American Economic Review 2009, 99:4, 1588–1607
We study ex post efficient policy responses to a run on the banking system and the ex ante
incentives these responses give to depositors. We focus primarily on system-wide runs, where
depositors rush to withdraw their funds from all banks in the economy simultaneously. Argentina
experienced such a run in the last two days of November 2001, with total deposits in the banking
system falling by more than 2 billion (US) dollars, or nearly 3 percent, on the second day of the
run alone.1 Such runs were a common occurrence in the United States in the late nineteenth and
early twentieth centuries and have also occurred in recent times in several developing countries,
including Brazil in 1990 and Ecuador in 1999.
A widespread bank run invariably provokes some intervention by the government and/or central
bank. A wide range of policy responses are possible and, in practice, the details of the response
vary across episodes. However, two key elements are typically present. First, at some point depos-
its are frozen, meaning that further withdrawals are strictly limited. In Argentina, deposits were
frozen for a period of 90 days beginning on December 1, 2001; this freeze was extended in various
ways until early 2003. Deposit freezes were also a regular feature in US banking history, with the
last occurring in March 1933 (Milton Friedman and Anna J. Schwartz 1963). Second, a reschedul-
ing of payments occurs. Some demand deposits might be converted to time deposits with a penalty
for early withdrawal. In addition, depositors may find that their access to funds is made contingent
on their ability to demonstrate an urgent need to withdraw. The court system in Argentina, for
example, was heavily involved in verifying individual depositors’ circumstances in 2001–02.
We focus on policy interventions that are efficient ex post, once a run is underway. Our objective
is to capture the effects of institutional features that prevent policymakers from being able to pre-
commit to follow a particular course of action in the event of a crisis. Instead, the authorities inter-
vene during the crisis and attempt to improve the allocation of resources given the situation at hand.
We show how the anticipation of such an intervention can generate the conditions necessary for a
self-fulfilling run to occur. In other words, when depositors anticipate that a run will be followed by
an (ex post efficient) intervention, this fact may give them an ex ante incentive to participate in the
run. In this sense, such interventions can have a destabilizing effect on the banking system.
Deposit freezes (sometimes called suspensions of convertibility) have been studied before,
but the focus has been almost exclusively on policies that are ex ante efficient. The classic paper
1 These figures include time deposits with penalties for early withdrawal. Demandable deposits (essentially check-
ing and savings accounts) fell by more than 6 percent on that day.
Bank Runs and Institutions:
The Perils of Intervention
By Huberto M. Ennis and Todd Keister*
* Ennis: Universidad Carlos III de Madrid, Calle Madrid, 126 28903 Getafe, Madrid, Spain, and Federal Reserve
Bank of Richmond (e-mail: firstname.lastname@example.org); Keister: Federal Reserve Bank of New York, 33 Liberty Street,
New York, NY 10045 (e-mail: email@example.com). We thank Roberto Chang, Doug Diamond, and seminar par-
ticipants at Rutgers University, the Federal Reserve Bank of Richmond, Universidad de Alicante, Universidad de San
Andrés, the Society for Economic Dynamics meetings, the Midwest Macro meetings, the North American Meeting
of the Econometric Society, the Cornell-Penn State macroeconomics workshop, and the SAET conference in Vigo,
Spain, for helpful comments. Ennis acknowledges the financial support of the Ministry of Science and Technology in
Spain (Projects 2008/00439/001 and 2009/00071/001). The views expressed herein are those of the authors and do not
necessarily reflect the position of the Federal Reserve Bank of New York, the Federal Reserve Bank of Richmond, or
the Federal Reserve System.
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ENNis ANd KEistER: BANK RuNs ANd iNtERVENtiON
of Douglas W. Diamond and Phillip H. Dybvig (1983) presented a model with demand deposits
in which a self-fulfilling bank run could occur, but then showed how an appropriate deposit
freeze policy would remove all incentives for depositors to run. In their setting with no aggregate
uncertainty, freezing deposits quickly enough in the event of a run guarantees that the banking
system will be able to meet all of its future obligations. Given this guarantee, depositors without
an urgent need for their funds have no incentive to withdraw and, therefore, a run will never
start. Importantly, deposits are never frozen in equilibrium; the threat of a freeze is sufficient to
convince depositors not to run.2
We show that the deposit freeze studied by Diamond and Dybvig (1983) is typically not ex post
efficient. In other words, if a run started and reached the point where deposits are to be frozen, a
benevolent banking authority would not want to follow through with the freeze. The intuition is
easy to see. Some of the depositors who have not yet withdrawn truly need access to their funds;
freezing deposits imposes heavy costs on these individuals. In most cases, a better policy would
be to delay the freeze or reschedule payments in a way that gives at least some funds to these
depositors. Hence, a banking authority that is unable to precommit to follow the complete-freeze
policy would not choose to do so once a run is underway.
