Rune Stenbacka Tuomas Takalo. Switching costs and financial stability

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1 Rune Stenbacka Tuomas Takalo Switching costs and financial stability ank of Finland Reseach Discussion Pape 06

2 SWITCING COSTS ND FINNCIL STILITY* Rune Stenbacka** Tuomas Takalo*** 4 Januay 06 We establish that the effect of intensified deposit maket competition measued by educed switching costs on the pobability of bank failues depends citically on whethe we focus on competition with established custome elationships o competition fo the fomation of such elationships. With inheited custome elationships intensified competition i.e. lowe switching costs destabilizes the banking maket wheeas it stabilizes the banking maket if we shift ou focus to competition fo the fomation of custome elationships. These findings imply that the popotion between new and locked-in depositos is decisively impotant when detemining whethe intensified competition destabilizes the banking maket o not. KEYWORDS: Deposit maket competition financial stability bank failues switching cost competition vesus stability tadeoff JEL: G; D43 *We ae gateful to Iftekha asan Esa Jokivuolle Diego Moeno Oz Shy and Otto Toivanen fo valuable discussions. **anken School of Economics P.O. ox elsinki Finland. Rune.Stenbacka@hanken.fi *** anken School of Economics P.O. ox elsinki Finland. Tuomas.Takalo@hanken.fi

3 . Intoduction Since the 990 s a spectum of influential studies compising theoetical policy-oiented as well as empiical ones has focused on the fundamental question of whethe thee is a tadeoff between competition and stability in banking see Caletti and atmann 003 fo a liteatue suvey and llen and Gale 004 fo a synthesis of vaious theoies. In this study we will e-addess this issue by applying a two-peiod switching cost model designed to chaacteize the effects of intensified competition in the deposit maket on the pobability of bank failues. Such a switching cost appoach to assess the elationship between competition and financial stability in banking is justified in light of convincing empiical evidence accoding to which switching costs ae a significant souce of maket powe in banking fo example Shy 00 Stango 00 and Kim et al 003. In the pesent study we demonstate that the effect of intensified deposit maket competition on the pobability of bank failues depends citically on whethe we focus on competition with established custome elationships o competition fo the fomation of such elationships. With inheited custome elationships intensified competition in the deposit maket destabilizes the banking maket wheeas it stabilizes the banking maket if we shift ou focus to the stage at which banks compete fo the fomation of custome elationships. Thus the popotion of new unattached depositos elative to the locked-in depositos is a decisively impotant facto when detemining whethe intensified competition tends to destabilize the banking maket o not. In his influential study Keeley 990 fomalizes the idea that inceased maket powe will educe the isk-taking incentives of banks. Though this mechanism thee will be a tadeoff between competition and stability in the sense that intensified competition will pomote fagility of the banking maket. oyd and De Nicolo 00 highlight the ole of banks as intemediaies lending to entepeneus with incentives of thei own implying that the etun distibutions of the banks ae endogenous. y incopoating such a modification oyd Keeley 990 efes to maket powe as the chate o fanchise value of banks.

4 and De Nicolo 00 find that intensified lending maket competition induces moe stable banking makets. Matinez-Miea and Repullo 00 extend the appoach developed by oyd and De Nicolo 00 by taking into account that a lowe lending ate does not only incease the pobability that a boowe can meet the debt obligation but it also educes the bank s etuns fom pefoming loans. Taking that effect into account Matinez-Miea and Repullo 00 show that thee will be a non-monotonic U-shaped elationship between competition and the isk of bank failues. To the best of ou knowledge thee ae no pevious studies that would have exploed the theoetical mechanisms undelying the elationship between switching costs and banking maket stability. own et al. 04 document how inceased switching costs slowed down withdawals fom two lage distessed banks in Switzeland in the financial cisis of Such a esult appeas to povide suppot fo asel III liquidity egulations that allow banks with stickie deposits to hold less liquidity. oweve one key contibution of ou study is to show that switching costs also have stability implications fom an ex ante pespective when banks compete fo deposits. Theefoe asel lll liquidity egulations emphasizing tighte deposito elationships as a stability-pomoting featue of bank funding may be patially misleading: While stickie deposits cetainly constitute a moe stable souce of funding fo banks they may not necessaily be conducive fo bank stability fom an ex ante pespective. Futhemoe ou esults suggest that policy poposals such as bank account numbe potability see e.g FC 0 with the aim of pomoting competition in the banking industy by loweing deposito switching costs should be assessed fom the point of view of stability. Policy discussions egading financial stability ae closely linked to views egading the elationship between competition and financial fagility. Fo example the adoption and design of capital equiements build on the idea that such equiements discipline the isktaking incentives of banks. ut as Repullo 004 emphasizes to the extent that capital egulation educes fanchising values of banks it may also pomote isk-taking in line with Koskela and Stenbacka 000 each a simila esult - the absence of a tadeoff between lending maket competition and financial stability - in thei analysis with endogenous lending volumes.

