Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. ... - PDF document

Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. 
...
Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. 
...

Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. ... - Description


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Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. Tinbergen Institute is the graduate school and research institute in economics of Erasmus University Rotterdam, the University of Amsterdam and VU University Amsterdam. More TI discussion papers can be downloaded at http://www.tinbergen.nl Tinbergen Institute has two locations: Tinbergen Institute Amsterdam Gustav Mahlerplein 117 1082 MS Amsterdam The Netherlands Tel.: +31(0)20 525 1600 Tinbergen Institute Rotterdam Burg. Oudlaan 50 3062 PA Rotterdam The Netherlands Tel.: +31(0)10 408 8900 Fax: +31(0)10 408 9031 Duisenberg school of finance is a collaboration of the Dutch financial sector and universities, with the ambition to support innovative research and offer top quality academic education in core areas of finance. DSF research papers can be downloaded at: http://www.dsf.nl/ Duisenberg school of finance Gustav Mahlerplein 117 1082 MS Amsterdam The Netherlands Tel.: +31(0)20 525 8579 Cheapbut ighty:howglobalimbalancescreate nancialfragilityToniAhnertyandEnricoPerottizMarch2015AbstractCanawealthshifttoemergingcountriesexplaininstabilityindevelopedcountries?Investorsexposedtopoliticalriskseeksafetyincountrieswithbetterpropertyrightprotection.Thisinducesprivateintermediariestoo ersafetyviainexpensivedemand-abledebt,andincreaseslendingintomarginalprojects.Becausesafetyconsciousfor-eignersescapeanyriskbyrunningalsoinsomegoodstates,cheapforeignfundingleadstolargerandmorefrequentruns.Beyondsomescale,foreignrunsalsoinducedomesticrunsinordertoavoiddilution.Whenexcessliquidationcausessociallosses,adomesticplannermaylimitthescaleofforeignin owsorcreditvolume.Keywords:capital ows,unstablefunding,safehaven,absolutesafety.JELclassi cations:F3,G2. WethankFernandoBroner,NicolaGennaioli,OlivierJeanne,AlbertoMartin,JavierSuarez,researchersattheNewYorkFedandseminarparticipantsatBankofCanada,CEMFI,theCEPR-IESEConferenceonFinancialStabilityandRegulation,theCEPR-CREIWorkshoponMacroeconomicsofGlobalInterdepen-dence,IMF,andNYUforusefulcomments.Theviewsexpressedaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasre ectingtheviewsoftheBankofCanada.yFinancialStudiesDivision,BankofCanada,234LaurierAveW,Ottawa,Ontario,K1A0G9,Canada.E-mail:tahnert@bankofcanada.ca.zUniversityofAmsterdam,CEPR,andTinbergenInstitute.AmsterdamBusinessSchool,Roetersstraat18,Amsterdam1018WB,Netherlands.E-Mail:E.C.Perotti@uva.nl 1IntroductionThescaleoftherecentcrisishasledtoasearchforglobalexplanations.Aleadingviewisthatexcesscreditwasdrivenbylowinterestrates,associatedwiththerecyclingoflargeglobalimbalancesintosafeUSassets.1AtatimeofdecliningUSsavingrates,thecreditboomwaslargelyfundedbyin owsseekingsafeassets,thusreducinginterestrates.Privateliabilitiescreatedby nancialintermediarieshelpedtosatisfyademandforsafetyinexcessofthesupplyofTreasurysecurities.Thee ectwasaportfolioreallocationthatincreasedtheriskconcentrationinholdingsbyUSresidents,whobecamemoreexposedtoshocks.2ThisnarrativeexplainswellhowglobalimbalancesmayleadtolargerriskbearingforUSinvestors.Itdoesnotsuggestane ecton nancialfragility,asforeignin owsareassumedverystable.Thispapershowshowsafety-seekingforeignfundingmaycreateriskbyincreasingthefrequencyofruns.Thisresultoccursunderoptimalcontractinginasimplesetupwithoutdepositinsuranceorbailouts,whenintermediariesbearallriskcreatedbytheirchoices.Itisdrivenbyspeci cfeaturesofmostcapitalin owsintodevelopedmarkets,namelytheirsafety-seekingnature.Historically,capitalmovedfromdevelopedtoemergingcountries,thoughlessthanim-pliedbyneoclassicaltheory(Lucas,1990).Developingcountrieshadtoborrowinforeigncurrencybecauseofexpropriationriskassociatedwithaweakinstitutionalframework,whichcausedsuddenreversalsand nancialcrises.Incontrast,foreignershavefordecadesaccu-mulatedclaimsinreservecurrencies(GourinchasandRey,2007).Netcapital owshaveinfactreversedsince1998,withdevelopingcountriesnowfundingthedevelopedworld(Prasadetal.,2007).Estimatesonin owsintotheUSare$7:8trillionoverthe2002-2007creditboom.Inadditiontowell-recordedin owsofocialreserves,81%oftheseUSexternallia-bilitieswereheldbytheprivatesector(Forbes,2010).Thesein owsoftenseekanonymity,andarechanneledvialegalentitiesino shorecenters. 1Bernanke(2005)discusseda\savingsglut"abroadasanexplanationforUStradede cits.2CaballeroandKrishnamurthy(2009):\[]theUSsellsrisklessassetstoforeignersandinsodoingraisesthee ectiveleverageofits nancialinstitutions."(p.584).1 Figure1:Leftpanel:Netin owsintotheUSfromo shorecenters.Assetsownedbyo shorecenterbankinvestedintheUS(solidblue)andassetsownedbyUSbankinvestedino shorecenters(dashedgreen).Rightpanel:Compositionofo shorecenterbankassetsinvestedintheUS.TotalinvestmentinUS(solidblueagain)andinvestmentinUSbanks(dottedred).Source:BISlocationalbankingstatistics.AllvaluesinbillionUSD.Figure1showstheremarkablegrowthofnetprivatein owsintheUSfromo shorecentersduringthecreditboom(leftpanel),andhowtheytargetedprivatelyintermediatedsafeassets(rightpanel).Thissuggeststhatastrongcomponentofforeignin owscomesfrominvestorsforwhichlegalanonymityisaformofsafety,andinvestthroughprivateinter-mediariesratherthanholdingassetsintheirownname.Identi cationrulesonUSinsureddepositsorUSTreasurypurchasesmayunderminestrictanonymity,sodirectholdingsofsafeassetsmaybeavoided.Thispaperanalyzestheconsequencesofsuchawealthshifttodevelopingcountryresidentsseekingtoinvestinmarketswithbetterprotectedpropertyrights.Largerforeignin owsarebene cial,astheysupporthigherdomesticlending.Theyaretraditionallyseenasverystable(CaballeroandKrishnamurthy,2009).Eveninthedepthofthecrisis,theUSdollarappreciated(Maggiori,2013).Ourcontributionistoshowthatdemandabledebtistheoptimalprivatecontracttoattractforeigninvestors,andhowsatisfyingtheirdemandforsafetyincreasesthefragilityof nancialintermediaries(Shin,2011).Intuitively,providingsafetytosaversunderuncertaintyrequireso