No 134 Frctons n the Interbank Market and Uncertan Lqudty Needs: Implcatons for Monetary Polcy Implementaton Monka Bucher, Achm Hauck, Ulrke Neyer July 2014
IMPRINT DISCUSSION PAPER Publshed by düsseldorf unversty press (dup) on behalf of Henrch Hene Unverstät Düsseldorf, Faculty of Economcs, Düsseldorf Insttute for Competton Economcs (DICE), Unverstätsstraße 1, 40225 Düsseldorf, Germany www.dce.hhu.de Edtor: Prof. Dr. Hans Theo Normann Düsseldorf Insttute for Competton Economcs (DICE) Phone: +49(0) 211 81 15125, e mal: normann@dce.hhu.de DISCUSSION PAPER All rghts reserved. Düsseldorf, Germany, 2014 ISSN 2190 9938 (onlne) ISBN 978 3 86304 133 5 The workng papers publshed n the Seres consttute work n progress crculated to stmulate dscusson and crtcal comments. Vews expressed represent exclusvely the authors own opnons and do not necessarly reflect those of the edtor.
Frctons n the Interbank Market and Uncertan Lqudty Needs: Implcatons for Monetary Polcy Implementaton Monka Bucher Achm Hauck Ulrke Neyer July 2014 Abstract Ths paper shows that dependng on the dstrbuton of banks uncertan lqudty needs and on how monetary polcy s mplemented, frctons n the nterbank market may renforce the effectveness of monetary polcy. These frctons mply that wth ts lendng and depost facltes the central bank has an addtonal effectve nstrument at hand to mpose an mpact on bank loan supply. Whle lowerng the rate on the lendng faclty has, taken for tself, an expansonary effect, lowerng the rate on the depost faclty has a contractonary effect. Ths result has nterestng mplcatons for monetary polcy mplementaton at the zero lower bound. JEL classfcaton: E52, E58, G21 Keywords: nterbank market, monetary polcy, monetary polcy mplementaton, zero lower bound, loan supply Henrch Hene Unversty Düsseldorf Department of Economcs, Unverstaetsstrasse 1, 40225 Duesseldorf, and Post-Graduate Programme Global Fnancal Markets, Halle and Jena, Germany, emal: monka.bucher@hhu.de. Portsmouth Busness School, Unversty of Portsmouth, Rchmond Buldng Portland Street, Portsmouth PO1 3DE, UK, emal: achm.hauck@port.ac.uk. Correspondng author. Henrch Hene Unversty Düsseldorf, Department of Economcs, Unverstaetsstrasse 1, 40225 Duesseldorf, Germany, phone: +49/(0)211/81 11511, emal: ulrke.neyer@hhu.de.
1 Introducton The nterbank market for overnght loans s mportant for monetary polcy mplementaton. By steerng the nterest rate n ths market, the central bank ams to nfluence short-term nomnal nterest rates, and thereby, through varous channels, the prce level and maybe aggregate output. In the euro area, the nterest rate channel and the credt channel play an mportant role. 1 Both transmsson mechansms rest on the central bank s ablty to nfluence bank lendng. Durng the recent fnancal crss, euro area nterbank markets sezed up. Ths led to concerns about the Eurosystem s ablty, or the lack thereof, to actually control bank lendng n tmes of malfunctonng nterbank markets, and t trggered a heated debate of whether the transmsson mechansm of monetary polcy mght be mpared. Our paper ams to contrbute to ths debate by studyng n how far frctons n the nterbank market for overnght loans nfluence the mpact of monetary polcy on bank loan supply and by dscussng the mplcatons for monetary polcy mplementaton. We develop a theoretcal model that has two central features. Frst, t accounts for nterbank market frctons. Second, t captures man elements of the Eurosystem s 2 operatonal framework. Frctons n the nterbank market emerge n the form of transacton costs. We broadly nterpret these transacton costs as search costs. Banks must fnd sutable transacton partners wth frst, matchng lqudty needs and second, a wllngness to conclude mutual agreements for trade. The former may be costly as, for example, banks have to splt large transactons nto small ones to work around credt lnes (Bartoln, Bertola, and Prat, 2001). The latter may be costly because lenders n the overnght nterbank market are typcally unwllng to expose themselves to any counterparty credt rsk (Hauck and Neyer, 2013). Consequently, they engage n costly checks of the credtworthness of potental borrowers who n turn must provde costly sgnals of ther credtworthness. 3 The man elements of the Eurosystem s operatonal framework captured by 1 For respectve emprcal analyses for the nterest rate channel see, for example, Čhák, Harjes, and Stavrev (2009); Angelon, Kashyap, Mojon, and Terlzzese (2003). In an emprcal analyss referrng, for example, to the Spansh credt market, Jménez, Ongena, Peydró, and Saurna (2012) confrm a hgh relevance of the credt channel. 2 The term Eurosystem stands for the nsttuton whch s responsble for monetary polcy n the euro area, namely the ECB and the natonal central banks n the euro area. For the sake of smplcty, the terms ECB and Eurosystem are used nterchangeably throughout ths paper. 3 One of the frst papers dealng explctly wth nterbank market transacton costs s the one by Bartoln, Bertola, and Prat (2001). They argue that nterbank market transacton costs are responsble for the relatvely hgh federal funds rate usually observed at the end of a reserve mantenance perod. Transacton costs also play a crucal role n Hauck and Neyer (2013). They argue that transacton costs, or partcpaton 2