We provide the first analysis of policy interventions that would be chosen ex post, once a run
is underway, in the classic Diamond-Dybvig framework. We focus on the types of interventions
observed in reality: deposit freezes and payment rescheduling with court intervention. We show
that, compared to the policy of immediately freezing deposits, interventions that are desirable ex
post are more lenient and allow more funds to be withdrawn. These withdrawals place additional
strain on the banking system and decrease the assets available to meet future obligations. This fact,
in turn, increases the incentive for a depositor to participate in the run. Taking the intervention that
is ex post efficient as a benchmark, we show that self-fulfilling bank runs can arise in the canoni-
cal Diamond-Dybvig model. Our approach thus provides one possible answer to the question of
“what’s missing?” in the Diamond-Dybvig model posed by Edward J. Green and Ping Lin (2000).
Our results identify an important time-inconsistency problem in banking policy. Banking
authorities would like depositors to believe they will be “tough” in response to a run. However,
if a run were to actually start, the authorities would not find it optimal to take a tough stand.
Instead, they would choose a more lenient policy, and this policy can end up justifying the origi-
nal decision of depositors to run. This type of time inconsistency was informally discussed by
Finn E. Kydland and Edward C. Prescott (1977) in the context of government investment in flood
control (see also the discussion in Robert G. King 2006). As in the Kydland-Prescott example,
we show that an inferior equilibrium exists if the government cannot precommit to a “tough”
course of action.
Whether the wave of withdrawals by depositors during a banking crises reflects, at least in
part, self-fulfilling behavior is an open question. System-wide banking crises are complex phe-
nomena that typically occur in conjunction with a variety of unfavorable financial and mac-
roeconomic factors, which makes answering this question difficult. Some important empirical
work has been done recently (see, for example, Charles W. Calomiris and Joseph R. Mason 1997,
2003), but the evidence remains inconclusive (Ennis 2003). Demonstrating, as we do here, that
this type of event is possible in a well-specified model—and identifying the circumstances that
make it possible—is therefore a critical contribution to the overall debate.
Governments have also responded to the possibility of bank runs by establishing deposit insur-
ance programs. While such programs have often proven effective in preventing runs, they have
2 Gary Gorton (1985), V. V. Chari and Ravi Jagannathan (1988), and Merwan Engineer (1989) have also studied
deposit freezes, but in each case the focus was again on the policy response that would be chosen ex ante, before a
tHE AmERiCAN ECONOmiC REViEW
significant shortcomings. First, a credible deposit insurance program requires that the govern-
ment be able to guarantee the real value of deposits in the event of a widespread run; this is not
always feasible. Depositors in Argentina in 2001, for example, likely anticipated that the govern-
ment’s resources were limited and that holders of insured deposits would suffer substantial real
losses. Second, deposit insurance programs generate moral hazard. The costs of this distortion
can be substantial, as shown during the savings and loan crisis in the United States in the 1980s
and 1990s. Evaluating the benefits of deposit insurance requires understanding what happens in
environments where it is not present and, in particular, whether other policy tools such as deposit
freezes can effectively prevent system-wide runs.3
In recent decades, many of the functions traditionally associated with banking have been
increasingly performed by nonbank institutions. Money market funds and other arrangements
perform maturity transformation by investing in long-term assets while offering investors the
ability to withdraw funds on demand. In any such arrangement, the issue of a run on the fund
potentially arises: what happens if a large fraction of the investors attempts to withdraw at once?
The reaction to a run on an investment fund is typically very similar to that for a bank run:
redemptions are temporarily suspended and there is some rescheduling of payments. The recent
turmoil in financial markets has witnessed several such cases.4 While our analysis is cast in
terms of banks and depositors, it also sheds light on factors that may contribute to runs on these
nonbank institutions. In particular, our analysis highlights the importance of thinking carefully
about arrangements that will be desirable ex post in the event of a run, and what incentives these
arrangements give to participants ex ante.
The remainder of the paper is organized as follows. In Section I we present the basic model,
including banking with demand deposit contracts and deposit freezes. In Section II we study the
decision of when to freeze deposits in response to a bank run, while in Section III we examine
interventions by the court system. In both cases, we derive conditions under which a self-fulfill-
ing run cannot be ruled out when the policy is chosen ex post, once the run is underway. Finally,
in Section IV we offer some concluding remarks.
I. The Basic Model
Our basic framework is the now-standard model of Cooper and Ross (1998), which generalizes
the Diamond and Dybvig (1983) environment by introducing costly liquidation and a nontrivial
A. the Environment
There are three time periods, indexed by t = 0, 1, 2. There is a continuum of ex ante identical
depositors with measure one. Each depositor has preferences given by
v(c1, c2; θ) = u(c1 + θc2),
3 In an environment similar to ours, Russell Cooper and Thomas W. Ross (2002) study the moral hazard costs of
deposit insurance financed with taxation. They show that the government will choose to offer only partial deposit
insurance in order to mitigate the moral hazard problem, and that this partial insurance can be insufficient to rule out
a self-fulfilling run. The run on the UK bank Northern Rock in September 2007 clearly highlights the limitations of
partial deposit insurance schemes.
