title: Three essays on the applications of multiplex networks in economics
Creators: name: Bonaccorsi, Giovanni
Publisher: name: IMT Alti Studi Lucca
Year: 2020

description: In the last years network theory has seen several theoretical advancements and an increasing number of interesting applications in various fields of knowledge such as in social, biological, human and economic networks. The use of network results in economics has led to fruitful developments in the theory of trade, of the economic effect of migration and of financial distress contagion. Moreover, in agent based modelling, a network structure is often employed as foundation for the behaviour of agents. Hence it has been demonstrated that the applications of network findings to different economic models can lead to new discoveries, showing that economic phenomena may obtain interesting explanations when network diffusion processes are taken into consideration. However, the main economic applications of network theory are often limited to single layer network results, where the networks employed represent one single type of relationship among the nodes and if more layers are analysed, they are considered independent. On the contrary an increasing number of publications by leading network scholars is focused on studying multilayer networks, where the same nodes have different types of links between them and their respective interdependence is recognized and studied. As a consequence, many of the single layer network concepts have been generalized to multilayer networks, improving previous analysis by adding the possibility to study different types of relations in an organic manner. In economics, in particular, network data regarding multiple relations among world countries has been employed over time but only recently the focus has shifted towards a more systematic approach. The first contribution of the present work is the harmonization of the majority of these sources in a consolidated dataset, the first merging together information from different fields: from flows of goods, to flows of financial contracts, to flows of people, to flows of citations. The final dataset spans over 40 years and 211 countries and reaches, in the more rich cross sections, 19 layers of data (ignoring duplicated and redundant sources). Since nodes are common across all layers the particular type of multilayer network we are using is a multiplex. In our first study on this new dataset we have measured the centrality of countries over time. We have identified two cross sections of layers, the years 2003 and 2010 (before and after the Great Financial Crisis), where the majority of the sources was present. Then we have harmonized the data filtering out excessive differences among the layers. Finally, we have applied on the dataset two recent multilayer algorithms which have generalized two of the most common centrality measures. The first is the MultiRank, the multilayer generalization of the PageRank algorithm, the second is the MD-HITS (MultiDimensional HITS) which generalizes the hubs and authority algorithm. Both the algorithms have been used to rank the importance of page results on the web and they highlight different features of the nodes: the first one refers to the property of webpages of being linked (cited) from other important ones, the second one instead is related to the status of a page as an important source of information (an authority) or as an important hub redirecting to authority pages. The interesting feature of both the multilayer generalizations of the algorithms is that they produce automatically two types of rankings: one for the nodes of the multiplex and one for the layers. This allows us to also identify which are the sources of importance of a certain country in the whole multiplex in an unsupervised manner. To obtain a measure of the relevance of these new methods we have compared the ranking of nodes obtained using the multiplex centrality measures with the ranking of countries by per capita GDP. We have found similarity in the rankings but not perfect correlation, signalling that our new dataset may contain some additional source of information to be exploited in explaining country development. After measuring country centrality, the second research question we have addressed with the aid of our new data sources regards the Great Financial Crisis. The collapse of the world financial markets in 2009, symbolically kick-started by the default of Lehman Brothers, made clear that economic theories were missing something, otherwise a crisis so deep and pervasive would have been avoided. One of the streams of research originated by this event is tightly related with network theory and it is the study of the propagation of contagious phenomena over networks, in particular financial distresses. However, contagion models are mostly theoretical and the empirical evidence on financial contagion is still scarce. Moreover, the econometric studies on financial crisis have yet to find a consistent and persistent explanation of why some countries are more affected than others during these events. Finally multilayer studies in this field are still rare. In this work we have used as starting point a consolidated set of evidences obtained in Feldkircher (2014). From a set of 95 economic and financial measures regarding world countries, they found only one which was significantly present in every model when trying to explain why countries have had different performances after the GFC: the growth of credit supply from domestic banks. Starting from this element we have integrated their analysis with a set of network variables obtained from each of our layers regarding topological features of the networks such as centrality (both at single and multilayer level), clustering and community structure. We have used their same methodology, Bayesian Model Averaging, to solve the issue of model selection and avoid bias in selecting the explanatory variables. With our final results we have improved on Feldkircher 2014 by finding a new variable which is consistently present in the majority of the analysed models: the kcore centrality of the investment layer. This result is important both because it confirms the relevance of network variables as explanatory candidates for economic models and because it introduces a new explanation for the different performance of countries after the crisis. Our last research question regards network embeddings and their use to predict missing links. In our dataset we have missing information due to unreported or censored data, to reconstruct it we have used the information available from the known part of the network to obtain predictions on the existence of the unobserved part. This is achieved employing the method of network embeddings both at single and multiple layer level: an embedding of a network is a mapping of the rich structure of the graph at node level to a lowerdimensional latent space where projections of nodes are optimized to be closer when they map to closer relations at graph level. By doing so networks can be used as features for machine learning tasks in a very flexible way. Among the network embeddings literature we have seen a recent development of several multilayer methods among which we have found the scalable multilayer network embeddings method (MNE, D. Zhang et al. (2018)) to be our best option for making predictions. By pairing the MNE binary prediction to the method of weighted stochastic block models (Peixoto, 2018a) to assign a weight to links we have predicted missing links in all the multiplex layers. Our results show that a certain level of reconstruction can be achieved, even though with wide variability by layer. To conclude, by answering these three research question we have shown how network measures can be of great help to improve the analysis of economic issues and in particular how the integration of different data sources mapping relation among countries can alter vividly the picture of the world that we have.