moral hazard under commercial and universal bank

8/13/2019 Moral Hazard Under Commercial and Universal Bank

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JOHN H. BOYD

CHUN CHANG

BRUCE D. SMITH

MoralHazard nderCommercial

andUniversalBanking

Many claims have been made about the potential benefits and the potential costs of

adoptinga system of universalbanlcing n the United States. We evaluate these claims

using a model where there s a moralhazardproblembetween banks and borrowers,

a moralhazardproblembetween banksand a deposit nsurer,and a costly state verifica-

tion problem.Underconditionswe describe,allowing banksto take equity positions in

firms strengthens heir ability to extract surplus, and exacerbatesproblems of moral

hazard.The incentivesof universalbanks o takeequitypositions will often be strongest

when these problemsare most severe.

FORMANYDECADES,ommercialbanks in the United States

have been prohibited rom makingequity investments n the firmsthey serve. Rather,

they are restricted o providing hem with loans in the form, essentially, of debt con-

tracts.This longstanding egulatory estriction1 esults n distinctlydifferentroles for

bank endersandequity investors,andhas had important mplications or the entirefi-

nancial sector.

The Americansystem of commercialbanking presentsa sharpcontrastwith the

bankingsystems of some othercountries,most notablyGermany, n which banks are

permitted o take equity positions. Under such universalbanking arrangements,

bankscan makeequity investmentsas well as loans, vote theirequity shares,andeven

hold seats on the boardsof directorsof nonfinancial irms.In general,they can be ac-

tively involved in all aspects of firmdecision malQing.n Germany, he control rights

The authorshave benefitted rom the helpful commentsof Doug Diamond,Joe Haubrich,Ross Levine,Stan Longhofer,Joao Santos, and an anonymousreferee. The views expressed herein are those of the au-thorsand not necessarilythose of the FederalReserve Bank of Minneapolisor the FederalReserve System.

1. The key legislation which constrainsU.S. banksequity investments s the Glass-SteagallAct of 1933.However, a numberof other aws also pertain o this issue, particularly he Bank Holding CompanyAct of1956 and ts 1970 amendments. ncidentally, hereare some important xceptions to the equity investmentprohibition. n default situations,banks are perrnitted o restructureoans into equity positions with the re-quirementof divestitureaftera few years (see James 1993). Also, bankholding companiesare permitted oform (separatelycapitalized)venturecapital subsidiaries or the expressedpurposeof investing in startupenterprises.

JOHNH. BOYDs a professor offinance in the CarlsonSchool of Managementat the Univer-sity of Minnesota and an adjunct consultant with the Federal Reserve Bank of Minneapolis.CHUNCHANGs an associate professor offinance in the CarlsonSchool of Managementat theUniversity of Minnesota. BRUCED. SMITHs a professor of economics at the UniversityofTexas atAustin.

Journal of Money, Credit,and Banking,Vol. 30, No. 3 (August 998,Part )

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JOHNH. BOYD, CHUN CHANG, AND BRUCED. SMITH : 427

of owner-banksarefurther nhancedby the fact thatthey can vote the sharesof other

agents which theyhold in trust auftragsstimmrecht).2

These importantdifferences in bankingarrangements ave notescaped the notice

of scholarsand there s a large iterature, oththeoreticalandempirical, hatcomparesthe two types of bankingsystems. Indeed,many academics as well as policymak-

ers have proposedthatthe United Statesadopta form of universalbankingand this

issue is underactive,ongoing debate in the Congress.3The obviouspoint is that this

subject s of significantpublic policy concern, as well as of academic nterest.

A second issue that ooms very large in discussions of bankingandbankregulation

is the control of moralhazardproblems.Moralhazard n bankingcan clearly take ei-

ther or both of two forms. Moral hazardproblemscan easily arisein the relationship

between banks andthe agents to whom they provide funds. In addition, t has long

been recognized thatthe presence of deposit insurancegives rise to a moral hazard

problembetween banksand the providersof deposit insurance the FDIC). [See, for

instance, Karekenand Wallace (1978) andMerton (1977).] And indeed, regulators

have often expressedthe concern that the establishmentof universalbanking in the

United States could extend the governmental afety net far too broadly,thatmoral

hazardproblemscould be exacerbatedas a consequence, and thatthey could, poten-

tially, be transmitted eyond the financialsector. [See, for example,Corrigan 1983,

1987) or Saunders 1994).]

In this paperwe investigate he severityof both kinds of moralhazardproblemsun-der both commercialand universal banking. In particular,we investigate optimal

bankbehaviorundereach regime, andthenpose the following two questions: i) How

severe is the moralhazardproblembetween banks and borrowers ;nd (ii) How se-

vere is the moralhazardproblembetween banksand the FDIC?

We begin by studyinga system of commercialbankingwhere banksare precluded

from takingequitypositions in the firms o which they lend. We show thatundercom-

mercial banking,banks will always take some actions to controlthe moral hazard

problembetween borrowersand themselves.These actions also tendto limit the im-

plied obligations of the FDIC, since the active control of moral hazardproblems bybanks implies that banks fail less often and,on average,have assets of greatervalue

when they do fail.

We then contrast his with a bankingsystem (universalbanking)where banks take

equity positions in the firmsthey serve.4When banksare allowed to take equity posi-

tions, and to assume some control rights, their incentives to controlmoral hazard

problemscan be substantiallyattenuated. ndeed,underuniversalbankingbanks can

2. The differentbankingregulationsundoubtedlyaffect the entirefinancial ntermediaryector, not just

banks.Restrictionson commercialbankingactivitieshave contributed o the developmentof a largeand ac-tive stock market n the United States. Not incidentally, he capitalizationof the Germanstock market srelatively small, and characterized y thin tradingandfew listings compared o the United States (Gortonand Schmid 1996).

3. For example, the so-called Shadow FinancialRegulatoryCommitteefavorsadoptionof a universalbankingsystem in the United States. See Criticism f FinancialReformOverblown,Shadow Panel Says,AmericanBanker,May 6, 1997.

4. As we show, in ourmodel banks deriveno advantageby taking mixed positions consisting of com-binationsof debt and equity.







428 : MONEY, REDIT, NDBANKING

share moreeasily in the benefits of misallocating unds,and they can more easily

pass losses onto the FDIC. Thisexacerbatesproblemsof moralhazardalong both di-

mensions.Moreover,by exercising theircontrolrights,bankscan force firms o mis-

allocate unds even whenthis is beneficialneither o the firmnor to society(althoughclearly it is beneficial to the bank). This alteration n the allocation of funds also has

adverseconsequences for the FDIC.Finally, we identify some economic factors that

areconducive to problemsof moral hazardbeing particularly evere underuniversal

banking.These factors nclude (i) low realreturnson savings, (ii) a relativelyhigh re-

turnto misallocatedfunds, (iii) a high cost to banks associated with deterringmoral

hazard, and (iv) banks obtainingrelatively large equity positions underuniversal

banking.

Having analyzed heseissues we then aska thirdquestion:.Whenwill abank, f giv-

en a choice between a debtand an equityclaim, choose to take an equityposition in afirm?Loosely speaking,we find thatbankspreferequityclaims when (i) the return o

misallocating unds is relativelyhigh, andhence the moralhazardproblem s relative-

ly severe; (ii) theirprobabilityof failure as a commercial bank is relatively high (it

will then be even higher underuniversalbanking,againreflectinggreatermoralhaz-

ard); iii) ex post state verificationcosts arerelatively ow; and (iv) the bank s able to

obtain a relatively largeequity position under universalbanking. (The latter factor

again is associated with moral hazardproblems being more severe under universal

banking.)Finally,we show thatthe two types of bankingsystemshave sharplydifferinggen-eralequilibriummplicationsfor resourceallocations. In particular,underuniversal

banking a largerportion of the surplusgeneratedby externally financed nvestment

accrues to banks, and less accrues to the originating nvestor. This clearlycan have

far-reaching mplications or aggregate nvestmentactivity. In addition,problemsof

moralhazard n investmentwill often, aswe have noted,be of greaterconcern under

universal han undercommercialbanking.Together,these observationssuggest that

universalbankingcan easily have adverseconsequencesfor the overallefficiency of

investment.Ourvehicle foraddressing he issues just described s a model in whichall deposits

are fully insuredby the FDIC. Such insurance s socially valuable in our framework

because, by assumption,banksare unableto perfectlydiversify risk and most deposi-

tor-savers are risk averse. Further, all savings and investment is intermediated

throughbanks. The FDICcharges a fixed-rate nsurancepremium o banks,5and, in

addition, he FDIC has recourseto taxationof saverswhenever necessaryto meet its

insurance liabilities. Symmetrically, any excess insurance receipts are returned o

savers.Besides banks, the FDIC, and savers, a fourthclass of agentsrounds out the

modeleconomy. These are entrepreneurs ho are endowed with access to produc-

tive investment echnologies which requireexternal inancing.

5. In the last several years, anattempthas been made (pursuant o the provisions of the FDICIA Act of1991 to set deposit insurancepremiaaccording o an insuredbank' riskclass. However, asimple flatrateinsurance cheme is still a good approximation o reality n the UnitedStates, for theoverwhelmingmajor-ity of banks arecategorized n the same (lowest) riskclass.







430 : MONEY,CREDIT,AND BANKING

This logic suggests quitecorrectly hatbanks will choose to organize as universal

banks when theirpotentialprivategainsfromfunds diversionarerelativelyhigh, andwhentheir ability to extractsurplus romborrowers s relativelygreat.Whatwe con-

clude,based on thisobservation,s that heremay wellbe reason orconcernabout heincentivescreatedby universalbanking.These concernswill typicallybeexacerbated

by the presenceof depositinsurance.

Prior o proceeding, t is useful to relateourwork to some of theexisting literature

on universalbanking.Boot andThakor forthcoming),or instance,examineshow al-

ternativebankingarrangements ffect the incentives for innovation n the financialsector.Berlin,John, and Saunders 1996) have studiedthe role that bankequity in-vestmentsmayplay (if permitted), n resolvingthe problemsof financiallydistressed

firms.Santos(1996a) hasexamined hewelfare mplicationsof restrictions n (orpro-

hibitionof) bankequity nvestments nnonfinancial irms.6 naddition, here s a largeempirical iterature hat solatesandquantifiesperformance ifferencesbetween vari-ous banking regimes. [Good examples include Allen and Gale (1995), Hauswald(1996), orGortonand Schmid(1996). A numberof otherrelatedstudies arediscussed

by SaundersandWalter(1994).] Thereis also a large literature xamining the provi-

sion of investmentbankingservices by universal banks. [See Krosznerand Rajan

(1994) or thereview by Santos (1996b).] Clearlyall of these studies(with theexcep-

tion of Santos1996a)have a substantiallydifferent ocus fromours.Our analysis fo-

cusses on the severity of bothendogenouslyarisingandpolicy-inducedmoralhazardundercommercialversusuniversalbanking.

Theremainder f thepaperproceeds as follows. Section 1 lays outthe modelenvi-

ronment,and section 2 describesthe behaviorof agents,and a generalequilibriumof

the modelundercommercialbanking.Section 3 considersuniversalbanking,and sec-tion 4 discusses when banks will preferto take equitypositions rather hanto hold

debt claims.Section 5 offers someconcludingremarks.

1. THEMODEL

We consider aneconomy that is populatedby a continuumof agentswho live for

two periods.These agents can be divided into three categories:Borrowers or entre-preneurs),bankers orpotentialbankers),anddepositors savers). Inaddition, here s

a government hatoperatesa depositinsurancesystem.We now describe each set of

agents.

A. Entrepreneurs

Borrowers entrepreneurs) omprise a fractiona E (0, 1) of the population.Each

borrowers endowed nperiodone with access totwoinvestmentprojects,althoughatmost one of theprojectscan be operated.A project hat is operated n the firstperiod

yields a randomgross returnof z, perunit invested, in periodtwo. For bothprojects,

we assume thatz E [0, z].