eringalessstableformoffunding.2 1980198519901995200020052010 centerbankinvested centers 1980198519901995200020052010 centerbankinvested centerbankinvested Becauserunsleadtocostlyearlyliquidation,long-termdebtwouldbedesirable.How-ever,foreignersseekingabsolutesafetywouldnotacceptsuchclaims,astheyaresometimesworthless.Thus,intermediariesneedtocarveoutanabsolutelysafeclaimfromtheirassetstoattractforeignin ows.3Theoptimalfundingarrangementisthenacombinationofsafedemandabledebtandalong-termclaimthatbearslossesinarun.Sincedomesticsaversareabletosatisfytheirsafetyneedsotherwise,theyo erinsurancebyacceptingthehighreturnriskyclaim.Thisenablesintermediariestocapturesomesafetyrents,bytargetingcheapdemandabledebttosafetyseekingforeigners.Sinceintermediariesneedenoughstablefundingtoinsuresuchinvestors,lendingmaybeconstrainedbyavailabledomesticfunding.Weshowthatundertheoptimalcontract,riskintolerantforeignerswithdrawwheneverinformationonassetvalueisimprecise,causingcostlyliquidationinsomegoodstates.Thusforeignfundingmaybecheap,butitislessstable.Theprivatefundingchoicewillacceptgreaterinstabilityinexchangeforahigherreturningoodstates.Wealsoshowthattheremaybeinsucientincentivesforarbitrageurstocounterinecientearlyliquidation.Theframeworkenablestoassessthee ectofanincreasingsupplyofforeignfundingonthescaleandriskpro leofdomesticcredit.First,itleadstoaversionofexcesslending,asthemarginalprojecthasanegativeNPVatthediscountratedemandedbysavers.Second,itcreatesincreasinglylargerunsingoodstates.The nalresultisanincreaseinrisknotjustforotherclaims,butalsointheaggregate.Thee ectisnotdrivenbyanincreaseinassetriskascreditincreases,butinacombinationofalargerscaleoflendingandlessstablefunding.Theprivatechoiceissociallyinecientinthepresenceofsocialcostsofdefault.Animportante ectofincreasedcreditisthatitrealisticallyinvolveslendingagainstassetswhosevalueisincreasinglyopaque,holdingconstanttheirrisk.(Forevidenceontheroleofhousing nanceincreditbooms,seeforexampleJordaetal.,2014.)Weshowhowinoursettingthisresultsinahigherfrequencyofruns.Thusultimatelyboththescaleandfrequencyof nancialfragilityarerelatedtothescaleofnon-speculativeforeignin ows. 3Gourinchasetal.(2010)showthattheUSprovidesinsurancetotherestoftheworld,intheformofaloweryieldduringnormaltimes,andatransferofwealthtoforeigninvestorsincrises.3 Wenextconsiderthecasewhensomedomesticinvestorsholddemandabledebt,e.g.forliquidityneeds.Asthesesaversarenotriskintolerant,theywouldnotrunsimplybecauseofin nitesimaluncertainty(thatis,whentheimprecisesignalsuggestsahighstate).How-ever,weshowthatonceforeignfundingreachesacertainscale,itwillinducealsodomesticdepositorstoruninthesecircumstances.Thisresultarisesnotoutorriskavoidance,butinordertoavoiddilutionoftheirclaim.Finally,weconsiderwhether\safe"domesticintermediaries(suchasmoneymarketfunds)mayinvestonbehalfofforeignersindomesticsafeassetstoavoidruns.Aslongasthemonitoringofassetchoiceisimperfect,leveragedintermediariesalwayshaveanincentivetoinvestinriskyassets,andcannotcrediblyprovideabsolutesafetyviatheirassetsholdings.KacperczykandSchnabl(2013)documenttherisk-takingbehaviorofmoneymarketfundsduringthe nancialcrisisof2007{2010.Thesimplesetupallowsalimitedwelfareanalysis.CheapforeignfundinginducesahighercreditvolumeintomarginalprojectswithanegativeNPVatdomesticrates,subsi-dizedbytheinsurancepremiaearnedfromforeigners.Thisisecientunderlinearprefer-ences,unlesstherearesocialcostsofexcessliquidation.Weshowhowasociallyoptimalbalancebetweenstabilityandaggregatecreditwilldi erfromtheprivatechoice.Thenourapproachmayrationalizemacroprudentialpoliciestargetingshort-termforeignin ows,suchasasystemicrisktaxonnon-corefunding(Hahmetal.,2013),tocomplementthecapitalandliquidityrequirementsproposedinBaselIII.Inthiscontext,publicguaranteesmaybedamaging,astheincreasedriskabsorptioncapacitywouldallowbankstoattractmoreunstablefunding.Thiswouldshiftbothexogenousandendogenousrisktopublicinsurance.Themodeldoesnotseektoo erafullanalysisofportfoliochoice.Weassumethatforeignerswhogainedsafetyviadomesticclaimsinvestanyresidualwealthintheirowncountry.Thismayre ectsomeadvantageinlocalinformation,whichensuresthemahigherreturnevenundersomeexpropriationrisk.4 LiteratureDemandforabsolutesafetyinourapproachisrationalizedbyaminimumsubsistenceconstraint.Uptothisthreshold,agentsactasin nitelyrisk-averseastheyneedtosecuresomeessentialneeds.Suchpreferencesareconsistentwithrecentevidenceonthestrengthandstabilityofdemandforsafeassets(KrishnamurthyandVissing-Jorgensen(2012);Gortonetal.,2012).Recentworkhasmodeledsuchdemandasarisingfromin nitelyrisk-averseagents(CaballeroandFarhi,2013).Inthepresenceofneglectedrisk,theycancauselargeshocks(Gennaiolietal.,2013).Gennaiolietal.(2013)pioneeredthenotionoflowprobabilityriskdrivingrunsbyin nitelyriskaverseinvestors.Inoursimpleversionthisriskisalwayssalient,butconsiderednegligiblebysomesetofagents.AstrictsegmentationbetweensavingsandinvestmentmarketsismodeledinAllenetal.(2014).Segmenteddemandmayarisefromnon-contingentpreferenceforliquiditytobackpayments,theclassic\moneyintheutilityfunction".Asmoney-likeclaimso ertransactionservices,theyarecheapertoissue(Stein,2012).Thisprivateincentivetoo erliquidclaimsneedstobebalancedagainstanyilliquidityexternality,suchas resales(PerottiandSuarez(2011);Stein,2012).Inourapproach,demandabledebtarisefromriskintoleranceratherthantransactionorliquidityservices,thoughabriefextensionconsiderstheinteractionbetweenthetwomotives.OurapproachisconsistentwiththeempiricalresultsinKrishnamurthyandVissing-Jorgensen(2013)onthee ectofchangesinthesupplyofgovernmentsafeassets.Adecreaseleadsnotjusttoanincreaseinnetshort-term nancialdebt,butalsoanincreaseinlong-terminvestmentsnetoflong-termfundingby nancialintermediaries.Here,thecreditexpansionisboostedbyabundant,lessexpensivefundingsupply,andisassociatedwithanincreaseinmaturitytransformation.Ourpapercomplementsarichinternational nanceliteratureonthe\originalsin".Mostcapitalin owsindevelopingcountriestaketheformofshort-termforeignloansbecauseofpoliticalrisk(EichengreenandHausmann,1999).Tirole(2003)explainssuchdemandableclaimsasadisciplinarydevice,re