our model are the man refnancng operatons and the two standng facltes. The man refnancng operatons are credt operatons wth a maturty of one week by whch the Eurosystem provdes reserves to the bankng sector. The two standng facltes, a depost faclty and a lendng faclty, allow banks to balance ther overnght lqudty needs. The nterest rates on the facltes form a corrdor around the rate on the man refnancng operatons wth the rate on the depost faclty to be lower and the rate on the lendng faclty to be hgher than the man polcy rate. 4 It s worth mentonng that although our model focuses on the Eurosystem s operatonal framework, our results apply to other operatonal frameworks as well, as long as they allow commercal banks to balance uncertan lqudty needs by usng a depost faclty and a lendng faclty offered by the central bank. The results of our model replcate several stylzed facts and mply nterestng mplcatons for monetary polcy mplementaton. The replcated stylzed facts observed before and durng the recent fnancal crss are: If there are no nterbank market frctons, the nterbank market rate wll equal the man polcy rate, reserves provded by the central bank to the bankng sector through ts man refnancng operatons wll correspond to the benchmark allotment, 5 and the standng facltes wll not be used. Ths s exactly what was observed n the euro area before the outbreak of the fnancal crss n 2007. Introducng nterbank market frctons n our model leads to results whch are broadly consstent wth the stylzed facts observed durng the fnancal crss. The nterbank market rate falls below the man polcy rate, reserves provded by the central bank exceed the benchmark allotment and the standng facltes are used whereas the use of the depost faclty outweghs by far the use of the lendng faclty. From our model results the followng mplcatons for monetary polcy mplementaton can be drawn: costs, can explan several stylzed facts observed n the euro area nterbank market durng the fnancal crss. Models explctly consderng a costly search process n the nterbank market can be found for example n Furfne (2004) and Ashcraft and Duffe (2007). Furfne analyzes the effectveness of standng facltes offered by a central bank at reducng the volatlty of the overnght nterbank rate. Ashcraft and Duffe show how the search process n a decentralzed nterbank market nfluences ntraday allocaton and the prcng of federal funds. 4 For a detaled descrpton of the Eurosystem s operatonal framework see European Central Bank (2012). 5 The Eurosystem s benchmark allotment s generally understood as the allotment n a man refnancng operaton that wll allow the banks to smoothly fulfl ther reserve requrements takng nto account future lqudty needs from reserve requrements and autonomous factors. For detals see European Central Bank (2014). 3
Irrespectvely of nterbank market frctons, the central bank can nfluence banks expected fundng costs, and therefore bank loan supply, by changng ts man polcy rate even f the frctons mply a total nterbank market freeze. If nterbank market frctons are suffcently hgh, they wll renforce the effect of a sole change of the man polcy rate on bank loan supply. The renforcng effect ncreases n the extent of uncertanty about banks actual lqudty needs. The renforcng effect wll be avoded f the central bank changes all ts nterest rates (rate on ts man refnancng operatons and on ts standng facltes) to the same extent. Obvously, ths may not be possble f the rate on the depost faclty s fxed at the zero lower bound. If nterbank market frctons are suffcently hgh, the central bank can use the rates on the facltes as an addtonal effectve monetary polcy nstrument by changng the wdth or the asymmetry of the nterest rate corrdor. A decrease of the rate on the depost faclty corresponds to a contractonary monetary polcy. Consequently, usng ths nstrument for conductng a contractonary monetary polcy wll not be possble f the zero lower bound becomes bndng. To llustrate the man dea behnd the mplcatons of our model results, let us assume that the central bank conducts an expansonary monetary polcy by lowerng solely the rate on ts man refnancng operatons. Then, borrowng reserves from the man refnancng operatons becomes cheaper whch mples that also the prce for reserves n the nterbank market, the nterbank rate, decreases. Ths