Limited Deposit Insurance Coverage and Bank Competition

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Limited Deposit Insurance Coverage and Bank Competition Oz Shy, Rune Stenbacka, and Vladimir Yankov 2014-53 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

∗ Limited Deposit Insurance Coverage and Bank Competition OzShy† RuneStenbacka‡ FederalReserveBankofBoston HankenSchoolofEconomics VladimirYankov§ BoardofGovernorsoftheFederalReserveSystem August6,2014 Abstract Deposit insurance schemes in many countries place a limit on the coverage of deposits in each bank. However, no limits are placed on the number of accounts held with different banks. Therefore, under limited deposit insurance, some consumers open accounts with different banks to achieve higher or full deposit insurance coverage. We compare three regimes of deposit insurance: No deposit insurance, unlimited deposit insurance, and limited deposit insurance. We show that limited deposit insurance weakens competition among banksandreducestotalwelfarerelativetonoorunlimiteddepositinsurance. Keywords: Limiteddepositinsurancecoverage,depositrates,bankcompetition. JELClassificationNumber: G21. (Draft=”deposit-124correctionAugust4”.tex2014/08/0608:55) Note: Thispapercontainshyper-referencesforeasiernavigation. Ifyoureadthisarticleona computer,youcanuseALT-leftarrow(Windows)orCommand-leftarrow(Mac)togoback tothereferringpageafterclickingonanyhyper-reference. ∗WethankJohnDriscollandJonathanRoseforcommentsonanearlierdraft.Theviewsexpressedinthispaperare thoseoftheauthorsanddonotnecessarilyrepresenttheviewsoftheFederalReserveBankofBostonortheFederal ReserveSystem. †E-mail:Oz.Shy@bos.frb.org.ResearchDepartment,FederalReserveBankofBoston,600AtlanticAvenue,Boston, MA02210,U.S.A. ‡E-mail:Rune.Stenbacka@hanken.fi.HankenSchoolofEconomics,P.O.Box479,00101Helsinki,Finland. §E-mail: Vladimir.L.Yankov@frb.gov. BoardofGovernorsoftheFederalReserveSystem,20thStreetandConstitutionAvenueN.W.,Washington,D.C.20551.

1. Introduction One feature of the 2008 financial crisis that sets it apart from other deep financial crises in U.S. economichistoryisthatdepositrunsonbanks,wheresmalldepositorssimultaneouslywithdraw theirdepositstriggeringilliquidityanddefaultonotherwisehealthyfinancialinstitutions,didnot occur as they did in the Free Banking Era and during the Great Depression.1 The financial crisis of2008broughtanewtypeof“bankruns”whichinvolvedthenon-traditional“shadow”banking systemwherefinancialinstitutionsranonotherfinancialinstitutions. ThemostsignificantinstitutionalchangesincetheGreatdepressionthatpreventedthetraditionalbankrunswasthepresence ofdepositinsurance. Thispaperfocusesontwoaspectsofthedesignofthedepositinsurancethat havenotreceivedmuchattentionintheacademicliteratureandtheimportanceofwhichbecame evidentduringthe2008financialcrisis. The first aspect of the deposit insurance design is that insurance is partial and subject to a limitation in terms of coverage. The second aspect is that the deposit insurance limit applies to oneinstitutionperdepositoraccountbutisunlimitedwithrespecttothenumberofaccountswith different banks all of which are subject to the same deposit insurance limit. Our paper addresses thequestionofhowlimiteddepositinsurancecoverageaffectstheintensityofcompetitioninthe deposit market. We also explore the effects of limited deposit insurance on consumer welfare as wellastotalwelfarecomparedwithsystemsofunlimitedornodepositinsurance. Westartouranalysisbyfirstdocumentingafewstylizedfactsonthedemandformultipledepositaccountsacrossdifferentbanks. WedocumentthatwealthierU.S.householdsholdmultiple depositaccountswithmultipledepositinstitutions. Thedemandformultipleaccountscorrelates positivelywiththefinancialwealthofU.S.households. Further,theaverageamountdepositedin accountsthatexceedthedepositinsurancelimitisapproximatelyatmostthreetimesthedeposit insurance limit, thus, making it feasible for depositors with partially insured deposit accounts to achieve full insurance by distributing their deposits among several banks. We further document that smaller banks, which are deemed riskier, attract more insured brokered certificates of deposits as compared to larger banks. During the recent financial crisis, however, both small and 1SeeGorton(2010)andGorton(2012)foranalysisoftherecentfinancialcrisisinhistoricalperspective. 1

largebanksexperiencedanequallylargeincreaseintheshareofinsuredbrokereddeposits. We next develop a stylized theoretical model of deposit market competition with the feature thatsomeconsumersdiversifytheirfundsacrossdifferentbanksinordertoqualifyforcomplete deposit insurance coverage. We establish that a system with limited deposit insurance coverage softens deposit market competition as compared to systems with unlimited or no deposit insurance. Wefurthershowthatlimiteddepositinsurancereducesconsumerwelfareandtotalwelfare notonlybyinducingdepositorstobearcostsofopeningseveralaccounts,butalsobyweakening competitioninthedepositmarket. We build on an extensive literature that has examined the role of deposit insurance for social welfare. Following the seminal contribution by Diamond and Dybvig (1983), the literature has typically analyzed deposit insurance systems within the framework of models focusing on bank runs. DiamondandDybvig(1983)demonstratedhowtheinteractionbetweenpessimisticdepositor expectations may generate bank runs as an inefficient Nash equilibrium, and how deposit insurance systems can eliminate such inefficient equilibria. Subsequently, an important and extensivecategoryofstudies,exemplifiedbyKeeley(1990),MatutesandVives(2000),andShyand Stenbacka(2004),hasexploredtheconsequencesofimperfectcompetitionfordepositsontherisktakingincentivesbybanks. Forexample,MatutesandVives(2000)characterizeindetailtheroles playedbylimitedliability,depositinsurancewithcompletecoverageanddepositmarketcompetition for the determination of risk-taking by banks. Also, Matutes and Vives (1996) characterize howthewelfareimplicationsofdepositinsurancewithcompletecoveragedependonthemarket structureofthebankingindustry. Furthermore, theoretical studies regarding the effects of deposit insurance have typically focusedoncompletedepositinsurancewithunlimitedcoverage. OneexceptionisManz(2009),who characterizes the optimal level of deposit insurance coverage as well as its determinants. However,Manz(2009)doesnotanalyzehowthedepositinsurancecoverageaffectscompetitioninthe depositmarket. Empirical studies have presented cross-country evidence regarding the effects of deposit insurancecoverageondepositrates. PenatiandProtopapadakis(1988)analyzemoralhazardissues 2

generatedbydepositinsurance. Demirgu¨c¸-KuntandHuizinga(2004)exploitcross-countrydifferences regarding the country-specific features of deposit insurance to conclude that the existence ofanexplicitinsurancepolicylowersdepositrates,whileatthesametimeitalsoreducesmarket discipline on bank risk taking. Bartholdy, Boyle, and Stover (2003) present evidence that the risk premium is on average over 40 basis points higher in countries without deposit insurance than in countries with deposit insurance. Bartholdy, Boyle, and Stover (2003) argue that the risk premium is a non-linear function of the deposit insurance coverage, a feature which they interpret to mean that the market recognizes that extended deposit insurance coverage makes the moral hazard problems more severe. Pennacchi (2006) shows that the combination of a deposit insurancedesignwhichfacilitatescompleteinsurancecoveragethroughmultipledepositaccountsand mispriceddepositinsurancepremiahasgivenbanksacompetitiveadvantageovermoneymarket fundsinprovidingsafehavenassetclasses. Since Merton (1978), who applied option pricing to characterize the arbitrage free pricing of deposit insurance premia under costly supervision, the debate on the deposit insurance design has focused on formulating actuarially fair premia that correctly reflect the credit risk that individualbanksface. Thisdebatewasintheearly1990saccompaniedwiththeintroductionofcapital requirements by the Basel committee that focused on controlling the individual bank credit risk. Since the financial crisis, the paradigm of both capital requirements and the design of deposit insurance premia shifted to analyze the pricing the systemic risk of financial institutions (see, Pennacchi (2009)). However, neither of these studies nor the policy debate has focused on the effectofthepartialinsurancedesignonbankcompetition. Itshouldbeemphasizedthatourstudyanalyzestheeffectsofdepositinsurancewithlimited coverage on deposit market competition without explicitly modeling banks’ risky lending decisions. Abstractingfrommoralhazardissues,wedevelopastylizedmodelinordertohighlightin atransparentwayhowdepositinsurancesystemswithlimitedcoverageinducesomeconsumers to diversify their deposits across several banks. 2 Our normative analysis is restricted to the in- 2Anumberofimportantstudies,forexample,Hellwig(1998)andWinton(1997),haveanalyzedtheperformanceof thebankingsystemfromtheperspectiveofdiversificationofeconomy-widerisks.Thesestudieshavetypicallyfocused onbanks’lendingactivities. Inourmodelthediversificationiscausedbythelimitedcoverageofdepositinsuranceas someconsumerssplittheirfundsacrossseveralbanks. 3

