国际清算银行-方便案例：CBDC设计选择如何影响货币政策传递（英）-2022年

BANKFORINTERNATIONALSETTLEMENTS

BISWorkingPapers

No1046

Thecaseforconvenience:

howCBDCdesignchoices

impactmonetarypolicy

pass-through

byRodneyGarratt,JiahengYuandHaoxiangZhu

MonetaryandEconomicDepartment

November2022

JELclassification:E42,G21,G28,Lil,L15.

Keywords:centralbankdigitalcurrency,interest

onreserves,paymentconvenience,depositrates,

banklending

BISWorkingPapersarewrittenbymembersoftheMonetaryandEconomic

DepartmentoftheBankforInternationalSettlements,andfromtimetotimeby

othereconomists,andarepublishedbytheBank.Thepapersareonsubjectsof

topicalinterestandaretechnicalincharacter.Theviewsexpressedinthemare

thoseoftheirauthorsandnotnecessarilytheviewsoftheBIS.

ThispublicationisavailableontheBISwebsite().

©BankforInternationalSettlements2022.Allrightsreserved.Briefexcerptsmaybe

reproducedortranslatedprovidedthesourceisstated.

ISSN1020-0959(print)

ISSN1682-7678(online)

TheCaseforConvenience:HowCBDCDesign

ChoicesImpactMonetaryPolicyPass-Through

RodneyGarrattyJiahengYuzHaoxiangZhux

Abstract

Banksof'clierentsizesresponddierentlytointerestonreserves(1OR)policy.For(ow1ORrates,largebanksarenon-

responsiveto1ORratechanges,leadingtoweakpass-throughqflORratechangestodepositrates.Inthesecircumstances,

acentralbankdigitalcurrency(CBDC)maybeusedtoprovidecompetitivepressuretodriveupdepositratesand

improvemonetaiypolicytransmission.Weexploretheimplicationsoftwodesignjeatures:interestrateandconvenience

value.IncreasingtheCBDCinterestratepastapointwhereitbecomesabinding

oor,increasesdepositratesbutleadstogreaterinequalityofmarketsharesinboth,depositand(endingmarketsandcan

reducetheresponsivenessofdepositratestochangesinthe1ORrate.Incontrast,increasingconvenience,Jromsuciently

highlevels,increasesdepositrates,causesmarketsharestoconvergeandcanincreasetheresponsivenessofdepositrates

tochangesinthe1ORrate.

Keywords:centralbankdigitalcurrency,interestonreserves,paymentconvenience,

depositrates,banklending

JELClassication:E42,G21,G28,L11,L15

Theviewsexpressedarethoseoftheauthorsanddonotnecessarilyre

ectthoseoftheBIS.WethankToddKeisterJbrmultiplediscussionsintheearlystagesofthisworkWealsothankYuAn,DavidAndol^fatto,Ben

Bernanke,DarrellDue,ZhiguoHe,MichaelKumhofJiaqiLi,DebbieLucas,MonikaPiazzesi,AlessandroRebucci,DanielSanches,AntoinetteSchoar,

HaraldUhlig,YuZhu,andFengZhu,aswellasseminarparticipantsattheBankofCanada,LuohanAcademy,MITSloan,NovaSBE,Microstructure

On-lineSeminarsAsiaPactc,theUniversityqfHongKong,theCanadianEconomicsAssociation,theJHUCareyFinanceCoriference,thePhiladelphia

WorkshopontheEconomicsofDigitalCurrencies,theCB&DCOnlineSeminar,BostonUniversity,theFederalReserveBankofNewYork,Shanghai

AdvancedInstituteofFinance,MITComputerScienceandAriiciatIntelligenceLab,the2021ECBMoneyMarketConference,AFA2022andtheFuture(s)

ofMoneyConference,Paris2022.

yBankjorInternationalSettlements.Email:rodney.garratt@

ofMaiwgcitxnt.Email：河

XMITSloanSchoolofX4ajugementaiufNBER.Email:zhuh@miteUu.HaoxiangZhu'sworkonthispaperwascompletedpriortoDecember10,2021,u4ienhejoinedtheLIS.SecuritiesandExchangeCommission.

