【行业研报】CBDC与金融稳定（英）_市场营销策划_重点报告20230802_doc.docx

AbstractWhatistheeffectofCentra1BankDigita1Currency(CBDC)onfinancia1stabi1ity?Weanswerthisquestionbystudyingamode1offinancia1intermediationwithanendogenous1ydeterminedprobabi1ityofabankrun,usingg1oba1games.Asana1ternativetobankdeposits,consumerscana1sostoretheirwea1thinremuneratedCBDCissuedbythecentra1bank.Consistentwithwidespreadconcernsamongpo1icymakers,higherCBDCremunerationincreasesthewithdrawa1incentivesofconsumers,andthusbankfragi1ity.However,thebankoptima11yrespondstotheadditiona1competitionbyofferingbetterdepositratestoretainfunding,whichreducesfragi1ity.Thus,theovera11re1ationshipbetweenCBDCremunerationandbankfragi1ityisU-shaped.Keywords:Centra1BankDigita1Currency,BankFragi1ity,DemandDeposits,G1oba1Games.JE1Codes:D82zG01,G21.1IntroductionCentra1banksaroundtheg1obe(BoarandWehr1i,2023)areresearchingthecostsandbenefitsofcentra1bankdigita1currency(CBDC).Theseeffortsarearesponsetothedec1iningimportanceofcashasmeansofpaymentandthecha11engesassociatedwiththepro1iferationofnewformsofprivatedigita1money(e.g.,stab1ecoins).Whi1eCBDCaimstopreservethero1eofpub1icmoneyandfendoffthreatstomonetarysovereignty,somepo1icymakersareconcernedaboutitspotentia11yadverseeffectsonthefinancia1system(Ahnerteta1.z2023).Oneissuethathasreceivedparticu1arattentionistheeffectofCBDConfinancia1stabi1ity(BankforInternationa1Sett1ements,2023).Itsstatusassafeassetwithpotentia11ypositiveremuneration-akeydifferencetophysica1cashcou1drenderitanattractivestoreofva1ueandthusincreasetheriskofbankrunsduringcrisisepisodes.Thispaperaimstoinformthisdebatebydeve1opingatwo-periodbank-runmode1withremuneratedCBDC.Initia11y,aprofit-maximizingbankwithaccesstoprofitab1ebutrisky1ong-terminvestmentopportunitiesraisesuninsureddeposits.Attheinterimdate,consumersreceiveanoisyprivatesigna1abouttheinvestment'sprofitabi1ity(''economicfundamenta1s,)anddecidewhethertowithdrawtheirba1ancesorro11themover.Whenfundsarenotkeptinthebank,consumerscanho1dthemincashoras(possib1yremunerated)CBDeJWeso1vefortheuniqueequi1ibriumatthewithdrawa1stageusingg1oba1-gamesmethods.Whenmakingtheirwithdrawa1decision,consumerstradeofftheva1ueofkeepingtheirfundsinthebankandtheoutsideoptionofconvertingthemintoCBDC(convertingprivateintopub1icmoney).According1y,ourmode1a11owsustostudyhowthetermsofthedepositcontractandCBDCremunerationaffecttheprobabi1ityofabankrun(ourmeasureoffinancia1fragi1ity).AsinMorrisandShin(1998)zGo1dsteinandPauzner(2005),andCar1ettieta1.(2023)ztheequi1ibriumischaracterizedbyathresho1dstrategy:whentheeconomicfundamenta1sarebe1owacertainva1ue,a11depositorsrunonthebank(Proposition1).,Ithismode1,theon1ydifferencebetweencashandCBDCistheirremuneration.According1y,apositive1yremuneratedCBDCisa1wayspreferredtocash.Inthiseconomy,anincreaseintheCBDCremunerationhastwoeffects.First,itmakeswithdrawa1sattheinterimdatemoreattractivebyincreasingthepayofffromstoringfundswiththecentra1bankforconsumptionatthefina1date.Thiszzdirecteffect"makesthebankmorefragi1e(Proposition1),consistentwiththe1ineofargumentunder1yingtheongoingpo1icydebate.Second,ahigherCBDCremunerationinducesthebanktooffermoreattractivedepositcontractsbecauseconsumerswou1dotherwisenotprovideanyfundingattheinitia1date.Asaconsequence,consumershave1owerincentivestowithdrawtheirfundsattheinterimdate.Thiszzindirecteffect,zrendersthebankmorestab1e(Proposition2).Inequi1ibrium,thetota1effectofCBDCremunerationonbankfragi1itydependsonthere1ativestrengthsofthesetwocountervai1ingforces.Theindirecteffectdominatesifandon1yifthee1asticityofthefai1urethresho1dwithrespecttothebankdepositrateexceedsone(1emma1).Asufficientconditionforthisisahighenoughprofitabi1ityofthebank'sinvestmentopportunityre1ativetotheremunerationonCBDC(Proposition3).Inthiscase,fragi1ityisminimizedforastrict1ypositive1eve1ofCBDCremuneration.Weconsidervariousextensionsofourmode1.First,po1icymakershaveadvanced1imitsonindividua1ho1dingsasapossib1etoo1toreducethefinancia1stabi1ityconcernsassociatedwithCBDC(Bindsei1eta1.,2023).Otherproposa1sinc1udetieredremuneration,assuggestedinBindsei1(2023).Ifthesecondtierisremuneratedatzeroorbe1ow,thisisequiva1enttoho1ding1imitsinourmode1becauseconsumerswou1dprefertoinvestincashanyamountnotcoveredbythefirsttier.Inourmode1,ho1ding1imitsreducetheeffectiveremunerationofdepositwithdrawa1sbecauseon1ypartoftheproceedscanbestoredinCBDC,withtheremainderbeinghe1dascash.According1y,ho1ding1imitscanhe1ptoattaintheoptima11eve1offinancia1fragi1ityifremunerationcannotbesetfree1y(e.g.becauseitisaimedatmonetarypo1icyobjectivesoutsideofourmode1).However,andin1inewithourpreviousresu1ts,ho1ding1imitshaveanambiguousimpactonbankfragi1ityiftheindirecteffectisSU仔icient1ystrong.Inthiscase,ho1ding1imitsincrease(decrease)fragi1ityfor1ow(high)1eve1sofCBDCremuneration(Proposition4).Second,westudyasettingwhereear1y1iquidationofthe1ong-terminvestmentdoesnot1eadto1osses.Inthiscase(Proposition5),bankrunsareneverdrivenbypanics,theycanon1ystemfromfundamenta1inso1vencies.Whi1etheindirecteffect(higherCBDCremunerationinducesbankstoof