BANK RUNS:DEPOSIT INSURANCE AND CAPITAL REQUIREMENTS *
B Y R USSELL
C OOPER AN
D T HOMAS W.R OSS 1
生活与哲学
Boston University,U.S.A.and University of British Columbia,Canada
Diamond and Dybvig provide a model of intermediation in which deposit insurance can avoid socially undesirable bank runs.We extend the Diamond±Dybvig model to evaluate the costs and bene®ts of deposit insurance in the prence of moral hazard by banks and monitoring by depositors.We ®nd that complete deposit insurance alone will not support the ®rst-best outcome:de-positors will not have adequate incentives for monitoring and banks will invest in excessively risky projects.However,an additional capital requirement for banks can restore the ®rst-best allocation.
1.INTRODUCTION
The publicly supported deposit insurance plans of a number of countries,most notably the United State禁毒手抄报的内容
s and Canada,have recently come under inten public scrutiny as concerns have mounted about the substantial contingent liabilities they have created for taxpayers.In the United States the savings and loan (S&L)crisis led to the transfer of a huge amount of bad debt,estimated recently at about $130billion,onto taxpayers'shoulders.2Created originally to support the banking ctor by building depositor con®dence,there is recognition that the insurance provided by *Manuscript received November 1998;revid October 1999.1This is a considerably expanded version of Section IV of our NBER Working Paper,#3921,November 1991.We have bene®ted from discussions on this topic with Paul Beaudry,Fanny Demers,Jon Eaton,Alok Johri,Arthur Rolnick,Thomas Rymes,Fabio Schiantarelli,David Weil,and Steven Williamson,and from helpful comments received from minar participants at Boston University,Brown University,Carleton University,the Federal Rerve Bank of Minneapolis,the University of British Columbia,and the University of Maryland.The extensive comments provided by three referees and the editor of this journal are gratefully acknowledged.Financial support for this work came from the National Science Foundation,the SFU-UBC Centre for the Study of Government and Business,and the Social Sciences and Humanities Rearch Council of Canada.The ®rst author is grateful to the Institute for Empirical Macroeconomics at the Federal Rerve Bank of Minneapolis for providing a productive working environment during preparation of parts of this manuscript.Some of this work was done while the c
ond author was visiting the Canadian Competition Bureau and he is grateful for the Bureau's assistance.The views expresd here are not necessarily tho of the Federal Rerve Bank of Minneapolis or of the Canadian Competition Bureau.Plea address correspondence to:Rusll Cooper,Department of Economics,Boston University,270Bay State Road,Boston,MA 02215.Fax:617-353-4449.E-mail:rcooper@bu.edu .2There is a considerable literature on the S&L crisis;e,for example,Feldstein (1991),Kormendi et al.(1989),and White (1991).
INTERNATIONAL ECONOMIC REVIEW Vol.43,No.1,February 2002
55
56COOPER AND ROSS
the plans has encouraged excessive risk taking by®nancial intermediaries.3The concerns have led to calls for the reform of deposit insurance and even suggestions that it be abolished.
This paper attempts to evaluate the trade-offs between risk sharing and moral hazard associated with the design of banking regulations.In particular,we focus on two policy instruments:deposit insurance and bank capital requirements.We are interested in how the instruments can be ud(a
nd misud)to control bank runs in an envi-ronment in which banks can make imprudent investments and depositors can monitor bank behavior.
Re¯ecting ongoing problems in the®nancial rvices ctor,there has been a great deal of rearch recently on lending behavior,bank stability,and optimal banking regulation.While a number of publications have considered parts of the problem addresd here,no individual contribution tackles the joint determination of optimal deposit insurance and capital requirements within a bank runs model with risk-aver depositors,depositor monitoring,and moral hazard.4Given the ongoing public debate over deposit insurance and capital requirements and the attention paid to the suppod trade-off between bank runs and moral hazard,a structure is needed that contains the elements.
With its emphasis on bank runs,the model of Diamond and Dybvig(1983)provides a convenient starting point for studying the issues.In the abnce of any moral hazard considerations,Diamond and Dybvig argue that publicly provided deposit insurance can be effective as protection against expectations-driven bank runs.5However,their
3Deposit insurance was created in the United States during the Great Depression(1934)to restore depositor con®dence.It came to Canada in1967.Concerns about the Canadian system are expresd in Smith and White(1988).