4 One example is the Local Government Investment Pool of Florida, a money market–style fund operated for state
and local government agencies, which halted redemptions on November 29, 2007, after experiencing heavy withdraw-
als. Redemptions were also suspended by some other money market and cash funds, as well as by a substantial number
of hedge funds.
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ENNis ANd KEistER: BANK RuNs ANd iNtERVENtiON
deposit freeze was declared. These institutional features that undermine a government’s ability
to precommit to a given course of action create precisely the type of situations we aim to draw
attention to with our analysis.
The issues we have highlighted here are also relevant for analyzing runs on nonbank financial
institutions and investment funds. In some cases, our analysis can be applied directly. Money-
market and related funds, for example, closely resemble the banks in our model. These funds
typically invest in relatively liquid assets, but disruptions in financial markets can cause their
assets to become considerably less liquid. Such funds can (and do) respond to a run by tempo-
rarily suspending investor redemptions and rescheduling payments. Our analysis suggests that
the susceptibility of such funds to a run could depend, in large part, on details of the expected
response and the ex ante incentives this response gives to investors.
More generally, a range of financial institutions rely on short-term funding in money markets
while holding long-term, illiquid assets. The recent period of financial turmoil has witnessed a
variety of events that resembled a run on such institutions. Beginning in August 2007, for exam-
ple, many firms that had previously been able to issue short-term debt in the form of commercial
paper suddenly found they could not roll over this debt; investors seemed to “run” away from
this market. Another example was the near-collapse of the US investment bank Bear Stearns in
March 2008, which Barry Eichengreen described as being “a lot like a 19th-century run on the
bank.”20 The specific features of these types of events may differ from those in our model; for
example, the policy options available to a government or central bank may depend on the type
of institution(s) experiencing a run. Nevertheless, we believe it is again critical in these cases to
study how the losses caused by a run will be distributed ex post and what ex ante incentives the
policy response creates. A logical starting point for any such analysis is to focus on the allocation
of resources that the interested parties will find to be ex post efficient, as we do here.
As a final remark, we note that our analysis may also be useful for studying phenomena in
asset markets. Observers often claim that certain episodes in these markets are analogous to
a bank run; examples include the stock market crash in 1987, the “mini-crash” in 1997, and,
more recently, the breakdown of the market for auction-rate securities in early 2008. Antonio E.
Bernardo and Ivo Welch (2004) and Stephen Morris and Hyun Song Shin (2004) have provided
important first steps in developing models of this type of market fragility. Major disruptions in
asset markets often trigger some kind of policy response, such as temporarily halting trade on an
exchange. We believe that studying the effects of ex post interventions on ex ante incentives, as
we have done here, is likely to provide critical insights into the potential sources of instability in
these settings as well.
PROOF OF PROPOSITION 2:
The banking system is fragile if and only if the efficient freeze point π s
equal to the threshold π t identified in Lemma 1. Under Assumption 1, the function cL(πs) defined
in (5) is strictly concave. Since the utility function u is also strictly concave, the objective func-
tion (4) is a strictly concave function of πs. Fragility obtains, therefore, if and only if W′(πt ) ≥ 0
holds. The derivative of the objective function is given by
E ) − (1 − π)u[cL(πs)] + (1 − πs)(1 − π)u′ [cL(πs)] dcL(πs)
m is greater than or
W′(πs) = u(c*
20 “Depression, You Say? Check Those Safety Nets,” New York times, March 23, 2008.
sEptEmBER 2009 1606
tHE AmERiCAN ECONOmiC REViEW
where, from (5), we have
dπs = R
1 − τ
(1 − π)(1 − πs)2 (1 − τi * − c*
Combining these two expressions and simplifying yields
W′(πs ) = u(c*
E ) − (1 − π)u[cL(πs)] + u′ [cL(πs)] R
1 − τ (1 − τi * − c*
(1 − πs)
Suppose we evaluate this derivative at the threshold point π t, which is defined by the condition
W′(πt ) = πu(c*
E. Then we have
E ) + u′(c*
E ) R
1 − τ (1 − τi * − c*
(1 − πt ) .
Solving the equation cL(πt ) = c*
E for πt yields
1 − τ (1 − τi * ) − (1 − π)c*
1 − τ c*
E − (1 − π)c*
which can be rewritten as
1 − τ c*
E − (1 − τi * )
(1 − πt ) = c*
E S R
1 − τ − (1 − π)T.
Substituting this expression into (A1) yields
W′(πt ) = πu(c*
E ) − u′(c*
E )Qπ − u′(c*
E S R
1 − τ − (1 − π)T
______ = u(c*
E ) S R
1 − τ − (1 − π)T R.
This final expression shows that W′(πt ) ≥ 0 holds, and hence the banking system is fragile,
if and only if (6) holds.
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