1

\lfallaCBDCdidwastosubstituteforcash{ifitborenointerestandcame

withoutanyoftheextraserviceswegetwithbankaccounts{peoplewould

probablystillwanttokeepmostoftheirmoneyincommercialbanks."|Ben

Broadbent,DeputyGovernoroftheBankofEngland,ina2016speech

1Introduction

Acentralbankdigitalcurrency(CBDC)\isadigitalpaymentinstrument,denominatedin

thenationalunitofaccount,thatisadirectliabilityofthecentralbank"(BIS,2020).Over

thelastfewyears,interestinCBDChasgrowntothepointwhereatpresent90percent

ofcentralbanksareinvestigatingoptionsforintroducingCBDCs(BIS,2021).As

indicatedinBroadbent'sremarks(intheepigraph),policymakersinitiallycontemplateda

CBDCthatduplicatedfeaturesofcash,withoutaddingdesigncharacteristicsthatwould

makeitmorelikelytocompetewithmoneyissuedbycommercialbanks{thesocalled

disintermediationproblem.However,morerecentlycentralbankshavetakenabroader

view,andhavebeenmoreopentothepossibilitythatCBDCscanhelpthemtofulII

theirmandates,eitherinthepresentorthefuture.Centralbanksareincreasingly

viewingCBDCsasawaytoimprovethepaymentsystem,promotenancialinclusion,

enhancemonetarypolicytransmission,andreducesystemicrisk(BIS,2020).

ThelikelihoodthataCBDCwillachieveanyofthedesiredcentralbankobjectivesdepends

uponitsdesignfeaturesandhowtheyinteract.CBDCscanoerbothpecuniarybenets,inthe

formofinterestpayments,andnonpecuniarybenets.Thesecanincludeahostoffeaturesthat

enhancetheperformanceofCBDCasamediumofexchange.Examplesincludethequalityof

theuserinterface,processingspeed,privacyandaccesstomarkets.

ApubliclyprovidedCBDCcouldbelessexpensivetouseandmorewidelyaccessiblethanexisting,

privatelyoeredpaymentmethods,anditcouldoeraccesstonewplatformsandservices.See,forexample,

theBankofEnglanddiscussionpaperonCBDC(BankofEngland,2020)whichdescribesthepotentialfor

third-partypaymentinterfaceproviderstoprovideoverlayservicesontopofCBDCbalances.ACBDCcould

alsoprovideprivacy.Policymakershavearguedthatthecentralbankisspeciallypositionedtoprovideprivacy

inpaymentsbecausethecentralbankdoesnothaveaprotmotivetoexploitconsumer

2

Welumpthesepossibilitiestogetherundertheheading\paymentconvenience."

Inthispaper,weexploretheimplicationsofintroducingaCBDCthatisinterest-bearingand

oerspaymentconvenience.Allelseequal,consumerswillprefertoholdacurrencythatpays

higherinterest.However,ifacurrencyiseasiertouse,oracceptedatmoreplaces,thenthese

non-pecuniarybenetsmayosetinterestpayments.Hencebothinterestrateandpayment

convenienceareimportantchoiceparametersforaCBDC,asbothwilldetermineconsumer

demandforCBDCandhenceitsultimateimpactonmonetarypolicyobjectives.

WeseektoevaluatedesignchoicesforCBDCinamodelthatisdescriptiveofthecurrent

USnancialsystem,whichischaracterizedbylargeexcessreservesandinwhichthemain

monetarypolicyvariableisinterestonreserves(IOR).2Crucially,wealsowantouranalysisto

captureheterogeneityinbanksize.Banksizemattersfortwokeyreasons.First,banksize

impactsthecostbasisofloans,asitdeterminesthelikelihoodofretainedreserves.Loan

issuanceinvolvesthecreationofdeposits.Whenthesedepositsarespentbytheborrower

thereisachancethattherecipientwillbelongtothesamebank,inwhichcasethereisno

associatedtransferofreservestoanotherbank.Thislikelihoodisnotnegligibleforthelargest

banksintheUSeconomyandhencetheimpactofretainedreservesshouldnotbeignored.3

Second,largebankdepositsmayoerahigherconveniencevaluethansmallbankdeposits.

Forexample,alargebankcouldhaveamoreexpansivenetworkofbranchesand

paymentdata(luigardc,2018).

2

IntheUnitedStates,IORhasbeenpaidsinceOctober2008.Sincethenanciatcrisisof2008-09,interestonexcessreserves(IOER)liasbecometheFederalReserve'smain

policytooltoadjustinterestrates.InJuly2021,theFederalReserverenamedIOERtointerestonreservebalances(IORB),asrequiredreserves

arecurrentlyzero.Forsimplicify,weusetheacronymIOR.