vestigationofhowdepositinsurancesystemswithlimitedcoverageaffectbankprofits,consumer welfare, and total welfare. We do not attempt to address the more challenging issue of how to characterize the socially optimal design of deposit insurance. Instead, the goal of this study is to pointoutsomedistortionsthatarisefrompartialinsuranceanddonotariseinsystemswithnoor unlimiteddepositinsurance. Thepaperisorganizedasfollows. Section2presentssomeempiricalfactsregardingtherealworld implementation of deposit insurance in the United States. Section 3 constructs a model of deposit market competition. Section 4 analyzes equilibrium deposit rates and profits as well as consumer and total welfare in the absence of deposit insurance. Section 5 introduces unlimited deposit insurance. Section 6 analyzes equilibrium deposit rates and profits as well as consumer and total welfare with limited deposit insurance. Section 7 presents the main results of our analysis by comparing the performance of the banking industry under the three regimes of deposit insurance. Section8extendsthemodeltoindependentbankfailuresandSection9presentssome concludingcomments. 2. Deposit Insurance: Facts SinceitsestablishmentwiththepassingoftheBankingActin1933,theFederalDepositInsurance Corporation (FDIC) in the United States was designed to insure bank deposits up to a certain dollar amount, called the deposit insurance limit.3 The rationale for the partial insurance design istwofold: toguaranteefinancialstabilitybypreventingbankruns,andtoprovidetheincentives forthemarketstomonitorthebanks. The intention behind the partial deposit insurance coverage is to protect small and unsophisticatedinvestors,whileatthesametimetoexposethewealthierandbetterinformedinvestorsto theindividualbank’screditrisk. Beingexposedtoabank’screditrisk,thewealthierandmoresophisticatedinvestorsareexpectedtoimposemarketdisciplineonbanksbywithdrawingdeposits from banks with lower asset quality. However, the deposit insurance design gives the option to 3Partialdepositinsuranceisalsothenorminmostcountrieswithexplicitdepositinsurance. AsurveybytheIMF Garcia (2000) documents that out of the 78 countries with explicit deposit insurance in 2000, 68 had implemented limiteddepositinsuranceandonly10countrieshadunlimiteddepositinsurance. 4

thesewealthyinvestorstoextendtheinsurancecoverageorevenachievecompletedepositinsurance by opening multiple deposit accounts with different banks. To achieve full insurance, the numberofaccountscanbecomputedbydividingtotaldepositamountsbythedepositinsurance limit. 4 The FDIC does not provide an official explanation of how the deposit insurance limit was determined and to what extent the two rationales for its design are met. Table 1 displays the historical values of the deposit insurance limit both in their nominal terms at the time they were setandtheirrealvaluesmeasuredin2010dollaramounts. Table1showsthatfortheaverageU.S. household the deposit insurance limit has always been sufficient to cover the average financial wealth held in deposits and most part of the total financial wealth. Similarly, Figure 1 shows the time series behavior of the real values of the deposit insurance limit and the average deposit andtotalfinancialwealthduringtheperiodsbetweentheinsurancelimitadjustments. Although the deposit insurance limit once set was continuously eroded by inflation, it was always reset to levels that guaranteed proper coverage of the average deposit balances. In this respect, the depositinsurancedesignachieveditsgoalofprotectingthesmalluninformedandunsophisticated investors.5 Regarding the second objective that targets the wealthy and sophisticated investors to disciplinethebanks,itcanbearguedthatthedesignwithanupperlimitofdepositinsurancecoverage createdastrongdemandformultipledepositaccounts. Whilewedonotaddressthequestionon howwelllargeandsophisticatedinvestorsimposedmarketdisciplineonthebanks,wearguethat 4For example, a depositor with $1 million could fully insure this amount under the current insurance limit by splittingtheamountequallyinaccountswithfourdifferentbanks. InAugust2013therewere6,938FDIC-insuredinstitutionsintheU.S.whichatthecurrentinsurancelimitof$250,000wouldallowanindividualtobefullyinsuredup to$1,734,500,000bysplittingthetotalamountacrossall6,938insuredinstitutions.Inaddition,theFDICwouldinsure amountsuptotheinsurancelimitperdepositor,perinsuredbank,foreacheligibleaccountownershipcategory. Eligibleaccountcategoriesincludesingleaccounts,certainretirementaccounts,jointaccounts,revocabletrustaccounts, irrevocabletrustaccounts, employeebenefitplan accounts, corporation, partnership, unincorporatedassociationaccountsandgovernmentaccounts. 5During the recent financial crisis, the insurance limit was deemed insufficient to guarantee the stability of the payment system and the FDIC implemented the Transaction Account Guarantee (TAG) program that fully insured non-interestbearingtransactiondepositaccounts.Interestbearingdepositaccountssuchasinterestcheckingaccounts, moneymarketdepositaccounts,timedepositsandcertificatesofdepositwerekeptsubjecttothelimiteddepositinsurance.Aspartoftheextraordinarymeasures,thedepositinsurancelimitwhichwasraisedto$250,000onOctober32008 from$100,000limitwhichhadbeeninplacesince1980. TheTAGprogramwastemporaryandexpiredonDecember 31,2012whilethenewdepositinsurancelimitwassetpermanentlywiththepassageoftheDodd-FrankWallStreet ReformandConsumerProtectionActonJuly21,2010. 5

threefactorshavecontributedtotheincreasingdemandforimproveddepositinsurancecoverage by these investors: First, real economic growth has increased the average incomes and financial wealthofmanyU.S.householdsabovethelevelsobservedinthe1970sand1980s. Second,growth inincomesandfinancialwealthhavebeendisproportionatelyhigherforthewealthiestU.S.households (see, Piketty and Saez (2003)). Finally, Figure 1 shows that inflation over the period from 1980 until 2008 reduced in half the effective deposit insurance coverage, thereby increasing the fractionofwealthyhouseholdsthatwerenotfullyinsured. 6 In order to characterize the magnitude of the demand for multiple deposit accounts, we use publicly available data on the average deposit balances from the regulatory reports of FDIC insured commercial banks and combine these data with survey data on individual depositor balancesfromtheSurveyofConsumerFinances. Fromthebanks’side,weusethepubliclyavailable data on the total number and the total balance of deposit accounts which fall above the deposit insurancelimittoestimatethedistributionofaverageuninsureddepositaccountbalances.7 Figure 2 plots the historical variation of the distribution of the average deposit account balances of the large denomination accounts at FDIC-insured commercial banks. In addition, Figure 3 plots the empirical cumulative density function of the average account balance held in depositaccountsexceedingthedepositinsurancelimitof$100,000inthesecondquarterof2008,just a quarter prior to the increase in the deposit insurance limit to $250,000. Approximately, 60 percentofthelargedenominationdepositaccountswerebelowthenewdepositinsurancelimitand most of the accounts were within two times the new deposit insurance limit. It is evident from thesetwofiguresthatformostofthetimesincethedepositinsurancelimitwassetto$100,000in 6Furtherindirectevidencefortherisingdemandformoreextensivedepositinsurancethroughmultipleaccounts withdifferentbanksisthecreationofamarketthatspecializesincollectingdepositsexceedingtheinsurancelimitand allocatingthemoverthenecessarynumberofdifferentbankstoachievefulldepositinsurancecoverage.Forexample, the Certificate of Deposit Account Registry Service (CADR) allows individuals, companies, non-profits and public fundstoinvestlargeamountsinoneaccountwhichCADRsplitsandplacesinanetworkofover3,000participating FDICinsuredcommercialbanks.TheCDARismanagedbyPromontoryInterfinancialNetworkandisprotectedbyU.S. patentsUS7376606,US7440914,US7596522. Formoredetailsseewww.cdars.com. CADRactsasatwo-sidedplatform connectinginvestorsseekingcompleteinsurancecoverageoftheirinvestmentswithFDICinsuredcommercialbanks seekingfunds.DepositscollectedandreallocatedthroughtheCADRareaccountedforasbrokereddepositsandwould showupinthemeasuresofinsuredbrokereddepositsshownabove. 7ThedatacomesfromtheregulatoryfilingsofU.S.commercialbankscalledtheReportsonIncomeandCondition or“CallReports”whichcontainquarterlydataonthebanks’balancesheetandincomestatements.Thedataispublicly availableatFederalFinancialInstitutionsExaminationCouncilhttps://cdr.ffiec.gov/public. 6

