Economic Quarterly—Volume 96, Number 1—First Quarter 2010—Pages 33–58
Reasons forBank Fragility
Huberto M. Ennis and Todd Keister
bank being taken into state ownership. In the United States, the investment
bank Bear Stearns and the commercial bank Wachovia both experienced a
rapid loss of funding and were taken over by other institutions to avoid their
outright failure. This same phenomenon affected other types of institutions as
well, including a large part of the money market mutual fund industry, which
experienced heavy withdrawals following the failure of the Reserve Fund in
These episodes are only the most recent examples of a phenomenon that
has been a recurrent theme in the history of banking. Banking panics, with
occurrence in the United States prior to the advent of government-sponsored
deposit insurance in 1933. Developing economies have also experienced runs
on their banking system, including episodes in Ecuador (1999), Argentina
(2001), and Russia (2004).
Observers of these episodes often claim that there is an important self-
fulfilling component to the behavior of depositors and/or investors. In this
view, each depositor fears that the withdrawals of other depositors will cause
the bank to fail and rushes to withdraw her funds before this failure occurs.
Collectively, these actions validate the original belief that a wave of with-
drawals will cause the bank to fail. During the height of the Panic of 1907
in the United States, J.P. Morgan was reported in the NewYork Times to have
ver the course of the recent financial crisis, several large financial
institutions experienced sudden, massive withdrawals of their usual
We would like to thank Borys Grochulski, Ned Prescott, and Juan S´ anchez for comments on
a previous draft. The views expressed here do not necessarily represent those of the Federal
Reserve Bank of New York, the Federal Reserve Bank of Richmond, or the Federal Reserve
System. E-mails: email@example.com; firstname.lastname@example.org.
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said, “If the people would only leave their money in the banks instead of with-
drawing it...everything would work out all right.”1In other words, Morgan
claimed that it was the behavior of the depositors themselves that was placing
the largest strain on the banking system. If this strain were removed, individ-
uals would be willing to leave their money deposited and a superior outcome
This view of events implies that banks and other financial intermediaries
are inherently fragile, in the sense of being susceptible to a self-fulfilling run
by their depositors. The degree to which one accepts this view has strong
implications for public policy. The desirability of government-provided de-
posit insurance, for example, and of other public interventions in the banking
system depends in large part on whether banking crises do indeed have an
important self-fulfilling component or whether they instead result from other,
more fundamental causes.
A substantial economic literature has developed that attempts to identify
the essential components that would justify a self-fulfilling interpretation of
events. Bryant (1980) and Diamond and Dybvig (1983) provided the first
early contributions is sufficient to explain banking and the fragility of banks
and other financial intermediaries, and which other elements, if any, may be
The approach taken in this literature has been to specify a complete phys-
ical environment and to study economic outcomes that agents in such an en-
vironment could achieve without imposing any artificial restrictions on their
ability to enter mutually beneficial arrangements. In following this approach,
the literature has become fairly technical and intricate. In this article, we aim
to provide an informal discussion of the issues and the results produced so far
in this literature. We hope that our endeavor will make the lessons obtained
from this body of work more readily accessible to readers who may be less
inclined to endure over the many technical issues involved in the subject.
We begin our discussion by reviewing the key theoretical contribution of
the seminal work by Diamond and Dybvig (1983). We discuss the basic ele-
the technical difficulties involved in designing an equilibrium concept that al-
lows for the possibility of a bank run. As will become clear in the discussion,
(or sequential service) constraint. In Section 2, we discuss how the litera-
ture has handled the specification of an explicit sequential service constraint.
Several important recent contributions in this literature have resulted from the
1New York Times, October 26, 1907, “Bankers Calm; Sky Clearing.”
H. M. Ennis and T. Keister: Bank Fragility 35
efforts to combine explicitly modeled sequential service with the presence of
aggregate uncertainty about the fundamental need for liquidity in the system.
We review those contributions and how they relate to each other in detail. In
Section 3 we discuss some potentially fruitful directions for further research
and, finally, we close the article with some brief concluding remarks.
