position regarding development than 10 years before! During the 90's, industries that were unrelated to the core of Argentina’s exports were shutdown and the few industries that emerged were located near the current industrial cumulus , as the tree’s topology shows. The simulations shows that complete branches remains undeveloped for a threshold bigger than 0.5.
The list of products that were exported in 1990 and weren’t exported in 2000 included products as: 6781 TUBES AND PIPES, OF CAST IRON; 7913 RAILWAY & TRAMWAY COACHES; 7922 AIRCRAFT; 7933 SHIPS, BOATS AND OTHER VESSELS. While the products that emerged in 2000 includes: 5530 PERFUMERY, COSMETICS AND TOILET PREPARATIONS; 5543 POLISHES & CREAMS, FOR FOOTWEAR, FURNITURE OR FLOOR; 5849 OTHER CHEMICAL DERIVATIVES OF CELLULOSE. These lists aren’t complete but the products in there play an import rol in the difference between the two diffusion processes.
The authors finished their work noticing that
“It is quite difficult for production to shift to products far away in the space, and therefore policies to promote large jumps are more challenging. Yet it is precisely these long jumps that generate subsequent structural transformation, convergence, and growth.”
Our little exercise shows it is also important to make an effort in order to preserve the long jumps previously made, i.e.: the industries far away in the product space. It also shows this tool (Product Space analysis) appears quite suitable to help policy makers on their task.
[1] Hidalgo, César A., Bailey Klinger, A.-L. Barabási, and Ricardo Hausmann. “The Product Space Conditions the Development of Nations.” Science 317, no. 5837 (2007): 482–87.