3'J

During2010-2020,basedonCallReportsdata,thetopjourlargestbankscaptures35%ofUSdepositmarketTheirdepositmarketsharesare

largeandstableover(helastdecade,withtheaverageslistedinthejbllowing：BankofAmerica(11%),Chase(10%),WellsFargo(10%),andCiti(4%).

Giventhestationarityofdepositshares,andthefactthatdepositsarecreatedthroughcommercialbanksmakingloans(BankofEnglandQuarterly

Bulletin,2014),thejradionofalentdollarthatultimately

owstoeachbankshouldapproximatethedepositshares,regardlessofthenumberoftransactionsortransfers.Hencethehighdepositmarketsharesof

thelargestbankshavenon-negtigibteimpactontheiropportunitycostsofmakingloans.Inlocaldepositmarkets,concentrationisalsosalient.Drechsler,

Savov,andSchnabl(2017)measurethisconcentrationbyHerndahlindex(HH1),calculatedbysummingupthesquareddeposit-marketsharesofall

banksthatoperateinagivencounty.Theircalculationindicatesthataround50%ofUScountieshaveanHH1thatishigherthan0.3(atleastonebanks

depositshareisgreaterthan30%),and25%ofUScountieshaveanHH1thatishigherthan0.5(atleastonebanksdepositshareisgreaterthan50%).

3

ATMs,abettermobileApp,orawiderrangeofother(unmodeled)services.Thehigher

conveniencevalueofitsdepositmayallowthelargebanktooeralowerdepositrate

thanthesmallbankandyetstillmaintainalargermarketshare.

Inourmodel,theCBDCisoeredthroughcommercialbanks.WhileCBDCbalancesare

thedirectliabilityofthecentralbank,weenvisionthatcommercialbankswillactasthe

centralbank'sagentstoconductKYC(KnowYourCustomer)andAML(Anti-Money

Laundering).This\tieredudesignofCBDCisconsistentwiththerecentpilotofE-Kronain

Sweden,theCBDCexperimentinChina,andtheBankingforAllActintheUnitedStates.4

Theheterogeneous-bankmodelwedevelopisnew.Therstpartofouranalysisseeksto

validatethemodelbydemonstratingthatitexplainsaspectsofUSdepositmarketsthatare

notexplainedbyexisting,homogeneous-bankmodelsoftheUSeconomywithlarge

reserves.Inparticular,weareabletoexplaintheobservedlackofinterest-ratepass-

throughinUSdepositmarkets.Interestratepass-throughintheUSeconomyisfarfrom

complete.Drechsler,Savov,andSchnabl(2017)ndthat\[f]orevery100bpsincreaseinthe

Fedfundsrate,thespreadbetweentheFedfundsrateandthedepositrateincreasesby54

bps."DueandKrishnamurthy(2016)documentasizabledispersionofabroadrangeof

moneymarketinterestrates,whichwidenedastheFedraiseditsinterestonreserves.Our

analysisshowsthatthelowcorrelationbetweenmovementsinpolicyratesthatdetermine

thefedfundsrateandmovementsindepositratescanbepartlyattributedtothedierential

impactthesechangeshaveonbanksofdierentsizes.

Theintuitionbehindthisresultisasfollows.Thelargebank'sabilitytooeralowerrate

thanthesmallbankmayplacethemata\cornersolution,'introducedbythefactthat

depositratescannotgobelowzero.Thelargebankwillsetadepositrateofzero,thatis

non-responsivetochangesinthepolicyrate,untilthatraterisestoalevelwherethezero

4TheActarguesthatDigitalDollarWalletsshouldprovideanumberofauxiliaryservicesincluding

debitcards,onlineaccountaccess,automaticbill-payandmobilebanking.Thesefeatures(inparticular

mobilebankingwhichcouldgiveaccesstoavarietyofplatformsthatcustomersofaparticularbankmight

otherwisenothaveaccessto)couldresultinaCBDCwithitsownconveniencevalue.Similarprovisions

areoutlinedintheECB'sdigitaleuroreport(2020).