5 Keeley s hypothesis theeby discouaging banking stability. Thus the design of an optimal policy with espect to capital equiements depends fundamentally on the elationship between competition and stability in paticula with banking makets chaacteized by impefect competition. The banking industy typically opeates within the famewok of an institutional and legal envionment such that stability concens ae addessed by financial supevisoy authoities often linked to the cental banks wheeas competition concens ae dealt with by the competition authoities. These authoities typically opeate vey independently fom each othe. oweve the existence of a potential systematic elationship between competition and stability leads Vickes 00 to ask whethe it is optimal that stability policies ae conducted independently of competition policy as fa as the banking industy is concened 3. s Vickes 00 points out fo example duing the financial cisis stability concens induced the Euopean Commission to suppot the banking industy in ways which wee hadly consistent with established Euopean competition policy egading state aid. Ou study poceeds as follows. In Section we descibe the two-peiod model of deposit maket competition with switching costs. Section 3 chaacteizes the peiod- deposit ate equilibium and exploes its popeties as fa as the implications fo banking stability ae concened. Section 4 conducts a simila analysis at the stage when banking elationships ae fomed. Section offes discussions egading impotant modelling featues. In Section 6 we pesent concluding comments. Fomal mathematical poofs can be found in the ppendix.. Deposit Maket Competition with Switching Costs: The Famewok We conside a isk-neutal economy with two banks and a continuum of depositos and thee dates t0. The banks apply the discount facto [ 0] pe peiod. Each deposito has one unit of capital at t0 and access to an outside investment oppotunity with a ate of etun nomalized to zeo. The banks compete fo deposits at t0 and t by offeing standad one-peiod deposit contacts that amount to a pomise to pay a fixed inteest 3 Simila issues have been aised by fo example eck 008 and eck et al 00. 3

6 ate at t on the deposito s unit of capital. Fo simplicity we assume that deposits ae fully insued. 4 s a esult the volume of deposits offeed to a bank depends only on the banks deposit ates. Retail deposits also constitute the only souce of funds fo the banks in ou model. The banks have exclusive access to a one-peiod stochastic investment technology meaning that the banks investment pojects mateialize each peiod. Moe pecisely we assume that the investment activities of bank i i at date t yields a goss etun of i easons of tactability we assume that ~ [ 0 ] distibuted on the inteval [ ] U at date t. Fo i t t i.i.d. In wods the etuns ae unifomly 0 and they ae identically and independently distibuted ove time and acoss the competing banks. Wheeas we take the banks investments as exogenous the banks influence thei isks and in paticula the pobabilities of bank failues via thei choices of deposit inteest ates. Stochastic etuns associated with the investment activities may ende the value of a bank s assets smalle than the value of its deposit liabilities both at t and t. In such a case the bank becomes insolvent. bank that is insolvent at t is not allowed to accumulate deposits and paticipate in the competition fo date- pofits. If the bank suvives it meets the contactual obligation to its depositos. Futhe fo simplicity we assume that at t a suviving bank distibutes all the pofits to its ownes and depositos consume the inteest ate eaned fom date-0 deposits. s a esult the deposit makets ae subject to identical capital endowments of banks and depositos at t0 and t. t t0 banks compete fo depositos who ae ex ante identical and competition is intense at this stage as thee ae no established competition baies. Deposit maket competition at t is constained by the pesence of switching costs fo the depositos. Such switching costs seve as a souce of maket powe fo banks. The pesence of switching costs is often consideed to be a typical featue of banking makets. Fo example the evidence pesented in Shy 00 Stango 4 s we focus on competition fo etail deposits ou assumption of complete deposit insuance seems to be a sufficiently good epesentation of the banking industy. Cuently deposit insuance coveage is limited to in the Euopean Union and to $0 000 in the United States. oweve in most counties no limits ae placed on the numbe of potected accounts held with diffeent banks. Shy et al 0 exploe the effects of limited deposit insuance coveage on the intensity of deposit maket competition on consume welfae and on total welfae. 4