Projectsaredifferentiated y theirscales of operation,and by theirprobabilitydis-







JOHNH. BOYD,CHUN CHANG,AND BRUCED. SMITH : 431

tributionsof returnsOroject 1 requiresq l > 1 unitsof first-period esources funds)to

operate.Projects are assumed to be indivisible, so that no projectcan be operated

withouta minimum investment,and investments n excess of the minimumare un-

productive. f q1 unitsare nvestedinproject 1, a random eturn is realized n the sec-ond period,with prob(z ' z) = G(z).We let g(z) denotethe pdf of this distribution,

andwe assume thatg(z) > 0 for all z E [0, z]. Finally,let zl denote theexpectedgross

return,per unitinvested,if project 1is operated.

Project2 requiresq2 units of fundsin thefirstperiod,with 1 ' q2< q1. If project2

is operated, hen prob(z ' z) = F(z), and we assumethat

F(z) ' G(z), for all z . (a.1)

Thus,the probabilitydistribution f returnson investments n project1 stochasticallydominates haton investments n project2. We also letfdenote the pdfof this distrib-

ution, and assumethatAz)> O or allz E [0,z]. The mean return perunit invested-

on project2 is Z2 Clearly22< zl holds.

We assume thatborrowers an operateeitherproject1 or project2. However,only

one projectcan be operated,andwe assumethat t is infeasibleto operateconvex com-

binationsof the two projects.Such assumptionsarestandard n modelsof moralhaz-

ardand costly state verification.

Borrowersare assumedto have no funds-otherthan those generatedby their in-

vestmentreturns in either period. Thus, to engage in any investment,borrowers

mustobtainexternal unding.If theyfail to do so, we assumethatthey engagein some

outside activitythatyields the (exogenously given) utility level u ' 0. We also as-

sumethatborrowersare riskneutral, o thatthey will wish to operateany investment

project hatyields an expectedpayoffno less thanu.

1. Information.We assumethat there aretwo kindsof informationalasymmetries

associatedwith the provisionof external inance.Oneis a standard ostly stateverifi-

cation problem (Townsend 1979; Diamond 1984; Gale and Hellwig 1985; and

Williamson 1986, 1987). In particular,or either type of projectthe randomreturncan be observedcostlessly only by the agentoperating he project.For certainother

agents the projectreturn an be observed(afterthe fact) by incurringa fixed cost of Y

unitsof effort. Herewe allow for the possibilitythatonly some agentscan engage in

stateverification,andthat verificationcosts are not necessarily the samefor all indi-

vidualswho can undertaket. We describethesefeaturesof the model in more detail

below.

The purposeof introducingcostly ex post state verification s to create some pre-

sumption hatdebtcontractsare not an inferiorcontractualorm if we abstract rom

stochasticmonitoring.For this reason, throughoutwe focus exclusively on ex post

monitoring hatoccursdeterministically.7

In addition o the state verificationproblem,we allow forthe presenceof a moral

hazardproblemassociatedwith projectchoice. In particular,we assume thatthe bor-

7. In addition,Boyd and Smith (1994) arguethat for realisticparametervalues-the welfare gainsfromstochasticmonitoringare likely to be small.








rower's choice of investmentproject s notobservable o thelenderex ante. Thus, if a

borrower eceives q1units of funds in periodone, he may either nvestin project 1, orhe maydivertq1- q2 and nvestinproject2. Thediverted undsyield perks oown-

ersof theproject:we describethese perks inmore detailbelow. A borrowerwho hasa second-periodncomeof y and who hasexpendedq1 - q2 unitsof funds on perksre-

ceives the lifetimeutilityy + 6(q1 - q2).We assumethatthepreferenceparametersatisfies O< 6 ' 1, andthatZ2> 6.8

While only theborrowerknows his own ex ante projectchoice, we assume thatbyengagingin what we call interimmonitoring,outsidelenderscanobserve thatchoiceat some cost. More specifically,after the projectinvestment has been made (and itis then no longerreversible),a lendercan engage in interimmonitoringat a cost in

effort-of k.9 If this cost is incurred, he lender earns theborrower'sprojectchoice.

We allow lenders to liquidatethe borrower'sproject at this point:projects of type jhave a liquidationvalue of L>; = 1, 2. We also allow interimmonitoring o be done

stochastically. 0

Interimmonitoring s one device by which a lendercan attempt o controlthemoral

hazardproblem.We also assumethat a second device is available. In particular,we

assume thateachborrower an deal withonly a single lender,and thus thatthelender

can control thequantityof funds obtainedby the borrower.Then, by restricting he

quantityof fundsextendedto q2,a lendercanalwayspreventa diversionof funds into

perks.However,whenever q1 > q2 is lent, a moralhazardproblem s alwayspoten-tially present.

B. Bankers

A fractionD E (O,1 of the population onsistsof potentialbankers.Each banker s

endowedwith one unit of fundsin thefirstperiod, alongwith some first-andsecond-

periodeffortthatcan be expendedoninterimandex postmonitoring, espectively.Byinvestingone unit of funds in thefirstperiod, apotentialbankeractuateshis ability to

engage in both types of monitoring. And,havingexpendedhis own funds, each op-

eratingbankermustclearly raise some depositsexternally.

We assume that nvestmentreturnsacrossentrepreneurs reindependentlydistrib-

uted. As a consequence,in view of the assumptionthat there is a large numberof

agents,there s no aggregateuncertaintyn thiseconomy. But,to make depositinsur-

ancevaluable, t is clearlynecessaryto confront hedepositorsof anybankwithsome

risk thatthatbankwill fail. We accomplish thisby assumingthat anygiven bank (or

8. This diversionf funds ormulationsrelatedo thatof GertlerndHubbard1988)orGertler nd

Rogoff 1990).Theassumptionhat ' 1 implieshat xpendituresn perksnevergeneratemoreutilitythan nequivalentmount f income. neffect, indexes owgoodasubstituteerks re orotherncome.Theassumptionhat 2 > 6 holds mplieshatnvestmentsnproject aremoreproductivehan xpendi-tures nperks onsumptionnot nclusive f thecostsof state erification).

9. Again hiscostmaydiffer cross gents n away hatwe describe elow.10.Theanalysiswouldbeaffectednonlyaminimalway f werestrictednterimmonitoringobe non-

stochastic.11. Thats, an nvestmentfoneunit srequiredy abank n orderor t tobe able oconductmonitor-

ingactivity.








banker)has a limited ability to service and monitor oans, and in particular-can

make only a finitenumberof loans. Given this assumption, omplete diversifications

impossiblefor anyspecific bank.In addition, okeep mattersas simpleas possible,we

restricteach bankto makingonly a single loan.12We assume thatbankers are risk neutral, and that they care only about second-

period income (consumption)and effort expendedon monitoring. Let y denote a

banker's second-period ncome, let eI E {O 1 } denote effortexpenditureon interim

monitoring eI = O( 1) implies that nterimmonitoringdoes not (does) occur],and let

eF E {0 1 } denoteeffortexpenditureon observingthe finalprojectreturn again, F

= O (1) indicates that ex post monitoringdoes not (does) occur]. Thenthe banker's

utilityis y-keI-yeF. Thusx (Y) s the cost of interim ex post) monitoring.

It will sometimesbe interestingto think about therebeing heterogeneityamong

banks, with some banks having high and some having low costs of monitoring.Let

,u (1 - ,u) denote the fraction of banks that have low (high) monitoringcosts. A

low- (high-) cost bank engages in interimmonitoringat a utility cost of XL (H). A

low- (high-)cost bank engages in ex post stateverificationat a utilitycost of YL (7H).

Clearlywe assumethatXL C XH andYL C YH with at leastone inequalitybeingstrict.

When we are not interested n differentiatingamong high- and low-cost banks,we

will simplyset ,u = Oor ,u= 1.

Finally,as thephrase potentialbanker uggests,each potentialbankerhasthe op-

tion of not runninga bank.In this case the potentialbanker imply saveshis singleunitof funds, n effectbecominga depositor.And to avoid a potential shortage f banks,

we assumethat ,B2 a holds so thatevery potentialborrowercan at least in princi-

ple findabank.l3

C. Depositors

A fraction1 - a - Dof the population s depositors.Depositors areeach endowed

with one unitof funds whenyoung, andthey careonly aboutsecond-period onsump-

tion. Thus, depositorseach supply their single unit of fundsinelasticallyin the first

period.

We also assume that depositorsare risk averse, so that they wish to be insured

whenold. This insurance s providedthrough he government theFDIC), since our

one bank-one borrower ssumptionpreventsbanks fromprovidingthis insurance

themselves.

Remark.At this point a brief remark s in orderregarding he role for banksin this

model.If q2 > 1holds, then each fundedentrepreneurequiresmoreresources hana

single savercouldprovide(even if saversdid nothave tomake an investment nmoni-

toring capacity).Familiararguments Diamond1984 andWilliamson1986) thenes-tablisha role for intermediationo avoid the duplicationof monitoringcosts. Such

12.Thisassumptions for simplicitynly.In practicet canbe thought f as eachbankmakesoansmostlyn a singlegeographicrea r industry,o that eturnsrecorrelatedcrossborrowers.imilar s-sumptionsn onebankne borrower remadeby John, ohn,andSaunders1994),Berlin, ohn, ndSaunders1996),orSantos 1996a).

13.Thisassumptions necessitatedy our onebankne borrower pecification.








argumentsalsoapplyhereeven though,underourassumptions,ntermediaries renotable to pool risks, as they arein manyothermodels. Risk sharing s described n thenext section.

D. Deposits andDeposit Insurance

Depositmarkets n our modeloperateas follows. All depositors as well as poten-

tialbankerswhoopt tobecome savers make a depositwith anactivebank.Banksof-fer to pay the gross marketrate of returnr per unit deposited.Banks who lend to

sufficientlysuccessful borrowerswill be able to make this payment. However, forbankswhose borrowers xperience ow returns, t will not be feasible to pay r perunitdeposited,and thebank will fail.

The fact thatdepositors are risk averse implies that they will wish to be insuredagainstbankfailures.Moreover, hefactthatthere s a largenumberof agents mpliesthat t is feasible for society to provide this insurance.We assumethatdeposit insur-anceis providedby thegovernment FDIC).Since one of ourprimary oncerns s withhow the provision of deposit insuranceby the governmentaffects the incentives of

commercialanduniversalbanksto controlmoralhazard, t is naturalor us to assumethatdeposit nsurance s governmentprovided. 4

TheFDICbehaves as follows. Forany bankthatmakes its promisedpaymentof r

per unit depositedin period two, the FDICtakesno action.However,when a bank

pays less thanrper unitdeposited hebank ails, andtheFDIC iquidates ts assetsandretains the proceeds. Of course, the FDIC,like otheragents,cannotdirectlyobservethereturnon anybank' assets. Thus,in order o liquidatea bank, the FDICmusten-gage in costly ex post stateverification.ForfailedbankstheFDICthen ascertains hevalueof the bank' assets, and uses theproceedsto payoff bankdepositors.1 To con-

ductex post stateverification he FDIChires privateagents,and we assume that the

cost of ex post stateverification o the FDICis YF. 16

Since theFDICcannotraiseenough resources romfailed banks tocover theloss-

es experiencedby depositors, t mustraise some additionalresources n other ways.We assume that n periodone theFDICimposes a flatratedeposit insurancepremiumof tper unit ent oneachbank. 7 TheFDIC-like otheragents mustthentransferheresources t obtainsbetweenperiods. To do so, we assume thatthe FDIC simplyde-

posits its taxincome withprivatebanks, and earnsthesame returns and s subject othe same risks as otherdepositors.This assumption s madebecause alternateas-

sumptionswouldresult in therevenue raisedby theFDIChaving aneffect on the to-

14. It wouldalso be natural o assume thatdeposit insurance s publicly provided f thefeasibility of in-suranceprovision n all statesrequired

potentialaccessto seignioragerevenue.15. Ineffect, a failure o payr perunitdeposited riggersa bankruptcy xactlyanalogous o those in con-ventionalcostly stateverificationmodels (Diamond 1984;Gale and Hellwig 1985; andWilliamson 1986,1987).

16. We allow forthepossibility thatYF 2 YH holds.Forexample, since FDICemployees do not havethesameclaim on the assets of monitoredbanksas lendersdo on borrowers, heFDIC may need to takecostlyactionsto verify that ts employees undertakeheirtasks in anappropriatemanner.

17. Givenourassumptions, his is equivalent o a flat ratetax on deposits. However,specifying a tax onlendingslightlysimplifies the calculations n the text.