1.THE DIAMOND-DYBVIG MODEL
This section presents an overview of the seminal contribution by Diamond
and Dybvig (1983) and sets the stage for the discussion of the more recent
and Dybvig’s theory, banks play an essential role in the process of maturity
transformation: they issue short-term (deposit) liabilities in order to finance
long-term productive investment. While maturity transformation may happen
through other channels in the economy, Diamond and Dybvig identify two
other essential features of banking arrangements: the fact that agents’ de-
mands must be dealt with on a first-come, first-served basis, and the fact that
agents’true liquidity needs remain private information. These three elements
constitute the foundations of Diamond and Dybvig’s theory of banking and
are also the source for the potential of bank fragility in their model.
The Physical Environment
Diamond and Dybvig (1983) consider an environment where a large number
of agents face idiosyncratic uncertainty about their intertemporal desire to
that can be used to transform these goods into (potentially more) goods in the
future. If investment is left in place long enough to mature, the net returns
are positive. However, some agents will discover that they are impatient and
need to consume before the investment matures. Other agents are patient and
able to consume after investment has matured.
Investment takes place before agents discover their intertemporal prefer-
ence for consumption. To the extent that the idiosyncratic desire to consume
early is not perfectly correlated among agents, there are insurance possibil-
ities to be exploited in this environment. In particular, there exists a clear
social benefit from pooling resources ex ante, before preferences are realized,
investing in the long-term technology, and then making payments ex post to
agents, contingent on their needs.
Diamond and Dybvig (1983) assume that an agent’s realized preference
type (patient or impatient) is private information. Any attempt to provide
for consumption must, therefore, rely on reports from agents. This fact could
complicate matters in two ways. First, the ex-post payments to agents must
Federal Reserve Bank of Richmond Economic Quarterly
be arranged in such a way as to create the right incentives for each individual
opens the door to the possibility of a coordinated misrepresentation by agents,
which may be interpreted as a run to withdraw from the pool. The insurance
possibilities associated with a pooling arrangement depend crucially on its
ability to avoid these two types of misrepresentation.
In principle, it would be beneficial to collect as much information as
possible about the total demand for withdrawals before making any payments
from the resource pool. However, Diamond and Dybvig (1983) assume that
agents who decide to withdraw early place their demands sequentially, and
that payments from the pool must be made at the time each demand is placed.
they call a sequential service constraint. Diamond and Dybvig argue that this
kind of restriction is a realistic description of how banks operate.2
ResourceAllocation and Optimality
Diamond and Dybvig’s simple environment provides a natural setup to think
about the institution of banking. In the model, agents initially deposit their
endowments in a pool, which can be interpreted as a “bank.” In exchange for
her deposit, an agent receives a claim to future consumption from this bank.
Afterdepositsaremade, thebankinvestsinthelong-termtechnology. Finally,
agents discover their consumption needs and contact the bank sequentially to
withdraw resources and consume. The bank makes payments to agents, on
demand, in a pre-arranged manner.
From a theoretical point of view, it is appealing to abstract from institu-
tional details and focus instead on allocations of consumption that are achiev-
the structure of information. Much of what is done in Diamond and Dybvig’s
(1983) article is consistent with this strategy. Following the basic principles
in the theory of mechanism design, the way to proceed is to set up a planning
problem that consists of choosing a (contingent) consumption allocation to
maximize the ex ante expected utility of agents subject to incentive compat-
ibility, sequential service, and resource feasibility constraints.3We will call
this allocation the constrained-efficient allocation.
2An important component of a formal sequential service constraint is the specification of
whether or not agents who decide to not withdraw early still contact the pool at that time. Diamond
and Dybvig (1983) implicitly assume that only agents who are attempting to withdraw contact the
pool. We return to this issue later in this article.