7 00 and Kim et al 003 suggests that banking makets ae chaacteized by significant switching costs and that these costs ae diffeentiated acoss customes. Futhe own et al 04 pesent evidence fo how switching costs may limit etail deposit withdawal even when banks face distess. Fomally the switching costs of a deposito indexed by s ae captued by c s s whee s is unifomly distibuted on the unit inteval [ 0 ]. We can attach two diffeent intepetations to the paamete. One intepetation is that the paamete captues the expected magnitude of the switching costs facing all depositos. ltenatively we could view as a measue of the heteogeneity of the switching costs acoss all depositos. In the pesent analysis we will not sepaate between the expected magnitude and the dispesion of the switching costs. We will simply efe to as a measue of the magnitude of the switching costs. In sum in the deposit maket banks compete at t0 fo unattached depositos by pomising to pay a goss inteest ate i i fo each unit of capital deposited at t. Contingent on the custome elationships fomed at t0 the banks compete again at t by offeing deposit ates i. We assume that the banks compete in unifom deposit ates which ae the same fo all depositos iespective of thei custome histoies. 6 Nonetheless we epeat that deposit ate It would be possible to sepaate the effects associated with the expected switching costs fom those associated with the dispesion by assuming that the switching costs ae distibuted on an inteval [ θ ω θ ω] such that θ measues the mean and ω measues the dispesion. oweve such an extension would take place at the expense of tanspaency of the pesentation as it would incease the numbe of model paametes. 6 The analysis could be conducted by focusing on histoy-based deposit ates such that each bank sepaates the deposit ates offeed to thei existing customes fom the poaching ates offeed to thei ival s customes. That would incease the numbe of elevant deposit ates offeed at t fom two to fou. Gehig and Stenbacka 007 analyze that type of histoy-based picing in thei study of infomation exchange in the lending maket. oweve histoy-based picing seems to play a bigge ole in the lending maket than in the deposit maket because factos such as asymmetic infomation egading boowes chaacteistics and the ability of banks to lean about the ceditwothiness of thei own customes povide a stong eason the application of histoybased lending ates.

8 competition at t is subject to bank maket powe geneated by the switching costs as well as to the switching option on behalf of the depositos. We analyze the model by poceeding backwads. We fist detemine the deposit maket equilibium at t conditional on the custome elationships inheited fom t0. The equilibium deposit ates detemine the pobability that a bank fails at t. Subsequently we chaacteize the date-0 deposit maket competition which detemine the failue pobabilities as well as the maket shaes of banks at t. 3. Deposit Rate Competition at t t t depositos choose whethe they continue the banking elationship established at t0 i.e. keep thei unit of capital in the same bank as they chose at t0 o whethe they tansfe thei unit of capital to the ival bank. We let µ 0 µ denote the maket shae inheited by bank fom t0 meaning that bank entes into date- competition with a maket shae of µ. Conside a deposito having an inheited custome elationship with bank. If bank offes the deposit ate and bank offes a custome with switching costs ŝ satisfying the condition sˆ / is indiffeent between staying loyal to bank and switching to bank. Clealy customes belonging to bank s inheited maket segment stay loyal if they have sufficiently high switching costs. Fomally bank s customes stay loyal if thei switching costs s satisfy the condition s sˆ wheeas they switch to bank if s ˆ < s. nalogously sˆ / is the switching theshold fo bank s depositos. We poceed unde the assumption that the switching thesholds s s ˆ ˆ belong to the unit inteval and late confim that the assumption is fulfilled in equilibium. ank detemines its deposit ate in ode to solve the following poblem max π µ µ sˆ d sˆ d. a 6

9 In the ight-hand side of a the fist tem captues the incumbency pofits that bank makes on its loyal customes wheeas the second tem measues the poaching pofits associated with depositos who switch fom bank. Futhe the deposit ate is the beakeven state of etun at which the pofit fom the investment activities matches the bank s costs of funds i.e. the deposit ate. If the ealized etun fom the bank s investment potfolio falls shot of the theshold etun the bank becomes insolvent. In that case the bank s depositos get the ealized and will be eimbused by the deposit insuance fo the emaining pat y limited liability the bank s shaeholdes get zeo. 7 nalogously to a bank sets its deposit ate to solve. max µ µ π s d s d ˆ ˆ. b y solving the optimization poblems a and b we ae able to epot the following poposition which is fomulated conditional on the assumption that banks and have inheited the maket shaes µ and µ espectively. Poposition a With inheited custome elationships the equilibium deposit ates ae given by µ 3µ. b The peiod- equilibium pofits ae given by π µ 3 µ 3 3 π. 3 7 y adjusting the pofit functions of the banks ou model could be extended to incopoate equity. Focing the bank to hold equity as a capital buffe would shift the insolvency theshold downwads but it would not qualitatively affect the esults insofa as the theshold would be an inceasing function of the peiod- deposit ates. 7