JOHNH.BOYD,CHUNCHANG,ANDBRUCED.SMITH435

tal supply of savingsin period one. In practice,we do not typically think thatan im-

portantaspect of deposit nsurance s how deposit nsurance axes affect the aggregate

supply of credit. 8

Finally, we wantto allow for the possibility thatthe FDIC's revenuefromdepositinsurancedoes notnecessarily cover its insurance osses. Since FDIC expendituresn

period two are perfectlypredictable n period one, we assume thatthe FDIC can levy

a lump-sum axof Xon all depositors(includingpotentialbankerswho do notchoose

to operatebanks) in the firstperiod to cover any shortfall.Again, the proceedsof this

tax aredepositedwith privatebanks.The valueXthenrepresents measureof the loss-

es incurredby theFDIC.

Remarks.Clearlyour intention s to stylistically representactualgovernmentpoli-

cy as it prevails n the United States.We believe thatthis is a natural hing to do, since

most of the discussionaboutproblemsof moralhazard hatwould be createdby mov-

ing towarduniversalbanking n the United Statespresume hat he current tructure f

deposit insurancewould continue in place. Of course, thereis no presumption hat

these deposit insurancearrangementsre in any way optimal.

It is also thecase that the FDIC has never had to obtain funding from generaltax

revenue, but it surely could and would if necessary.Indeed, such tax funding

was actually authorizedas recently as the FDICIA Act of 1991 (but then proved

unnecessary).

The FDICIAAct also providedfor deposit insurancepremiato be determinedac-cording to a bank's risk class, as opposed to the simple flat-rate cheme assumedin

our analysis. However, the assumptionof a flat-rate nsurancepremium does little

violence to realityat the present, as an overwhelmingmajority of banks are in the

same (lowest) risk class. And, of course, until recentlyall banks were chargedthe

same premium.

A naturalquestion s whethercountries hatcurrentlyallow universalbankinghave

deposit nsurancemechanisms n placesimilar o the one we model? In some cases the

answer is yes: Germanyprovides virtuallycomplete insurance o depositors (Saun-

ders 1997), andTurkeyalso has a deposit insuranceprogram. n addition,we believethatthe reality s that n most countnesinformal toobig to fail policies rendervirtu-

ally all depositors nsured, rrespectiveof theirformal nsuranceschemes. Fora vari-

ety of reasons, ncludingthe existenceof highly concentratedbankingsystemswith a

relatively small numberof large banks,governmentsarewont to toleratebank fail-

ures. Thatreluctancehas been quite evident n the recentbankingproblems n Europe,

South America,and Asia.

Finally, the banks in our model haveno outside equityholders. Here this is actual-

ly optimal, since agents with equityshares n banks would be obligated to duplicate

monitoringeffort.But this would be an interesting eatureof the analysis to modify in

futureresearch.

18. In an expandedmodel we mightthinkof oursas an overlappinggenerations conomy where he gov-ernmentraises resources from the currentyoung to make paymentsto the currentold depositorsof failedbanks.Our assumptionon FDIC behavior s intended o give the analysis this kind of flavor.







436 : MONEY, CREDIT,AND BANKING

2. COMMERCIALBANKING

We now analyze the behaviorof banksandborrowers and discuss the determina-

tion of a full generalequilibrium under wo alternativebankingarrangements:om-mercial banking and universal banking. In this section we exogenously impose a

commercialbankingstructure;by this we mean thatbanks are restricted o entering

into debt contractswithborrowers. n thenext section we considerbanks hattake eq-

uity positions in the firmsthey lend o. Then, in section 4, we comment on when

banks thatare free to enter into any type of contractualarrangementwith borrowers

will choose to take equitypositions.

The timing of events is as follows. Each potentialbanker(knowing deposit rates

and contract erms)chooses whether o open a bank.Those who do notact as bankers

become depositors (deposit their unit of funds with a bank). Those who do act asbankers nvest in monitoringcapacity.

Once theset of banks s determined, ach banktakesdeposits andenters nto a con-

tractualarrangement the natureof the contractualarrangement epends on the type

of banking system in place) with one borrower.After the contracthas been entered

into, the borrowermakes a choice of which investment project to operate (among

those that are feasible given his funding).Subsequent o projectchoices being made

the bankcan, if it desires,engage in interimmonitoring which it may do stochastical-

ly). At this point the bankcan also if it wants liquidate the project and call the

loan.

If the loan is not called, the randomreturnz is realizedat the beginning of period

two. Thenpaymentsaremade from the borrower o the bank, andverificationof the

projectreturn s undertaken y the bankascalled for by the contract. f it is feasible to

do so, thebank then pays r per unitdeposited, andpockets any residual.If this is not

feasible, the bank s liquidatedby theFDIC.

Under commercialbanking, banks are restricted o entering into a debt contract

withborrowers.Ournotionof a debt contracthere closely follows the one that s stan-

dard n thecostly stateverificationiterature Diamond1984; Gale and Hellwig 1985;andWilliamson1986,1987). In particular, debt contract pecifies thefollowing: (a)

A probability,denotedp, that interimmonitoringwill be undertaken; b) A set of ex

postverification tates,which we denoteby A. Ex post state verificationdoes not take

place if z E B = [O,z]-A; (c) A repayment chedule (per unit borrowed)of R(z), for

all z E A; (d) An uncontingentpayment(that is, a gross rate of interest)x if z E B.

Clearly, B = [x, z], as in Diamond (1984) and Williamson (1986, 1987); (e) A loan

quantityq. Here, it clearly suffices toconsiderq E {q2' ql }

Withthese preliminanes, we now proceed to considerthe behavior of banks and

borrowersundercommercialbanking.

A. BankStrategies

Since a funded borrowercan invest only in project 1 or project 2, any individual

bank' strategiesare verylimited. In this section as well as section B we take the








set of active banks,the rateof intereston deposits,andthedeposit insurancepremium

as given. We theninvestigatethe optimalbehaviorof banksof differentkinds.We be-

gin by consideringeach potentialbank strategy n turn.

Strategy

Onestrategy hat can be undertaken y a bank s as follows. Lendql to a borrower.

It is thenfeasible for the borrower o undertake ither project.To deter the borrower

from investingin project2 and consumingperks, engage in interimmonitoring,and

liquidate he investment f the borrowers foundto have invested in thatproject.1 Of

course under this strategy,the interim monitoringprobabilityp must be set high

enoughto determoralhazard.

If abank ollows strategy1, we denotethe interestrate tchargesbyxl . Thenthe ex-pectedgross return o a bankfrom following strategy1, notinclusiveof interimmoni-

toringcosts (andper unit lent) is given by

xl [1- G(xl ] + l zg(z)dz (-)G(x) = xl - | G(z)dz (-) G(xl _ 5.(xlQl;) ( 1

if its ex post monitoringcost is y. The expectedreturn o the borrowerrom choosing

project 1 is

ql Izi - xl[1 G(xt ] - | zg(z)dz = ql Izl - xl + | G(z)dz;.

A crucial questionin our analysisis, when is there a moral hazardproblemunder

strategy1? Undercommercialbanking,and in the absence of interimmonitoring,a

borrowerwho receivesq1 units of fundscouldinvest in project2 andsimultaneously

spendq1 - q2 onperks.20A borrower ollowing this course of actionwould defaulton its loan if q2z< qlxl. As a result,the expectedpayoff to the borrower rominvest-

ing in project2 is absent nterimmonitoring-

q2z2+6(ql -q2)-qlxl ll -F ( I )Xl i-q2 1 Zf(z)dz

(q,lq2 )Xl

= q2Z2 + 6(ql - q2) - qlXl + q2 | F(Z)dz.o

19. We assume throughouthatthe lendercan commit in advance o liquidate he investment f it is dis-coveredthatthe borrowerhas invested in project2. Thus renegotiations not a possibility.

20. All of these perkswould be consumedby the borrower, ince thebankhas no ownershippositioninthe firm.








Consequently, here s a nontrivialmoralhazardproblem understrategy1 iff

Xl (ql/q2 )Xl

q2Z2 + 6(ql - q2 ) 2 qlzl + ql | G(Z)dz q2 | F(z)dz. (a.2)

o o

In keeping with our focuson moralhazardproblemsunderdifferentbankingarrange-

ments, we henceforthassumethat (a.2) holds.2l For analyticalsimplicitywe also as-

sume that

z > ( ql )x (a.3)q2

Assumption(a.3) simply assertsthat whena borrowerdivertsfunds understrategy 1,

this does not imply thathe defaultson his loan with probabilityone.

When (a.2) holds, a bankfollowing strategy1 must engage interimmonitoring o

determoralhazard. f thebankengages in interimmonitoringandthe borrowerhas di-

verted funds into expenditureson perks, we assume thatthis perks consumptionoc-

curs before the project can be liquidated;hence the borrower gets 6(ql - q2).

However, if interimmonitoringdoes notoccur, a borrowerwho divertsfunds gets the

expected payoffdescribedabove. Thus, in order o determoralhazard, he bankmust

choose an interimmonitoringprobability hat satisfies the following incentivecom-patibilityconstraint:

S Xl ] S (ql/q2 )Xl n

qlfzl -xl + |G(z)dzJ2(1-P)iq2z2 -qlxl +q2 | F(Z)dZJ+6(ql -q2). (2)

Since interimmonitorings costly, clearlythe bankwantsto setp as smallas possible.

Consequently,he bank' interimmonitoringprobabilitys given by22

r (ql/q2 )Xl

P = f q2Z2 + 6(ql - q2 ) - ql zl + q2 | F(Z)dzo

I g F (ql/q2 )Xl )

-ql| G(Z)dzJ lq2Z2 -qlXl +q2 | F(Z)dzJ-p(Xl). (3)o o

It is easy to verify thatp'(xl) > Oholds, so thatthe probabilityof interimmonitoring

must increase(the moral hazardproblembecomes more severe) as the interest ratechargedunder strategy 1 becomes higher.It is also easy to verify thatthe value of p

given by (3)satisfiesp ' 1 iff

21. Whether(a.2) holds or not depends, in general,on the equilibriumvalue of xl . We describe its de-terminationbelow. Note that (a.2) is more likely to hold the larger is xl; that is, moral hazardproblemsappearwhen rates of interest on loans are sufficiently high.

22. Assumptions a.2) and (a.3) imply thatp > O.







JOHNH.BOYD,CHUNCHANG, NDBRUCED. SMITH : 439

xl

qlzl - 6(ql - q2) 2 qlxl - ql G Z ) d Z (4)

o

holds. Therefore, here s an upperboundon the interestratethatcan be chargedunderstrategy 1: interestrates exceeding this boundrender t impossibleto determoralhaz-

ard.Let x denotethe solution to (4) atequality.Thenxl ' x must hold.

Togetherourobservations ndicatethatthe expected payoffto a bank fromfollow-

ing strategy 1, andfrom chargingthe interestratexl is given by (not inclusiveof the

cost of funds) qlz(xl, ql; y)-Xp(xl). We now discuss thedetermination f the inter-

est ratexl.

a. Interest Rate Determination.As is well-known (Williamson 1986, 1987), the

functionz(x, ql; y) is typically not monotone in x. Excessively high rates of interest

lead to high probabilitiesof default,high expected monitoringcosts, and low returnsto lenders.Theprobabilityof interimmonitoring s also increasing n x. This adds an

additional actor eading lendersnotto want to chargeoverlyhigh rates of interest.

When the expectedreturn o a lender is not monotonically ncreasing n therate of

interest, his opensthe possibility thatcredit can be rationed.In particular, f the sup-

ply of funds is low relativeto the potentialdemand or funds,borrowerswill compete

with each otherfor scarce oans. But there s a limit to how much they can do so, for if

they offer excessively high ratesof interest hey will makethemselves unattractive o

lenders.

To simplify our discussion, we henceforthassume that credit is rationed.23This

makesthe determination f loan ratesvery straightforward;orrowersbid theseup to

the level thatmaximizesa lender' expectedpayoff. Definexl by

xl - argmax qlz(x, ql; y) - Xp(x)] (5x<x

Then, understrategy1, creditrationing mplies thatxl = xl.24

b. The Costof Funds. In orderto evaluate the net expectedpayoff to a bank from

following strategy1, it is necessaryto describe the bank's cost of funds underthatstrategy.A bankfollowing strategy 1 must raise ql unitsof funds to make its loans,

and in addition t must raise tql units of funds to pay its depositinsurancepremiums.