1980anduntilitsrevisionin2008,thelargedenominationpartiallyinsureddepositaccountswere withintwoorthreetimesthedepositinsurancelimit. Fact1. Fortheperiod1986–2008, theaveragebalanceofmostofthelargepartiallyinsureddenomination accountswaswithintwoorthreetimesthedepositinsurancelimit. The empirical fact 1 is a statement about the observed distribution of the average size of the partially-insured large denomination deposit accounts. Because we do not have information on how many of the existing deposit accounts below the deposit insurance limit are owned by the sameindividual,wecanonlymakestatementsregardingthedepositaccountsthathavenotbeen distributed into multiple institutions. The evidence suggests that the average balance left uninsuredcouldbespreadovertwoorthreebankstoachievefulldepositinsurance. Furtherevidenceregardingthedemandformultipledepositaccountsinordertooptimizethe depositinsurancecoveragecanbeobtainedbyexaminingtheshareofinsuredbrokereddeposits.8 Commercial banks are required to report the total amount of brokered deposits on their balance sheetandabreakdownintoinsuredanduninsured. Figure4plotsthetimeseriesvariationofthe share of insured brokered deposits on the books of three size classes of banks—small banks with assetsbelowthe75th percentile,mediumlargebankswithassetsbetweenthe75th percentile,and the 99th percentile and large banks with assets in the top one percentile of assets. We summarize theinformationinthegraphinthefollowingempiricalfact. Fact2. Formostoftheperiod1986–2008,smallerbanksattractedalargershareofbrokeredinsureddeposits compared with medium and large size banks. At the onset of the financial crisis as aggregate default risk increased,thedemandfordepositinsuranceincreasedatbanksofallsizes. We can think of three reasons that explain the fact that smaller banks carried a higher share of insured deposits. First, on average, smaller banks are more volatile as these banks operate in limitedgeographicareasandhavemuchlessscopefordiversificationcomparedwithlargebanks operatinginmultiplegeographicalmarkets. Consequently,thesebanksrelyonretaildepositfunding and rarely borrow from the wholesale funding markets. Second, larger banks are implicitly 8ForalegaldefinitionofbrokereddepositsseeFDIC(2011)whichwascommissionedasaresponsetoregulation introducedbytheDodd-FrankActfordefinitionofbrokereddeposits. 7

covered by a too-big-to-fail guarantee which is hard to measure but lowers the perceived likelihood of default. Finally, large banks are more likely to attract larger clients with larger deposit accounts and serve as their primary account custodians. Smaller banks, on the other hand, due to their larger number and the symmetric treatment by the deposit insurance limit, could serve assecondaryaccountsofdepositorswhowanttoachievehigherdepositcoveragebydistributing their deposits among multiple banks. At the onset of the 2008 financial crisis,the share of insuredbrokereddepositsincreasedinalltypesofbanks,wherethemostpronouncedincreasewas documented in large banks. The evidence suggests that the demand for high deposit insurance coverageincreasedduringthisperiod. Shifting our attention to the investors, the Survey of Consumer Finances (SCF) provides evidence regarding the demand for multiple deposit accounts. The survey collects information on the size and allocation of financial assets over different financial institutions from a representative sample of U.S. households. In particular, it surveys households regarding the different bank accounts they have with different financial institutions and their corresponding balances. In Figure5,weexaminetheallocationofcertificatesofdepositsoverdifferentbankaccountsinthe2007 SCF.ThereisalargefractionofwealthyU.S.householdsmaintainingdepositaccountswithmultiple deposit institutions. We attribute part of the demand for multiple deposit accounts to the demandforlargerinsurancecoverage. Fact3. According to the Survey of Consumer Finances, a large fraction of wealthy households maintain multipledepositaccountswithmultipledepositinstitutions. Thereisastrongpositivecorrelationbetween theaveragenumberofCDaccounts,theaverageamountdeposited,andthenumberofbankstheseaccounts areheldwith. 3. A Model of Bank Competition 3.1 TheBanks There are two financial institutions (“banks” in what follows) that pay interest on deposit accounts. Let r and r denote the interest rates paid by bank A and bank B, respectively. On A B each$1deposit,abankearnsρbylendingthemoneytoariskyprojectorbyinvestingthemoney 8

in other ways (buy bonds, stocks, credit default swaps, real estate, and other derivatives).9 The project(andhencetheinvestingbank)failswithprobabilityφmeaningthattheexpectednetreturn tobankAandBona$1depositis(1−φ)(ρ−r )and(1−φ)(ρ−r ),respectively. Therefore,abank A B thatfailslosesitsentiredepositamountandisnotabletopaybacktheprincipalandthepromised interesttodepositors. Forreasonsoftractabilitywewillfocusonperfectlycorrelateddefaultrisks for banks, but in Section 8 we extend the model to cover independent failure probabilities across banks. 3.2 Depositors Eachconsumerisendowedwith$2,andthisendowmentisinitiallydepositedeitherinbankAor in bank B. Each consumer has the option to shift the entire deposit ($2) or part of it to the rival bank. Openinganewaccountiscostlytodepositors,butitallowsdepositorstotransfermoneyto thecompetingbank. The depositors are differentiated with respect to two characteristics: the history and the costs associated with opening a new account. We refer to consumers who initially have their entire $2 depositedwithbankA(bankB)astypeA(typeB)depositors. TypeA(similarly,typeB)depositorsareindexedbytheircostsofopeninganewaccountwithadifferentbanks,where0 ≤ s ≤ n. More precisely, the cost of opening a new account to a consumer indexed s is σs, where σ > 0 is aparametercapturingtheintensityofthiscostofswitchingallorpartthedeposits. Wecaninterprettheparameterσ asameasureoftheintensityofdepositratecompetitionbetweenthebanks. Further, we assume these switching costs to be uniformly distributed. 10 As shown in Figure 6, depositorswithlowshaveahigherincentivetoopenanewbankaccountthandepositorswitha highs. Atypei,i = A,B depositorwhoisindifferentbetweenopeningandnotopeninganewbank accountisdenotedinFigure6bys ,wherei = A,B. i 9Both, thebanks’projectreturn(ρ)andtheinterestratespaidtoindividualdepositors(r A andr B)couldalsobe viewedasrealrates. Infact, atthetimeofcompletingthisarticle(June2014), theinflationrateintheUnitedStates exceeds2percent,whereasinterestratesondepositaccountsarebelow1percent.Therefore,ouranalysisdoesnotrule outnegativerealinterestrates. 10Thereisampleevidencethatswitchingcostsareempiricallysignificantinbankingmarketsandthattheswitching costsaredifferentiatedacrossconsumers;see,forexample,Shy(2002),Kim,Kliger,andVale(2003),andYankov(2014). 9

3.3 Assumptions We analyze three regimes of deposit insurance and compute the equilibrium deposit rates under each regime. In order to facilitate the formal analysis of the effects of partial deposit insurance on competition, we have to impose some technical conditions on the relationship between the returnonthebanksoutsideinvestmentprojectρandthebankruptcyprobabilityφ. Thefollowing conditions are sufficient for ensuring that the equilibrium deposit rates are non-negative in all threeregimes. ASSUMPTION 1. (a) Thereturnona$1investmentbyabankisbounded. Formally, 2nσ nσ(2+φ) −1 < ρ < −1. φ(2−φ) φ(2−φ) (b) Theprobabilityofbankfailureisbounded. Formally,φ < 2/3. Assumption1(a)isneededinSection6(limiteddepositinsurance). Thelowerboundonρensures existenceofequilibriumwhensomedepositorssplittheirsavingsbetweentwobanks. Theupper boundensuresthatsomeconsumerschoosenottodosoduetosufficientlyhighswitchingcosts, as reflected by the parameter σ. Note that the interval where ρ is bounded is nonempty as its length equals nσ/(2−φ) > 0. Assumption 1(b) seems very reasonable to capture environments wherebankfailuresarenotahighlyfrequentphenomenon. 4. No Deposit Insurance Withnodepositinsurance,consumerslosetheirentiredeposit(s)withprobabilityφ. TheexpectedutilityofatypeAdepositors ∈ [0,n](initiallyinvestedinbankAonly)isgiven by (cid:40) (1−φ)2r −φ2 ifdoesnotopenasecondbankaccount A u (s) = (1) A (1−φ)2r −φ2−σs ifopensasecondaccountandtransfers$2tobankB. B Note that (1) ignores a potential third option where a type A depositor opens a second account withbankB,buttransferslessthan$2therebykeepingapositivebalancewithbothbanks. Inthe absenceofdepositinsurance(andalsounderunlimitedinsurance),thisoptionisnotbeneficialto 10

the depositor because once the depositor maintains two accounts, the depositor has an incentive transfertheentireamounttothebankthatpaysthehighestinterest. The first term in the first row in (1) , (1 − φ)2r , is the expected interest payment on the $2 A depositkeptinbankA. Thesecondterm,φ2,reflectstheexpectedlossresultingfromafailureof bankAthatisunabletopaybackthe$2depositamount. Thesecondrowisverysimilartothefirstone,exceptthatthedepositorholdstheentire$2with bankB insteadofbankA. Theadditionalterm,σsmeasuresthecostofopeninganaccountwith bankB bornebya typeAdepositorindexedbys. Theparameterσ > 0capturestheintensityof thiscost,and,likeswitchingcosts,itcanbeviewedasameasureoftheintensityofdepositmarket competition. For instance, the case σ = 0 implies that all depositors can open a second account at no cost. In contrast, higher levels of σ makes this operation more costly and also widens the variation of this cost across depositors, thereby enhancing differentiation across depositors with differentvaluesofs. Similarto(1),theexpectedutilityofatypeB depositors ∈ [0,n](initiallyinvestedinbankB only)isgivenby (cid:40) (1−φ)2r −φ2 ifdoesnotopenasecondbankaccount B u (s) = (2) B (1−φ)2r −φ2−σs ifopensasecondaccountandtransfers$2tobankA. A The utility function (1) implies that a type A depositor s opens an account with bank B and transfers the entire $2 deposit if (1−φ)2r −φ2−σs > (1−φ)2r −φ2. Similarly, the utility B A function (2) implies that a type B depositor s opens an account with bank A and transfers the entire$2depositif(1−φ)2r −φ2−σs > (1−φ)2r −φ2. Therefore,typeAdepositorswho A B openasecondbankaccount(withbankB)andtransfertheirdepositsarecharacterizedby    0 ifr A ≥ r B   2(1−φ)(r B −r A ) σn s < s A d=ef σ ifr B − 2(1−φ) < r A < r B (3)   σn    n ifr A ≤ r B − 2(1−φ) . According to (3), type A depositors who face high cost of opening a new account (s > s ) A decide not to open a new account. Similarly, type B depositors who open a new bank account 11

