Unformatted text preview: to pay its creditors in full, who may
be unable to pay their creditors in full, and so forth. The original shortfall in payments can cascade
through the system, causing more and more banks to default through a domino eﬀect. The EisenbergNoe
framework shows how to compute a set of payments that clear the network, and it identiﬁes which nodes
default as a result of an initial shock to the system. The number and magnitude of such defaults depend
on the topological structure of the network, and there is now a substantial literature characterizing those
structures that tend to propagate default or alternatively that tend to dampen it (Gai and Kapadia 2010,
Gai, Haldane, and Kapadia 2011, Haldane and May, 2011, Acemoglu, Ozdaglar, and TahbazSalehi 2013,
and Elliott, Golub, and Jackson 2013).
Much of this literature proceeds by examining the eﬀects of ﬁxed shocks applied to particular nodes
rather than fully specifying the distribution that generates the shocks. In this paper we analyze the
probability of contagion and the expected losses generated by contagion when the joint distribution of
shocks is given. We then apply the framework to answer the following questions about the impact of
network eﬀects. First, how likely is it that a given set of banks will default due to contagion from another
node, as compared to the likelihood that they default from direct shocks to their own assets? Second,
how much does the network increase the probability and magnitude of losses compared to a situation
where there are no connections?
To compare systems with and without interconnections, we proceed as follows. First, we deﬁne our
nodes to be ﬁnancial institutions that borrow and lend on a signiﬁcant scale, which together with their
obligations to one another constitute the ﬁnancial network. In addition, such institutions borrow and
lend to the nonﬁnancial sector, which is composed of investors, households, and nonﬁnancial ﬁrms. We
compare this system to one without connections that is constructed as follows. We remove all of the
obligations between the ﬁnancial nodes while keeping their links with the nonﬁnancial sector unchanged.
We also keep node equity values as before by creating, for each node, a ﬁctitious outside asset (or liability)
whose value equals the net value of the connections at that node that were removed. We then apply
the same shock distributions to both systems, with the shocks to real assets originating in the external
sector and the ﬁctitious assets (if any) assumed to be impervious to shocks. We can ascertain how much
the network connections contribute to increased defaults and losses by comparing the outcomes in the
two systems.
One might suppose that the comparison hinges on what shock distribution we use, but this turns
out not to be the case: we show how to compute general bounds on the increased losses attributable to
network contagion that hold under a wide variety of distributions. The bounds also hold whether the 2 shocks are independent or positively assoc...
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This document was uploaded on 02/20/2014 for the course ECON 101 at Pontificia Universidad Católica de Chile.
 Spring '11
 Traferri

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