10 Fo the poof of Poposition we efe to the ppendix. The switching cost paamete can be viewed as a measue of the intensity of deposit maket competition as a highe value of endows the banks with stonge maket powe. With this intepetation the equilibium deposit ates fomalize the intuitive view that intensified competition meaning a lowe value of induces banks to offe highe deposit ates. Futhemoe Poposition a demonstates that the peiod- deposit ates would be asymmetic if the banks inheited diffeent maket shaes fom the pevious peiod. Nevetheless identical maket shaes µ in peiod would imply a symmetic deposit ate equilibium in peiod. Fom Poposition we can also conclude that an incease in the paamete intensifies deposit ate competition theeby aising the peiod- deposit ates. Consistent with this popety an incease in the paamete educes the equilibium pofits in peiod as fomally shown by 3. s the deposit ates define the costs of funds fo the banks ou model has immediate implications fo financial stability. Since the pobability that a bank fails in peiod is given by i / the equilibium deposit ates immediately yield the following conclusion egading financial stability in peiod. Poposition With inheited custome elationships intensified competition in the deposit maket destabilizes the banking maket by inceasing the pobability of bank failues. In light of Poposition with inheited custome elationships thee is a tadeoff between competition and stability. The qualitative featues of this esult esemble the classic esult obtained by Keeley

11 We will next shift ou attention to deposit maket competition at the stage when the custome elationships ae fomed. In paticula we exploe the effects of intensified competition at that stage on the stability of the banking secto. 4. Deposit Rate Competition at t0 The banks decide on the date-0 deposit ates in ode to maximize the discounted sum of the pofits accumulating ove the two-peiod hoizon. t t0 the banks compete fo unattached depositos and we denote the maket shae acquied by bank as µ wheeas the maket shae of bank is µ. Clealy the maket shaes µ and µ ae detemined by the peiod- deposit ates. Regading the mode of peiod- competition we assume that µ g with g>0 and g / / µ. These popeties captue the idea that the demand fo deposits of a bank is inceasing its own deposit inteest ate and deceasing in the ival s ate. Thus the paamete g measues the sensitivity of a bank s maket shae in peiod to an incease in its deposit ate at date t0. Fo the moment we conside g to be exogenous. oweve if depositos wee fully fowadlooking it would be plausible to think that changes in would affect g. We will exploe this paticula featue in geate detail in Section. whee we also pesent an explicit example of peiod- competition allowing g to depend on the paametes of the model. ank detemines its deposit ate at t0 in ode to maximize the discounted value of the twopeiod pofits accoding to max µ d π Π 4 whee π is bank s equilibium pofit in peiod as chaacteized in 3. s 3 shows depends on µ and theeby on π. The fist tem in 4 denotes the pofit of bank at t unde cicumstances whee the ealization of the bank s investment potfolio is sufficiently successful so that it can meet its debt obligations to its depositos. The second tem captues the expected 9

12 discounted value of the peiod- pofit when also taking into account that the deposit ate chosen by bank at t0 affects its insolvency isk at t. Fomally the facto / denotes the pobability that bank suvives so that it can compete fo peiod- pofits. ank detemines its peiod-0 deposit ate in an analogous way. The last tem of the objective function 4 fomalizes the featue that a failed bank is eplaced by a new bank so that the stuctue of the banking maket emains stable. This could captue fo example a configuation whee the opeation of a failing bank is taken ove by a foeign bank fo which this takeove facilitates maket enty. simila fomalization has been adopted in fo example ellmann et al. 000 yytinen and Takalo 00 and Repullo 004. We discuss the implications of this simplifying assumption togethe with altenative fomalizations in Section.. In the ppendix we pove the following esult: Poposition 3 t the stage whee banks compete fo the fomation of custome elationships the equilibium deposit ates ae given by i G i 4 whee 3 and G. g g The equilibium deposit ates given by equation imply that the pobability of a bank failue at t is given by i G. 6 4 We next use 6 in ode to exploe the effects of competition as measued by and the discount facto on financial stability. We can fomulate the following findings: 0

