Three essays on the applications of multiplex networks ineconomics
2020
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.
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