Three essays on the applications of multiplex networks in economics

In the last years network theory has seen several theoreticaladvancements and an increasing number of interesting applicationsin various fields of knowledge such as in social,biological, human and economic networks.The use of network results in economics has led to fruitfuldevelopments in the theory of trade, of the economic effectof migration and of financial distress contagion. Moreover,in agent based modelling, a network structure is often employedas foundation for the behaviour of agents. Hence ithas been demonstrated that the applications of network findingsto different economic models can lead to new discoveries,showing that economic phenomena may obtain interestingexplanations when network diffusion processes are takeninto consideration.However, the main economic applications of network theoryare often limited to single layer network results, where thenetworks employed represent one single type of relationshipamong the nodes and if more layers are analysed, they areconsidered independent. On the contrary an increasing numberof publications by leading network scholars is focused onstudying multilayer networks, where the same nodes havedifferent types of links between them and their respective interdependenceis recognized and studied. As a consequence,many of the single layer network concepts have been generalizedto multilayer networks, improving previous analysisby adding the possibility to study different types of relationsin an organic manner.In economics, in particular, network data regarding multiplerelations among world countries has been employed overtime but only recently the focus has shifted towards a moresystematic approach. The first contribution of the presentwork is the harmonization of the majority of these sources ina consolidated dataset, the first merging together informationfrom different fields: from flows of goods, to flows of financialcontracts, to flows of people, to flows of citations. The finaldataset spans over 40 years and 211 countries and reaches,in the more rich cross sections, 19 layers of data (ignoring duplicatedand redundant sources). Since nodes are commonacross all layers the particular type of multilayer network weare using is a multiplex.In our first study on this new dataset we have measured thecentrality of countries over time. We have identified two crosssections of layers, the years 2003 and 2010 (before and afterthe Great Financial Crisis), where the majority of the sourceswas present. Then we have harmonized the data filtering outexcessive differences among the layers. Finally, we have appliedon the dataset two recent multilayer algorithms whichhave generalized two of the most common centrality measures.The first is the MultiRank, the multilayer generalizationof the PageRank algorithm, the second is the MD-HITS(MultiDimensional HITS) which generalizes the hubs and authorityalgorithm. Both the algorithms have been used torank the importance of page results on the web and they highlightdifferent features of the nodes: the first one refers to theproperty of webpages of being linked (cited) from other importantones, the second one instead is related to the status ofa page as an important source of information (an authority)or as an important hub redirecting to authority pages. The interestingfeature of both the multilayer generalizations of thealgorithms is that they produce automatically two types ofrankings: one for the nodes of the multiplex and one for thelayers. This allows us to also identify which are the sourcesof importance of a certain country in the whole multiplex in an unsupervised manner. To obtain a measure of the relevanceof these new methods we have compared the rankingof nodes obtained using the multiplex centrality measureswith the ranking of countries by per capita GDP. We havefound similarity in the rankings but not perfect correlation,signalling that our new dataset may contain some additionalsource of information to be exploited in explaining countrydevelopment.After measuring country centrality, the second research questionwe have addressed with the aid of our new data sourcesregards the Great Financial Crisis. The collapse of the worldfinancial markets in 2009, symbolically kick-started by the defaultof Lehman Brothers, made clear that economic theorieswere missing something, otherwise a crisis so deep and pervasivewould have been avoided. One of the streams of researchoriginated by this event is tightly related with networktheory and it is the study of the propagation of contagiousphenomena over networks, in particular financial distresses.However, contagion models are mostly theoretical and theempirical evidence on financial contagion is still scarce. Moreover,the econometric studies on financial crisis have yet tofind a consistent and persistent explanation of why some countriesare more affected than others during these events. Finallymultilayer studies in this field are still rare.In this work we have used as starting point a consolidated setof evidences obtained in Feldkircher (2014). From a set of 95economic and financial measures regarding world countries,they found only one which was significantly present in everymodel when trying to explain why countries have had differentperformances after the GFC: the growth of credit supplyfrom domestic banks. Starting from this element we haveintegrated their analysis with a set of network variables obtainedfrom each of our layers regarding topological featuresof the networks such as centrality (both at single and multilayer level), clustering and community structure. We haveused their same methodology, Bayesian Model Averaging, tosolve the issue of model selection and avoid bias in selectingthe explanatory variables. With our final results we have improvedon Feldkircher 2014 by finding a new variable whichis consistently present in the majority of the analysed models:the kcore centrality of the investment layer. This result isimportant both because it confirms the relevance of networkvariables as explanatory candidates for economic models andbecause it introduces a new explanation for the different performanceof countries after the crisis.Our last research question regards network embeddings andtheir use to predict missing links. In our dataset we havemissing information due to unreported or censored data, toreconstruct it we have used the information available fromthe known part of the network to obtain predictions on theexistence of the unobserved part. This is achieved employingthe method of network embeddings both at single and multiplelayer level: an embedding of a network is a mappingof the rich structure of the graph at node level to a lowerdimensionallatent space where projections of nodes are optimizedto be closer when they map to closer relations at graphlevel. By doing so networks can be used as features for machinelearning tasks in a very flexible way. Among the networkembeddings literature we have seen a recent developmentof several multilayer methods among which we havefound the scalable multilayer network embeddings method(MNE, D. Zhang et al. (2018)) to be our best option for makingpredictions. By pairing the MNE binary prediction to themethod of weighted stochastic block models (Peixoto, 2018a)to assign a weight to links we have predicted missing links inall the multiplex layers. Our results show that a certain levelof reconstruction can be achieved, even though with widevariability by layer.To conclude, by answering these three research question wehave shown how network measures can be of great help toimprove the analysis of economic issues and in particular howthe integration of different data sources mapping relation amongcountries can alter vividly the picture of the world that wehave.