Thus, the bankwill have deposits equalto (1 + t)ql. It will be feasible for the bankto

pay r on each of these deposits iff its borrowerhas z-r(l + t). Hence, the bank will

fail with probabilityG[r( 1 + t)].

If the bank does not fail, it pays rql(l + t) to depositors.If it does fail, all its assets

are liquidated o pay depositors.Let <?l[r(l + t)] denotethe expected transfer rom

banksto depositorsor the FDIC, as a functionof r and t, understrategy1 (andper unitdeposited).Then ¢1 satisfies

23. We emphasizethat his is by no meansessential to most of ourdiscussion. We show below thatcred-it rationingmust obtain f a > (2 + q2)- 1, andif d is sufficiently ow.

24. Of course, in order for borrowers o participaten the loan market,ql {z^l xl + Jol G(z)dz} 2 umust hold. If this conditionis violated by xl, then the interestrate mustbe lowered until borrowersare in-differentbetween obtaining,and not obtaining,credit.Of course n this case credit s not rationed.We mustconfine our attention o the situationwherecredit s rationed n the text.








r(l+t) r(l+t)

O1 r(l + t)]_ r(l + t) {1 G[r(l+ t)] } + | zg(z)dz= r(l+ t) - | G(z)dz. (6)o o

ClearlyO1> Oholds, so increases n ror theinsurancepremium raise thebank' cost

of funds.

c. Net Payofs underStrategy . Fromour previousobservations t is immediate

thata bank' net expectedprofitunderstrategy1, and assuming hatcredit s rationed,

is given by q1{z(x1 q1, y) - 4>1[r(l + t)]} - Xp(xl).We now comparethis with the

expected payoffsavailableunderother strategiesopen to a bank.

StrategyAnotheroption open to a bank would be simply to lend a borrowerq2.Under this

strategy t is not feasible for a borrower o invest in project1 or to divertfunds, since

if funds arediverted t will be clear thatno projectwas undertaken.Thus, understrat-

egy 2 a borrower ust invests in project2, which is an alternativemethodof dealing

with the moralhazardproblem.25

When strategy2 is followed, clearly no interim monitoringis necessary by the

lender.Moreover, f x2 denotesthe interestratecharged, he borrowerdefaults f Z2 <

x2. Thus theexpected payment rom the borrowero thebank s given by

r X2 1 X2

q2f x2 [1 - F(x2 )] + | ;t(z)dZ q2 X2 - | F(z)dzo o

Then the bank's expectedreturnunder strategy2 (per unit lent), not inclusive of its

cost of funds,but inclusiveof ex post verificationcosts is given by

xo X

X I F Z ) d Z - J F X 2 ) - q 2 4 X q 2 ; Y )

The remarkswe made above about the nonmonotonicityof z(-) apply equally to

t(-). It follows that, undercredit rationing,a bank following strategy2 will charge

the interestrate26 2 = argmaxX(x, q2;y)-x2, and its expected gross return exclu-

sive of its costs of funds)equals q24(x2,q2,y).

a. TheCostof Funds.A bank pursuingstrategy2 needs q2( 1 + t) unitsof funds to

make its loansand pay its deposit insurancepremiums. twill be feasiblefor the bank

25. Recallthatthere s a cost to letting the borroweroperateproject2, since zl > Z2

26. For the same reasons as before

q2 tZ2 - 2 + I F(Z)dz 2 u

must hold for x2 to be charged.If x2 violates this condition, the same comments as in footnote 29 apply.








to pay its depositorsrq2(1 + t) iff its borrowerhas z ' r(l + t): therefore he bank

fails with probabilityF[r(l + t)]. If O2[r(1 + t)] denotesthe expected paymentby

banksto depositorsand the FDIC(per unit deposited)understrategy2, it follows that

r(l+t) r(l+t)

¢2 [r(l + t)] = r(l + t) {1 F[r(l + t)] } - | (z)dz = r(l + t) - | F(z)dz. (8)

o o

Assumption a.l) implies that¢?2[r(l + t)] < Ol[r(l + t)]: that is, the cost of funds

per unit s lower understrategy2 thanunderstrategy1. It is also apparenthat 2 > °

holds.

b. NetPayofs underStrategy2. Fromtheprecedingdiscussion it is apparent hata

bank'snet expected profitsunderstrategy2 are given by q2{4(x2,q2;y) - O2[r(1 +t)] }, if credit s rationed.

Strategy3

A bank engaged in strategy1 or strategy 2 attemptsto address the moral hazard

problem n some form.There is a thirdoption availableto the bank: t might ignore

moral hazardaltogether.To be more specific, suppose thata bank lendsql to a bor-

rower, that(a.2) holds, and thatthe bank engages in no interimmonitoring.Then the

borrowerwill invest in project2, and consumeql - q2in perks.27Under strategy3,the bank simply allows this to happen.28

In order o hide the fact that t is following strategy3, the bankmustact as if it is fol-

lowing strategy1. Then,in particular,t mustchargetheinterestratexl.29If it does so,

since theborrowerborrowsql, a loan defaultoccurs if q2z< ql xl. Thusthe probabil-

ity of default s F[(ql/q2)xl], andthe expectedgross return o the bank inclusiveof

ex postmonitoring osts is

qlxl|l-F (ql)xl |+q2 | zf(z)dz-yF (ql)xl -q24 (ql)xlq2; . (9)

a. Cost of Funds.In order o pursuestrategy3, a bankneeds ql(l + t) units of funds

to lend ql and pay its deposit insurancepremium.Thebank can pay depositorsr per

27. As before all perksconsumptionaccrues to theborrowerbecause no one else has an ownershippo-sition in the borrower' project.

28. If thebank ent q E (q , q 1 to theborrower, t would be clear to the FDIC thatthe bank was not at-temptingto control the moral2hazard roblem.We assumethat this is unacceptable o the FDIC. Howev-

er, if the bank lends ql, the FDIC cannot distinguishbetween a bank following strategy 1, and a bankfollowing strategy 3.

29. Of course this strategymay not be feasible, since

q2Z2 + 6(ql - q2 ) - Xl + | F(z)dz 2 uo

need nothold. The discussionin the text assumes thatthisconditiondoes hold.








unitdeposited iff q2z > rql(l + t), since the bank's loans are invested in the small

scale project(project2). Thus the bankfails withprobabilityF[(q1/q2)r(1 + t)], and

the bank' expectedpayments o depositorsand the FDIC are

r - -] (ql/q2 )r(l+t)

qlr(1+ t)41- F ql j r l t) JLq2 | zf(z)dz

(ql q2 )r(l+t) A

= qlr(1+ t) - q2 | F(z)dz = q2¢2 ql j r l t)

b. Net PayoJfs underStrategy 3. Consolidating the discussion of the preceding

paragraphs,t is apparenthat the net expected profitof a commercialbank pursuingstrategy3 is given by theexpressionq2{4[(ql/q2)Xl sq2; 7] - ¢2[(ql/q2)r(l + t)] }. We

now proceedto rank hedifferentstrategiesavailableto a commercialbank.

B. A ComparisonofAlternativeStrategies

In thissection we pose the question:which lendingstrategywill be preferred y any

given bank?The main resultof the sectionis as follows.

PROPOSITION1: For every commercialbank,strategy2 is strictlypreferred o strat-

egy3.

Proposition 1 is proved in Appendix A. The propositionmakes a strong assertion:

strategy3 cannotbe optimalundercommercialbanking.Thus acommercialbankwill

always takesome actionsto addressthe moral hazardproblemconfronting t, either

by restricting he size of its loans, or by engaging in interimmonitoring.As we will

show, ananalogousstatement annotbe made underuniversalbanking.

Intuitively,a bankpursuingstrategy3 holds a claim on the same assets as a bank

followingstrategy2. In addition, t is moreconstrained n its choice of a loan rate,and

it mustraise a largerquantityof depositsthan a bankfollowing strategy2. Finally, itcannot share n the perksthat accrueto theborrowerunderstrategy3, since it has no

ownershipclaim on the firm.Thus, a commercialbankwill never choose to allow its

borrowers o divertfunds.

A comparisonof strategies 1 and 2 is far less straightforward. rom our previous

discussionit is easy to show thatany bankprefersstrategy1 to strategy2 iff

(ql) (ql) ( ql )r(l+t) A

_ | G(z)- q2 | F Z ) dz- (10)o ql )

The expression n ( 10)reflects severalconsiderations hatarise in ranking trategies1

and 2. First,z(xl, ql; y)-(Sql)p(xl) > (q21ql)4(x2, 2;y) holds iff X is sufficiently







JOHNH. BOYD,CHUNCHANG, NDBRUCED. SMITH : 443

small. This expressionis obviouslynecessaryforthe satisfactionof (10): strategy1 is

superior o strategy2 only if the costs of interimmonitoringare sufficientlysmall.30

Second,engaging in strategy1 requires hat the bankraisemorefunds than would

be required o follow strategy2. This is expensive,and it becomes more expensive as

r( 1 + t) increases. Thus high valuesof r, or highvaluesof teteris paribus favor

banksfollowing strategy2.

Third,the expected cost of ex post state verificationunder strategy 1 (2) equals

yG(x1)[yF(x2)].If F(x2)> G(xl) holds,3l thenstrategy2 involves higher expectedex

post monitoring osts thanstrategy1. This works n favorof strategy1. Moreover, his

last observationhas an interesting mplication:other things being equal, higherex

postmonitoringcosts increasethe attractiveness f strategy1 relativeto strategy2 (if

F(x2) > G(x1)).But, in general,as these observationsmake clear, either strategy 1

or strategy 2 might be preferredby any bank, dependingon the configurationofparameters.

C. BankHeterogeneity,andSome Scenarios

Whenthere s heterogeneityamongthe set of potentialbankers as when thereare

low- and high-costbanks there areseveral possible scenarioswithrespectto which

banksoperate,andwith respectto whichstrategies hey follow. We now outlinesome

of thepossibilities.

Scenario1. If the interimand ex post monitoringcosts of high-costbanks are toohigh, then it is possible thatonly low cost bankswill operate, n equilibrium. n this

case the low-costbanksmayfollow eitherstrategy1 or strategy2.

Scenario2. If low- andhigh-costbanks have relativelysimilarmonitoringcosts,

then it is possible thatbothtypes of bankswill operateand,moreover, hatboth types

of bankswill havethe sameoptimalstrategy.

Of course, when eitherscenario 1 or scenario2 is played out in equilibrium-

nothingvery interestinghappensas a resultof allowing forbankheterogeneity.Thus,

whenwe want to discuss theimplicationsof having differentkindsof banks, we will

focus on the thirdof our scenarios.Scenario3. High-costbanksdo nothave monitoring oststhatareso high as to deter

themfrom operating.However,eitherthe interimor the ex post monitoringcosts of

high- and ow-costbanksdiffer sufficiently hatthey havedifferentoptimalstrategies.

Whenscenario3 transpires,t maybe either hehigh- orthe low-cost banksthat ind

it optimalto follow strategy 1. It will be the low-cost banks that follow strategy1

when they have relatively low (and high cost banks have relatively high) interim

monitoringcosts, and when ex postmonitoringcosts are relativelysimilaracrossthe

banks.On the other hand, it will be high-costbanks that favor strategy1 if interim

monitoringcosts are similaracross banks, if F(x2) > G(xl), and if high-costbanks

haveex post monitoringcosts thatareenoughhigherthanthose of low-costbanks.

The last pointis of interest or the following reason. Underscenario3, some banks

30.The aststatementresumeshat a.2)holds, o thatP(21 > °-31.There remany easonswhyF(x2)> G(xl might esatisfied.ndeed,ssumptiona.1 implieshat

thisconditionmustbe satisfiedfx2> xl The nequality2 > 21willnecessarilyoldf 22violates4). Sucha violationanresultwhenever(ql - q2)/ql s sufficientlyarge.







444 : MONEY,CREDIT,AND BANRNG

follow strategy1, while othersfollow strategy2. The formerset of bankswill have a

largervolume of loans and deposits, and a lowerprobabilityof failure.When interim

monitoringcost differences differentiatehigh- and low-cost banks, the large banks

will also have relativelylow operatingcosts. But, when ex post monitoringcost dif-ferences differentiatethese banks and when F(x2) > G(xl) the relatively large

bankswill have highoperatingcosts. In short, here s no logical presumption hat t is

the mostefficient banks that are also the largestbanks.