ectinggreateragencycostinacontextofpoliticalrisk.Ourresultsderivedirectlyfromthenatureofforeigninvestmentintosafehavens,inacontext5 ofsymmetricbutimpreciseinformation.Acriticalassumptionintheliteratureisthatforeignersneedanintermediarytoaccessdomesticassets(CaballeroandKrishnamurthy,2009).Inoursettingthismaybejusti edbytheneedforsafe-keeping,orfortheanonymitygainedbyinvesting(possiblyviaano shorecenter)intoadomesticlegalentity.4OcialdatasuggeststhatthecompositionofUSnetexternalassetsisskewedtowardsriskyassets,whileforeignersinvestinsafedollarassets.Thereisabundantevidencethatforeignersseekingsafetyacceptalowerratesofreturn(Caballeroetal.,2008).Forbes(2010) ndsthatforeigninvestorsintheUSearnlessthanUSinvestorsearnabroad,evenafteradjustingforexchangeratemovementsandroughmeasuresofrisk.ForeignerswithlessdevelopeddomesticbondmarketsinvestcomparativelymoreintheUS,con rminganeedforsafety.ThehistoricalaccumulationofUSde citsnetofocialreservessuggestsasubstantialbuild-upinthestockofforeigncapital,thoughgranularevidenceisimpairedbyapreferenceforanonymity.However,newevidencelinkspoliticalriskinspeci ccountriestocapital ightintosafehavens(BadarinzaandRamodorai,2014).Mendozaetal.(2009)showhowcountrieswithbetterprivatecontractualenforcementbene tbyattractingforeigninvestmentin ows,andareabletoexplaintheirdecliningnetassetholdings.Ourapproachiscomplementaryaswehighlightdi erencesinprotectionfrompublicexpropriation,andthusdescribenonspeculativecapital ows.Ourassumptionofasubsistencelevelinpreferencesmaybeseenasanextremeversionofhabitformationmodels,whicharewellsupportedbyevidenceinassetpricingandmacroe-conomics.5Intuitively,asagentsbecomewealthier,theyadjusttheirlifestylerequirementsorincreasetheirobligations,requiringahigher\safe"componentofwealth.ThismayalsoexplainthestableshareofUSsafeassets(Gortonetal.,2012).Underthisinterpretation,thedemandforsafetyfromemergingcountrieswillincreaseastheybecomewealthier.Hence,bothcreditvolumeandinstabilityincountrieswithgoodpropertyrightswouldrise. 4Secrecyisahallmarkofcapital ight.In2011,a$32bndiscrepancywasreportedinAngola'snationalaccounts,widelyattributedtorentextractionfromitspoliticalelite.Estimatesofannualcapital ightfromRussiaareamultipleofthisamount.Taxevasionandmoneylaunderingareotherreasonsforanonymity.5HabitformationinAbel(1990)andCampbellandCochrane(1999)o eranexplanationfortimeseriesanomalies,suchasthesizeoftheequitypremium.Fuhrer(2000)usesittoexplainthe`hump-shaped'gradualresponseofspendingandin ationtoshocks.6 Oursettingderivesdemandabledebtasanoptimalcontracttosatisfysaversseekingabsolutesafety.Traditionally,demandabledebtisexplainedbycontingentliquiditydemand(DiamondandDybvig,1983),alsoessentialfortheadverseselectionapproachinGortonandPennacchi(1990).Inatwo-periodsetting,demandforliquidityisindistinguishablefromsafetydemandforearlywithdrawals.6Alsointhisapproachinvestorpreferencesareextreme,assomesaversvalueconsumptiononlyattheinterimdate.However,latewithdrawingsaversmaysu erdefault,whichisincompatiblewithabsolutesafetypreferences.Suchpreferencesalsocreatelargescaleinstabilityundersalientbeliefsonrisk(Gennaiolietal.,2013).Demandabledebtisalsorationalizedasanoptimalcontracttoresolveagencycon icts(DiamondandRajan(2001);CalomirisandKahn,1991).InDiamondandRajan(2001),demandabledebtrunsactasathreattocontrolagency.Thepresenceofjitteryinvestorsmakesthisthreatcostlysincerunsmayoccurinsolventstates.2ModelTheeconomyextendsoverthreedatest2f0;1;2g.Itispopulatedbydomesticandforeignsaversandacontinuumofdomesticintermediariesi2[0;1]thatraisefundingfromsavers.Eachintermediaryhasaccesstoaspeci cpoolofriskyinvestmentIi0thatyieldsR(I)withprobability 2(0;1)atthe naldate(highstate)andzerootherwise(lowstate).Liquidationattheinterimdateyields 2(0;1)inallstates,soliquidationisecientinthelowstate.Investmenthasdecreasingreturnstoscale,whereR0(I)0andR00(I)0.Thus,marginalrevenueinthehighstate,MR(I)IR0(I)+R(I),decreasesininvestment.Attheinterimdatethereisalwaysanimprecisepublicsignalabouttheinvestmentreturn.Inaddition,inthehighstate,thereisaprecisesignalwithprobability2(0;1)(contingencyG).Ifthereisnoprecisesignal,someresidualuncertaintyremains.Theimpre-cisesignalmaycorrectlysuggestthatthestateishigh(contingencyM)orlow(contingencyB),butisincorrectwithprobability&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.93; 0 ;&#xTd [;0(contingenciesXandE).Figure2summarizes. 6Inadynamicconsumptionsmoothingsetup,liquidityneedscannoteasilyexplainthehugestockofdemandabledebtheldbyhouseholds.7 Figure2:Theinformationsstructureofthemodel.Forsimplicity,henceforthweassumethatuncertaintypersistsonlyaftertheimprecisesig-nalsuggeststhehighstate(soweeliminatecontingencyX).7Therefore,conditionalonnoprecisesignal,theBayesianprobabilityofthehighstateis (1�)(1�) (1�)(1�)+(1� )1.AllsaversneedabsolutesafetyforaminimumamountS2(0;1)oftotalconsumption,anamountrequiredforsubsistence.Oncethislevelisattainedineitherperiod,saversactasrisk-neutralinvestorswithnotimediscounting,wherectdenotesconsumptionatdatet:U(c1;c2)=8&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ ;� -2;.51; Td;&#x [00;&#x]TJ ;� -2;.51; Td;&#x [00;&#x]TJ ;� -2;.51; Td;&#x [00;:c1+c2c1+c2Sif�1c1+c2S(1)Foreignsavershaveworseaccesstoasafestoreofvalue,re ectingalowerdegreeofpropertyrightprotectionintheircountry.Domesticsavershaveaccesstosafeshort-termstoragewithunitreturnattheinterimdate,andtolong-termstoragewithreturnT&#x-278;1atthe naldatethatcannotbeliquidatedearly.Incontrast,thereturnon(short-orlong-term)foreignstorageisx2[S;T).Therefore,foreignsaverscansatisfytheirabsolutesafety 7Whileasymmetricallyimprecisesignalismoregeneral,ourresultsareinvarianttothissimpli cation.8 StatesignalContingency needsviaforeignstorageorbyinvestinginadomesticintermediary.AsinCaballeroandKrishnamurthy(2009),weabstractfromforeigners'riskyinvestmentbyassumingittakesplaceintheirowncountryandfrominvestmentabroadbydomesticsavers.Table1summarizestheendowmentsattheinitialdate.Foreignsavershaveaunitendowment,sotheirmassWmeasurestotalforeignwealth.Asanormalization,theunitmassofdomesticsaversisendowedwith1+S=T.AsdomesticsaverssatisfytheirabsolutesafetyneedslocallybyinvestingS=Tinlong-termdomesticstorage,oneunitofdomesticwealthisavailabletoinvestinriskyclaims.ItsrequiredreturnistheopportunitycostT. Agents