withbankAandtransfertheirdepositsarecharacterizedby    0 ifr B ≥ r A   2(1−φ)(r A −r B ) σn s < s B d=ef σ ifr A − 2(1−φ) < r B < r A (4)   σn    n ifr B ≤ r A − 2(1−φ) . The nature of the thresholds defined in (3) and (4) implies that if s > 0 then s = 0 and if A B s > 0 then s = 0. Intuitively, type B depositors will open a new bank account (with bank A) B A onlyifbankApaysahigherdepositratethanbankB,r > r ,inwhichcase,typeAdepositors A B wouldlosefromopeninganaccountwithbankB. Withnolossofgenerality,wederivetheequilibriumdepositratesbyexaminingthecasewhere r ≥ r so that s = 0. In this case, the total volumes of deposits maintained by bank A and A B A bank B are 2(n + s ) and 2(n − s ), respectively. Therefore, the optimization problem facing B B bankAistotaketheinterestratesetbybankB asgivenanddecideonitsinterestrater inorder A tomaximizeπ = (1−φ)(n+s )2(ρ−r ),whereρ−r istheprofitperunitofdepositand1−φ A B A A is the probability that this bank does not fail. Similarly, bank B determines its interest rate r in B ordertomaximizeπ = (1−φ)(n−s )2(ρ−r ). Substituting(4)fors intotheprofitfunctions, B B B B theequilibriuminterestratesandtheresultingprofitlevelsarefoundtobe σn rN = rN = ρ− and πN = πN = σn2, (5) A B 2(1−φ) A B wherethesuperscript“N”referstoequilibriumvalueswithnodepositinsurance. Itshouldbe pointedoutthatwithnodepositinsurances = s = 0ifbothbanksofferthesamedepositrate, A B becausewithidenticalinterestratesdepositorscannotbenefitfromopeninganewaccount. Next, consumer welfare with no deposit insurance is defined by cwN = nu +nu , where n A B isthenumber(measure)ofconsumersofeachtype. Substituting(5)into(1)and(2)yields cwN = 2n[(1−φ)2ρ−σn−2φ]. (6) Finally, we define total welfare as the sum of consumer welfare and profits of the banks and we subtracttheexpectedbailoutcostsassociatedwiththeprevailingsystemofdepositinsurance(di). 12

Of course, with no deposit insurance di = 0. Hence, from (5) and (6), with no deposit insurance totalwelfare(wN)isgivenby wN = cwN +πN +πN −di = 4n[(1−φ)ρ−φ]. (7) A B From the deposit rate equilibrium (5) as well as welfare expressions (6) and (7) we can apply straightforwarddifferentiationtodrawthefollowingconclusions: Result1. Supposethatbanksoperatewithoutanydepositinsurance. (a) The equilibrium interest rates (rN and rN), the consumer welfare (cwN), and the total welfare (wN) A B increase in response to an increase in banks’ investment return (ρ), whereas the banks’ equilibrium profits(πN andπN)areinvariant. A B (b) An increase in consumers’ cost of opening a new bank account (σ) reduces the equilibrium deposit rates(rN andrN)andconsumerwelfare(cwN),itincreasesbanks’profits(πN andπN),whereastotal A B A B welfare(wN)isinvariant. (c) The equilibrium deposit rates (rN and rN), the consumer welfare (cwN), and the total welfare (wN) A B decrease in response to an increase in banks’ failure probability (φ), whereas the banks’ equilibrium profits(πN andπN)areinvariant. A B Result 1(a) reveals that competition between banks guarantees that the gains from higher investment returns forbanks flow to the depositors inthe form of higher deposit rates. Depositors benefitfromincreasedcompetitionbecausetheyearnhigherinterestratesontheirdeposits. The intuition behind Result 1(b) can be formulated as follows. An increase in the parameter σ induces a higher degree of differentiation between the banks. This means that the banks have stronger market power, leading to lower equilibrium deposit rates and higher profits. Such an increase in σ induces a redistribution of surplus from consumers to banks. However, because all individuals deposit all their funds with the two banks, this redistribution is neutral from total welfareperspective. Result 1(c) characterizes the equilibrium response to a more fragile banking industry. The qualitative findings reported in Result 1(c) are the mirror image of those reported in Result 1(a). 13

Thisfeaturereflectsthefactthatthebanks’expectedreturns(1−φ)ρaremultiplicativewith(1−φ) andρasfactorsandthereforedeclinewiththedefaultprobabilityφ. 5. Unlimited Deposit Insurance Inthissectionweshiftourattentiontoanenvironmentwithunlimiteddepositinsurance,thatis, a system such that all bank accounts are insured to their full amount. In this case, consumers do notfaceanyriskassociatedwiththeirdeposits. Inaneventofabankfailingtomeetitsobligation, depositorsreceivetheirprincipalandthepromisedinterestfromtheinsuringagency. Underunlimiteddepositinsurance,consumers’expectedutilities(1)and(2)aresimplifiedto (cid:40) 2r ifdoesnotopenasecondbankaccount A u (s) = (8) A 2r −σs ifopensasecondaccountandtransfers$2tobankB. B (cid:40) 2r ifdoesnotopenasecondbankaccount B u (s) = (9) B 2r −σs ifopensasecondaccountandtransfers$2tobankA. A The utility function (8) implies that a type A depositor s opens a new account with bank B (and transfers the entire $2 deposit) if 2r −σs > 2r . Similarly, the utility function (9) implies B A that a type B depositor s opens an account with bank A (and transfers the entire $2 deposit) if 2r − σs > 2r . Therefore, with unlimited deposit insurance, the thresholds (3) and (4) are A B transformedtobe     0 ifr A ≥ r B   0 ifr B ≥ r A   2(r −r ) σn 2(r −r ) σn s d=ef B A ifr − < r < r and s d=ef A B ifr − < r < r A B A B B A B A σ 2 σ 2   σn   σn  n ifr A ≤ r B −  n ifr B ≤ r A − . 2 2 (10) Applying an optimization procedure analogous to the previoussection, we now find that the equilibriumdepositratesandtheresultingequilibriumprofitsunderunlimiteddepositinsurance aregivenby σn rU = rU = ρ− and πU = πU = (1−φ)σn2, (11) A B 2 A B 14

where the superscript “U” denotes equilibrium values under unlimited deposit insurance. Note that in equilibrium it holds true that s = s = 0, because depositors cannot benefit from open- A B ing a second account if all banks offer the same interest rate and if all banks are insured to the full amount. Substituting the equilibrium deposit rates (11) into (8) and (9) yields the consumer welfare cwU = nu +nu = 2n(2ρ−σn). (12) 1 2 Next,unliketheconfigurationwithnodepositinsuranceanalyzedintheprevioussection,the presenceofdepositinsuranceintroducesaneconomy-widecostoffundingsuchaninsurancesystem. Thus,theexpectedcostofthedepositinsurancesystemshouldbesubtractedfromconsumer welfare or profit in order to obtain the relevant expected total welfare. The expected bailout cost ofdepositinsuranceis diU = φn2(1+rU)+φn2(1+rU) = φ2n[2(1+ρ)−σn]. (13) A B Equation (13) captures formally the expected cost of bailing out two failing banks. This expected bailout cost is the product of the failure probability (φ), total amount deposited in a bank ($2n)andthepromisedinterestpayment. The deposit insurance system can be viewed as a redistributive taxation system. Following anestablishedtradition,weassumethatitisfundedbyalumpsumtaxsothatwecandisregard potential distortions created by this form of taxation. Of course, such distortions could easily be incorporated into the analysis by multiplying the raised tax with a multiplier (larger than one) thatrepresentsthesocialcostsassociatedwiththosedistortions. Finally, the expected total welfare is obtained by subtracting the expected bailout costs (diU) fromthesumofexpectedconsumerwelfareandindustryprofits. Hence, wU = cwU +πU +πU −diU = 4n[(1−φ)ρ−φ]. (14) A B From the deposit rate equilibrium (11), the welfare expressions (12) and (14), as well as the 15

bailoutcost(13),wecanconductordinarycomparativestaticstodrawthefollowingconclusions: Result2. Supposeallbankaccountsarecoveredbyunlimiteddepositinsurance. (a) The equilibrium interest rates (rU and rU), consumer welfare (cwU), bailout costs (diU), and total A B welfare(wU)allincreaseinresponsetoanincreaseinbanks’investmentreturn(ρ),whereasthebanks’ equilibriumprofits(πU andπU)areinvariant. A B (b) Anincreaseinconsumers’costofopeninganewbankaccount(σ)reducestheequilibriuminterestrates (rU andrU),bailoutcosts(diU),andconsumerwelfare(cwU);itincreasesbanks’profits(πU andπU), A B A B whereastotalwelfare(wU)isinvariant. (c) An increase in banks’ failure probability (φ) reduces the equilibrium profits (πU and πU) and total A B welfare (wU); it increases the bailout costs (diU), whereas the equilibrium interest rates (rU and rU) A B andconsumerwelfare(cwU)areinvariant. Result2(a)verifiesthatcompetitionbetweenbanksensuresthatthegainsfromhigherinvestment returns by thee banks flow to the depositors in the form of higher deposit rates also with unlimited deposit insurance. In this respect, it is qualitatively identical to Result 1(a) with the exceptionthatahigherreturnalsoimplieshigherbailoutcosts. The intuitive explanation for Result 2(b) is identical to that for Result 1(b). The new element included in Result 2(b) is that the induced reduction in deposit rates also reduce the expected bailoutcosts. Finally, Result 2(c) formalizes the very intuitive idea that, with unlimited deposit insurance, depositorsareperfectlysecuredagainstincreasesinbanks’failurerate. 6. Limited Deposit Insurance Asdiscussedintheintroduction,inmanycountriesdepositinsuranceisnotunlimited. Thisobservationisthemainmotivationforourformalanalysisoftheeffectsoflimiteddepositinsurance. In ordertoexhibittheeconomicmechanismsinaverytransparentway,weintroduceaparticularly simpleformoflimiteddepositinsurance: Eachaccountisinsuredupto$1worthofdeposits.11 11The assumption that the insurance limit equals exactly half of the initial deposit amount saves us a tremendous amount of algebra, because under the computed equilibrium deposit rates, low-cost consumers who open a second 16