We will referto scenario3a (3b) as the situationwhere bothtypes of banksoperate,

and low- (high-) cost banks follow strategy 1.Under scenario3a (3b), equation(10)

holds for low- (high-)cost banks,while the same equation ails for high- (low-) cost

banks.

D. GeneralEquilibrium

It remainsto determinea full general equilibriumof the model with commercial

banking.Therearetwo components o such a determination.First, he assumptionhat

p ' a, coupled with the assumption hat not all potentialborrowersarefunded (ra-

tioningof credit), mplies thatnotall potentialbankerscan operatebanks,in equilib-

rium. Thus the marginalbankermust be indifferentbetween operatinga bank and

actingas a depositor. n effect, themarginalbankmustearna normal xpectedprof-

it. Second,the FDIC must breakeven.We now proceed as follows.

We assumethat the FDIC exogenously sets a value for the deposit insurancepre-mium parameter . Given t, the remainingendogenous variables n the model are the

deposit interestrate,r, and the lump-sum ax levied by theFDIC, In particular, iv-

en t, the FDIC's expectedlosses depend on r, both directlyand indirectly.32Thus, in

equilibrium,he lump-sum ax thatthe FDICmust impose to balance tsbudgetneeds

to be determined long with r. We now describe he remainingequilibrium onditions

of the model.

1. Normal'9Profitsfor Banks.We begin by stating the condition under which

banks earnnormalprofitswhen all potentialbankersare identical,ex ante.We then

give therequiredmodificationwhenthere s heterogeneityamong potentialbankers.

When all potentialbankersarealike, agents who operatebanks will either pursue

strategy1 or strategy2. Then, as per our previousdiscussion, their expected profits

will be given by

Q[r(1 + t); rys _ max{ql [lt(Xl,ql; 7)-(iql)p(x1)-Ol [r(1 + t)]],

q2[4(X2'q2; 7)-¢2[r( 1 + t)]] } ( 1 1

On the other hand, agentswho do not operatebanks will simplybecome depositors.

Such agentspay the lump-sumtax , and deposit 1-X with a bank. Theirpayoff is

32. TheFDIC's (expected)paymentsdependon r directly,because eachdepositorof a failed bankmustbe paid the difference between r and theper depositorvalue of the bank's assets. They dependon r indi-rectly because r influencesthe optimal endingstrategyof each active bank,and hence theprobability hatany given bank will fail.








r(1 - ). Thus,potentialbankersare indifferentbetweenoperatingand not operating

a bank ff

Q[r(1 + t); 7, k] = r(1-) . (12)

Given t, equation 12) describesa relationbetween randXthat s depicted n Figure

1. The locus definedby (12) is upwardsloping, since Q is a decreasing unctionof r.

Intuitively, as X rises the FDIC is engaging in increasinglyheavy subsidizationof

banks at the expense of depositors.Thus, to maintainan equality of payoffs the de-

posit rate of interestmust rise. This benefits depositorsand is costly to banks.There-

fore r andXmustmove together f banks are to earnonly normalprofits.

a. Heterogeneity.When thereareboth low- and high-cost banks,mattersaresome-

what more complicated.In particular, ependingon the fractionof low-cost banks n

the bankerpopulation(,u)and the extent of credit rationing, t may be the case that

only low-cost banksoperate.Or, it is possible that both low- and high-cost banksop-

erate.We describeeach case in turn.

When only low-cost banks operate, then the marginalbankerobviously has low

costs. Then (12) must be replacedwith

Q[r( 1 + t); YL XL] = r( 1-) ( 13)

We now describewhat s required n order or only low-costbanksto operate, n equi-

librium.

Let 0 denote thefractionof borrowerswho receive funding.When only onetype of

bank s active, each fundedborrowergets ql (q2) units of funds,if strategy1 (2) is pre-

ferredby banks.Define the functionq[r(1 + t)] by

ql; if strategy1 is preferred by a low-cost bank)

q[r(1 + t)] =

q2; if strategy2 is preferred by a low-cost bank) (14)

Then uses of funds of given by Oaq[r(1+ t)].

/ (12)

dl+t)

FIG. 1. A BankEarns Normal Profits f (12) Holds








With respect to sources of funds, there is one unit of funds supplied by every

agent who is notan activebankorborrower.33 ince the measureof active banksmust

equal themeasureof fundedborrowers, ourcesof fundsare 1 - af1 + 0). Hence, an

equalitybetweensourcesand uses of fundsrequires hat

0 (l-a)t 1 l (15)

a t l + q[r(l + t)]J

In orderfor it to be feasible foronly low-cost banksto operate, t must be the case

thatOa 5 holds. Thus, anecessary(butnot sufficient)condition or low-costbanks

alone to operate is that,u5(l + ql) ' 1-a. If this condition fails, some high-cost

banksmustoperate, n equilibrium.

Of course, if only low-cost banksoperate,there is no heterogeneityamong active

banks in ourmodel. Therefore, n the futurewhen we allow for bankheterogeneity,we will assume that somehigh-cost banksoperate.As we havenoted,this will be the

case if

1-a>R(1+ql) (a.4)

Moreover,when some high-cost banksoperate,clearly the marginalbankermust

be a high-costbanker.Therefore hemarginalbankerearns zeroprofits ff

Q[r(l + t);GIH'H] r(l-T) (16)

Finally,we have arguedthatheterogeneityamong banks is interesting f and only if

somebanks follow strategy 1,while othersfollow strategy2. To fix ideas, we hence-

forth assume (when thereare high- andlow-cost banks) thatlow-cost banksprefer

strategy 1,whilehigh-cost bankspreferstrategy2.34Then (16) reducesto

q2{4(X2s q2; YH)-¢2[r(l + t)]} = r(l-) . (16t)

Inaddition, hisconfiguration f optimalbankstrategiesrequires hatequation 10) be

satisfied orlow-cost banks, while the samecondition s violatedforhigh-cost banks.2. TheFDIC Break-Even ondition. sbefore, we beginby describingwhat is

required or theFDIC to breakeven when all potentialbankersareidentical,ex ante.

We then show how the analysis must be modified when there is bankheterogeneity.Severalfactors need to be analyzed n order o statethe condition thatmustbe sat-

isfied for theFDIC budgetto balance.First, we must know how many banks are inoperation.Second, we must knowthe expectedloss of each bank.This,of course, de-

pends on the optimal ending strategyof banks.Third,we mustknowthe probability

of failure or eachbank,asthisdetermines he FDIC's cost of ex post monitoring.This

33. This is trucesince theFDIC reinvests all its taxrevenue n credit markets.

34. Ofcourse, as we havenoted, this is not theonly possibility.







JOHNH. BOYD, CHUN CHANG,AND BRUCE D. SMITH : 47

failure probabilityalso depends on the banks' optimal oan strategy.We begin with

the measureof banksthat are active.

Our assumptionof one bank-one borrower mplies that the measure of active

banks must equal the measure of fundedborrowers.Thus, as indicatedby equation(15), the mass of banks n operation s aO = (1 - a)lf 1 + q[r(l + t)] }. For futureref-

erence we note thatcredit must be rationed 0 < 1 must hold)if

l-a<a(l+q2) (a.5)

as we henceforthassume.

WhenaO is themeasureof activebanks,the FDIC collects aOtq[rf 1 + t)] indeposit

insurancepremiums,and it collects [1 - a(1 + 0)] in lump-sum axes paidby bank

depositors.TheFDIC, by assumption, einveststhis incomein the creditmarketearn-ing r per unit deposited in period two. Thus total second-periodFDIC income not

inclusive of theassets of liquidatedbanks is given by the expression

r{aotq[r(l + t)] + [1-a(l + 0)]T} = r(l-a)(t + T)q[r(l + t)]/

{1 + q[r(l + t)]} .

Total FDIC obligations in periodtwo are calculatedas follows. Each bank has an

expected payment o depositorsandthe FDIC (if it fails) of qlOl[r(l + t)] (q2<D2[r(1

+ t)]), if strategy1 (2) is optimal.Thus,by the law of largenumbers,FDIC payments

to depositors(including tself) net of income from asset liquidation-equal ql {r(l

+ t)-¢1[r(l + t)]} (q2{r(1 + t) - ¢2[r(1 + t)]})ifstrategy 1 (2)isbeingfollowed

by banks.35Multiplying the appropriate uantityby aO (the mass of active banks)

gives the differencebetween FDICobligations to the depositorsof failed banks and

FDIC income fromasset liquidation.

The otherrevenueraised by the FDICmust cover this difference, and it must also

cover the monitoringcosts incurredby the FDIC in the processof asset liquidation. fbanksare engaged in strategy 1 (2), thena fractionG[r(1 + t)] (F[r(l + t)]) of banks

fail, and the FDIC's cost of ex post state verificationarePyFG[r(1 t)] (yFF[r(l +

t)]). Then if c[r(l + t)] denotes the second-periodcosts of the FDIC net of its in-

come from liquidating he assets of failedbanks c[r(1 + t)] satisfies

(1 + ql ){ ( + t) 4)I[r(1+ t)] + (7F )G[r(l + t)]};

if strategy1 is optimal for banks

(l-a)(l+q2 ){r(l+t) (>2[ ( (q2 ) }

if strategy2 is optimal for banks.

35. In particular,he FDIC must cover the average difference between the promisedpaymentper unitdeposited, r, and the amount hatbankspay outto depositorsand the FDIC.








/ (1

l

<1+t)

Slr 1 Slrategg 2

oplimal qXimal

/ (1

Kl+t)

stratca 1 Stalty 2

qimal qhmal

FIG. 2. FDIC Break-EvenCondition

The FDIC breakseven iff

r(1-a)(t + )q[r(1 + t)]/{ 1 + q[r(1 + t)] } = c[r(1 + t)] . (17)

We now depict the locus definedby (17) diagrammatically. t has several possible

configurations, wo of which are depicted n Figures 2.a and 2.b. In those figures,the

optimal ending strategy or banks s strategy 1 (2) if r(1 + t) lies to theleft (right)ofthe dottedvertical ine. Thefunctionc[r(1 + t)] will typically not becontinuousat the

value of r(1 + t) thatmakes banks ndifferentbetween the two strategies.Moreover,

it is easy to show thatc[r(1 + t)] can either increaseor decrease as banks shift from

strategy 1 to strategy 2, depending on parametervalues. In Figure 2.a (2.b), the

FDIC's costs rise (fall) discretely as the optimal strategychanges from strategy 1 to

strategy2.

If G(z)/zand F(z)lz areboth nondecreasing n z, then it is straightforwardo show

that (17) defines a locus that is eithermonotonically ncreasing,as in Figure 2.a, or

thatfails to be increasingonly whenstrategy1 andstrategy2 yield thesame expectedpayoff to a bank,as in Figure 2.b.3637Of course, it is also possible thata single lend-

36. That s, the locus definedby (17) can fail to be increasingat most a single value of r(1 + t); the val-ue thatrendersbanks ndifferentbetween strategies 1 and 2.

37. If G(z)/zor F(zlz) can be decreasing n z thereare clearly severalotherpossibleconfigurations f thelocus definedby ( 17). We do notexhaustthe set of possibilities here.








X , (12)

/(1

dlft)

X ,, (12)

l/ (1D

</

/dlft)

FIG.3. GeneralEquilibrium:CommercialBanking

ing strategy s optimalfor all values of r(l + t): in this case the locus definedby (17)

is continuous.

The determination f r andX in a general equilibrium s depicted in Figure3. As

shown there, here s considerable copefor multipleequilibria o arise. Acrossdiffer-

ent equilibriahighervalues of r are accompaniedby higher ump-sum axes and larg-

er FDIC losses. Of course, as shown in Figure 3.b, there need not be multiple

equilibria or arbitraryonfigurations f parameter alues.

a. BankHeterogeneity.As before,when thereare bothhigh- and low-cost banks n

operationwe fix ideas by assuming hat ow- (high-) cost banksoptimally ollow strat-

egy 1 (2) in lending.We now state the condition underwhich the FDIC breakseven

when this transpires.

