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Product Progression Network


Is there a common path on countries development, or each country must follow his own way? In order to produce cars, one has to learn how to produce wheels before? To answer to these questions, we have imagined countries as walkers in a directed network made of goods, defined such that if a country steps on one product, it will export it. Obviously, paths can be very different: while Germany has already explored much of the available space, underdeveloped countries have a long road ahead. And, obviously, direction matters, as one should aim at technological progress. Which are the best paths in the product network?

The general idea is that products are defined by means of the set of skills which are needed for a country to be able to produce it, and the presence (or the absence) of a product in a country’s export basket will represent a hint on the capability basket of the country itself, i.e. all the ingredients that are needed to build the products it exports (i.e. specific technological skills, materials, industrial infrastructures). Usually the starting point consists in building a network of products in which two nodes are connected if they share some capabilities. However, these are practically impossible to measure so, in practice, what one usually does is to link two products if many countries produce both of them. However, our research activity aims at building a different network of products, in which two products are connected not only if they are similar, but also if the first is usually a preliminary step to produce the second, like transistors for smartphones, cows for leather, and wheels for cars. In this kind of network links have to be directed: a country usually goes from one product to another, but not vice versa.

We called this structure the taxonomy network: nodes (such as products) are connected by a directed link, which represents the causality relationship between them. We have studied the influence of the structure of our network on countries’ development and, in particular, we have focused on the industrialization of South Korea, noticing for many components a diffusion from the center (root product) towards the borders of the components, where more complex products are located. Driven by this example, we analyzed all countries in our database, finding that when countries get industrialized they walk in the taxonomy network following the directed links from one product to another, retracing the structure of our network. In other words, we are able to spot which products are connected by a sort of causal relationship, that is, which products are helpful to start to export new products. Moreover, we have found that once countries are industrialized, they start to specialize again, but now in complex products. These results suggest paths in the network of products which are easier to achieve, and so can drive countries’ policies in the industrialization process.

Recently, we proposed a significant improvement of this methodology. This approach, called Product Progression Network, provides two major improvements with respect to previous attempts in the literature:

1. the Product Progression Network takes explicitly into account the time evolution of the export baskets, computing a time-delayed projection of two and not one bipartite networks, and

2. the filtering procedure is made by selecting the statistically significant links with respect to a suitable null model.

In the figure we show the Progression Network for a database constituted by both physical goods and services, in which we have kept only those links that are statistically significant at the p=0.0001 level. Blue nodes are goods-only sectors, while yellow nodes represent services. At a glance, one notices that services are not segregated, in the sense that they do not constitute a cluster on their own: on the contrary, they are fully integrated with the industrial sectors, indicating that they share a high number of capabilities. This is true, in particular, for the high complexity services such as Research and Development and Intellectual Property, that are highly connected with sophisticated industrial sectors, such as Aircraft and Spacecraft and Pharmaceutical. We point out that, in these cases, there is no net flux of information going from a sector to the other: instead, all these sectors benefit from the presence of the other sectors in the same country at the same time. On the left a textile sector is present, containing Leather, Footwear, and Knitted Clothing, while in the lower corner one can find raw materials and basic agriculture.

The centrality of complex services such as finance, research and development, business consulting, and intellectual property provides new insights with respect to the goods-only approach. These complex services can help countries gain competitiveness in (a) other services such as air-transport, sea-transport, and business services, and (b) advanced manufacturing components in the world trade network, such as pharmaceuticals, photographic, cinematic goods, and electrical machinery. The centrality of complex services reinforces the idea that ignoring services specialization will misinform about production structure and potential opportunities for countries.


Comparison among some of the main predicting methodologies.

More details will be given in [4].

Method/Metric AUC Best F1
Autocorrelation* 0.68 0.15
Random Forest 0.74 0.12
pvalue BiCM 0.70 0.10
weighted BiCM 0.72 0.11
Taxonomy, best 80 links 0.70 0.10
Assist matrix, best 80 0.72 0.11
Product Space 0.67 0.085










* trained on an extended dataset.


[1] A. Zaccaria, M. Cristelli, A. Tacchella, and L. Pietronero, How the Taxonomy of Products Drives the Economic Development of Countries, PLoS ONE 9 (12): e113770, (2014)

[2] E. Pugliese, G. Cimini, A. Patelli, A. Zaccaria, L. Pietronero, and A. Gabrielli, Unfolding the innovation system for the development of countries: co-evolution of Science, Technology and Production, arXiv:1707.05146, (2017)

[3] A. Zaccaria, S. Mishra, M. Cader, and L. Pietronero, Integrating services in the economic fitness approach, World bank policy research working paper, WPS8485, (2018)

[4] I. Baybusinov, et al. Forthcoming