Mass Endowment Foreignsaver W 1 Domesticsaver 1 1+S=T Banker 1 0 Table1:Agentsandendowments.Theexpectedmarginalrevenueofinvestmentis MR(I)+(1� )(1�) .Weassumethatinvestmentinitiallydominateslong-termstoragebut,becauseofdecreasingreturns,domesticfundingsucesforecientinvestmentinautarky: MR(0)+(1� )(1�) �T� MR(1)+(1� )(1�) (2)Theresidualdomesticendowmentisstoredlong-termtoequalizetheexpectedmarginalrevenue,soautarkyinvestmentIAut2(0;1)satis es MR(IAut)+(1� )(1�) =T.Attractingcheaperfundingfromabroadenablesalargerscaleofecientinvestment.Intermediariesaresubjecttolimitedliabilityandmaximizetheexpectedvalueofeq-uity,equaltoinvestmentproceedsafterdebtpayments.Investmentreturnsarepubliclyobservableatthe naldatebutnon-veri able,sowerestrictattentiontodebtcontracts(HartandMoore,1998).Whenfundedwithdemandabledebt(sothatintermediariesarebanks),weabstractfromrunsbasedonpurecoordinationfailure(AllenandGale,1998).Wenextconsidertheoptimalfundingarrangement.Eachintermediaryhasuniqueaccesstooneunitofdomesticfundingdi1,providedtheexpectedreturno eredisno9 smallerthanT.(Thiscouldariseinamodelofspatialcompetitionwithsomedis-utilityofdistance.)IntermediariescompeteforforeignfundinginaWalrasianmarket.Attheinitialdate,eachintermediarymayo erclaimstoraisedomesticfundingdi0andforeignfundingfi0inordertoinvestIidi+fi.Weclosethedescriptionofthemodelwithanobservationsabouttheintermediaries'abilitytoo erabsolutesafety.Inordertoattractforeignfunding,anintermediaryhastoensurefullrepaymentalsointhelowstate.Ifforeignsavershadverypoorownstorageoptions, x,theirrequiredreturnissatis edwithoutinsurancefromotherlendersevenincaseofearlyliquidation.Inthisextremecase,foreignsaversactuallyprovideinsurancetodomesticsavers.Wehenceforthexcludethiscasebyassuming x.BenchmarkWeestablish rstthebenchmarkwhenagentsareperfectlyinformedinallstates(!0).Banksalwaysterminateinvestmentecientlyinthelowstate,ensuringareturnof .Lemma1summarizestheoptimalfundingarrangementinthiscase.Lemma1Debtseniorityunderecientliquidation.Underperfectinformation(!0),theoptimalfundingcontractisamenuofseniorlong-termdebtandjuniorlong-termdebt.Foreignsaversselectseniordebt,whiledomesticsaversselectjuniordebt.ProofSeeAppendixA.Thebenchmarkoptimalfundingcontractusessenioritytoensuretheabsolutesafetyofforeignfunding.Domesticsaversreceiveahigheryieldtocompensatefortheirsubordination.Incentivecompatibilityholdssincedomesticsaverspreferthehigherexpectedreturnofthesubordinateddebtcontract,whileforeignsaversseektheabsolutesafetyofseniordebt.Long-termdebtprecludesthepossibilityofinecientliquidationattheinterimdate,triggeredbysafety-seekingforeignsaverswhentheprecisesignalisnotobserved.10 3Unstablein owsandendogenousriskWeturntothemainmodel,whereagentsmakeraremistakesinthelowstate.Asaresult,seniorlong-termdebtleadstoacompletelossincontingencyE,violatingtheabsolutesafetyneedsofforeignsavers.Thisalterstheoptimalfundingcontractradically.Proposition1Optimalfundingcontracts.Supposeinvestmentisnotalwaystermi-natedinthelowstate(�0).Domesticfundingisattractedwithlong-termdebt.Foreignfundingcanonlybeattractedwithdemandabledebt,providedasucientamountofloss-absorbingdomesticfundingisattractedtoo erabsolutesafetyinthelowstate.Foreignsaverswithdrawearlyunlesstheprecisesignalisobserved.Theoptimalcontractingproblemisfairlysimpleinthisenvironment.Foreignsaversneveracceptthelong-termdebtcontractwithfacevalueLasitdoesnotprovideabsolutesafety.However,theyacceptdemandabledebt,providedthereabsolutesafetyneedsaremetinallcontingencies.Therefore,thebank'sabilitytoo erabsolutesafetyrequirestheliquidationvaluetobehighenoughtocoverthedemandabledebtclaim: Iixfi;(3)whichrequiresasucientamountofloss-absorbingdomesticfunding,dix� fi.Underthiscondition,theintermediarycano erabsolutesafetytoforeignsaversinallcontingen-cies.However,thesafety-seekingnatureofforeignfundingcreates nancialfragilityundertheoptimalfundingcontract.ToavoidthecompletelossincontingencyE,foreignsaverswithdrawwhenevertheprecisesignalisnotobserved.Corollary1Ifforeignfundingisattracted,therearesometimesrunsinthehighstate,leadingtotheliquidationofinvestment.Whileliquidationisecientinthelowstate,thesewithdrawalscreateaneciencylossincontingencyM,whichincreasesinthescaleofforeignfunding.Undertheoptimalfundingcontract,thepromisedamountforearlywithdrawalsissetaslowasconsistentwithabsolutesafety.11 Whileattractingforeignfundingundertheoptimalcontractingenablestoexpandin-vestment,italsocausesearlywithdrawalswheneverthereisuncertaintyaboutthehighstate.Thisde nesabasictrade-o betweencostandstabilityofforeignfunding.Theresultindicatesthatdomesticintermediariesattractforeignfundingonlyifitslowcostcompensateforthelossescausedbysafety-seekingrunsincontingencyM.WhiledemandabledebtrunsalsoforceecientliquidationincontingencyE,thisexpectedbene ciale ectisin nitesimalrelativetoitsaveragecost.Table2summarizesallpayo swhenforeignfundingisattracted. State Probability Return F D Bi G  R(Ii) X L RIi�Ldi�Xfi M (1�) R(Ii) x minL;RIi�R xfi di maxfRIi�R xfi�Ldi;0g B (1� )(1�) x minL; Ii�xfi di maxf Ii�xfi�Ldi;0g E (1� ) 0 x 0 0 Table2:Payo swhenforeigncapitalisattracted.DandFarethepayo stodomesticandforeignsavers,respectively,whileBiisthepayo tobanki.Weconsidernowthesupplyanddemandforforeignin ows.ForeignsaverscansatisfytheirabsolutesafetyneedsbyinvestingS xinself-storage,orinademandabledebtcontract(X1;X2)withreturnofatleastxinallcontingencies.Thefacevalueofdemandabledebtatthe naldateX2XmayexceedX1xifthereisstrongcompetitionforforeignfunding.Lemma2Supplyofforeignfunding.Foreignfundingissuppliedundertheconditionthattheintermediarycano erabsolutesafety.Underthiscircumstance,foreignfundingcanbeattractedwithdemandabledebtoffacevalues(x;X).Theaggregatesupplyis:f(X)=8���&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;:0Xx0;WS xifX=xWS xX�x(4)Bank'sfundingchoiceTheprivatelyoptimalfundingchoicemaximizesthebank'sex-pectedpro t,equaltoexpectedinvestmentreturnnetoffundingcosts.DomesticfundinghasanaveragecostofT.ForeignfundingcostsXincontingencyG,R(Ii) xincontingencyMduetocostlyliquidation,andxincontingencyB.