4

lowerboundondepositratesisnolongerbinding.Wewillshowthatthezerolower

boundondepositratesbindsonlywhenIORrateislow.HenceforlowlevelsofIORwe

expectdepositratessetbyalargeshareofthebankingsectortobenon-responsiveto

changesinIOR.ForhighlevelsofIOR,thelowerboundisnotbindingandweexpectall

bankstoadjustdepositratesinresponsetochangesinIOR(orthefederalfundsrateif

thisbecomestherelevantopportunitycostoflending).Wedemonstratethatbothof

thesemodelpredictionsseemtobetrueempirically.

Inlightoftheseobservationsregardingweakpass-throughforlowIORrates,we

examinehowoutcomesinboththedepositmarket(depositsharesatthedierentbanks

anddepositrates)andthelendingmarket(loanvolumesandrates)maybeimpactedby

thechoiceofdesigncharacteristicsofaCBDC.First,wevarytheCBDCinterestrate.

IncreasingtheCBDCinterestratewhileholdingtheIORrateandtheCBDC

conveniencevaluexedraisesthedepositratesofbothbanks,thusbringingtheir

weightedaverageclosertotheIORrate.SettingtheCBDCinterestrateequaltothe

interestrateonreserveswouldresultinfullmonetarypolicypass-through.However,by

forcingbothbankstoraiseinterestrates,ahigherCBDCinterestratemakesitmoredi

cultforthesmallbanktocompetewiththelargebankbyoeringhigherdepositrate.

Thus,ahigherCBDCinterestratereducesthemarketshareofthesmallbankin

depositandlendingmarkets,furtherwideningthelargebank-smallbankgap.

Second,wevarytheCBDCconveniencevalue,holdingtheIORrateandCBDCinterest

ratexed.MakingtheCBDCmoreconvenientweakensthemarketpowerofthelargebank

bynarrowingtheconveniencegapbetweenthetwobanks.Forexample,byhostinga

convenientCBDC,asmallcommunitybankpartially\catchesup"withlargeglobalbanksin

oeringpaymentfunctionalities.ThemostimmediateimplicationisthataconvenientCBDC

resultsinalowerdepositrateatthesmallbank,becausethesmallbankdoesnothaveto

compensatedepositorsasmuchforforgoingthelargebank'sconvenience.Thedeposit

rateatthelargebankinitiallyremainsunchanged,andhencetheaveragedepositratefor

5

themarketfallsasconvenienceisincreasedfromzero.However,asconveniencerises,

apointiseventuallyreachedwherethelargebankisnolongerconstrainedbythezero

lowerboundandstartstoraiseitsdepositratetocompetewiththesmallbank.The

resultisanincreaseintheaveragedepositrate.Theimplicationisthatforanygiven

levelofIOR,pass-throughofIORtodepositratesisreducedforlowlevelsof

convenienceandincreasedforhighlevelsofconvenience.

Finally,weaddresstheissueofhowagivenCBDCdesignimpactsthesensitivityof

depositratestochangesintheIORrate.Intheequilibriumwherethelowerboundon

depositratesisnotbinding,pass-throughiscompleteregardlessofthelevelsoftheCBDC

interestrateorconveniencevalue.Inequilibriawherethelowerboundisbinding,we

establishtworesultsthatholdundersomedistributionalassumptions.First,withinthe

constrainedequilibrium,wherethelargebank'sdepositrateisnon-responsivetochanges

intheIORrate,theresponseofthesmallbank'sdepositratetoincreasesintheIORrate

decreasesastheCBDCinterestrateincreasesandincreasesasconvenienceincreases.

Second,higherlevelsoftheCBDCinterestrateincreasetherangeofIORratesforwhich

thelargebank5sdepositrateisnon-responsiveandhigherlevelsofconveniencedecrease

therange.Thus,apositiveinterestonCBDCnecessarilyweakensmonetarypolicy

transmissionfromIORtodepositrateswhentheIORrateislow,whileincreasing

conveniencenecessarilyincreasesmonetarypolicytransmission.

Thepaperisorganizedasfollows.Section2providesaliteraturereview.Section3intro­

ducesthemodelandcharacterizestheconstrainedandunconstrainedequilibrium.Thereisa

criticallevelofIORrateatwhichtheeconomytransitionsfromthetheconstrainedtoun­

constrainedequilibrium.Hence,thisanalysisprovidesanexplanationforweakpass-throughof

IORratetodepositratesatlowlevelsofIORandstrongpass-throughathighlevels.Section4

separatelyevaluatesthedirectimpactondepositratesofincreasingtheCBDCinterestrates

andconveniencelevelvondepositrates.Section5examinesthesensitivityofdepositratesto

changesintheIORrateunderdierentCBDCdesigns.Section6concludes.