13 Poposition 4 t the stage when banks compete fo the fomation of custome elationships a intensified competition in the deposit maket deceases the pobability of a bank failue b a highe discount facto inceases the pobability of a bank failue. Fo the poof of Poposition 4 we efe to the ppendix. ccoding to Poposition 4 a at the stage when custome elationships ae fomed intensified competition measued as a eduction in the switching cost paamete of depositos stabilizes the banking makets. The eason is that a lowe switching cost paamete educes the value of a custome elationship theeby educing the incentives fo banks to offe high deposit ates in ode to acquie customes. This mechanism lowes the investment etun theshold above which banks stay solvent meaning that the pobability of a bank failue is educed. In light of Popositions and 4a we can conclude that the effect of intensified competition on banking maket stability depend citically on whethe we focus on competition with established banking elationships o competition fo the fomation of such elationships. In the pesence of new unattached depositos as well as locked-in depositos the elative popotions of these diffeent custome categoies would detemine whethe competition with established custome elationships o competition fo the fomation of such elationships is the dominant mode of competition theeby detemining whethe intensified competition tends to destabilize the banking maket o not. Fo example ou model pedicts that intensified competition pomotes financial stability in an emeging economy with a gowing deposito base wheeas the effect of competition on stability would be evese in developed counties with matue banking makets. Keeley s 990 well-established agument egading the detimental effect of competition on stability aises because stonge maket powe implies highe bank chate values which induces banks to educe thei isk taking. In line with Keeley Poposition 4 a suggests that

14 intensified competition measued as a decease in the switching cost paamete dilutes the chate value. In ou model howeve the esult is elaxed competition at the stage when custome elationships ae fomed and theeby a moe stable banking maket. This insight is confimed by Result 4 b which shows the effect of the discount facto on bank stability. In geneal a highe discount facto enhances the weight of futue pofits in banks decision making. In ou model this featue geneates two opposing effects. Thee is the standad chate value effect which inceases the banks willingness to avoid insolvency at t theeby making competition fo depositos at t0 less aggessive. oweve in ou model a highe discount facto also induces banks to invest moe in ode to acquie locked-in customes who can be exploited in the second peiod. high deposit ate at t0 is the mechanism fo the acquisition of such customes. Poposition 4 b suggests that the latte effect dominates ove the fome effect. s a esult a highe discount facto inceases the initial deposit ates destabilizing the banking maket at the intemediate stage. In paticula we can immediately obseve fom 6 that when 0 the pobability of a bank failue at t is i g / / and positive discount factos aise this failue pobability monotonically.. Extensions With the intention to highlight the effects of switching costs on bank stability in a tanspaent way a numbe of impotant featues ae outside of ou model. In this section we will comment on and biefly analyse some selected issues of obustness. Futue eseach should addess these issues in geate detail.. Fowad-looking Depositos So fa we have assumed that the effect of a bank s deposit inteest ate on the bank s maket shae at t0 is given by the positive constant g. This assumption common in the liteatue captues the simplified view accoding to which depositos ae myopic in the sense that thei eaction to a bank s inteest ate change is invaiant to a change in the switching costs o in

15 the depositos discount facto. With fully fowad-looking depositos one would expect that µ / < 0. This fomalizes the plausible featue that highe switching costs ende a bank s maket shae less sensitive to its own deposit ate at t0 because depositos ealize that the bank will have highe maket powe in setting its deposit ate at t. Similaly we would expect that µ > 0 i.e. that highe switching costs ende a bank s maket shae less / sensitive to the ival s deposit ate at t0. It would theefoe be a plausible hypothesis that g would be a deceasing function of. n analogous agument applies to the elationship between g and. Moe pecisely if depositos become moe patient they will place a highe weight on the bank s maket powe at t when they select a bank at t0. Fomally we would expect that the paamete g to depend on as well as on g in such a way that g / < 0 and g / < 0. llowing g to be a deceasing function of and would leave the qualitative popeties of ou basic analysis and Popositions -3 intact but with this genealization the equilibium deposit ate in peiod is given in implicit fom. This means that the analysis of the effects of switching costs and the discount facto on bank stability at t is moe complex since and have an additional effect on the equilibium failue pobability / via g. In paticula if g is a deceasing function of and banks have weake incentives to aise inteest ates t0 to acquie locked-in customes. ence inceases in and ae less detimental to bank stability at t than in the case analysed in Section 4 whee g is independent of and. i Fo bevity ou fomal analysis hee focuses on as the analysis concening would be qualitatively identical. Let us denote the elasticity of g by ε i.e. ε g' / g. In the ppendix we pove the following esult: Poposition If the elasticity with espect to the switching cost paamete of the bank s sensitivity to the peiod- deposit ates is sufficiently small i.e. if ε is sufficiently small intensified competition at the stage whee custome elationships ae fomed deceases the pobability of a bank failue. 3