By opening a second account, and bearing the cost σs, a consumer can benefit from complete deposit insurance. More precisely, through diversification by allocating $1 to each bank, the depositor’s entire wealth would be fully insured. In contrast, maintaining a single bank account wouldsaveadepositorthecostσs, butwouldleave$1(outof$2)uninsured. Thus, withlimited deposit insurance the depositor faces the following tradeoff: To accept exposure to the risk of a bank failure while avoiding the cost σs of opening a new account or to diversify away the risk causedbyapotentialbankfailurebybearingthecostassociatedwithopeningasecondaccount. Underlimiteddepositinsurance,consumers’expectedutilities(1)and(2)aremodifiedto12 u (s) = A    1r A +(1−φ)1r A −φ1 doesnotopenasecondbankaccount  1r +1r −σs opensasecondaccountandtransfers$1tobankB (15) A B   1r +(1−φ)1r −φ1−σs opensasecondaccountandtransfers$2tobankB. B B u (s) = B    1r B +(1−φ)1r B −φ1 doesnotopenasecondbankaccount  1r +1r −σs opensasecondaccountandtransfers$1tobankA (16) B A   1r +(1−φ)1r −φ1−σs opensasecondaccountandtransfers$2tobankA. A A Theexpectedutility(15)demonstratestheconsequencesoflimiteddepositinsurance. Without diversification, a type A depositor is guaranteed a return of r on a $1 deposit only. The excess A depositof$1willprovideareturnonlywithprobably1−φ,whereasthedepositorwilllosethe$1 principalwithprobabilityφ. Thesefeaturesarecapturedbythefirstrowin(15). Thesecondrow in(15)showsthatthisdepositorcaneliminateallrisksbyopeningasecondaccountandsplitting accountwilltransferexactlyhalftheirinitialdeposittothesecondaccounttherebymaintainingfullinsurancecoverage. Assumingotherwisewouldgenerateoscillationswiththefeaturethateachbankattemptstoattractconsumersto transferdepositamountsexceedingtheinsurancecoverage.Priceoscillationsarecommonlyreferredtoas“Edgeworth PriceCycles,”andoccurinoligopoliessellinghomogeneousproductsorservices. MaskinandTirole(1988)tacklethis problembyusingaMarkovPerfectEquilibrium,whichisbeyondthescopeofourpaper. 12Forthesakeofsimplicity, thespecificationoftheutilityfunctions(15)and(16)isincompleteastheyomitother possibletransfersoflowerthan$1andamountsstrictlybetween$1and$2.AppendixAindeedshowsthat,inequilibriumwithalimiteddepositinsurance,consumerswhoopenasecondaccountwilltransferexactlytheamountofthe depositinsurancelimit,whichis$1. 17

the deposit into two separate bank accounts that do not exceed the insurance limit. Lastly, the third row in (15) captures a depositor who opens a second account and completely transfers the entireinitialdeposittothenewaccount. Inthiscase,openingasecondaccountwouldnotresultin anyriskreductionforthisconsumerbecausethetransferstillleaves$1uninsured(withadifferent bank). Moreover,AppendixArulesoutsuchanequilibrium. Therefore,thethirdrowwillnotbe analyzedinthissection. Theutilityfunction(15)impliesthatatypeAdepositorsopensanaccountwithbankB (and transfers$1)ifr +r −σs > r +(1−φ)r −φ. Therefore, withlimiteddepositinsurance, (3) A B A A and(4)become     0 ifr A ≥ r 1 B − + φ φ r −(1−φ)r +φ s A d=ef  B σ A if rB+ 1− φ− φ σn < r A < r 1 B − + φ φ   n ifr ≤ rB+φ−σn A 1−φ     0 ifr B ≥ r 1 A − + φ φ r −(1−φ)r +φ and s B d=ef  A σ B if rA+ 1− φ− φ σn < r B < r 1 A − + φ φ (17)   n ifr ≤ rA+φ−σn. B 1−φ Figure7illustrateshowthetwotypesofconsumersallocatetheirdepositsbetweenoneortwo accounts. InviewofFigure7,thebanks’profitfunctionsaregivenby π = (1−φ)(ρ−r )[2(n−s )+s +s ] (18) A A A A B π = (1−φ)(ρ−r )[2(n−s )+s +s ]. B B B B A From the perspective of bank A, the profit function (18) consists of three components. First, bankAmaintainsthevolume$2(n−s )ofdepositsfromtypeAdepositorswhoremainloyaland A do not open a second account. Second, the bank keeps the volume $s of deposits from type A A depositors,whodecidetosplittheirresourcesbetweenthetwobanks. And,third,bankAattracts the volume $s of type B depositors, who each decide to diversify $1 to bank A. Substituting B 18

(17) into (18), we find the equilibrium deposit rates and the associated equilibrium profits under limiteddepositinsurancetobe 2σn 4(1−φ)σn2 rL = rL = ρ− and πL = πL = , (19) A B 2−φ A B 2−φ wherethesuperscript“L”denotesequilibriumvalueswithlimiteddepositinsurance. Next, substituting (19) into (17) shows that the equilibrium thresholds determining market segmentationaregivenby φ[(2−φ)(1+ρ)−2σn] sL = sL = . (20) A B σ(2−φ) Thethresholds(20)areproportionalthecostofopeninganewaccountatwhichthedepositoris indifferentbetweendiversifying$1totherivalbankinordertoqualifyofcompletedepositinsuranceorremainingloyaltoitspresentbankingrelationship. Fordepositorswithacostofopening a new bank account exceeding this threshold, the benefit from a complete deposit insurance are insufficienttojustifythecostofdiversificationacrosstwobanks,whereastheoppositeholdstrue for costs below this threshold. Technically, Assumption 1 guarantees that 0 < sL = sL < n. In A B particular, Assumption 1 implies that in equilibrium with limited deposit insurance, the benefits of full deposit insurance exceed the cost of opening a second account for some depositors, more precisely for those with relatively low switching costs. This feature somewhat complicates the computations of consumer welfare, because, as illustrated in Figure 7, depositors are heterogeneouswithrespecttotheirdecisionsregardingwhetherornottoopenasecondbankaccount. Formally, by combination of consumers’ utility functions (15) and (16), the equilibrium deposit rates (19), and the associated equilibrium segmentation thresholds (20), we find aggregate consumerwelfareunderlimiteddepositinsurancetobe 19

sL (cid:90)A cwL = cwL +cwL = (rL +rL −σs)ds+(n−sL) (cid:2) rL +(1−φ)rL −φ (cid:3) A B A B A A A 0 sL (cid:90)B + (rL +rL −σs)ds+(n−sL) (cid:2) rL +(1−φ)rL −φ (cid:3) (21) A B B B B 0 16n2σ2(φ−1)+2nσ(φ−2) (cid:2) ρ(φ2+4φ−4)+φ(φ+2) (cid:3) +φ2(ρ+1)2(2−φ)2 = . σ(2−φ)2 The first component in the first and second rows of (21) is the difference of the deposit rates and the costs of opening a second account for the depositors with a sufficiently small switching cost. The second component in each row is the sum of utilities for those depositors who do not openasecondaccount,andthereforedonotbearcostsofopeninganewaccount. Next,inviewofFigure7,withlimiteddepositinsurancetheexpectedcostofbailingoutfailing banksbyinsuringagencyisgivenby diL = φsL(1+rL +1+rL)+φ(n−sL)(1+rL)+φsL(1+rL +1+rL)+φ(n−sL)(1+rL) A A B A A B A B B B 2φ[2nσ+(ρ+1)(φ−2)][nσ(3φ−2)+φ(ρ+1)(φ−2)] = . (22) σ(2−φ)2 Thefirstterminthefirstrowin(22)istheexpectedcostofbailingouttypeAdepositorswho split their $2 evenly between the two banks. The second term applies to type A depositors who do not open a second account, in which case only $1 is insured (out of a total of $2 deposit). The thirdandfourthtermsreferinananalogouswaytotypeB depositors. Using(19),(21),and(22),totalwelfareunderlimiteddepositinsuranceisgivenby wL = cwL+πL +πL −diL (23) A B 4n2σ2φ2+4nσ(φ−2) (cid:2) ρ(2φ2−3φ+2)+2φ(φ−1) (cid:3) +φ2(ρ+1)2(φ−2)2 = − . σ(2−φ)2 Finally,underlimiteddepositinsurance,sL depositorsoftypeAandsL depositorsoftypeB A B 20