6

2Literature

Ourworkbuildsonpreviousliteraturethathasmodelleddepositandlendingmarketsinthe

currentregimeoflargeexcessreserves.InMartin,McAndrews,andSkeie(2016),aloanis

madeifitsreturnexceedsthemarginalopportunitycostofreserves,whichcanbeeitherthe

federalfundsrateortheIORrate,dependingontheregime.Ourmodeldiersinthatwe

havemultiplebanksandhencelentmoneymayreturntothesamebankasnewdeposits.

Hence,ouropportunitycostoflendingislower.Nevertheless,wesharetheconclusionthat

theaggregatelevelofbankreservesdoesnotdeterminethelevelofbanklending.

ThereisnowagrowingliteraturethatseekstoexaminetheimpactofCBDCon

depositandlendingmarkets.Theconclusionsvaryanddependuponthelevelof

competition,theinterestrateontheCBDC,andotherfeatures(e.g.,liquidityproperties

ofCBDCandreserverequirements).KeisterandSanches(2021)considera

competitivebankingenvironmentinwhichdepositratesaredeterminedjointlybythe

transactionsdemandfordepositsandthesupplyofinvestmentprojects.IftheCBDC

servesasasubstituteforbankdeposits,thenitsintroductioncausesdepositratesto

rise,andthelevelsofdepositsandbanklendingtofall.

Incontrast,ifbankshavemarketpowerinthedepositmarket,theintroductionofa

CBDCdoesnotdisintermediatebanks,asbankscanpreventconsumersfromholdingthe

CBDCbymatchingitsinterestrate.Thislowerstheirprotmargin,butdoesnotlowerthe

levelofdeposits,andmayevenincreaseit.ThisistrueinthemodelproposedbyAndolfatto

(2021),wherethebankisamonopolist.Inthatpaper,aninterestbearingCBDCcauses

depositratestoriseandthelevelofdepositstoincrease.Likewise,inthatpaper,banks

havemonopolypowerinthelendingmarket,and,asinMartin,McAndrews,andSkeie

(2016),lendingisnottieddirectlytothelevelofdeposits,Hence,aCBDCdoesnotimpact

theinterestrateonbanklendingorthelevelofinvestment.

Chiu,Davoodalhosseini,Jiang,andZhu(2019)alsoconsiderbankswithmarketpower

andshowthataninterest-bearingCBDCcanleadtomore,fewerornochangeindeposits,

7

dependingontheleveloftheCBDCinterestrate.Inanintermediaterangeofrates,the

CBDCimpactsthedepositmarketinamannersimilartoAndolfatto(2021)inthatbankso

erhigherdepositratesandincreasedeposits.Since,similartoKeisterandSanches(2021),

lendingistiedtothelevelofdeposits,addingtheCBDCresultsinincreasedlending.

OurworkisclosesttoAndolfatto(2021).Wedonotspecifytheoverlappinggenerations

frameworkthatheusestomakemoneyessential.However,likeAndolfatto(2021),inourmodel,

reservesareabundant,lendingisdeterminedbyaperformancethreshold,andbankshave

monopolypowerinlendingmarket.Hence,lendingisdeterminednotbydepositlevels,but

insteadbytheopportunitycostoffunds.Inourmodel,thisopportunitycostislowerthanthe

IORrate,sinceweallowfortherealisticfeaturethatreservescomebacktothelendingbank

withaprobabilitythatdependsonthedepositmarketshare.UnlikeAndolfatto(2021),andthe

otherworksmentionedabove,weincorporatetwokeydesignaspectsofCBDC,interestrate

andconveniencevalue,andweexaminethecombinedimpactthesefeatureshaveonmarket

outcomesinanenvironmentwithheterogeneousbanks.

TheimpactofaddingaCBDCcanbericherinthepresenceofotherfrictions.Ina

modelwithrealgoodsandcompetitivebanks,PiazzesiandSchneider(2020)ndthat

theintroductionofCBDCisbenecialifallpaymentsaremadethroughdepositsandthe

centralbankhasalowercostinoeringdeposits.However,theyalsondthattheCBDC

canbeharmfulifthepayerpreferstouseacommercialbankcreditline,butthereceiver

preferscentralbankmoney.Parlour,Rajan,andWalden(2022)arguethatawholesale

CBDCthatenhancestheeciencyofinterbanksettlementsystemcouldexacerbatethe

asymmetrybetweenbanksiftheCBDCdoesnotdistinguishnet-payingandnet-

receivingbanks.Agur,Ari,andDeirAriccia(2022)consideranenvironmentwhere

householdssuerdisutilityfromusingapaymentinstrumentthatisnotcommonlyused.