16 Poposition genealizes Poposition 4a to the case whee depositos ae fully fowad-looking. We can conclude that the genealization is valid wheneve the elasticity with espect to the switching cost paamete of depositos eaction to the peiod- deposit ates is limited. Condition 6 in the ppendix chaacteizes mathematically the theshold fo the elasticity. s long as the elasticity is below this theshold intensified competition fo new depositos will stabilize the banking secto. Futhemoe the ppendix veifies that Poposition 4a always holds tue if it wee the case that an inceased switching cost paamete would make depositos moe sensitive to the peiod- deposit ates i.e. g / > 0. Poposition 4b can be extended based on analogous aguments... Example In ode to illustate the effects of allowing dependence g to depend on and we conside the well-known otelling model of competition between the two hoizontally diffeentiated banks. Following the standad otelling model we assume that depositos ae unifomly distibuted on the unit inteval and that the banks ae located at the opposite ends of this inteval. ssuming that the paamete τ > 0 captues the deposito s tavel costs i.e. the deposito s disutility of using sevices of an existing bank athe than the deposito s ideal combination of sevices we show in the ppendix that with otelling competition g is given by g. 7 τ Fom 7 we can conclude that g / τ < 0 and g / τ < 0 meaning that g is a deceasing function of and theeby veifying ou conjectues above about the plausible elationship between g and and. The equilibium deposit ates as well as the associated implications fo financial stability can now be chaacteized by substituting 7 into and 6 keeping in mind that with a symmetic equilibium µ /. 4

17 .. ank Failues and Maket Stuctue s we mentioned when commenting on 4 ou model does not incopoate any stategic incentives associated with the potential effects of a bank failue on maket stuctue. ctually ou model shaes this featue with many influential models focusing on the effects of capital egulation on isk taking fo example ellman et al 000 and Repullo 004. n altenative modelling appoach taking the stategic incentives associated with maket stuctue effects into account would be to modify 4 in the following way. The discounted value of bank s suvival pofits in 4 could be decomposed into two tems: a component with duopoly pofit ealized with the pobability that both banks suvive / and a component with monopoly pofit ealized with the pobability that bank is the only suviving bank. Such an appoach would captue a configuation whee the / assets of a failed bank ae sold o tansfomed to the suviving ival. Peotti and Suaez 00 analyse the effects fo isk-taking behavio associated with the maket stuctue effect i.e. the featue that the numbe of banks decease in esponse to a maket failue. 8 Futhe chaya and Youlmaze exploe how the option fo suviving banks to take ove failing banks may affect potential time-consistency poblems associated with bank closue policies. 6. Concluding Comments This study has analytically established that the effect of intensified deposit maket competition measued by educed switching costs on the pobability of bank failues depends citically on whethe we focus on competition with established custome elationships o competition fo the fomation of such elationships. With inheited custome elationships intensified deposit maket competition destabilizes the banking maket wheeas it stabilizes the banking maket if we shift ou focus to the stage at which banks compete fo the fomation of custome elationships. These findings imply that the popotion of new 8 lso llen et al 0 exploe this maket stuctue effect within the famewok of a two-peiod duopoly model of stakeholde govenance.

18 unattached depositos elative to the locked-in depositos is a decisively impotant facto when detemining whethe intensified competition tends to destabilize the banking maket o not. In its attempt to highlight the mechanism ceated by switching costs as a geneato of a elationship between the intensity of competition and financial stability in banking makets ou model has abstacted fom a numbe of impotant factos that should be incopoated in a futue analysis. Fo example we have chaacteized the etun distibutions associated the banks investments lending activities as an exogenous featue of ou model. oweve it is likely that changes in switching costs affect the banks lending and investment decisions in ways eminding of the effects of changes in vaious egulatoy policies see e.g. ellman et al. 000 and Repullo 004 fo the effects of capital equiements and Moeno and Takalo 0 fo the effects of tanspaency egulation on banks asset isk taking. Likewise Matutes and Vives 000 show how impefect competition in the deposit maket togethe with limited liability and deposit insuance affects the banks asset isk-taking incentives. Ou model could be modified to analyse the effects of foeign enty in configuations whee all depositos belong to the inheited maket segment of the incumbent bank. Ealie studies see e.g. Sengupta 007 have highlighted the benefits of foeign enty in banking makets. oweve if the domestic bank s depositos face switching costs inceased competition via foeign enty would not only lead to highe deposit ates but potentially also to less stable banking maket in line with the casual evidence fom fo example the effects of coss-bode enty of Icelandic banks in vaious makets in the ealy yeas of the 000s. Futhemoe as emphasized by asel III liquidity egulations and the findings in own et al. 04 tighte deposito elationships consistent with highe switching cost baies ae likely to make depositos ceteis paibus less likely to un on a bank in a cisis. To make a compehensive evaluation of the stability implications of switching costs one should build a bank un model with multiple banks whee depositos can switch deposits fom one bank to anothe see e.g. Chen and asan 006 fo a contibution in this diection. 6