We continueto denote the fractionof fundedborrowersby 0. Only fundedborrow-

ers who borrow rom low-cost banksget a loan of ql; the oa-5 borrowerswhobor-

row from high-costbanksget a loan of q2. Hence uses of funds areoaq2 + ,u(ql-

q2). As before, sources of funds are 1 -a(l + 0). Thus, an equality between

sources and uses of funds implies that

0 1 - a - ,U(q1 - q2 )

a(l+q2)

Clearly,credit s rationed 0 < 1 holds) iff

1 < a(2 + q2) + R(ql - q2)(18)








In addition,high-costbanks must be active if Oa< R. This condition is satisfied ff

1 - a>R(l + ql) (19)

When (18) and (19) hold, there arebanks of mass ,u (0a - 5) following strategy

1 (2). Thus, the FDIC collects t[0aq2 + ,ul3(ql-q2)] in period one in deposit insur-

ance premiums, and it also collects [1-a(l + 0)] in lump-sum taxes. It is then

straightforwardo show that the FDIC's second-period ncome not inclusive of in-

come from the liquidationof failed banks is given by

r(t + ){(1 - a)( 1 + q2 ) R ( 1 + q2 )}

In addition, he FDIC's netobligationsto the depositorsof the ,uG[r(1 + t)] low-cost

banks that fail, plus its costs of monitoring these banks, equal ,u5{ql[r(1 + t) -

¢1 [r(1 + t)]] + PyFG[r(l+ t)] } TheFDIC's net obligations to the depositorsof the

(0a-R)F[r(l + t)] high-cost banks that fail, plus its costs of monitoring these

banks,equal (0a-,u){q2[r(1 + t)-¢2[r(1 + t)]] + PyFF[r(l+ t)] }. It is then easy

to show thatthe FDICbreakseven iff

{ (1 + C2 ( 1 + q2 )} 5(7FG[r(l + t)] + qi | G(Z)dz}

f r(l+t) ]

+ (0a - A5)j7FF[R(1 + t)] + q2 | F(Z)dzi. (20)o

When(16') and (20)have a solution rj ) such that(10)holds (fails) forlow- (high-)

cost banks,then we indeedhave anequilibriumwhere low- (high-) costbanks follow

strategy1 (2).

3. UNIVERSALBANKING

In this section we analyze optimalbankbehavior,as well as thedetermination f a

full generalequilibrium,undera systemwhere all banks are universalbanks.By this,

of course, we mean simplythatall bankstake equity positions in the firms hey lend

to.38In thenext section we then compareuniversalwithcommercialbanking.

Whenbanks take an equity position in the firmsoperatedby their borrowers, wothings happen.First, thetransferbetweenthe firmandbank must alwaysbe nontrivi-

ally statecontingent.Absent stochasticmonitoring, hisobligates the bank to engage

in ex poststateverificationor (almost)all projectreturn ealizations.Thisobservation

38. We do not consider the possibility in thispaper hat some banksare commercialbanks while others








impliesthata cost of Py,he bank n effectbecomes fully informedabout he investment

returnof thefirm.There s, therefore,no gain fromthebankandthe borrower ntering

into any kindof contractotherthanan equitycontract.Thusthe bank s happyto take

an equity position alone, ratherthan enteringinto a more complicatedcontractualarrangementhatmight haveboth a debt andan equitycomponent.

Second,when a bankholdsequity in a firm, t canshare n the consumptionof perks

generatedby the diversionof fundsaway fromproject nvestments.As we will show,

this ability to sharein perks consumptioncan substantiallyalter the set of optimal

lendingstrategies or a bank.

Throughouthe analysis,we let w E [0, 1]denotethe shareheld by the bank n the

firm'sproject.And, as before, there are only two claimants: he operatorof the firm

andthe bank itself. (This arrangement an again be regardedas a type of delegated

monitoring.)Finally,we assumethat f a bankhas aclaim on a fractionw of thefirm'

profits, t alsohas aclaim on a fractionw of theperksgeneratedby anydiversionof in-

vestmentfunds, if the bankhas agreedto-and is awareof this diversion.We now

considerthestrategiesavailableto a universalbank.

A. BankStrategies

As in section2, we beginby takingthe set of activebanksand the rateof intereston

depositsas given. We then investigatethe optimalbehaviorof banks.

As before, thereare only three strategiesopen to banks. A bankcantransferql to a

firmand if there s a moralhazardproblem-engage in interimmonitoring o deter

it. Or, a bankcan transferustq2 to a firmand, de facto,forcethe firmto investin pro-

ject 2. Finally,a bankcan transferql to a borrowerwiththe ideathatthe borrowerwill

investin project2. Inthis case, the bankandthe firm ointly expendql-q2 on perks.

Wenow considereachstrategy n turn.

Strategy1. Supposethata bank nvestsql in an entrepreneur'project,andtakes an

equitypositionof wl. Thenthe expectedpayoff to theentrepreneurs (1 - wl)qlzl, if

theentrepreneurnvests in project 1.On theotherhand, f the entrepreneurnvestsinproject2, withoutthebank'sknowledge,his expectedpayoff is (1-wl)q2z2 + 6(

- q2).39Thus,there s a moralhazardproblem understrategy1 iff

Z1 < (-) Z2 +ql (1 - W1 )ql

It is easy to show that (a.2) implies the satisfactionof the above inequality.Thus,

whenever here s a moralhazardproblem ora commercialbank ollowing strategy1,

there s also a moralhazardproblem or a universalbankfollowing strategy1. There-fore,a universalbank following strategy1 must engagein interimmonitoring.

Let p denotethe probability hata universalbankfollowing strategy 1 will engage

39. In particular,f theentrepreneur ivertsfunds without he bank's knowledge,we assumethatthe en-trepreneur oes not haveto shareperksconsumptionwiththe bank.In effect, then, there s a managerialn-centiveproblem.








in interimmonitoring.Clearly,p mustbe set high enough to deter an entrepreneur

fromdiverting unds. As in section 2, we assumethat f fundsare diverted,perkscon-

sumptionoccursbeforethe bank has anopportunity o liquidate he borrower'spro-

ject. Thus,anentrepreneurwhodoesdivert undsenjoysutility6(ql-q2) fromperks.Inaddition,withprobability1-p, thediversionof funds will not be discovered,and

theentrepreneurwill have anexpectedsecond-periodncomeof (1 - wl)q2z2. Thus,

Fmust be chosen to satisfy the incentiveconstraint

ql(l-wl)zl ' (1-p)q2(1-wl)z2 + 6(ql-q2) (21)

Since interimmonitoring s costly, clearlyF will be chosen to satisfy(21) at equality.As is clear froman inspectionof (21), if the banktakestoo large anequityposition,

it will notbe possible to determoralhazardunderanycircumstances. n effect, then,there is an upperboundon the equity positionthat can be taken by a bankfollowing

strategy1,and

wl ' 1 - 6(ql - q2)/ql2l (22)

must hold.When(22) is satisfied,equation 21) impliesthata bank ollowing strategy1will engage in interimmonitoringwithprobability

P= {q2Z2- qlzl + [6(ql - q2)/(1 - wl)]}/q2z2-F(wl). (23)

Clearly,F'(wl) > Oholds, for all wl satisfying(22) as a strict nequality.Moreover,

since the bankmust engage in ex post stateverification n (almost) all states,the ex-pected return o the bank not inclusiveof thecost of funds fromfollowing strate-gy 1 is given by wlqlzl - XF(Wl)- y

a. Costof Funds. A bankfollowing strategy 1 requiresql(l + t) units of funds tomake its loan and to pay its deposit insurancepremiums.Then the bank fails iff z <

r(1 + t)/wl holdsex post.40 t follows that hebank's expectedpayments o depositorsand theFDIC (in theevent of a failure)equal

ql |r(l + t) 1 - G(r(1 + t) ) + wl | zg(z)dz = w q o r(1 + t)Wl O I -

Finally,we notethata universalbankwill be willing to follow strategy 1 only if

r( 1 + t)/z < wl * (24)

Equation 24) implies thatthe bankwill not fail with probabilityone.

40. Notice hat, oranygivenvalueofr,theprobabilityhat bankollowingtrategy willfail s high-erunderuniversal anking hanunder ommercialanking. hesame s trueof strategies and3. Ofcourse,tbears mphasishat hisargumentspurely f apartialquilibriumature.








b. Net Expected ayoffsunderStrategy . It follows from our previous observa-

tions that a bank' netexpected profitunderstrategy1 equals

Wlq1Z1 Xp w1 - Y - wIqlol r(1+ t) _ p(wl )W1

The definitionof ¢1 implies that p(wl) ' Oholds iff wl satisfies

q z +q | G(z)dz2q r(l+t) +( 7 )+( X jp(w ) (25)o W1 xvl wl

It will subsequentlyprove useful to knowhow the bank' expected net profitvaries

with the bank' equityposition. Proposition2 states a result on this issue.

PROPOSITION2:Suppose hat

(7 + )/ 2 qlZl[qlZl - 6(ql - q2)]1q2Z26(ql - q2) (a.6)

holds.Thenp'(wl) > Of r all wl satisfying22) and(25).

Proposition 2 is proved in Appendix B. The propositionasserts that if Py s large

enoughrelativeto X, hen a bank' expectedprofitunderstrategy1is increasing n w 1

for all feasible values of wl consistentwithnon-negativeexpected profits.We hence-

forthassumethat(a.6) is satisfied.

Strategy .Understrategy2, a bank nvests q2 in an entrepreneur'project,andthis

entitles the bankto a sharew2 of the borrower' investmentreturn.4lSince any diver-

sion of funds is impossible, there is no moral hazardproblem. Clearly, then, the

lender's expected return from follpwing strategy 2 not inclusive of his cost of

funds is w2q222 Y

a. Costof Funds.Abankfollowing strategy2 must raiseq2( 1 + t)units of funds to

make a loan of q2, andto pay a deposit insurancepremiumof tq2. Thus, a bank en-

gaged in strategy2 canpay rper unitdeposited n the secondperiod iff W2Z > rf1 +t). It follows that the bank will fail with probabilityF[r(1 + t)/w2]. n addition,the

bank' expected second-periodpayments o depositorsand theFDIC are given by

I - (1 )-- r(l+t)/w2 | (1 )-

_ _ 2 __ o _ W2 _

b. NetExpected royits nderStrategy . It follows from theseremarks hata bank

pursuingstrategy2 has a net expected profitof w2q2{22 ¢2[r(1 + t)/w2]} - Py.

Strategy . The thirdstrategyavailableto a universalbank s as follows. The bank

41. Note thatw2 can, andtypically will, be different rom wl.








lendsaborrowerqlwith the intention hat heborrowerwill invest in project2, anddi-

vert ql-q2 units of funds towardexpenditureson perks consumption.The bank

claims a fraction,W3, of both theex post projectreturn,and of perksconsumption.

Underthisstrategy, heexpectedpayoff of theentrepreneurs (1-w3)[q2z2 + 6(ql-q2)]. If instead the entrepreneur ould invest in project 1, his expected income

would be (1 - w3)ql2l. Since our assumptions mply thatqlzl > q2z2+ 6(ql-q2),

theentrepreneurlearly prefers o invest inproject 1.However, f he does so, noperks

consumptionwill be generated,and the bankwill be alerted hatthefirmhasdeviated

fromthe intended nvestment strategy.Thus,by threatening o liquidatethe invest-

ment if no perksconsumptionoccurs, the bank can deter the entrepreneur rom in-

vesting in project 1. Or, in other words, under strategy 3 there is no costly moral

hazardproblem hatarises between the bankand the firm.In effect, in this situation,a

universalbankcanexercise its controlrights over the firm.

It follows thatthe expectednet return o the bank fromfollowing strategy3 in-

clusive of perks consumption,but not inclusive of the cost of funds is given by

W3[q222 + a(ql-q2)]-a. Cost of Funds. A bankpursuing trategy3 needs deposits n theamountql(l + t)

to make a loan of ql andto coverits deposit nsurancepremiums.Thebankwill there-

fore be able to pay its depositors n the second period iff its second-period ncome,

w3q2z,is no less than rql(l + t). In other words, the bank fails with probability

F[(qllq2)r(1 + t)/W3]. And, the bank's expected second-periodpayments to itsdepositorsand to the FDIC equal

ql (r(l+t) l-F (ql ) ( ) +(q2 )W3 | zf(z)dz|

= q2W3¢2 (ql ) ( )q2 W3

b. Net ExpectedProfits under Strategy 3. It follows from our discussion that a

bank' net expectedprofit romfollowing strategy3 is equal to w3[q2z2+ 6(ql-q2)]

Y q2W3¢2[qlrf 1 + t)lq2w3].

