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Unformatted text preview: o be of greater importance is crises of conﬁdence in the credit
3 See Shleifer and Vishny (2011) for a survey and Cifuentes, Ferrucci, and Shin (2005) for an extension of the EisenbergNoe framework with ﬁre sales. 3 quality of particular ﬁrms. If a ﬁrm’s perceived ability to pay declines for whatever reason, then so does
the market value of its liabilities. In a marktomarket regime this reduction in value can spread to other
ﬁrms that hold these liabilities among their assets. In other words, the mere possibility (rather than the
actuality) of a default can lead to a general and widespread decline in valuations, which may in turn
trigger actual defaults through marktomarket losses.4 This is an important phenomenon in practice:
indeed it has been estimated that marktomarket losses from credit quality deterioration exceeded losses
from outright defaults in 20072009.5
We capture this idea by reinterpreting the EisenbergNoe framework as a valuation model rather
than as a clearing model. Declines in conﬁdence about the ability to pay at some nodes can spread
to other nodes through a downward revaluation of their assets. This mechanism shows how a localized
crisis of conﬁdence can lead to widespread losses of value. Our analysis suggests that this channel of
contagion is likely to be considerably more important than simple domino or spillover eﬀects.
The rest of the paper is organized as follows. In Section 2 we present the basic EisenbergNoe
framework and illustrate its operation through a series of simple examples. In Section 3 we introduce
shock distributions explicitly. We then compare the probability that a given set of nodes default from
simultaneous direct shocks to their outside assets, with the probability that they default indirectly by
contagion from some other node. In Section 4 we examine the expected loss in value that is attributable
to network contagion using the comparative framework described above. We show that one can obtain
useful bounds on the losses attributable to the network with almost no knowledge of the speciﬁc network
topology and under very general assumptions about the shock distributions. In Section 5 we introduce
bankruptcy costs and show how to extend the preceding analysis to this case. Section 6 examines the
eﬀects of a deterioration in conﬁdence at one or more institutions, such as occurred in the 200809
ﬁnancial crisis. We show how such a loss of conﬁdence can spread through the entire system due to
marktomarket declines in asset values. In the Appendix we illustrate the application of these ideas to
the European banking system using data from European Banking Authority (2011). 2
2.1 Measuring systemic risk
The EisenbergNoe framework The network model proposed by Eisenberg and Noe (2001) has three basic ingredients: a set of n nodes
¯
N = {1, 2, ..., n}, an n × n liabilities matrix P = (¯ij ) where pij ≥ 0 represents the payment due from
p
¯
4 This mechanism diﬀers from a bank run, which could also be triggered by a loss of conﬁd...
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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
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