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Unformatted text preview: iated and thus capture the possibility that institutions have
portfolios that are exposed to common shocks (see for example Caccioli et al. 2012).
Two key ﬁndings emerge from this analysis. First we compute the probability that default at a given
node causes defaults at other nodes (via network spillovers), and compare this with the probability that
all of these nodes default by direct shocks to their outside assets with no network transmission. We
derive a general formula that shows when the latter probability is larger than the former, in which case
we say that contagion is weak. A particular implication is that contagion is always weak unless there is
substantial heterogeneity in node sizes as measured by their claims outside the ﬁnancial sector. More
generally, contagion will tend to be weak unless the originating node is large, highly leveraged, and –
crucially – has a relatively high proportion of its obligations to other ﬁnancial institutions as opposed to
the nonﬁnancial sector. Second, the analysis shows that the total additional losses generated by network
spillover eﬀects are surprisingly small under a wide range of shock distributions for plausible values of
model parameters. Both of these results are consistent with the empirical and simulation literature on
network stress testing, which ﬁnds that contagion is quite diﬃcult to generate through the interbank
spillover of losses (Degryse and Nguyen 2004, Elsinger, Lehar, and Summer 2006, Furﬁne 2003, Georg
2011, Nier et al. 2007). Put diﬀerently, our results show that contagion through spillover eﬀects becomes
most signiﬁcant under the conditions described in Yellen (2013), when ﬁnancial institutions inﬂate their
balance sheets by increasing leverage and expanding interbank claims backed by a ﬁxed set of real assets.
These results do not imply that all forms of network contagion are unimportant; rather they show that
simple spillover or “domino” eﬀects have only a limited impact at realistic levels of payment obligations
between banks. This leads us to examine other potential sources of contagion. The prior literature
has focused on the role of ﬁre sales, that is, the dumping of assets on the market in order to cover
losses.3 Here we shall focus on two alternative mechanisms that are more immediate extensions of the
simple spillover mechanism in the Eisenberg-Noe model and thus allow a more immediate comparison:
bankruptcy costs and losses of conﬁdence.
Bankruptcy costs magnify the costs associated with default both directly, through costs like legal
fees, and indirectly through delays in payments to creditors and disruptions to the provision of ﬁnancial
intermediation services necessary to the real economy. We model these eﬀects in reduced form through a
multiplier on losses when a node defaults. This approach allows us to estimate how much the probability
of contagion, and the expected losses induced by contagion, increase as a function of bankruptcy costs. A
somewhat surprising ﬁnding is that bankruptcy costs must be quite large in order to have an appreciable
impact on expected losses as they propagate through the network.
A second mechanism that we believe t...
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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