B. A Determinationof theEquityPositions

Wenow discuss how the valueof a bank' equityposition is determinedundereach

of the threepossiblebankstrategies.In each case we proceed as in section 2, and as-

sume that societal savings are insufficient to meet all of the potential demand for

funds.42 n section 2 this led to the rationingof credit. As we will show, mattersmay

be differentwhen banks can hold equitypositions in firms.We begin with the deter-

minationof wl.

42. As in section 2, this must be the case if assumption a.S) is satisfied.








Strategy .Assumption(a.6) impliesthatany bank' expectedprofits understrat-

egy 1 are ncreasing n w1 (for all feasiblevalues of w 1consistentwith non-negative

expected profits).Thus, competitionamong entrepreneursor funds implies that w1

must be bid up to the lower of two values:w1 must eitherbe bid up to its largestfeasi-ble level, or it must be bid up to the level at which there s no longer competitionfor

funds. Under strategy 1 funded entrepreneurs eceive the expected payoff (1 -

w1)ql2l; thus competitionfor funds ceases when (1 - wl)qlzl = u.

Define the value w1by

wl=min{(ql IA ), (ql I (ql q2))} (26)

The argument ust given implies thatwhen banks follow strategy 1, wl = wl holds.

If

6(ql-q2)>U (a.7)

is satisfied, hen understrategy 1 therewill be unfundedborrowerswho would like to

get funding.They cannot,because if they offer a bankera largerequity claim, strate-

gy 1 will cease to be feasible. Thus, thepursuitof strategy 1 by banks can be consis-

tent with a phenomenonanalogousto credit rationing.To fix ideas, we henceforthassume that(a.7)holds.

Strategy . It is straightforwardo show thatthe expectedprofitof a bankfollowing

strategy2 W2q222 Py w2q2¢2[r(1 + t)/w2], is monotonically increasingin w2.

Hence, competitionamong entrepreneursor funds implies that w2 must be bid up to

the level where a borrower s just indifferentbetween receiving and not receiving

funding.Since a fundedborrowerunderstrategy2 receives the expected payoff (1-

w2)q222,t follows that

w2 = (q222-u)lq222 (27)

Strategy .The expected profita bankreceives when it follows strategy3, w3[q222

+ 6(ql - q2)] - 7 - W3q2¢2[(ql1q2)r(l + t)/w3], s also increasing n w3.Aus, arepetitionof the argument ust given implies thatW3mustbe bid up until fundedand

unfundedborrowersreceive the same expected utility. Since a funded borrowerhas

the expected utilitylevel (1 - w3)[q222+ 6(ql - q2)], it follows that

W3 = q2Z2 + 6(ql - q2 ) - U (28)

q2Z2 + a(ql - q2 )

C. A ComparisonfAlternativetrategies

We now consider the relative rankingsof the strategiesavailable to a universal

bank.We begin with a comparisonof strategies1 and 3.








1. Strategy versusStrategy . When (a.7) holds, we have wl = [ql2l-6(ql-

q2)]/ql2l, and the expectedprofitof a bankunderstrategy1 is given by43

r(l+t)/wl

wlQlzl- Py X - qlr(l + t)+ Wlql | G(z)dz.o

In additionsw3 = [q222+ 6(ql-q2)-u]l[q2z2 + 6(ql-q2)], andthe expectedprof-it of a bankpursuingstrategy3 equals

(qllq2 )r(l+t)/w3

w3q2Z2 + 6(ql - q2 )] - 7 - ql r(1+ t)+ q2 w3 | F(z)dz.o

We now statea result on therelativerankingsof strategies1 and 3.

PROPOSITION: Strategy is preferredo strategy , underuniversal ankingf

X + [6(q1-q2) U] > q121-q222-6(q1-q2) * (29)

Proposition3 is proved n Appendix C. The propositionasserts that a universalbank

will preferstrategy3 to strategy1 if eitherXor [6(ql-q2)-u] is relatively arge, and

if project 1 is not too productiverelativeto project2 (inclusiveof the perksconsump-tion madepossible by the diversionof funds.)

When(29) holds, the relativerankingof strategies1 and3 underuniversalbanking

is exactly the opposite of their rankingunder commercialbanking. Why is this the

case? Thereare threebasicanswers o this question.

First, when (a.7) holds, there is a strictupper imit on how large wl can be while

strategy 1 is still feasible. This is not trueunderstrategy3. Thus, strategy3 allows a

bankto own a larger ractionof a firm han s possible understrategy1. In effect, even

though the total surplus not inclusive of the cost of funds)is largerunderstrategy

1, the bankgets a larger ractionof this surplusunderstrategy3. When(29) holds, thebankprefersa larger ractionof a smaller pie.

Second,the bank' cost of funds s always lower understrategy3 thanunderstrate-

gy 1 here.44In particular,by following strategy 3 a bankfails more often, ceteris

paribus,andpasses largerexpected costs to the FDIC.

Third,a universalbankhas a greateropportunityo share n the perks generatedby

the diversion of funds than does a commercialbank.By itself, though, this factor

would be insufficientto induce a universalbank to pursuestrategy3. The other two

factorswe have mentionedmust be present or the bankto preferstrategy3.A Remark.When p(wl) = 1 holds, strategy1 is socially preferred o strategy3 iff

ql21 - q222 - 6(ql - q2) > X (30)

43. Note thatp(wl)-1 holds.

44. This factis demonstratedn AppendixC.








(q21ql)z2 > 6,45 and c)r(1 + t) is sufficientlylose to 6. Inpmicular, herewill be arelatively everemoralhazard roblem nder niversal ankingwhen herealrateofinterest n depositss relativelyow, when hedeposit nsurance remiums relative-

ly low, whenperksarea relatively oodsubstituteorother ncome,andwhenbankshaveconsiderableower o extract urplusrom borrowers.

We henceforthssume hat 29) and heconditions f proposition aresatisfied.46Then all active bankswill pursue trategy3, in equilibrium.t will therefore ethe case thatuniversal anking reates severemoralhazard roblem: anksdo notattempto control and, n facttheycondone the diversion f fundsby borrowers.This clearly constitutes marked ontrastwith the situationundercommercialbanking.

D. AGeneralEquilibrium

As in section2, therearetwo requirementsf equilibriumeyondwhatwe havediscussed hus ar.First, he marginal ankmustearna normal xpectedprofit.Second, heFDICmustbreak ven.We now describe hecorrespondingquilibriumconditions.

When all banksfollow strategy3, each active bank earnsthe expectedprofit

W3{q2Z2 + 6(ql-q2)-q2¢2[(ql1q2)r(l + t)lW3]}-7, withW3 = [q2Z2 + 6(ql-q2)-u]l[q222 + 6(ql-q2)]. Agentswhocouldoperate anks, utchoosenot o, pay

the lump-sumax anddeposit1-. In the secondperiod heirutility s r(1-).

Hence,activebanks arn normal rofitsff47

w3 q2z2+ 6(ql - q2 ] - Y = r(l - t) + W3q2(I)2 ( ql ) ( ) * (35)

q2 W3

Equation35) s depicted iagrammaticallyn Figure .In order o describewhat s requiredor theFDIC o break ven,we must irstde-

scribe hemassof activebanks.As before, et0 denote he raction f funded orrow-ers. Underour assumptionsach fundedborrower btainsql unitsof funds.Thus,

uses f funds saOq1 Sources of fundsderive rom hesingleunit avedby agentswho neither orrow, oroperate anks.Hence,sourcesof fundsare 1 - a(1 + (3).

Then ources ndusesof fundsareequatedwhen

(3=(1 -a)/a(1 +q1).

Ourprevious ssumptionsmply hat < 1, and hemassof funded orrowersnd-by implication activebanks s (3a = (1-a)/(1 + ql).

Each undedborrower, s we havenoted, eceivesa loanof ql. It follows hat he

46. When therearehigh- and ow-cost banks,we assume that hese conditionsare satisfied or bothtypesof banks.

47. If there are low- and high-cost banks that are both active in equilibrium, 35) must hold only forhigh-cost banks.








G eqpiw uni g

FIG. 4. General quilibrium:niversalanking

FDICcollects Oaqlt= t(l-a)ql/(l + ql) in deposit insurancepremiums n the first

period,and [1 - a(l + 0)] = (1-a)ql/(l + ql) in lump-sum axes.Since all reve-

nues aredeposited, n periodtwo the FDIChas incomeof r(l-a)(t + )ql/(l + ql),

not inclusiveof the incomegeneratedby liquidating ailedbanks.

Whenall banksfollow strategy3, a fractionF[(qllq2)r(1 + t)/w3] of all bankswill

fail in the secondperiod.Hence, theF9IC incursmonitoringcosts of yFF[(qllq2)r(1

+ t)/w3].In addition,the FDIC's obligationsto the depositorsof failed banks less

the FDIC's income from bank asset liquidation is given by qlr(l +t) -

w3q2¢2[(ql1q2)r(1+ t)/w3].Thus, theFDICbreakseven if

r(l - a)(t + )ql /(1+ ql) = qlr(l + t) - w3q2¢2 (-)q2 W3

*7 F (ql )r(l+t) (36)

q2 W3

Equation 36) is depicted diagrammaticallyn Figure4 underthe assumption hat

F(z)lz is nondecreasingn z. If (35) and (36) have a solutionwhere r(l + t) satisfies

(31), thenthere s an equilibriumwhere all active banksfollow strategy3. And,clear-

ly, multipleequilibriaare a realpossibility

4. A COMPARISONOF COMMERCIALVERSUSUNIVERSALBANKING

In section 2 we exogenously imposed thatall bankswere commercialbanks(as

wouldbe the case if bankswere precluded romtakingequitypositions).We thende-

rivedoptimalbankbehavior,and the requirements f a generalequilibriumunder his

assumption.In section 3, we exogenously imposed thatall bankstake equity posi-

tions. We similarlyderivedoptimalbank behavior and the conditionsof a general

equilibrium under this requirement. n this section we endogenize bank choices

over whetherto acquiredebtor equity claimson borrowers. nparticular,we now








pose the following question: aking r and t as given, when would any individualbank

preferto take an equity position in a firm,rather hanto hold a debt claim? When the

values of r andXthat satisfy (35) and (36) as well as the exogenously given value of

t imply that each active bank would preferan equity position to a debt claim, thenthere is indeed an equilibriumwhere all banks prefer to operate as universal rather

thancommercialbanks.When this transpires,we have seen thatmoralhazard n bank-

ing can potentiallybecome a severe problem, f universalbanking s permitted.48

To fix ideas, in this section we proceed as follows. We assume that all potential

bankersare identical, ex ante. We also assume that strategy2 is the optimal lending

strategyundercommercialbanking,while strategy3 is the optimalstrategyunderuni-

versal banking.49Under these assumptions, he expected profitof a universalbank s

(ql Iq2 )r(l+t)/w3

q2Z2+ 6(ql - q2 - u - Y - ql r(l + t) + q2w3 | F(Z)dz

o

withw3 [q2Z2 + 6(ql-q2) - U]/[q2Z2 + 6(ql-q2)] Theexpectedprofitofacom-mercialbank s

, ^ A

q2{4(X2q2;7) - ¢2 [r(l + t)] } = q2 X2- | F(Z)dz - yF(x2 ) - q2r(l + t)V o )

r(l +t)

+ | F(z)dz.

o

In addition, n orderfor borrowers o take debt contracts, t must be the case that the

expected utility of a fundedborrower s no less thanu. In otherwords,

X2

q2Z2-q2 X2- |F(Z)dz 2u (37)o

must hold.

It follows that from these observations hat a bank would strictly preferan equity

position over a debt claim if

48. Of course, if the values r andXsatisfying (35) and (36) do not have the property in conjunctionwitht) thatbankspreferequity to debt claims, then there s no equilibrium n which all banks operateas univer-sal banks. In this case, if the values r andX satisfying (12) and (17) have the property hat all banks preferdebt to equity claims, then there s an equilibrium n which all banks operateas commercialbanks.Clearlymultipleequilibriaare possible as well. So are equilibriawhere banks are indifferentbetween taking debtand equity positions, and where they take some of each.