19 7 ppendix Poof of Poposition : y substitution of s ˆ and s ˆ into a and b we see the objective functions can be ewitten accoding to max d µ µ π a. max d µ µ π b The objective functions a and b imply the eaction functions 0 d µ π a 0 d µ π. b Solving the system of equations defined by a and b yields the equilibium deposit ates 3 µ µ as given by. Substitution of the equilibium deposit ates back into the objective functions yields the equilibium pofits µ π µ π which ae epoted in 3. These equilibium pofits can also be witten as π π. QED

20 Poof of Poposition 3: y applying Leibniz s ule when diffeentiating 4 we find that bank s eaction function is given by µ µ µ π µ π µ 0. 3 Substitution of 3 fo the second-peiod pofits imposing symmety µ / and defining x the fist-ode condition 3 can be simplified accoding to x x G 0 4 whee we have intoduced the notation that / g 3 / and G /g. Thee ae two solutions to equation 4. ut as we can ignoe the negative oot the unique equilibium peiod- deposit ate is given by x / / 4 G which is equivalent to the peiod- deposit ate epoted in Poposition 3. This solution to equation 4 satisfies the sufficient second-ode condition because the second-ode deivate of bank s pofit function is - g x g 0 when evaluated in a < neighbohood of the solution to 4. QED Poof of Poposition 4: a y diffeentiation of 6 with espect to we find that i F 4 G whee and G ae defined in Poposition 3 and whee we have intoduced the F / 4 G G. y investigation notation / of F we find that F < 0 if and only if / 4 G > /6g /. 8

21 9 Staightfowad calculations veify that the last inequality holds tue fo all values of. Theefoe we can conclude that 0 4 > F G i meaning that elaxed competition inceases the pobability of a bank failue. b nalogously to pat a by diffeentiation of 6 with espect to we find that 4 D G i whee we have defined D accoding to / 4 / G G D. We find that 0 < D if and only if / /6 4 / g G > which holds tue fo all values of. Consequently we each the conclusion that 0 4 > D G i meaning that a highe discount facto inceases the pobability of bank bankuptcy. QED Poof of Poposition : ssume that g is a function of. Fom the poof of Poposition 4 we have that the sign of / / i is given by the sign of F whee 4 G G F

22 0 as befoe. We want to chaacteize the cicumstances when 0 F. Let us suppess the agument fo bevity in what follows. Compaed with the poof of Poposition 4 the diffeence is that now 6 ε R g g and ε g R G whee we have defined. / R fte substitution of these fomulas fo and G in F and some algeba we get that the sign of F is given by the sign of 4 ε R G whee > G g R. That 0 > is the essence of the poof of Poposition 4. Since also 0 > R g R it is immediate fom that 0 F if. 4 ε R G 6

23 Clealy this condition holds as a stict inequality if ε 0. y continuity it also holds if ε < 0 but small. QED The Details associated with Example of Section..: Let us conside the well-known model of competition between the two hoizontally diffeentiated banks. ssume that depositos ae unifomly distibuted on the unit inteval and that the two banks and ae located at the opposite ends of this inteval. Conside a x 0 on the unit line. If she deposits at bank located at the deposito with an addess [ ] 0-end of the unit line at t0 he payoff is given by u x τ x 7 µ whee the paamete τ > 0 as mentioned in Section. denotes the deposito s tavel costs and u is the deposito s utility at t when she has an inheited custome elationship µ with bank which has a maket shae µ. In light of this utility is given by u µ µ µ. 8 Note that we assume fo simplicity that switching a bank at t involves no explicit tavel costs. n intepetation is that tavel cost paamete τ eflects the intensity of competition ex ante at t0 and the switching cost paamete captues the intensity of competition ex post at t. We may also think that potential tavel costs at t ae embodied in the switching costs. nalogously if at t0 the deposito located at x chooses bank located at the -end of the unit line he utility is given by whee afte using we have u x τ x u 9 µ