4Some of this literature is reviewed in the recent books by Dewatripont and Tirole(1994)and Freixas and Rochet(1997).The articles clost in purpo to this one include Giammarino et al. (1993),Matutes and Vives(1996),Besanko and Kanatas(1993),Holmstrom and Tirole(1993), Kupiec and O'Brien(1997),and Peck and Shell(1999).Each considers some aspect of our problem, but none combines the elements we view as important here.For example,Giammarino et al.(1993) consider optimal deposit insurance premia in markets with bank moral hazard but no bank runs. Matutes and Vives(1996)study the effect of competition on bank fragility with deposit insurance. Besanko and Kanatas(1993)consider the provision of funds to®rms from both banks(through loans)and capital markets in a model with bank moral hazard but no bank runs.Studying bank lending behavior(without deposits or bank runs),Holmstrom and Tirole(1993)®nd that borrower moral hazard can be controlled by requiring that borrowers contribute some of their own fundsÐa requirement not unlike the capital requirements that banks face.Finally,Peck and Shell(1999)also examine policies that might in¯uence the probability of bank runs,but focus on deposit contracts that permit the suspension of convertibility and on government restrictions on banks'portfolios of loans. 5Further,Wallace(1988)has argued that there is an inconsistency in the Diamond±Dybvig model's treatment of deposit insurance.The spatial paration that motivates banking appears inconsistent with the ability of governments to provide deposit insurance.However,Wallace goes on to point out th
at``...this argument does not say that any kind of deposit insurance is infeasible.It only says that the policy that Diamond and Dybvig identify with deposit insurance is infeasible¼''(p.13). We are in complete agreement;clearly the®nancing of deposit insurance must be credible to eliminate certain equilibria.Therefore,in contrast to Diamond and Dybvig,we rely on the prence of an outside group of agents(``taxpayers'')as a tax ba.Esntially,the government has enough information to tax labor income without needing to overcome any spatial paration constraints.
model does not incorporate the moral hazard considerations en to be central to recent policy debates.Deposit insurance avoids bank runs but has adver incentive effects:it implies less monitoring by depositors,which allows banks to hold riskier portfolios.In fact,if deposit insurance is complete enough,depositors'and banks'interests are aligned:both types of agents are eager to hold high-risk portfolios,effectively gambling with taxpayers'money.Thus a trade-off emerges between providing insurance against bank runs and monitoring incentives.By characterizing this trade-off,our model permits a derivation of the optimal degree of deposit insurance.In general,deposit insurance with depositor monitoring is not suf®cient to support the ®rst-best outcome.However,appropriately designed capital requirements can eliminate the incentive problem caud by deposit insur-ance and support the ®rst-best allocation.From the perspective of our model,the experience in the U.S.during t
he 1980s suggests two forms of regulatory failure.First,capital requirements were inadequate.Second,the relaxation of Regulation Q allowed banks to more aggressively compete for deposits,which,along with deposit insurance,led to excessively risky investment.This is certainly not a novel story but one that appears here in a consistent,formal framework.