Theyexaminetrade-osfacedbythecentralbankinpreservingvarietyinpayment

instrumentsandshowthattheadverseeectsofCBDConnancialintermediationare

hardertoovercomewithanon-interest-bearingCBDC.

8

Fernandez-Villaverde,Sanches,Schilling,andUhlig(2021)extendtheanalysisof

CBDCtoaDiamondandDybvig(1983)environmentinwhichbanksarepronetobank

runs.Inthissetting,thefactthatthecentralbankmayoermorerigiddepositcontracts

allowsittopreventruns.Sincecommercialbankscannotcommittothesamecontract,

thecentralbankbecomesadepositmonopolist.Providedthatthecentralbankdoesnot

exploitthismonopolypower,therst-bestamountofmaturitytransformationinthe

economyisstillachieved.

BrunnermeierandNiepelt(2019)andFernandez-Villaverde,Sanches,Schilling,and

Uhlig(2021)deriveconditionsunderwhichtheadditionofaCBDCdoesnotaect

equilibriumoutcomes.Keytotheirresultisthecentralbank'sactiveroleinproviding

fundingtocommercialbanksinordertoneutralizetheCBDC'simpactontheirdeposits.

3ModelandEquilibrium

3.1Setup

Theeconomyhasalargebank(L)andasmallbank(S).*5ThereareX=Xs+XLreservesinthe

bankingsystem,whereXsdenotesthereserveholdingofthesmallbankandXLdenotesthe

reserveholdingofthelargebank.6Forsimplicity,thebanksstartoholdingreservesastheir

onlyasset,balancedbyexactlythesameamountofdeposits.FollowingMartin,McAndrews,

andSkeie(2016),weassumethatthelevelofreservesXisexogenouslydeterminedbythe

centralbankandisassumedtobelarge.Thecentralbankpaysthetwocommercialbanksan

exogenouslydeterminedinterestratefontheirreserveholdings,which

5Theassumptionoftwobanksis,ofcourse,asimplication.However,thesituationmayaccurately

describetheretaildepositors'decisionmakingprocess.Usingsurveydata,Honka,Hortacsu,andVitorino

(2017)ndthatUSconsumerswere,onaverage,awareofonly6.8banksandconsidered2.5bankswhen

shoppingforanewbankaccount.Morethan80%consideredfewerthan3bankswhenshoppingfora

newbankaccount.

6Wenormalizethesizeofanindividualloantobe$1,soreservesareinunitsofthestandardloansize.

Forexample,ifaloansizeis$1millionandtheactualreserveis$1trillion,theninourmodel,Xis

interpretedas$1trillion=$1million=106.

9

iscalledinterestonreserves(1OR).ThelargeandsmallbankspaydepositorsendogenouslydetermineddepositratesrLand

fS,respectively.Thus,ifnothingelsehappens,bankjJstotalprotwouldbeXj(flj).

Commercialbankdepositsarevaluablenotjustjbrtheinteresttheypay,butalsoforthepaymentservicestheyprovide,the

beiietofwhichwerefertoasconveniencevalue.Theconveniencevalueofdepositsinthesmallbankisnormalizedtobezero.

Theconveniencevalueofdepositsinthelargebankisarandomvariableothathasthetwicedierentiable,cumulative

ctistributionJiAncfionG.WemakefheJb[lowingassumptiononGthatweimpose

throughoutthepaper:

Assumption1.ThefunctionGsatisesG°()=f<G°°()<G°()=fforany[o；f

2

s+v]:

Thisconditionensuresthesecondorderconditionofabank'soptimizationproblemissatised.Theconditionisalsoused

inthecomparativestaticsanalysis.BoundingthecurvatureofGbounctsthemassesofagentswhovaluelargebank'sdeposits

highlyandlowly,andensures(hatbothbankswillcompetetowinadditionaldepositorsbyraisingtheirdepositrateswhenf

andotherparameters,whichweintroduceinthefollowingparagraphs,change.Eachdepositorintheeconomydrawstheir

large-bankconveniencevalueindependentlyfromthedistri