24 u µ µ µ. 0 s usually we assume that the configuation of paametes is such that the maket is fully coveed e.g τ is sufficiently small. Then the equation ~ u x u ~ x defines the location ~ x [ 0 ] of a consume who is indiffeent between whethe to deposit in bank o bank at t0. Fom the well-known natue of the otelling model the maket shaes ae diectly detemined by the location of this indiffeent consume. Making use of 7-0 we find that the equilibium maket shaes ae given by ~ x µ. τ In tems of ou model this diectly implies that which is equation 7 of the main text. µ g τ Refeences chaya V. and T. Youlmaze Too Many to Fail n nalysis of Time-inconsistency in ank Closue Policies. Jounal of Financial Intemediation 6: -3. chaya V. and T. Youlmaze Cash-in the-maket Picing and Optimal Resolution of ank Failues. The Review of Financial Studies : llen F. E. Caletti and R. Maquez. 0. Stakeholde Govenance Competition and Fim Value. Review of Finance 9: llen F. and D. Gale Competition and Financial Stability. Jounal of Money Cedit and anking 36:

25 eck T ank Competition and Financial Stability: Fiends o Foes? Wold ank Policy Reseach Pape 466. eck T. D. Coyle M. Dewatipont X. Feixas and P. Seabight. 00. ailing Out the anks: Reconciling Stability and Competition. CEPR Repot. oyd J. and G. De Nicolo. 00. The Theoy of ank Risk-Taking and Competition Revisited. Jounal of Finance 60: oyd J. G. De Nicolo and. Jalal The Theoy of ank Risk-Taking and Competition Revisited: New Theoy and New Evidence. IMF Woking Pape WP/06/97. own M.. Guin and S. Mokoette. 04. Deposit Withdawals fo Distessed Commecial anks. Woking Pape Univesity of St.Gallen. Caletti E. and P. atmann Competition and Stability: What s Special about anking? In: Mizen P. ed Monetay istoy Exchange Rates and Financial Makets: Essays in onou of Chales Goodhat. Edwad Elga. Chen Y. and I. asan Tanspaency of the anking System and the Efficiency of Infomation-based ank Runs. Jounal of Financial Intemediation : Financial Conduct uthoity FC. 0. Making Cuent ccount Switching Easie: The Effectiveness of the Cuent ccount Switch Sevice CSS and Evidence fom ccount Numbe Potability. FC Repot Mach 0 Gehig T. and R. Stenbacka Infomation Shaing and Lending Maket Competition with Switching Costs and Poaching. Euopean Economic Review : ellmann T. K. Mudock and J. Stiglitz Libealization Moal azad in anking and Pudential Regulation: e Capital Requiements Enough? meican Economic Review 90: yytinen. and T. Takalo. 00. Enhancing ank Tanspaency: Re-ssessment. Euopean Finance Review 6:

26 Keeley M Deposit Insuance Risk and Maket Powe in anking. meican Economic Review 80: Kim M. D. Klige and. Vale Estimating Switching Costs and Oligopolistic ehavio. Jounal of Financial Intemediation : -6. Koskela E. and R. Stenbacka Is thee a Tadeoff between ank Competition and Financial Fagility? Jounal of anking & Finance 4: Matinez-Miea D. and R. Repullo. 00. Does Competition Reduce the Risk of ank Failue? Review of Financial Studies 3: Matutes C. and X. Vives Impefect Competition Risk Taking and Regulation in anking. Euopean Economic Review 44: -34. Moeno D. and T. Takalo. 0. Optimal ank Tanspaency. Jounal of Money Cedit and anking fothcoming. Peotti E. and J. Suaez. 00. Last ank Standing: What Do I Gain if You Fail? Euopean Economic Review 46: Sengupta R Foeign Enty and ank Competition. Jounal of Financial Economics 84: 0-8. Shy O. 00. Quick-and-Easy Method fo Estimating Switching Costs. Intenational Jounal of Industial Oganization 0: Shy O. R. Stenbacka and V. Yankov. 0. Limited Deposit Insuance Coveage and ank Competition. SSRN Woking Pape 4 Novembe 0. Stango V. 00. Picing with Consume Switching Costs. Evidence fom the Cedit Cad Maket. The Jounal of Industial Economics 0: Vickes J. 00. Cental anks and Competition uthoities: Institutional Compaisons and New Concens. IS Woking Papes No 33. 4

27 ank of Finland Reseach Discussion Papes 06 ISSN online /06 ino Silvo The inteaction of monetay and macopudential policies in economic stabilisation ISN online /06 Rune Stenbacka Tuomas Takalo Switching costs and financial stability ISN online

28 ISN ISSN online