(IncontingencyE,thebankisbankrupt).12 Lemma3Demandforfunding.Theintermediarychoosesonlydomesticfunding(au-tarky)ifuncertaintyistoohigh.Incontrast,if� 2(0;1),thereexistsauniquethreshold XT �(1� )(1�) x�1� x R(IAut)suchthat:Ifforeignfundingisexpensive,X X,autarkyisoptimal:fi=0anddi=IAut.If X�XX x MR�x x� �x� T ,thesafetyconstraintbinds:di=�x� fi.Bothdomesticandforeignfundingisattracted,wherefiisuniquelyde nedby: MRx fi=T+ xh X�Ti:(5)Inthisinteriorsolution,theexpectedmarginalrevenueofinvestmentequalstheexpectedmarginalcostofbothdomesticandforeignfunding.Ifforeignfundingischeap,XX ,thecornersolutiondi=1andfi= x� obtains.Theintermediaryraisesthemaximumamountofforeignfundingconsistentwithabso-lutesafety,giventhelimitedamountofdomesticfunding.ProofSeeAppendixB,whichalsocontainsthede nitionof .Uniquenessfollowsfromthedecreasingmarginalrevenueofinvestment.Aggregationisstraightforwardunderacontinuumofidenticalintermediaries,sofRi2[0;1]fidianddRi2[0;1]didi.Wenowstatetheequilibrium.Proposition2Uniqueequilibrium.Considerthecaseofsmallmistakes�0andsucientlylowuncertainty,� .Thereexistsauniqueequilibriumifforeignwealthisabundant,W�W 2(0;1),wherethislowerboundisimplicitlyde nedby: MRS W + (1�)R(IAut)+(1� )(1�) =T:(6)ProofSeeAppendixC.13 Figure3:Equilibriuminthemarketforforeignfunding:supply(straightblue)anddemand(dashedgreen).Theleftpaneldepictstheunconstrainedcase,whilethelimitedsupplyofdomesticfundingmaybindintherightpanel(X �x).Corollary2summarizesthetwopossiblecases,illustratedinFigure3.Corollary2UndertheconditionsofProposition3,theamountofsafetyseekingforeignwealthdeterminestheequilibriuminthemarketforforeignfunding.IfX �x,therearetwocases:IfW W W Sx x� ,theequilibriumisinterior:foreignfundingisfi=f=WS xanddomesticfundingisdi=d=x� xWS2(0;1).Theequilibriumfacevalueofdemandabledebtis:X=x MRS W�x� T (7)IfforeignwealthisabundantW W,thecornersolutiond=1andf= x� occurs.Inthiscase,theamountofinexpensiveforeignfundingthatcanbeattractedislimitedbytherisk-absorptioncapacityofdomesticfunding.IfX x,thereisaninteriorequilibriumwithadi erentupperboundonforeignwealth:MRS W=x� xT + :(8)14 f f Wecannowassesstheriskcreatedbysafety-seekingforeigncapital.Proposition3Financialfragility.Whenforeignfundingisattracted,withdrawalsbyforeignsaversleadtofullliquidationofinvestment.Theresultingeciencylossincontin-gencyMequalstoS R�S WWforW2(W ; W)andtoR�x x� x x� forW W.ProofSeeAppendixD.Corollary3ForeignwealthandnegativeNPV.Wheneverforeignfundingisattracted,thevolumeofdomesticinvestmentincreasesinforeignwealth,whileitsnetpresentvalueatdomesticdiscountratesdecreasesinforeignwealth.IfX xand R�x x� +(1� )(1�) T,thenthereexistsauniquewealththresholdW2�W ; WsuchthatthenetpresentvalueofinvestmentisnegativeatdomesticdiscountratesforallW�W.ProofSeeAppendixE.Wecannowsummarizetheaggregatee ectofcapitalin ows.Underourinitialassump-tion,condition(2),theNPVofinvestmentinautarkyispositive,NPVAut IAut(�R0(IAut) T�0.Whilenotanessentialassumption,itensuresthatsomecapitalin owsareecient.Ifforeignwealthisabundantandthusforeignfundingcheap,investmentexpandsuntilitearnsanegativeNPVatdomesticdiscountrates.Notethatthisinducedexpansionincreditisecientunderlinearpreferences:foreigncapitalinducesmorecreditnotjustbecauseitexpandsavailablefunding,butbecauseitreducesitsmarginalcost.Asinvestorswhosupplycheapforeignfundingaresatis ed,theirmarginalrequiredrateofreturnbecomestheappropriatediscountratefordomesticbanks.15 4Extensions4.1UncertaintyoverassetreturnInoursetup,impreciseinformationmayleadtorunsbyriskintolerantinvestors,sointerme-diarieshaveanincentivetoprioritizemore\transparent"assets.Westudyheretherealisticcasewhenlendingmorerequiresinvestinginmore\uncertain"assets.Tokeepourfocusdistinctfromthetraditionalriskshiftingincentiveinbanking,weassumethatmorelendingdoesnotinvolveinherentlyriskierassets,butassetsthataremoreopaque.Thisnotionisconsistentwithevidencethatcreditboomstendtofundrealestateinvestment.Speci cally,assumethatuncertaintyoverassetvaluesatt=1increasesinthecreditvolume,asthechanceofaprecisesignalfalls.Thisimplies=(Ij)withd dIj0.Itiseasytoshowthatthisleadstoagreaterfrequencyofruns,sincecontingencyMoccursmoreoften.Astheintermediarybearsallcost,theimpactofmoreopaqueinvestmentisfullyinternalized,anditisstraightforwardtogeneralizetheresultsofLemma3.Theautarkyallocationisnota ected,giventhatonlylong-termdebtiso eredtodomesticsavers.AutarkyisnowoptimalwheneverXXT�(1� )(1�)x� (1�(IAut))x R(IAut) (IAut):(9)Ifforeignfundingischeap,XX,theintermediarywouldstillattractasmuchforeignfundingaspossible,constrainedbytheabsolutesafetyconditionfi= x� di.Thenewlevelofforeignfundingraisedfi(X)isimplicitlygivenby: (Ii)MR(Ii)=T+ xh X�T� 0(Ii)x R(Ii)�Xi:(10)Relativetothebaselinecase,nowamarginalincreaseinforeignfundedinvestmentleadstomorefrequentliquidationinthehighstate.Sincethebankernowincursmorefrequentcostlyliquidationduetoforeignruns,itschoiceofthescaleofforeignfundingislower.16 Thisnaturalextensionshowshowrisk-intolerantforeignfundingislikelytoincreasethefrequencyofruns,inadditiontotheirscale.4.2SocialcostofexcessiveliquidationOurcontractingresultwithitstrade-o betweenthecostandstabilityoffundingistheoptimalchoiceforriskneutralintermediaries.Aproperwelfareanalysismustconsiderthepossibilitythatthisprivatechoicehassocialconsequences.Asidefromriskaversion,anaturalcaseinoursetupisthatexcessliquidationmaycausesomesocialcostsassociatedwithearlytermination.Runsmayinvolvebankruptcycosts.Largerrunswilla ecttheliquidationpriceofassets,orunderminecon denceindomesticintermediaries,bothcausinganegativeexternalitye ect(Stein,2012).Weconsiderherethesimplecaseofasocialcostofexcessliquidation�0perunitofassetsterminatedearly,inthegeneralcasewithendogenousuncertaintyoverassets(asinthepreviousextension).Recallthatinthecaseofautarky,therearenosuchcostsasfundingislongterm.Weexcludeanycostinthecasewhenliquidationisecient,namelyinthelowstate.Consider rsttheinvestmentandfundingchoiceofaconstrainedplanner.Theplanner(P)internalizesthesocialcostofexcessliquidation,takingthesupplyofforeignanddomesticfundingasgiven(thatis,itisawareoftheabsolutesafetyconstraintofforeignsavers).Forsucientlycheapforeignfunding,thesocialoptimumofinvestmentIP(andthusthevolumeofforeignfunding,fP)isgivenby: (IP)MR(IP)=T+ xh X�T� 0(IP)x R(IP)�Xi+socialcostz }| {h (1�(IP))� x 0(IP)fPi:(11)Relativetotheprivatechoice,theplanner'sproblemincorporatesthesocialcostofexcessiveliquidation.Itiseasytoseethatthisimpliesalowervolumeofcredit,andagreaterdegreeofstability.Inparticular,thesocialdemandforforeignfundingislowerthantheprivate17 demand,sincethesocialcostofinvestmentexceedstheprivatecostbythehighlightedamountinequation(11).Supposeloss-absorbingdomesticisnotconstrained(sodP1)andforeignwealthisabundant(sothecostofforeignfundingisX=xevenintheprivateequilibrium).Theplannerthenchoosestoattractlessforeignwealthinordertoreduceliquidationvolumesinthehighstate.8Thesecondbene tfromareducedintermediationvolumeisalowerfrequencyofruns,asassetuncertaintyislower(contingencyMoccurslessoften).Figure4showsthiscase. Figure4:Thesocialandprivateoptimumofforeignfunding.ThecostXversusthevolumeofforeignfundingf.Thesupplyofforeignfundingisagainthestraightblueline,whereastheprivateandsocialdemandforfundingarethedashedgreenanddashedredlines,respectively.ThecaseofX xisdepicted.Theimplicationisthatmoreforeignfundedcredithasadirecte ectnotjustontheamountbutalsothefrequencyofexcessliquidation,bothcontributingtosystemicrisk.Thuscapitalrequirementshouldbecomplementedbystablefundingnorms(asenvisionedintheBaselIIIrecommendations,sofarnotintroduced),thatrecognizethelowerstabilityassociatedwithsafety-seekingforeignin ows.Inaddition,thecalibrationofliquidityrisk 8Ifforeignwealthisscarce,thedownwardshiftinthedemandforforeignfundingdoesnota ecttheallocation,butreducesthecostofforeignfunding(verticalsupplycurve).Ifaccessofforeignsaverstosafestoragewereheterogeneous,theresultwouldagainbelesscredit,aswellaslowerforeignfunding.18 f weightsshouldrecognizethesensitivityofout owstoassetopaqueness,asdistinctfromassetliquidity.4.3PrivatearbitrageWeconsidernextwhetherdomesticinvestorscouldresolvetheinecientliquidationbyactingasarbitrageurs,relyingontheirsuperiorriskabsorptioncapacityrelativetoforeigners.Thisentailsstoringsomeresourcesuntiltheinterimdate,whichhasanopportunitycostofthetermpremiumT�1.Thesearbitrageurscouldbuyclaimsfromwithdrawingforeignsaverswhentheimprecisesignalindicatesahighstate,andnegotiatewiththebanktoappropriatethepro tfromavoidingliquidationincontingencyM.Considerthemaximumpossiblebene tfromthisposition,namelywhenthearbitrageurhasallthebargainingpower.Anarbitrageurwithaunitofcapitalatt=1canbuy1=xunitsofrunningdemandableclaimsincontingenciesMandE(recallthatthereremainssomeresidualuncertaintywhentheimprecisesignalispositive).Next,theseclaimsmaybetradedforalong-termclaimworthatmostR(I) xperclaim.ThisstrategygeneratesR(I) incontingencyM,whichoccurswithprobability (1�),andacompletelossincontingencyE,wherethestateislow.ForanygivenI,asucientconditiontoexcludethepossibilityofdomesticarbitrageursis:T�1� (1�)R(I) :(12)Insum,aprivatesolutiontotheineciencyalwaysfailswhenitsopportunitycost(thetermpremium)exceedsthemaximumexpectedgainincontingencyM.Formoregeneralbargaininggames,orinthepresenceofspeci ccosts,theconditionwillbelessstringent.Notethatitisimpossibleforthearbitrageurtoleverupinordertoincreaseitsexpectedpro ts.First,foreignfundingcannotbeattractedasthearbitrageurmakesomein nitesimalerrors.Second,otherdomesticsavershavethesameopportunitycostT�1.19 4.4Moneymarketmutualfundsandrisk-takingincentivesWehavesofarassumedthatdomesticintermediariescannotinvestdirectlyinsafestorage,becausetheyseekanonymity,orbecausedomesticsafestoragerequiressomelocale ort(e.g.forsafekeepingormaintenanceofarealasset).Alternatively,safetydemandbydomesticorforeignsaversmayhaveuseduptheavailablestock.Inthiscase,safeassetsmustbecarvedoutofriskyinvestmentbyintermediaries.Considerthecasewhenthereisnoexcessdemandforsafety,inthesensethatsomeamountofliquidsafeassetsisavailableforinvestment.Thiscreatestheoptionfordomesticintermediaries,suchasmoneymarketmutualfunds,toinvestingovernmentdebttosatisfysomesafetydemand.Supposetheseintermediariescaninvestinlong-termstorage,withasafereturnofT.Competitionamongsuchintermediarieswillimprovereturnsforforeignsaversuntilthesupplyofsuchsafeassetsisfullyexhausted.Beyondthispoint,theoutcomewillbeasinourmodel.However,thissolutionisfragileinacontextofextremeriskaversion.Supposethereisatinychancethattheassetchoiceisnotfullyobserved(governancerisk),andthattheseintermediariescanaccessthesameinvestmentopportunitiesasbanks.Becauseoftheirleverage,theseintermediarieshaveanincentivetomakesomeriskyinvestment,sinceitsreturnexceedsT.Asaresult,suchintermediariescouldnotattractsafety-seekingforeignfunding.KacperczykandSchnabl(2013)documenttherisk-takingbehaviorofmoneymarketfundsduringthe nancialcrisisof2007{2010.4.5InducedrunsWeconsidernowthee ectofforeignfundingondomesticsaversholdingdemandabledebt.Supposeamass!�0ofdomesticsaverschoosesademandableclaim,duetoexogenousreasonssuchaseaseofpaymentortimingofliquidityneeds.Let betheliquiditydis-countthatdomesticsaversarewillingtoaccept,where1� x,sothattheyacceptthedemandabledebtcontracttargetedatforeignin ows.Forsimplicity,theavailableamount20 ofrisk-absorbingdomesticfundingisunchanged,ensuringanunchangedcapacitytoinsuresafety.Asaresult,somedemandabledebtisheldbyrisktolerantdomesticsavers,whomaychoosetorollovertheclaimevenwhenthereisonlysomesmalluncertaintyoverthehighstate(thatis,whentheimprecisesignalsuggestsassetvaluesarehigh).Thosedomesticsaversoptimallychoosetorolloverif: (1�)(1�) (1�)(1�)+(1� )minnX;R(I)I�R(I)x fX !X+Lox:(13)wherethe rsttermistheprobabilityofthehighstateconditionalonafavorableimprecisesignal;thesecondisthepromisedreturnXatthe naldate,ortheirexpectedshareoftheresidualprojectreturnincaseofdefault.