2.MODEL
水浒传主要内容
The model is a modi®ed version of Diamond±Dybvig (1983).There are N ,ex ante identical,agents in the economy who are each born with a unit endow-ment,which they deposit with an intermediary in period 0.6At the start of period 1,agents are informed about their taste types.A fraction p learn that they obtain utility from period 1consumption only (early consumers),while the others obtain utility exclusively from period 2consumption (late consumers).As in the ®rst part of Diamond and Dybvig (1983),assume that p is nonstochastic and known to all agents.7Denote by c E and c L the consumption levels for early and late con-sumers,respectively,and let U (c )reprent their utility function over consump-tion.Assume that U (á)is strictly increasing and strictly concave,U H (0) I ,and U (0) 0.There are two technologies available for transferring resources over time.First,there is a productive technology that is not completely liquid.This technology provides a means of shifting resources from period 0to 2,with a return of R >1over the two periods.However,liquidation of projects
using this technique yields only one unit in period 1per unit of period 0investment.Second,there is a storage tech-nology,available to both intermediaries and consumers,that yields one unit in 6
In Cooper and Ross (1998)we allow consumers to make their own investments rather than using an intermediary and prove that using an intermediary in this structure always weakly dominates autarky.7In the last part of their article they consider the importance of aggregate uncertainty to argue further in favor of deposit insurance instead of policies that suspend convertibility.57
DEPOSIT INSURANCE AND INCENTIVES
period t +1per unit of period t investment,t 0,1.While not as productive as the illiquid technology over two periods,storage provides the same one-period return.8The intermediary operates in a competitive environment,which compels it to offer contracts that maximize consumers'ex ante expected utility subject to a break-even constraint.If the ex post consumer taste types were costlessly veri®able it would therefore offer a contract d à (c ÃE ,c ÃL )solving
max c E ,c L优雅图片
p U (c E ) (1Àp )U (c L )s.t.1 p c E (1Àp )c L R
关于阅读的手抄报
(1)
From the ®rst-order conditions,the optimal contract satis®es U H (c ÃE ) RU H (c ÃL )
(2)Since R >1,the strict concavity of U (á)implies that c ÃE `c ÃL for (2)to hold.Diamond and Dybvig establish that when consumer tastes are private information,multiple equilibria may exist.The contracting problem can be formulated with three stages.First,the contract is t by the intermediary,which speci®es a consumption level for each type of consumer independent of the number of consumers claiming to be each type.9Second,agents learn their preferences and the are announced to the intermediary.Finally,the allocation of goods to agents is determined by the contract.The ®rst-best outcome with the contract d Ãwill be one equilibrium of this game.Truth telling is a dominant strategy for early consumers while truth telling by late consumers is a best respon to truth telling by all other late consumers.Under d Ãthere may also exist an equilibrium in which all late consumers mis-reprent their tastes and announce that they are early consumers.This can be an equilibrium if the intermediary does not have suf®cient resources (including liqui-dated illiquid investments)to provide c ÃE to all agents.As in the Diamond±Dybvig model,the late consumers who do not withdraw in period 1obtain a pro rata share of the bank's period 2asts.This equilibrium with misreprentation is termed a ``bank run.''The ®rst-best allocation is vulnerable to runs iff c ÃE b 1:o
therwi,the interme-diary would have suf®cient resources to meet the demand of c ÃE by all agents in period 1.Diamond and Dybvig (1983)show that if agents are suf®ciently risk aver,then c ÃE will exceed 1.
8
In this tup,which comes from Diamond and Dybvig,returns on investments made in this productive technology are always (weakly)greater than tho in the alternative (storage).In Cooper and Ross (1998)we extend the model by adding a liquidation cost to the illiquid projects that renders the one-period return to liquidated investments less than the alternative.This expands the t of conditions under which bank runs can occur and in¯uences agents'investment and contract choices.It does not,however,have implications for the results described below so we have chon to work with the simpler model here.9Thus,in particular,it is not feasible for the bank to accumulate information about withdrawals and make payments to depositors contingent on this information.Further,agents are unable to meet at a common location after period 0,thus eliminating the types of ex post markets considered in,for example,Jacklin (1987).58COOPER AND ROSS
As described in Alonso (1996)and Cooper and Ross (1991,1998),there are esntially two ways the i
张治中将军