49. As we have seen, this will be the optimal configuration f strategies f interimmonitoringcosts arerelativelyhigh, if (q21q1 Z2 > 6, and if rF + t) is relatively ow.







JOHNH. BOYD,CHUN CHANG, AND BRUCED. SMITH : 46 l

- -

X2

q2Z2 - q2 X2 - | F(z)dz - U + 6)(ql - q2 ) - 7[1 - F(x2 (38)o

(qx Iq2 )t(1+t)/W3 r(l+t)

+ q2W3 | F(z)dz-q2 | F(z)dzzr(l+t)(ql -q2)

O O

is satisfied.We now state a conditionunderwhich(38)holds.

PROPOSITION: Suppose hat

(ql-q2){6)-r(l + t)[l-F(r(l + t))]} ' 7[1-F(x2)] . (39)

Then quation38)is satisfied.

Proposition5 is proved n AppendixE. Theproposition ndicatesthat any bankgiven

a choice will operateas a universalbank if (a) 6 is sufficiently arge(perksconsump-

tion is a good substitute or other ncome), (b) the probabilityof failure as a commer-

cial bank (F[r(l + t)]) is sufficiently large, and (c) the cost of ex post state

verification, is sufficiently small.Note in particular hat the maindisadvantageof

universalbankingstems from the large amountof ex post monitoring hat t requires.

When ex post monitorings notvery costly, this does not serve as a strongdeterrent o

bankstakingequitypositions.

Finally, we note that PropositionS gives a relative weak suJficientonditionfor

banksto preferequitypositionsover debt claims.It is by no means necessarythat6 >

rf1 + t){ 1 - F[rf1 + t)]}hold in order orequity positionsto be desired.

5. CONCLUSIONS

Manyclaims havebeen made aboutthe potentialbenefitsand thepotentialcosts ofadoptinga system of universalbanking n the United States.Opponentsof a universal

bankingsystem haveargued hatuniversalbankingcan easily exacerbateproblemsof

moralhazard,and increase perhapsdramatically the potential insuranceobliga-

tions of the FDIC relativeto a systemof commercialbanking.

For at least some configurationsof parameter alues, our analysisis quite support-

ive of these arguments.And, even when universal banking does not increase the

severity of moral hazardproblems n our model, a bankgiven the choice betweena

debt claimand an equitypositionwill choose to hold equitylargelybecausethis either

enables it to extracta largerportionof the profits rom investment,or to pass a larger

portionof its costs onto the FDIC. Universalbanks, in short,have few intrinsiceffi-

ciency advantagesover commercialbanks n the worldwe have described.

One might suspect that this fact is due entirely to our focus on an environment

where costly stateverificationproblems arepresent in financialmarkets.As is well







462 : MONEY, REDIT, NDBANNNG

known (Diamond 1984; Gale and Hellwig 1985; Williamson 1986, 1987), the exis-

tence of costly state verification ends to favor debt as an optimal contractual orm.

However, our results go well beyond this observation.Indeed, they indicate condi-

tions under which debt instrumentsare also wellesuited to addressingproblems ofmoralhazard.This result was not previouslyknown, at least to us. Moreover, t is the

case thatone can easily obtainclose analogsof our results n a purerisk-shiftingmod-

el where costly state verification s entirely absent. Thus, we believe that our results

will obtain n a much broaderclass of economies than ust the one we have described

here.

Another eatureof our analysisthatmeritscomment s as follows. In practice,many

believe that the benefits of universal banking derive from the fact that that arrange-

ment allows banksto hold both debt andequity claims on firms.As we have noted, our

model has the property hata bank takingan equity position in a firmhas no reasontoacquirea debt claim as well. Thus it may appear hat n this way we have stacked he

deck againstuniversalbanking.However, we do not believe this to be the case. Our

main points are that (a) the ability to take equity positions aligns the incentives of

banksand borrowers potentiallyat the expense of the FDIC, (b) thatwhen funds are

scarce, the ability to take equity positions enables banks to extractadditionalsurplus

from borrowers,and (c) banks may be able to extractmaximumsurplusby distorting

resourceallocations.We see no reasonwhy these points shouldbe overturned y find-

ing an environment n which there is a simultaneousrole for both debt and equityclaims.

Finally, a crucial aspect of our model is the assumptionthat banks can share in

perksconsumption ff they hold an equity position in a firm.Whatdo we have in mind

here? While harderto model than perks consumption, in practice large universal

bankshold controlrights n any numberof differentfirms.This enables them to engi-

neer transactions mong these firms hatarebeneficialto the bank althoughnot nec-

essarily beneficial to all parties to the transactionor their other outside claimants.

These powers would be harder o exercise with no equity positions in firms.Thus, for

us, perksconsumption tands n broadly or an ability to benefit at the expense of oth-er claimantsby takinghiddenactions. We think t is highly plausiblethat his ability s

enhancedby holding an equity position in a firm.50

As a last remark,we wish to emphasizethatwhen credit s rationed,a system of uni-

versal banking substantiallyalters the set of conditions that determinea full general

equilibrium n any given economy. This observationargues for a broaderuse of gen-

eral equilibriummethodsto evaluatethe relativemeritsof commercialversus univer-

sal banking.This is a topic we hope to pursue n greaterdetail in the course of future

research.

50. See Akerlof and Romer (1993) for an alternativediscussion of how differentcontractual orms giverise to similar types of problems. They also provide a numberof illustrativeexamples in the context ofbanking.








APPENDIX

A. Proof of Proposition 1

A commercialbank strictlyprefersstrategy2 to strategy3 iff

t(X2 sq2; 7) - ¢2 [r(l + t)] > t[(ql / q2 )X1 sq2; 7] - ¢2 [(ql / q2 )r(l + t)]. (A-1

By definitions (x2,q2;Y) t[(qllq2)xl,q2;Y]must hold. In addition, 2[(ql/q2)r(1+ t)]> ¢2[r(1+ t)] holds as well, since ¢2 > O. This establishesthe claim.z

B. Proof of Proposition2Clearly

P'(W1 ) = qlZl - Xp'(wl ) + ql | G(z)dz _ q r(l + t) G r(l + t) (A 2)o W1 _ _ W1 _

Thereforep'(w1)> Oholds for all w1 satisfying (25) if

(r /w,) + (x / wl [v(wl - wlpt(wl]+ ( ) {1- G ( ) } > O. (A.3)W1 W1

Then obviously a sufficientconditionfor p'(w1)> O o obtain,for all w1obeying (25),

is that

Y/k 2 wlp'(wl ) - p(w1 (A.4)

Now the condition(A.4) has the following equivalentrepresentation:

7 1 2 [(ql Zl - q2Z2 )/q2Z2 ] + [6(ql - q2 ) Iq2Z2 ](2w1 - 1) (1 - w12 . (A.4t)

Therefore, ince the right-hand ide of (A.4') is increasing n w1, p'(wl) > Omusthold

for all w1 satisfying (22) and (25) if

(7 + ) / X 2 (qlzl lq2Z2 ) + (qlzl ) {1 - [26(ql - q2 ) /ql Zl ] } / q2Z26(ql - q2 )- (A.5)

Rearranging erms n (A.S) gives (a.6). z

C. Proof of Proposition 3

The observations n the text imply thata universalbankprefersstrategy3 to strate-

gy 1 iff








(A.6)(ql Iq2 )r(l+t)/w3

Io

q2Z2 + 6(ql - q2 ) - U + q2W3F(Z)dz

r(l+t)/wl

> qlzl - 6(ql - q2 - X + qlwl | G(z)dz.o

Wenow show hat

(ql Iq2 )r(l+t)/w3 r(l+t)/wl

q2W3 | F(Z)dzqlwl | G(z)dzo o

(A.7)

is necessarily satisfied.Then (29) is obviously sufficientfor (A.6) to hold.

To establish (A.7), we begin with the following result.

LEMMA1 q1W1-q2W3 holds

PROOFFLEMMA1 The conditionqlwl > q2w3 s easily shownto be equivalent o

Z2 Z1 - 6)(ql - q2 ) + [6Zl (ql - q2 ) / q2 ] 2 [6 (ql - q2 )2/ q2 ] - Z1U. (A.8)

But (A.8) must hold since zl > 6.

We now show that (A.7) obtains.To do so, note that(A.7) is equivalent o

qlWlj(q2W3) , q2 1) (l+t)/wl t'(l+f)/W,

(A.9)

We now make use of the following result.

LEMMAA2. Define he unctionH(s)by

sr( I +t)/ wl r( I +t)/ wl

H(s) _ 5-1 | F(z)dz- | G(z)dz.o o

ThenH(s) ' O, or all s-1.

TogetherLemmasA1 and A2 imply thatH[(q2w3)/(ql l ]-0, implyingthat(A.7) is

satisfied.Ourproof is thereforecompletedby the following:

PROOFOFLEMMA . Assumption a. 1) implies thatH(1) ' O. n addition,

sr(l+t)/wl

| F(Z)dzo

G(z)dz} 2 0.

H'(s) = 5-1 r(l+t) F sr(l+t) _ -2_ W1 - - W1

>5-1 r(l+t) F sr(l+t) _ -1 r(l+t) F sr(l+t) 0

W1 _ _ W1 _ _ W1 _ W1 _








It is then immediate hatH(s) > OV s > 1. z

D. Proof of Proposition4

A universalbankprefersstrategy3 to strategy2 iff

(ql Iq2 )r(l+t)lw3

[r(l + t) - 6](ql - q2 ) / q2 < (W3 - W2 ) | F(z)dz + W2 (A. 10)

o

(qlw2 Iq2w3 )r(l+t)/w2

| F(z)dzr(l+t)/w2

is satisfied.Moreover,

W3 - W2 = U 6(ql - q2 ) Iq2Z2 [q2Z2 + 6(ql - q2 )] > °-

We now prove part(a) of the proposition.

(a)Using the expressionsstated n the text for w2 andW3, it is straightforwardo ver-

ify thatqlw2 > q2w3holds iff

ql - q2 > u (ql - q2)(q2z2+ bQl)l (q2z2)[q2z2+ 6(ql - q2)] (A.11)

Rearrangingerms n (A. 11 gives (32) in the text.

(b) If (32) holds, then satisfactionof (33) implies thesatisfactionof (A. 10).This es-

tablishespart b) of theproposition.

(c) When (32) holds, a sufficientconditionfor (33) to be satisfied s that

_

F ( ) [(qlw2 q2w3 - 1] 2 (ql - q2 [r(l + t) - 6] /q2r(1+ t). (A. 12)W2

Moreover,

(qlw2 Iq2w3 ) - 1 > (ql Iq2 )W2 - 1 = [(ql - q2 )q2Z2 - qlU]l(q2 ) Z2 -

It follows that (A. 12) must be satisfied f

F ( ) {q2Z2 - [qlU /(ql - q2 )] } > [r(l + t) - 6]q2z2/r(l+ t)* (A. 13)W2

Finally, (a.7) implies thatq2z2-[qlu/(ql-q2)] < q2Z2-ql6. It follows that(34) im-

plies the satisfactionof (A. 12),completing he proof.z








D'(s)=q2 J F(z)dz-ql[ ( )F(ql) ( )

< q (q /q )[r(l + t)]F (ql ) r(l + t)

_q [ r(l + t) ]F ( ql ) r(l + t) = O

ThenD(s)> D(1), forall s ' 1, establishingheclaim.LemmaA3 implies hat

(ql Iq2 )r(l+t)/w3 r(l+t) (41 Iq2 )r(l+t)

q2w3 | F(z)dz q2 | F(z)dz> q2 | F(z)dz (A.16)o o o

r(l+t) (ql Iq2 )r(l+t)

-q2 | F(z)dz=q2 | F(z)dzO r(l+t)

is satisfied.Moreover,

(ql Iq2 )r(l+t)

q2 | F(z)dz2 F[r(l + t)]r(l + t)(ql - q2 (A.17)r(l+t)

But(A.16) and A.17) together ield (A.15), and herefore39) implies he satisfac-tionof (38).

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moral hazard under commercial and universal bank

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