carrythecostsofopeningasecondaccount. InviewofFigure7,theaggregatecostsofopeninga secondaccountarethereforecomputedtobe sL sL (cid:90)A (cid:90)B φ2[2nσ+(ρ+1)(φ−2)]2 SL = σs ds+ σs ds = . (24) σ(2−φ)2 0 0 Itshouldbeemphasizedthatthiscostisacomponentoftheconsumerwelfareascomputedin (21). As the next section shows, this aggregate switching cost plays a key role when distinguishing the regime with limited deposit insurance from those associated with either no or unlimited depositinsurance. 7. A Comparison of Three Regimes of Deposit Insurance Wearenowreadytocharacterizetheeffectsoflimiteddepositinsurancecoverageonequilibrium depositrates,associatedindustryprofits,consumerwelfare,bailoutcostsandtotalwelfarebased on a comparison among the investigated three deposit insurance regimes (no insurance, unlimited, andlimitedinsurance). Westartbyfocusingontotalwelfare. Comparing(7), (14), and(23), yieldsthefollowingresult: Result3. A regime with limited deposit insurance coverage yields lower total welfare than either no or unlimited deposit insurance. Formally, wL < wU = wN. Moreover, the reduction in total welfare caused bylimiteddepositinsurancecoverageequalsthedepositors’aggregatecostsofopeningasecondaccount. ThesecondpartofResult3canformallybeverifiedbyaddingdepositors’aggregatecost(24) to(23),whichyieldswL+SL = wU = wN. In our model, the regimes with no deposit insurance and unlimited insurance are efficient fromtheperspectiveoftotalwelfare. Undertheregimewithlimiteddepositinsurance,consumers withsufficientlylowswitchingcostshaveanincentivetoqualifyforcompletedepositinsurance, therebyeliminatingalltheirrisksbydiversifyingacrossbanks. But,theswitchingcostsassociated withopeningnewaccountsgenerateasocialdeadweightloss. Bycomparingtheequilibriumdepositrates(5),(11),and(19)weobtaintherelationshipsrU − k rN = nσφ/[2(1−φ)] > 0andrN−rL = nσ(2−3φ)/[2(1−φ)(2−φ)] > 0,foreachbankk = A,B. A k k k 21

comparisonof(5),(11),and(19)alsoimplies,foreachbankk = A,B,thatπU −πN = −n2σφ < 0 k k and πN −πL = −n2σ[3−4/(2−φ)] < 0, because φ < 2/3 by Assumption 1. These inequalities k k provethefollowingresults: Result4. (a) A system with limited deposit insurance coverage softens competition in the deposit market compared with no or unlimited deposit insurance. Furthermore, competition is more intense with unlimitedthanwithnodepositinsurance. Formally,rU > rN > rL,foreachbankk = A,B. k k k (b) The nature of the deposit insurance system determines the banks’ equilibrium profits according to the followingrelationship: πL > πN > πU,foreachbankk = A,B. k k k AccordingtoResult4(a), limiteddepositinsurancecoveragesoftensdepositratecompetition betweenbanks. Thisfeaturecanbeexplainedaccordingtothefollowingmechanism. Limiteddepositinsurancerelaxescompetitionforconsumerswithlowswitchingcosts. Fortheseconsumers the benefits associated with deposit insurance outweigh the benefits offered by competition. In fact,ourformalmodelendowstherivalbankwithamonopolypositionovertheconsumerswith lowswitchingcosts. Themonopolypowermakesitpossiblefortherivalbanktolowerthedeposit ratewithoutlosingthiscategoryofconsumers. Limited deposit insurance coverage essentially relaxes deposit market competition by inducing some depositors to transfer money between banks in order to improve their insurance coverage. From a theoretical perspective, this mechanism resembles how information exchange between lenders (who have established customer relationship) softens lending rate competition by improving banks’ ability to target their poaching activities towards specific borrowers from the rival bank. Formal two-period models capturing how information exchange softens competition in lending markets have been developed by Bouckaert and Degryse (2004) and Gehrig and Stenbacka(2007). In addition, Result 4(a) captures the idea that consumers can benefit more from deposit rate competition in a system with unlimited deposit insurance compared with a system offering no deposit insurance. This can be explained as follows. In these two regimes banks compete for deposits in a symmetric way with the only difference that bank competition is supported by a transfer from the insurance agency to depositors under unlimited deposit insurance, and this 22

transferintensifiesthecompetitionbetweenbankswhichresultsinhigherdepositrates. Result4isillustratedinFigure8, whichshowsasimulationofhowequilibriumdepositrates and profits depend on the system of deposit insurance. In particular, Figure 8 demonstrates that limiteddepositinsuranceleadstohigherindustryprofitsthanunlimitedornodepositinsurance simplybecausebothbankspaylowerinterestondepositaccounts. The following result summarizes our comparison of the three regimes of deposit insurance withrespecttoconsumerwelfareandthecostofbailingoutbanks: Result5. (a) Consumerwelfarewithunlimiteddepositinsuranceexceedsthatwithlimitedornodeposit insurance. Formally,cwU > max (cid:8) cwL, cwN(cid:9) . (b) Expected cost of bailing out banks increases with the limit on deposit insurance. Formally, diN < diL < diU. From Result 3 and Result 4 we can directly conclude that consumers are better off with unlimited (U) compared with limited (L) deposit insurance coverage. That is, because diU > diL and πU < πL, it cannot hold true that wU > wL unless it also holds true that cwU > cwL . In k k other words, consumers unambiguously benefit from unlimited compared with limited deposit insurancecoverage. When comparing limited (L) deposit insurance coverage with no (N) deposit insurance, we can first make use of Result 3 and Result 4 to conclude that the introduction of limited deposit insuranceimposeslossesonsocietyintheformofexpectedbailoutsoronconsumersintheform of switching costs or lower deposit rates. In particular, we know from Result 3 that the sum of these losses exceeds the benefits to banks associated with limited deposit insurance. However, ourmodelisformulatedatsuchalevelofgeneralitythatitdoesnotincorporatesufficientlymuch structure so as to facilitate an unambiguous ranking between cwL and cwN . Figure 8 exhibits simulations illustrating a configuration where consumer welfare is higher with limited deposit insurancethanwithnodepositinsurance. But,asourargumentaboveshows,thisrankingcould alsobereversed. Result 5(b) does not require a formal proof. It captures the intuitive idea that the expected bailoutcostsincreaseasafunctionoftheinsurancecoverage. 23

Overall,inlightofResult3,Result4andResult5wecandrawtheconclusionthatlimiteddepositinsuranceintroducesadistributionalconflictbetweenbanksanddepositors. Limiteddeposit insurancecoveragepromotesmarketpowerofbanksoverconsumerswithsmallswitchingcosts andthismechanismisthesourceoftheredistribution. Furthermore,wehaveestablishedthatthe benefittobanksfallsshortofthecoststoconsumersandsocietywhenthebailoutcostsaretaken into account. Thus, limited deposit insurance generates a social deadweight loss compared with systemsofunlimitedornodepositinsurance. 8. Independent Bank Failures Our analysis so far has focused on perfectly correlated default risks for banks. In this section we will explore the robustness of our results regarding this assumption by analyzing the configurationwherebanksfaceindependentdefaultrisks. Forsimplicitywerestrictourselvestosymmetric banks facing identical default risks, measured by the bankruptcy probability φ. Under such circumstances, both banks fail with probability φ2, only one bank fails with probabilities φ(1 − φ) and(1−φ)φ,respectively,andnonefailswithprobability(1−φ)2. We proceed in this section by examining each of the three deposit insurance regimes separately,andshowthattheequilibriaderivedundercorrelatedbankruptcyrisksareidenticaltothe equilibriaunderindependentbankruptcyrisks. 8.1 IndependentBankFailures: Nodepositinsurance Section4establishedthat,inequilibrium,depositorsdonotopenasecondaccount. Furthermore, according to Section 4, if a consumer opens a second account, this consumer transfers the full volumeofdeposits,i.e.$2,tothebankthatpaysthehigherinterest. Underindependentbankfailures,wenowexaminethepossiblecasenotcoveredbySection4, namelythecasewheresomeconsumersopenasecondaccountandtransferhalfoftheamountso they maintain $1 with each bank as a diversified portfolio bearing independent risks. In this case, 24

theutilityfunction(1)becomes    (1−φ)2r A −2φ ifdoesnotopenasecondbankaccount;  u A (s) = (1−φ)2(r A +r B )+(1−φ)φ(r A −1) ifopensasecondaccountand (25)   +φ(1−φ)(r −1)+φ2(−2)−σs transfers$1tobankB. B The first row in (25) is the same as in (1). It characterizes the utility of type A depositors, who keep their entire deposit with bank A. The second alternative in (25) (the second and third rows)capturestheexpectedreturnassociatedwithopeningupasecondaccountandmaintaining two independent accounts. The consumer earns r + r interest if neither bank A nor bank B A B fail, which happens with probability (1 − φ)2. If only bank B fails (probability (1 − φ)φ) the consumer earns interest r from bank A, but loses the $1 deposit with bank B. If only bank A A fails(probabilityφ(1−φ))theconsumerearnsinterestr frombankB,butloses$1depositwith B bankA. Finally,theconsumerlosesallhis$2depositsifbothbanksfail(probabilityφ2). Comparingthetwoutilitiesin(25)revealsthattypeAdepositorswhoopenasecondaccount andtransfer$1tobankB arecharacterizedby (1−φ)(r −r ) s < s d=ef B A , (26) A σ wherewedonotdisplaythecornersolutionsforthesakeofbrevity. Thevalueofs in(26)is A proportionaltothatin(3). ThisimpliesatypeAconsumeropensasecondaccountonlyifr > r . B A However, inthiscase, theconsumerisbetterofftransferringthewholedeposit($2)fromAtoB, whichreplicatestheanalysisinSection4undercorrelatedbankfailures. 8.2 IndependentBankFailures: Unlimiteddepositinsurance Under unlimited deposit insurance, consumers do not bear any risk and therefore will not open a second account unless the rival bank offers a higher interest. Hence, the analysis of Section 5 applies also to the case of independent bank failures. Still, it is worthwhile to check whether the expectedcostofbailingoutbanksunderindependentfailuresisthesameaswithcorrelatedbank failures,computedin(13). 25

