On the fundamental reasons for bank fragility
ABSTRACT A substantial body of literature has now developed as a result of efforts to identify the fundamental reasons for the fragility of financial intermediaries in the Diamond-Dybvig theory of banking. Many of these articles focus on the interaction between sequential service and uncertainty about the aggregate need for liquidity in the economy. The articles in this literature are inevitably technical and focus somewhat narrowly on the implications of specific assumptions. Here, we provide a more accessible discussion of the main ideas and findings in this literature. Our discussion can be used as an introduction to the more technical articles or as an organizing framework for understanding the relative contribution of the main articles in this literature.
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ABSTRACT: Sequential service in the banking sector, as modeled by Diamond and Dybvig (1983), is a barrier to full insurance and potential source of financial fragility against which deposit insurance is infeasible (Wal-lace, 1988). In this paper, we pursue a different perspective, view-ing the sequence of contacts as opportunities to extract information through a larger message space with commitment to richer promises. As we show, if preferences satisfy a separating property then the de-sired elimination of dominated strategies (Green and Lin, 2003) occurs even when shocks are correlated. In this manner the sequential service promotes stability.03/2011;
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: firstname.lastname@example.org; email@example.com.
Federal Reserve Bank of Richmond Economic Quarterly
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 Fragility37
To understand the implications of agents possibly misrepresenting their
imposing the incentive constraints. We will call the solution to this modified
problem the unconstrained-efficient allocation.4
In general, the incentive compatibility constraint for an individual agent
in this environment depends on the assumed behavior of the rest of the agents.
While it may be incentive compatible for an agent to not misrepresent her
consumption needs when all the other agents are also not misrepresenting, the
situation may be different when the other agents are expected to misrepresent.
This payoff complementarity is important because it creates the potential for
strategic coordinated responses that may result in substantial inefficiencies.
induced by a given contingent consumption allocation, i.e., a complete pay-
ment scheme. In the withdrawal game, agents decide when to contact the
resource pool (the bank) to demand payment. An allocation is implementable
(under truthful representation) if there is a Nash equilibrium of the induced
withdrawal game in which all impatient agents withdraw early and all patient
also called incentive feasible, in the sense that it satisfies the incentive com-
patibility constraint for each individual agent given that all the other agents
are not misrepresenting their consumption needs. If the equilibrium of the
withdrawal game is unique, we say that the allocation is strongly (or fully)
implementable. As we will see, implementable allocations in the Diamond-
Dybvig model are sometimes not strongly implementable. In those cases,
there exists another Nash equilibrium of the withdrawal game in which some
patient agents misrepresent their need to consume and attempt to withdraw
early, in effect running to obtain payment from the pool before its resources
Diamond and Dybvig (1983) make some additional simplifying assump-
tions that turn out to have significant implications for their results. In par-
ticular, they assume that there is a continuum of agents in the economy and
that preference types (patient or impatient) are independent and identically
distributed (i.i.d.) across agents. The combination of these two assumptions
and the law of large numbers implies that the total need for early consump-
tion is completely predictable. In other words, if the bank believes that only
impatient agents will withdraw before investment matures, then it knows the
total demand for liquidity even before agents begin placing their requests.
4The unconstrained-efficient allocation is the best allocation that can be attained when pref-
erences of agents are observable. Since we consider the sequential service constraint a reflection
of a feature of the physical environment (Wallace 1988), the unconstrained-efficient allocation must
satisfy sequential service in the same way that it must satisfy resource feasibility.