蚂蚱肚ntermediary can optimally respond to the possibility of multiple equilibria.One is to ®nd the best contract available that is not vulnerable to runs.This best runs-preventing contract comes from solving (1)with the added constraint c E 1so that there are always suf®cient resources available in period 1to pay all consumers.Concavity arguments demonstrate that if the ®rst-best contract is vulnerable to runs (i.e.,c ÃE b 1),the best runs-preventing contract will involve c E 1and c L R .As an alternative,one might construct a model of the equilibrium lection pro-cess and solve for the optimal contract.One simple model relies on the existence of publicly obrvable,but not contractible,variables (sunspots)that correlate agents'behavior at a particular equilibrium of the game.10Instead of preventing runs,the intermediary adjusts the contract to reduce the impact of runs in the event they ari.Suppo that with probability q there is a wave of economy-wide pessimism that determines the beliefs of depositors.If the outstanding contract has a runs equilib-rium the pessimism leads to a bank run.With probability (1)q ),there is optimism and no run occurs.In this way,the beliefs of depositors are tied to a move of nature that determines their actions.The intermediary recognizes this dependence in de-signing the optimal contract.Taking the probability of liquidation,q ,as given,the contract solves (assuming c E >1)
max c E ,c L
(1Àq )[p U (c E ) (1Àp )U (c L )] qU (c E )(1a c E )s.t.1 p c E (1Àp )c L R
(3)
Let d (q )be the contract solving this problem.11Cooper and Ross (1998)show the existence of a critical q ÃP (0,1)such that the best runs-preventing contract domi-nates the best contract with runs if q b q Ãand the rever holds if q `q Ã.3.SUPPORTING THE FIRST-BEST:DEPOSIT INSURANCE
AND CAPITAL REQUIREMENTS
The previous ction characterizes the optimal respon of a private bank facing the prospect of a run.Regardless of whether the intermediary optimally adopts a runs-preventing contract or allows runs,the possibility of bank runs clearly lowers expected utility below that attainable in the ®rst-best solution.This naturally rais 10
Bental et al.(1990)and Freeman (1988)also adopt a sunspots approach.In contrast to our work,tho articles allow for sunspot-contingent contracts.While it is convenient to think of sunspots as determining which equilibrium of the subgame will be obrved,contracts contingent on the events are assumed to be infeasible.11Here an agent receives c E with probability 1/c E in the event of a ru
n,which occurs with probability q .Note that if the solution to (3)involved c E £1it would in fact be runs-preventing and therefore be dominated by the best runs-preventing contract (c E 1and c L R ).59
DEPOSIT INSURANCE AND INCENTIVES
60COOPER AND ROSS
the question of whether some government intervention in the form of deposit in-surance or other instrument could prevent runs and thus improve welfare.12 Deposit insurance is a contract t by the government that provides a payment to depositors in the event that the bank is unable to meet its obligations.13Diamond and Dybvig argue that a simple deposit insurance scheme will eliminate bank runs in their model.However,their argument leaves aside the adver incentive effects of deposit insurance on both the investment strategy of the intermediary and the monitoring decisions of depositors.We study this by adding both moral hazard and monitoring by depositors to our model.Our main result in this ction is that an appropriately designed capital requirement coupled with deposit insurance can avoid bank runs without creating vere moral hazard problems.
3.1.Extended Model.We modify the basic model in a number of ways,detailed in the subctions that
follow.First,we introduce a richer investment choice for the banks.Second,we allow for a monitoring decision by depositors.Third,we introduce both deposit insurance and capital requirements as policy instruments for the gov-ernment.
生活中的大数有哪些The quence of events in period0is as follows:First,the government ts a deposit insurance policy.In general,the government contract stipulates payments to early and late consumers as a function of the deposit contract in the event the intermediary is unable to make its promid payments.We denote the payments to early and late consumers as I(c E)and I(c L)respectively.Since the government is unable to obrve the types of private agents,it too must rely on the agents'an-nouncements.Put differently,tho agents who appear at the intermediary in period 1are termed early consumers and are eligible for the government insurance over c E in the event the intermediary is unable to meet its obligations.Likewi,an agent who makes the announcement of being a late consumer is eligible for government insurance over c L if the bank fails in period2.Importantly,if a bank fails in period1, then late consumers will not receive insurance over c L.Instead,they will receive the same payment as early consumers if a bank fails in period1.Note that we assume that government insurance policy depends on the deposit contract offered by the intermediary.
Second,the competitive banks offer a contract,d.Depositors then decide on the allocation of their end
owment and whether to monitor the bank.If the bank
12For the purpos of this exerci,we do not consider private deposit insurance schemes.
13For simplicity,assume that the tax obligations to®nance deposit insurance fall upon agents who are not depositors.Hence we do not consider the possibility that intermediaries make payments into a deposit insurance pool but rather focus on the obligations of taxpayers to the system.Here we imagine a government policy that provides deposit insurance to agents who arrive at the bank after the bank has exhausted resources and then taxes,say,the endowment of a group of agents in the economy not involved with the intermediary or even the endowment of the next generation of depositors,as in Freeman(1988),to®nance the transfers.We assume that the social welfare function is such that providing this insurance is desirable.The key point is that there must be a government taxation scheme that is not inconsistent with isolation that is capable of generating the needed revenues.