The expected total bailout cost under unlimited deposit insurance with independent failures isgivenby diU = φ2[2n(1+r )+2n(1+r )]+φ(1−φ)[2n(1+r )]+(1−φ)φ[2n(1+r )]+(1−φ)20 A B A B = 2nφ[2(1+ρ)−σn], (27) wherethesecondrowisobtainedbysubstitutingtheequilibriuminterestratesfrom(11)into thefirstrow. Thefirstrowin(27)sumsupfourterms: Theexpectedcostofbailingouttwofailing banks, theexpectedcostofbailingoutbankAonly, theexpectedcostofbailingoutbankB only, andthezerocostofnotbailingoutanybank(ifnofailingbank). Comparing (27) with (13) reveals that the expected bailout cost is the same independently of whetherwefocusonindependentbankfailuresorperfectlycorrelatedfailures. 8.3 IndependentBankFailures: Limiteddepositinsurance InviewofFigure7,withlimiteddepositinsurance,s ands low-costdepositorsopenasecond A B accountanddeposit$1witheachbank. Therefore,theequilibriumderivedinSection6holdsalso underindependentfailures. The expected bailout cost to support limited deposit insurance with independent failures is givenby diL = φ2[s (1+r +1+r )+(n−s )(1+r )+s (1+r +1+r )+(n−s )(1+r )] A A B A A B B A B B +φ(1−φ)[s (1+r )+(n−s )(1+r )+s (1+r )] (28) A A A A B A +(1−φ)φ[s (1+r )+(n−s )(1+r )+s (1+r )]. B B B B A B The first row in (28) is the expected insurance cost of bailing out two failing banks, where in view of Figure 7, s and s type A and type B consumers split their deposits between two A B banks,whereasn−s andn−s consumersleavetheirentiredeposit$2inasinglebankaccount A B with only half of this amount being insured under limited deposit insurance. The second row is 26

the expected cost of bailing out bank A only, where s type B depositors also keep $1 of their B deposits. Similarly,thethirdrowistheexpectedcostofbailingoutbankB only. Substituting the equilibrium interest rate (19) and the segmentation thresholds (20) into (28) reveals that the expected insurance cost under independent failures (28) is the same as under perfectlycorrelatedfailures(22). Assubsections8.1,8.2and8.3demonstrate,theresultsderivedundertheassumptionthatthe bankfailuresareperfectlycorrelatedalsoapplytoamodelwherethebankfailuresarerealizedas independentevents. 9. Conclusion Inthisstudywehavecomparedtheperformanceofasystemwithlimiteddepositinsurancecoverage to the performance of systems with unlimited or no deposit insurance. In order to achieve this goal, we have developed a stylized model to highlight in a transparent way how a deposit insurancesystemwithlimitedcoverageinducessomeconsumerstodiversifytheirdepositsacross severalbanks. Withinsuchaframework,wedemonstratethatlimiteddepositinsurancecoverage softens competition among banks, thereby introducing a redistribution of income to the banks. Furthermore, we establish that the benefits to banks of limited deposit insurance fall short of the costs to consumers and society when bailout costs are taken into account. Thus, limited deposit insuranceleadstoalossintotalwelfarecomparedwithunlimitedornodepositinsurance. The simple model we have designed abstracts from many important issues, and could therefore,beextendedindifferentdirections. Mostimportantly,weabstractfrommoralhazardissues associatedwiththelendingorinvestmentdecisionsofbanks. Modelsincorporatingmoralhazard associated with banks’ lending/investment activities typically emphasize that deposit insurance offersanoptionvalueforbanksandthatthisoptionvalueismonotonicallyincreasingasafunctionoftheinsurancecoverage. Inourmodelthevaluetothebanksofthedepositinsuranceisvery differentinnature,becauselimitedinsurancecoverageismoreprofitabletobanksthanunlimited insurancecoverage. Further,wedonotformallyaddressthefollowingquestion: Aredepositorsalwaysguaranteed 27

toreceivetheinsuredamountinthecaseofbankfailure? Thisneednotalwaysbethecasebecause theFDICdoesnothavesufficientreservestobailoutallbanks. However,recentexperienceshows thatgovernmentstendtousetaxpayermoneytobailoutbankswhentheinsuranceagency(such as the FDIC) does not have sufficient funds to cover bank losses.13 But, of course, the funding of such bailout programs would cause distortions which would affect welfare evaluations. The welfareanalysiscouldbeextendedtoincorporatethesocialcostsofsuchdistortions. Forreasonsoftractability,wehavefocusedondepositorsdifferentiatedbythecostsassociated withopeninganewaccount,buthomogeneouswithrespecttothevolumeoftheirdeposit($2). A natural extension would be to analyze a deposit market where consumers are differentiated also withrespecttotheiravailablefunds. Thiswouldmakethewelfareanalysismorecomplicatedas some consumers would not be affected by the deposit limit at all, whereas others would benefit fromopeningmultipleaccountsinordertoqualifyforcompletedepositinsurance. Finally,wehaverestrictedourattentiontoanevaluationoflimiteddepositinsurancecoverage bycomparingitwithsystemswithunlimitedornodepositinsurance. Clearly,apromisingdirection for extending our approach would be to characterize the socially optimal deposit insurance coverage. Withsuchanapproachitwouldbepossibletomorefundamentallycharacterizewhich particularfactorsdetermineoptimaldepositinsurancepolicy. Appendix A Existence and Uniqueness of an Equilibrium with Limited Deposit Insurance The derivation of the equilibrium interest rates (19) under limited deposit insurance ignored the possibility that depositors who open a second account may benefit from transferring more than $1(depositinsurancelimit). Thethirdrowsintheutilityfunctions(15)and(16)displaytheutility gainedwhenconsumerstransfer$2andmaintainzerobalancewiththeirinitialaccount. Ourfirstobservationisthatinanysymmetricequilibriumwherebankspaythesameinterest on deposits (so that r = r ), depositors who open a second account transfer exactly $1. This is A B 13SeeaMay28,2013WallStreetJournalarticlebyAlexPollockentitled“DepositsGuaranteedUpto$250,000–Maybe,” whichdiscussesthelegalquestionwhetherFDICinsuredaccountsarebackedbythe“fullfaithandcreditoftheUnited StatesGovernment.” 28

becauseanyotherwayofdistributingthe$2totalamountbetweenthetwobanksdoesnotresult in higher expected interest payment but increases the risk by leaving some amount uninsured. Therefore,toprovethatthederiveddepositrates(19)constituteaNashequilibriumweonlyneed toruleoutadeviationwhere,say,bankB raisesthedepositrateabovetheequilibriumlevel(19) in order to attract type A depositors to transfer $2 to bank B instead of just $1. This appendix showsthatsuchandeviationisnotprofitableforbankB. LetbankA’sdepositrate(rL)begivenby(19). Then,inordertoattracttypeAdepositorswho A openanaccountwithbankB totransfer$2insteadof$1,bankB hastoraiseitsdepositratetor(cid:48) B satisfying 1rL +1r(cid:48) −σs > 1r(cid:48) +(1−φ)1r(cid:48) −φ1−σs. This basically says that the expected A B B B utility captured by the third row in A’s utility function (15) exceeds that captured by the second row. Substituting(19)forrL yields A r +φ (2−φ)(ρ+φ)−2nσ r(cid:48) > r d=ef A = . (A.1) b (cid:98)B 1−φ (1−φ)(2−φ) ForthisdeviationtobeprofitableforbankB,theinterestr paidtodepositorscannotexceed (cid:98)B thereturnρthatbankB makesina$1investment. However,itcanbeshownthat 2nσ ρ > r ifandonlyif ρ > −1, (A.2) (cid:98)B φ(2−φ) whichcontradictsAssumption1. ThiscompletestheproofshowingthatbankB willnotdeviatefromtheequilibriuminterestrate(19). References Bartholdy,Jan,GlennBoyle,andRogerStover.2003. “DepositInsuranceandtheRiskPremiumin BankDepositRates.” JournalofBankingandFinance27(4):699–717. Bouckaert,JanandHansDegryse.2004. “SofteningCompetitionbyInducingSwitchinginCredit Markets.” JournalofIndustrialEconomics52(1):27–52. Demirgu¨c¸-Kunt, Asli and Harry Huizinga. 2004. “Market Discipline and Deposit Insurance.” JournalofMonetaryEconomics51(2):375–399. Diamond, Douglas and Philip Dybvig. 1983. “Bank Runs, Deposit Insurance, and Liquidity.” JournalofPoliticalEconomy91(3):401–419. 29

