Problems of ranking and dynamics of complex bipartite networks

A recent new line of research that aims to couple network theory and economics has grown in the last decade, thanks to its ability to capture information from large datasets of exports and cast it into human-readable measures to rank nations and commodities. With Economic Complexity, we aim to infer as much as possible meaningful information about the nodes of the network of worldwide exports and, possibly, use this information to deduce the future topology of the economic network. In this thesis, we will present a new algorithm to measure the complexity of nations and the ubiquity of products, based on a self-consistent use of the Shannon entropy function that makes full use of the exports dataset information. We will discuss how these new entropic measures differ from the usually used complexity measures in the economic complexity framework, such as Fitness and Economic Complexity Index (ECI), highlighting the improvements. An original discussion about the dynamics of the measure will be presented, constructing an entropy-income plane by coupling the entropic complexity measure to some macroeconomic monetary indicator. A coarse-grained analysis of the plane will unveil a flow structure, individuating a laminar dynamics region thanks to the entropic dimension of nations. Moreover, we will observe how entropy and economic stability are strongly correlated. Finally, we will use the dynamical information of the entropy-income plane to predict Gross Domestic Product (GDP) growth at five years. We will use an algorithm developed in the context of Fitness, the selective predictability scheme bootstrap. This algorithm is an example of the method of analogues, firstly developed in the context of atmospheric prediction, as we will look at historical dynamics of nations with comparable entropy and GDP, hence at the analogues, to infer future growth. However, in the original formulation of the algorithm the problem to choose the right ”comparable” nations’ dynamics was not addressed. We will individuate and solve this problem using a statistical learning approach to historical data, combined with an update of the algorithm towards kernel regression. The use of the maximum information available in the dataset of exports, their stability against noisy data, the relevant dynamical information, and the improvement in accuracy of a 20% with respect to the International Monetary Fund prediction of growth make this measure an excellent candidate to rank nations and products according to their relevance in the trade market.