3Going back to the interpretation of the theoretical constructions in terms of the institutions
of banking, it can be demonstrated that under certain conditions the solution to this planning
problem is equivalent to the outcome that would obtain when profit-maximizing banks compete
H. M. Ennis and T. Keister: Bank Fragility55
consistent with equilibrium. In other words, bank fragility is possible in the
Ennis-Keister version of the Diamond-Dybvig model with limited commit-
ment, even though there is no fundamental source of aggregate uncertainty in
the model. Interestingly, the equilibria of the model have a natural “dynamic”
structure, which derives from the fact that agents have information about their
position in the order of early withdrawal opportunities (as in Green and Lin
). An equilibrium bank run consists of an initial wave of withdrawals,
which is followed by a reaction from policymakers. Following this reaction,
the run may end or it may continue with another wave of withdrawals taking
place, which would lead to another reaction from policymakers, and so on.
This interplay between the withdrawal decisions of agents and the reaction of
policymakers seems to be an important feature of real-world banking crises.
There is a long tradition in policy of regulating the activity of banking. One
common approach has been to restrict the type of investments that banks are
allowed to undertake. For example, for more than 50 years, banks in the
United States that accepted deposits from the public were prohibited from
engaging in certain asset management activities, which were reserved for a
different set of institutions called investment banks. These restrictions were
imposed partly as a way to address the possibility of bank fragility. When
those policies were designed, a formal theory of banking was not available.
Diamond and Dybvig (1983) and the literature that followed have provided
such theory and, hence, it is natural to ask how this kind of policy influences
outcomes in the models within this tradition. Peck and Shell (2010) address
Peck and Shell (2010) consider an environment with an indivisibility in
consumption, which is aimed at capturing the payment function of demand
deposits: A check written for a purchase, for example, either pays the bearer
at par or may not be useful for exchange. Peck and Shell consider an envi-
ronment with two investment technologies: one technology is as in the stan-
dard Diamond-Dybvig model and the other has higher long-run return but is
completely illiquid in the short run. They analyze two regulatory systems for
banks—a unified system and a separated system. In the unified system, banks
system, however, banks cannot invest in the illiquid technology and agents do
that directly. Somewhat surprisingly, Peck and Shell show that runs can hap-
pen in the separated system but not in the unified system. They conclude
that policies that impose restrictions on the investment strategies of banks can
actually have unexpected, counterproductive effects by inducing fragility in
Federal Reserve Bank of Richmond Economic Quarterly
Understanding the root causes of the banking crises that have been observed
around the world is an extremely difficult task. Some commentators claim
that self-fulfilling behavior on the part of depositors and investors plays a
critical role, while others emphasize more fundamental factors related to the
value of banks’assets. Banking crises are complex phenomena that typically
occur in conjunction with a variety of unfavorable financial and macroeco-
nomic factors, making it difficult to determine the true underlying cause of an
event. In spite of these difficulties, progress has recently been made in several
directions. This article reviews the progress in one of these directions.
The literature we have discussed shows that it is possible to provide an
internally consistent explanation for the self-fulfilling interpretation of bank
runs. However, this literature also shows that the details of the environment
are important. In other words, the fragility of banks in these models is the
result of physical and informational frictions, but only specific combinations
of these frictions lead to fragility. In particular, information about the actions
of agents must not flow too quickly, so that the bank makes a significant
amount of payments to depositors before discovering whether or not a run is
of convertibility clauses in deposit contracts either undesirable or ineffective.
How important are self-fulfilling factors in the explanation of observed
crises? It may very well be the case that the types of frictions described in this
had a considerable self-fulfilling component. If these theories are a useful
reflection of reality, however, it is important to realize that natural changes in
the way information flows in the economy (because of, for example, techno-
logical innovation) could have substantial implications for bank fragility in
the future. In addition, it seems important to recognize that our understanding
of the issues involved remains fairly limited. Identifying appropriate policies
to deal with bank fragility, then, must be an ever-evolving activity that takes
into account changes in the structure of the financial system as well as fur-
ther developments in our understanding of the issues. The theories we have
discussed here provide a solid foundation for pursuing these important and
H. M. Ennis and T. Keister: Bank Fragility 57
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