(Aunitmassofdomesticsaverswithlong-termdebtoffacevalueLandamass!ofdomesticsaverswithdemandabledebtoffacevalueXreceiveanequalshareoftheproceeds,netofliquidationrequiredtoserveforeignsavers.)Thisallowstostudythecomparativestaticofanincreaseinthesupplyofunstableforeignfunding.Inequilibriumthishasseverale ects.First,moreforeignfundingreducestheequilibriumfacevalueofdemandabledebtatthe naldate,X.Second,itincreasestheamountofforeignfundingfattractedinequilibrium,whichleadstolargerrunsandthusmorecostlyliquidationincontingencyM.Third,therewillbeamarginale ectoninvestmentvaluebecauseofdiminishingreturns.Itisimmediatetoseethatallthesee ectsincreasetheincentivesofdomesticsaverstowithdrawattheinterimdate.Itiseasytoshowthatthereisathresholdlevelofforeignfundingsuchthatinequilibriumdomesticsaverswithdrawtheirdemandabledebtwheneverthereisuncertainty,andthusevenwhenassetvalueisalmostcertainlyhigh.Inconclusion,anincreasingrelianceonunstableforeignfundingmayfeedintogreaterinstabilityofdomesticfundingeveninthegoodstate,astheyanticipatelargelossesduetoaforeignrun.Herethelocalsaversarenotdrivenbyriskintoleranceastheforeignsavers,butbytheincentivetoavoiddilutionoftheirclaim.21 5ConclusionThispaperhassoughtafoundationforthewidespreadviewthatglobalimbalancesshapedthecreditboomandultimatelythe nancialcrisis(CaballeroandKrishnamurthy,2009).Weshowhowtheaccumulationofwealthincountrieswithaweakprotectionofpropertyrightscreateademandforabsolutesafetytobeprovidedbyintermediariesinsafecountries.Theoptimalcontractualarrangementshapesthefundingstructureofdomesticintermediaries,creatingaclearlinkbetweeninexpensivefunding,creditexpansionandinstability.Ourmainresultisthatpressuretoprovideabsolutesafetydoesnotjustredistributeriskamongsavers,butincreasesriskvialargerandmorefrequentruns.Thisresulthasclearpolicyimplications,asthesociallypreferredfundingstructurewouldinvolvelesscreditvolumeandlowerinstabilitythantheprivatechoice.Whilelargeglobalimbalancesre ectmajorshiftsinwealthawayfromdevelopedcoun-tries,alargefractionhas ownbackasinexpensiveliabilitiesofdomesticintermediaries,enablingtoexpandcreditattimesofdecliningsavings.Weshowthatthesafetyseekingnatureofthese 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AProofofLemma1Considerthesupplyoffunding rst.Domesticsaverssatisfytheirabsolutesafetyneedslocally,sodomesticfundingdi2[0;1]canbeattractedbyintermediaryiwithaclaimthatyieldsatleastTinexpectation(asdoeslong-termdomesticstorage).Thisisbestachievedwithlong-termdebt,sincedomesticsaverswhoseekexpectedreturnhavenoincentivetowithdrawprematurely.EachforeignsaverinvestsS xinforeignstorageinautarkytosatisfytheabsolutesafetyneeds.Therefore,foreignfundingissuppliedtodomesticintermediariesifaminimalreturnofxisensuredinallcontingencies.ForanintermediarytosatisfythisabsolutesafetyconstraintincontingencyMandB,it(i)o ersaseniorclaimtoforeignsaversand(ii)attractsasucientamountofrisk-absorbingdomesticfunding, (di+fi)xfi.Thisrequireseitherfi=0ordi�x� fi�0.Sincesafety-seekingforeignsaverswouldcauseinecientliquidationofinvestmentincontingencyM,itisoptimalfortheintermediarytoo erlong-termdebtcontractsonly.Se-niorityensuresthesafetyneedsofforeigners,providedenoughdomesticfundingisattracted.LetLSxdenotethefacevalueofseniorlong-termdebtandLJTdenotethefacevalueofjuniorlong-termdebt,wherethelowerboundsarisefromtheparticipationconstraintsofsavers.Furthermore,theincentivecompatibilityconstraintofforeignsaversismet,sincejuniorlong-termdebtcontractdoesnotguaranteeabsolutesafety, Ii�LSfixdi.ThereisaWalrasianmarketforforeignfunding,soallintermediariesandforeignsaverstakeLSasgiven.Hence,theaggregatesupplyofforeignfundingis:f(LS)=8&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;&#x]TJ ;� -2;.52;&#x Td ;&#x[000;:0LSx0;WS xifLS=xWS xLS�x(14)Increasesinforeignwealthshiftsoutthesupplycurveofforeignfunding.26 Conditionalonattractingforeignfunding,Table3summarizesthepayo stothein-termediaryandsaversinallcontingencies.TheintermediaryalwaysdefaultsincontingencyB,leadingtoatleastpartialdefaultonjuniorclaims,whichareheldbydomesticsavers. State Probability Return F D Bi G  R() LS LJ R(Ii)Ii�LJdi�LSfi M (1�) R() LS LJ R(Ii)Ii�LJdi�LSfi B 1� minLS; Ii fi max0; Ii�LSfi di 0 Table3:Payo swhenforeigncapitalisattractedIntermediaryimaximizesitsexpectedequityvaluebychoosingtheamountofforeignanddomesticfundingandthefacevalueofjuniorlong-termdebt.SinceahigherfacevalueLJreducesexpectedpro tsbutmakestheparticipationconstraintofdomesticsaversslacker,itisalwaysoptimalfortheintermediarytosetitatthelowestvalueconsistentwithparticipationofdomesticsavers:LJ=T �1� max0; Ii�LSfi di (15)Therearetwocases.Case(I)describescompletedefaultondomesticsaversincontingencyM,LSfi Iixfi,whilecase(II)describespartialdefaultincontingencyM,LSfi Ii.Itisalwaysoptimaltoattractsomedomesticfunding,di&#x-278;0.Proofbycontradiction:ifdi=0,thenfi=0fromtheabsolutesafetyconstraint.Hence,theexpectedpro tsarezero,whichisdominatedbytheautarkyallocationwithstrictlypositivepro ts,AutIAut[ R(IAut)+(1� ) �T]&#x-278;0.Thisestablishestheclaim.Weshowedthattheoptimalfundingcontractwhenagentsareperfectlyinformedislong-termdebt.Seniorityisgiventoforeignsaverstosatisfytheirabsolutesafetyconstraint.Sinceforeignfundingisweaklycheaperthandomesticfunding,someofwhichisattractedinequilibrium.Speci cexpressionsforthefacevaluesofdebtcontractandthecompositionoffundingcanbeobtainedbysolvingtheconstrainedoptimizationproblemdescribedabove.27 BProofofLemma3Westartbyshowingthatthebank'sproblemsimpli esasstatedbelow.Domesticfundingisexpensive,asimpliedbytheparticipationconstraintofdomesticsavers:E[D]= L+ (1�)min(L;R(Ii)Ii�R(Ii) xfi di)+(1� )(1�)minL; Ii�xfi diT:Theexpectedpro tofbankiis:E[i]= [R(Ii)Ii�Ldi�Xfi]+ (1�)maxR(Ii)Ii�R(Ii) xfi�Ldi;0+(1� )(1�)maxf Ii�xfi�Ldi;0g:Eachintermediaryimaximizesitsexpectedpro tsE[Bi]bychoosingitsfundingpro le(di,fi)andthefacevalueoflong-termdebtL,takingthefacevalueofdemandabledebtXasgiven.Thesechoicesareconstrainedbytheparticipationconstraintofdomesticsaversandtheabsolutesafetyconstraint.Thefacevalueoflong-termdebtreducesthebank'sexpectedpro tsbutmakestheparticipationconstraintofdomesticsaverslessbinding(withouta ect-ingtheabsolutesafetyconstraint).Hence,thebanksetsLfortheparticipationconstraintofdomesticsaverstobind.Thus,thebank'sproblemcanbereducedtothefollowingproblem:maxfi2[0;1);di2[0;1]^i=Ii[ R(Ii)+(1� )(1�) ]�diT(16)�fi X+x (1�)R(Ii) +(1� )(1�)s.t. IixfiIi=di+fiTheobjectivefunctionistheexpectedrevenuefrominvestmentnetofthecostofdomesticandforeignfunding.Wenowsolvethisstandardconstrainedoptimizationproblem.LetLitheLagrangianoftheproblemandibetheLagrangemultiplierassociatedwiththeabsolutesafetyconstraintofbanki.The rst-orderconditionsare:28 dLi ddi= MR(Ii)+(1� )(1�) �T� (1�)xR0(Ii) fi+idLi dfi= MR(Ii)+(1� )(1�)( �x)� X� (1�)x [R0fi+R]�x �1iandi0anddix� fiwithcomplementaryslackness.B.1SlackabsolutesafetyconstraintConsiderthecaseinwhichtheconstrainttoprovideabsolutesafetydoesnotbind(i=0).Therearetwosubcases:(A)foreignfundingismoreexpensive,(B)foreignfundingischeaperthandomesticfunding.