FDIC.2011. “StudyonCoreDepositsandBrokeredDeposits: SubmittedtoCongresspursuantto theDodd-FrankWallStreetReformandConsumerProtectionAct.”. Garcia,Gillian.2000. “Depositinsurance: actualandgoodpractices.” InternationalMonetaryFund WorkingPaper (197). Gehrig,ThomasandRuneStenbacka.2007. “InformationSharingandLendingMarketCompetitionwithSwitchingCostsandPoaching.” EuropeanEconomicReview51(1):77–99. Gorton,Gary.2010. SlappedbytheInvisibleHand: ThePanicof2007. OxfordUniversityPress. ———.2012. MisunderstandingFinancialCrises: WhyWeDon’tSeeThemComing. OxfordUniversity Press. Hellwig, Martin. 1998. “Banks, Markets, and the Allocation of Risks in an Economy.” Journal of InstitutionalandTheoreticalEconomics154(1):328–345. Keeley, Michael. 1990. “Deposit Insurance, Risk, and Market Power in Banking.” American EconomicReview80(5):1183–1200. Kim, Moshe, DoronKliger, andBentVale.2003. “EstimatingSwitchingCosts: TheCaseofBanking.” JournalofFinancialIntermediation12(1):25–56. Manz,Michael.2009. “TheOptimalLevelofDepositInsuranceCoverage.” FederalReserveBank ofBoston,WorkingPaperNo.09-6. Maskin,EricandJeanTirole.1988.“ATheoryofDynamicOligopoly,II:PriceCompetition,Kinked DemandCurves,andEdgeworthCycles.” Econometrica56(3):571–599. Matutes, Carmen and Xavier Vives. 1996. “Competition for Deposits, Fragility, and Insurance.” JournalofFinancialIntermediation5(2):184–216. ———. 2000. “Imperfect Competition, Risk Taking, and Regulation in Banking.” European EconomicReview44(1):1–34. Merton, Robert. 1978. “On the Cost of Deposit Insurance When There Are Surveillance Costs.” JournalofBusiness51(3):439–452. Penati, Alessandro and Aris Protopapadakis. 1988. “The effect of implicit deposit Insurance on Banks’PortfolioChoicesWithanApplicationtoInternationalOverexposure.” JournalofMonetaryEconomics21(1):107–126. Pennacchi, George. 2006. “Deposit Insurance, Bank Regulation, and Financial System Risks.” JournalofMonetaryEconomics53(1):1–30. 30

———.2009. “DepositInsurance.” Workingpaper,DepartmentofFinance,UniversityofIllinois– Champaign. Piketty,ThomasandEmmanuelSaez.2003. “IncomeInequalityintheUnitedStates,1913–1998.” QuarterlyJournalofEconomics118(1):1–41. Shy, Oz. 2002. “A Quick-and-Easy Method for Estimating Switching Costs.” International Journal ofIndustrialOrganization20(1):71–87. Shy, OzandRuneStenbacka.2004. “MarketStructureandRiskTakingintheBankingIndustry.” JournalofEconomics82(3):249–280. Winton,Andrew.1997. “CompetitionAmongFinancialIntermediariesWhenDiversificationMatters.” JournalofFinancialIntermediation6(4):307–346. Yankov, Vladimir. 2014. “In Search of a Risk-Free Asset.” Available at SSRN: http://ssrn.com/ abstract=2044882. 31

Table1: FDICinsurancelimits1934-present Year Limit(nominal) Limit(real) Fin.wealth(real) Deposits(real) 1934 2,500 40,218 NaN NaN 1935 5,000 78,434 NaN NaN 1950 10,000 89,460 119,581 20,439 1966 15,000 99,497 184,555 37,293 1969 20,000 117,384 194,933 39,321 1974 40,000 174,658 181,028 47,361 1980 100,000 261,263 208,522 49,177 2008 250,000 250,000 370,674 69,176 NOTE:Allrealvaluesarecomputedusingtheconsumerpriceindexforallitemswithbaseyear2008, thefinancialwealthanddepositsaretheaveragerealvaluesperU.S.household. SOURCE: TheFDIC,“ABriefHistoryofDepositInsuranceintheUnitedStates”,FREDdatabase,Census BureauandtheFlowofFunds. Figure1: Thedepositinsurancelimit,averagehouseholdfinancialwealthanddeposits(in2008USD) Deposit insurance limit 500 Average financial assets Average deposits 250 100 40 30 20 1935 1950 19661969 1974 1980 2008 NOTE:Allrealvaluesarecomputedusingtheconsumerpriceindexforallitemswithbaseyear2008, thefinancialwealthanddepositsaretheaveragerealvaluesperU.S.household. SOURCE: FDIC, “A Brief History of Deposit Insurance in the United States”, FRED database, Census BureauandtheFlowofFunds 32

Figure2: Theinter-quartilerangeofaveragepartially-insureddepositaccountbalances1986–2006 4 3.5 3 2.5 2 1.5 1 Interquartile P(25)/P(75) Median Jan86 Jan88 Jan90 Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 NOTE: Thefigureplotstheinter-quartilerangeofthepartiallyinsureddepositaccountbalancesasa fractionoftheinsurancelimitof$100,000fortheperiod1986Q2to2006Q1. Theaverageaccountbalance foreachbankiscomputedasthetotalamountofdepositaccountsexceeding$100,000(itemrcon2710) dividedbythenumberofsuchaccounts(itemrcon2722). SOURCE: ReportsonIncomeandCondition(CallReports) 33

Figure3: Empiricalcumulativedensityofaverageaccountbalancesheldindepositaccountsexceeding$ 100,000in2008Q2 1 0.9 0.8 0.7 0.6 57.9 % of accounts below $ 250,000 0.5 ← $ 235,000 median account balance 0.4 0.3 0.2 0.1 0 100 150 200 250 300 350 400 450 500 Average account balance in thousands NOTE: The figure plots the empirical cumulative density function of the average deposit account balancefordepositaccountsexceeding$100,000reportedbyallFDICinsuredUScommercialbanksin 2008Q2. The variable is constructed from the Call Reports as the ratio of the total deposit amount in accountsexceeding$100,000(itemrconf051)tothenumberofsuchaccounts(itemrconf052).Ascompared toFigure2,hereweusethereviseditemsintheCallreports–itemrconf051replaceditemrcon2710and itemrconf052replaceditemrcon2722in2006.ThesenewreportingitemsontheCallreportsalsoreflected thechangeintheFDIClimit.TheFDIClimitwasraisedto$250,000onOctober3,2008. SOURCE: ReportsonIncomeandCondition(CallReports) 34

Figure4: Shareofinsuredbrokereddeposits Shareofinsuredbrokereddeposits 0.9 Smallbanks:below75pctile Mediumlargebanks:75-99pctile 0.8 Largebanks:Top99pctile 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Jul82 Jan85 Jul87 Jan90 Jul92 Jan95 Jul97 Jan00 Jul02 Jan05 Jul07 Jan10 Jul12 NOTE:Computedastheratiooftotalinsuredbrokereddeposits(itemrcon2343)andthetotalamount ofbrokereddeposits(itemrcon2365). SOURCE: TheReportsonIncomeandCondition(CallReports) 35

Figure5: NumberofCDcontractsandnumberofinstitutions )01 dedoc pot( stnuocca DC :snoitutitsni fo rebmuN 01 8 6 4 2 0 0 5 10 15 20 Number of CD contracts (top coded at 20) Total deposit amount at banks: 100K − 1 mln more than 1 mln NOTE: Households in the 2007 Survey of Consumer Finances (SCF) with total deposits exceeding thedepositinsurancelimitof$100,000aregroupedintwogroups-thefirstgrouparehouseholdswith depositwealthbetween$100,000and$1,000,000,thesecondgrouparehouseholdswithdepositwealth exceeding$1,000,000. Thescatterplotdepictsthenumberofcertificateofdeposit(CD)contractsagainst thenumberofFDICinsuredcommercialbanksthesecontractsareheldwithforthetwogroupsofhouseholds. The relative size of the marker corresponds to the size of the fraction of households with the particulardepositwealthallocationforthetwogroups. ThenumberofCDcontractsandthenumberof institutionsinthepubliclyavailableversionoftheSCFaretopcodedat20and10,respectively. SOURCE: SurveyofConsumerFinances,2007 Figure6: Division of type i ∈ {A,B} depositors between those who open and do not open a new bank account. (cid:45) s 0 Openasecondbankaccount s i Donot n 36

Figure7: Division of type A (top) and type B (bottom) depositors between those who open and do not openasecondbankaccount. (cid:45) s 0 PrimarybankaccountA($1) s A BankAonly($2) n SecondarybankaccountB ($1) (cid:45) s 0 PrimarybankaccountB ($1) s B BankB only($2) n SecondarybankaccountA($1) 37

.ecnarusnitisopedfosemigereerhtfosnoitcnufsatsoctuoliabecnarusnitisopeddna,tfiorp’sknab,eraflewremusnoC :8erugiF 0.2 )wc( eraflew remusnoC )r( setar tisopeD 5.1 ) p+ p( tiforp yrtsudni gniknaB B A )id( tsoc tuoliab ecnarusni tisopeD 0.1 5.0 0.0 detimilnU detimiL enoN emiger ecnarusni tisopeD -libaborperuliaf’sknab,70.1 = ρtnemtsevnis’knabnonruteR :seulavretemarapgniwollofehtnodesaberasnoitalumiS :ETON .5.0 = nknabhcaehtiwsrotisopedfoerusaemlaitinidna,2.0 = σretemaraptsoc,50.0 = φyti 38