(A)moreexpensiveforeignfundingSupposethatforeignfundingisexpensiverelativetodomesticfunding,XT �(1� )(1�) x�1� x R(Ii).Then,noforeignfundingisattracted,fi=0,andtheautarkylevelofinvestmentoccurs,di=IAut.Thepro tlevelisAutIAut[ R(IAut)+(1� )(1�) �T].Weneedtocon rmtwosuppositions.First,theabsolutesafetyconstraintistriviallyslack,i=0.Second,forforeignfundingtobe(prohibitively)expensive,werequire:X XT �(1� )(1�) x�1� x R(IAut):(17)Autarkyistheuniqueequilibriumif Xx.However,weimposealowerboundonuncer-taintyinordertoallowforanequilibriuminwhichforeignfundingisattracted.Inshort:� 0 R(IAut)+(1� )(1�) � xT [R(IAut)� ]2(0;1)(18)(B)foreignfundingischeaperthandomesticfundingIfforeignfundingischeaprelativetodomesticfunding,XT �(1� )(1�) x�1� x R(Ii),thentheintermediarywould29 wishtoattractonlyforeignfunding,fi�0,andnodomesticfunding,di=0.Thisallocationviolatestheabsolutesafetyconstraint,however.Contradiction.B.2BindingabsolutesafetyconstraintConsidernowthecaseinwhichtheconstrainttoprovideabsolutesafetybinds(i�0).Hence,di=�x �1fiandIi=x fi.Optimalityrequiresfi�0,sowehavedLi dfi=0.SolvingthisequationfortheLagrangemultiplieryields:i= x� MR(Ii)�(1� )(1�) �  x� X� (1�)x x� [R(Ii)+R0(Ii)fi]:(19)InsertingthemultiplierindLi ddiyields:dLi ddi= x x� MRx fi�T�  x� X:(20)First,ifdi2(0;1],thendLi ddi=0,sotheoptimalamountofforeign(anddomestic)fundingisimplicitlyde nedby:MRx fi=x� xT + xX:(21)Theleft-handsidestrictlydecreasesintheamountofforeignfundingsinceMR0()0.Theright-handsideisapositiveconstant.Notethattheleft-handsideatzerostrictlyexceedstheright-handsideforallX X.Therefore,thereexistsauniqueinteriorsolutionfi(X)�0forallX X.9Thedemandforforeignfundingindownward-sloping,dfi(X) dX0,sincetheright-handsideincreasesinthepriceofforeignfunding.Sincedomesticfundingisbounded,di1,werequirealowerboundonthepriceofforeignfundingtoguaranteeaninteriorsolution:XX x MRx x� �x� T :(22) 9Thatis,R(0)x� xT + xXforallX Xbecauseofthe rstboundaryconditionandthede nitionoftheautarkyinvestmentlevel.30 IfXX ,thentherethecornersolutiondi=1andfi= x� prevails.Foraninteriorsolutiondi1toexist,werequireX Xthatimposesalowerboundontheinformativenessofforeignfunding:� 1 R(IAut)+(1� )(1�) �T R(IAut)�MR�x x� 2(0;1):(23)Finally,weneedtoestablishthati�0assupposed.Insertingtheoptimalitycon-ditionintheexpressionfortheLagrangemultiplieryieldsanupperboundonthepriceofforeignfundingX~X,whichisimplicitlyde nedby:~XT �(1� )(1�) x�1� x RIi(~X):(24)NotethatlimX!~XIi(X)�IAutandlimX!~Xfi(X)�0.Thisfollowsfrom rst-ordercondition,equation(21),andthede nitionofautarkyinvestment: RIi(~X)+ Ii(~X)R0Ii(~X)+(1� )(1�) =T:(25)NotethatlimX! XIi(X)�IAutandlimX! Xfi(X)�0.Thisfollowsfrom rst-ordercondition,equation(21),andthede nitionofautarkyinvestment: R�Ii( X)+(1�)R�IAut+Ii� XR0�Ii( X)+(1� )(1�) =T:(26)Hence,Ii( X)�Ii(~X).Sinceinvestmentdecreasesinthefacevalueofforeignfunding,wealsohave X~X.B.3Whenisautarkyoptimal?Theexpectedequityvalueoftheintermediarythatchoosesautarkyis:AutIAut[ R(IAut)+(1� )(1�) �T]= �IAut2(�R0(IAut)):(27)31 ForX2[X ;~X],abank'sexpectedequityifchoosingtoattractforeignfundingis:i(X)= x fi(X)Rx fi(X)� Xfi(X)�Tx� fi(X);(28)wherefi(X)2(0; x� ]isdeterminedasdescribedabove.Bytheenvelopetheorem,theexpectedpro tstrictlydecreasesinthefacevalueofforeignfunding,di dX0.SupposeaswitchingthresholdofforeignfundingXSexists.ThisimpliesthatautarkyispreferredforXXSandattractingforeignfundingispreferredforXXS.Twoconditionsarerequired:atthelowerboundX ,attractingforeignfundingmustbepreferable,whileautarkyispreferableattheupperbound X.Onecanshowthatthe rstconditionismorerestrictiveandimposesanotherlowerboundontheinformativenessofforeignsavers.Speci cally,theexpectedpro tattheupperbound X{wheretheforeignfundinglevelisfi( X)de nedabove{is:i( X)=Ii( X) R�Ii( X)+ (1�)R(IAut)+(1� )(1�) �T(29)Hence,i( X)Autisimpliedbyalowerboundontheinformativenessofforeignsavers:&#x-278; 2Ii( X)�IAut Ii( X) R(IAut)+(1� )(1�) �T R(IAut)�R(Ii( X))2(0;1)(30)Then,thee ectivelowerboundis maxf 0; 1; 2g.CollectingthevariouscasesyieldsthedemandforfundingstatedinLemma3.CProofofProposition2ThisproofsbuildsonLemma2andLemma3.Toensureexistenceofequilibrium,werequirealowerboundonforeignwealth.ThislowerboundW isgivenbytheinteractionbetweenthesupplyofforeignfunding,f=WS x,andthedemandforforeignfundingasimpliedbythesolutiontotheintermediary'sproblem.Thede nitionstatedinthePropositionfollows32 immediately.Toensureaninteriorequilibrium,werequire X�x.Thisconditioncanbeexpressedasalowerboundontheinformativenessofforeignsaversthatwederivedbefore.Thiscompletestheproof.DProofofProposition3ThisproofbuildsonLemma2,Lemma3,andProposition2.Foreignfundingisattractedwheneverforeignwealthissucientlyabundant,W�W .Fortheseequilibria,theabsolutesafetyconstraintbinds, Ii=rfiforeachintermediaryi.Hence,therearenoresourcesleftafterforeignsaverswithdrewattheinterimdateincontingencyM(seeTable2).Thus,thebankmakeszeropro tsandfullydefaultsondomesticsavers.ThetotaleciencylossisR(I) xf.FocusingonthemoregeneralcaseofX �x,wehavetworelevantrangesofforeignwealth.First,forW2(W ; W),wehavethatI=S Wandf=S xW,whichyieldsaneciencylossofR�S WS W.Second,forW W,wehavethatI=x x� Wandf= x� W,whichyieldsaneciencylossofR�x x� x x� .Thiscompletestheproof.EProofofCorollary3IrrespectiveofwhetherX �xornot,thenetpresentvalueofinvestmentatdomesticdiscountratesforalevelofforeignwealthbelowtheupperbound Wis:NPV= R�WS +(1� )(1�) T�1:(31)33 Hence,thenetpresentvaluesdecreasesinforeignwealth:NPV0(W)= R0�WS S T0:(32)IfX �x{whichisimpliedbyx� T [MR(x x� )� ]{thenthecornersolutionwithI=x x� occursforsucientlyabundantforeignwealth.Thus,thegrosspresentvalueofinvestmentneversmallerthan R(x x� )+(1� )(1�) T.Bycontinuity,theresultinCorollary3follows.34

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