means that banks expected margnal fundng costs declne whch has a postve mpact on ther loan supply. However, frctons n the form of transacton costs n the nterbank market mply that the nterbank rate devates from the central bank s man polcy rate. If these costs are that hgh, that the nterbank rate wll be already at ts lower bound, whch s determned by the rate on the central bank s depost faclty, the above descrbed prce mechansm wll not work anymore. Therefore, borrowng reserves from the central bank s refnancng operatons remans to be relatvely cheaper as compared wth an nterbank market loan. As a consequence, banks ncrease ther borrowng from the refnancng operatons. The prce effect (lower nterbank rate) s replaced by a quantty effect (ncreased borrowng from the refnancng operatons). Ths quantty effect mples that the expansonary effect of the ntal monetary polcy mpulse s renforced as the senstvty of banks fundng costs to the monetary 4
polcy mpulse s hgher. The central bank can steer the extent of the renforcng effect by changng the rate on ts depost faclty. Ths rest of ths paper s organzed as follows. Secton 2 presents related lterature. Secton 3 descrbes the framework of the model. Sectons 4 and 5 derve the optmal behavor of commercal banks. Secton 6 dscusses the equlbrum of the model. Takng a closer look at ths equlbrum n Secton 7, we analyze the mpact of monetary polcy on bank loan supply and dscuss the consequences for monetary polcy mplementaton. Secton 8 brefly summarzes the paper. 2 Related Lterature Our paper contrbutes to three strands of lterature. The frst strand focuses on the nfluence of monetary polcy on bank lendng. A huge part of ths lterature consders asymmetrc nformaton n credt markets and argues that these frctons amplfy the effects of monetary polcy on bank lendng and, therefore, on aggregate demand. 6 Ths credt vew of monetary polcy can be dvded nto the balance sheet channel and the bank lendng channel. Wth respect to the balance sheet channel, the crucal pont s that a monetary polcy mpulse changes the borrowers net worth. A contractonary monetary polcy decreases the borrowers net worth whch mples an ncrease n adverse selecton and moral hazard problems leadng to a declne n bank lendng. Semnal papers are those by Bernanke and Gertler (1989) and Bernanke, Gertler, and Glchrst (1999). Wth respect to the bank lendng channel, the drvng force s that monetary polcy has an mpact on bank deposts. A contractonary monetary polcy reduces bank deposts mplyng a declne n bank loan supply. Important papers dealng wth ths tradtonal bank lendng channel are, for example, those by Gertler and Glchrst (1993) and Kashyap and Sten (1995). Ths tradtonal approach of the bank lendng channel has been crtczed as t neglects, for example, that banks can replace deposts by market-based fundng. However, Dsyatat (2011) shows that a greater relance on market-based fundng creates a new approach of the bank lendng channel. Crucal s that a stronger relance on market-based fundng ncreases the senstvty of banks fundng costs to monetary polcy as the banks health, n terms of leverage, asset qualty and n percepton of rsk, becomes more mportant. 6 For a short survey on ths so called credt vew of monetary polcy see, for example, Bovn, Kley, and Mshkn (2010) and Peek and Rosengreen (2012). 5
The second strand of lterature deals wth frctons n the nterbank market. Untl the outbreak of the fnancal crss n 2007, the nterbank market was typcally regarded as frctonless, also n the theoretcal lterature. As a consequence, the nterbank rate was assumed to be dentcal wth the monetary polcy rate or the nterbank market was entrely neglected. The fnancal crss challenged ths vew and nspred a growng lterature dealng wth nterbank market mperfectons, prmarly focusng on asymmetrc nformaton about credt rsks. Frexas and Jorge (2008) consder the mpact of ths nterbank market frcton for the transmsson of monetary polcy. They show that prvate nformaton n the nterbank market wth respect to credt rsks may nduce ratonng of frms n credt markets. Wth respect to the transmsson mechansm of monetary polcy ths mples that asymmetrc nformaton n the nterbank market may be responsble for a) a magntude effect,.e. the aggregate mpact of monetary polcy may be large gven the small nterest elastcty of nvestment, and b) a lqudty effect,.e. that the mpact of monetary polcy s stronger for banks wth less lqud balance sheets. Heder, Hoerova, and Holthausen (2009) argue that banks nformatonal dsadvantage wth respect to counterparty credt rsks nduces them to hold more lqudty. Dependng on the rsk dsperson, ths may result n ether adverse selecton or a dry-up of the nterbank market. However, banks may learn about counterparty credt rsks by repeatedly tradng wth each other so that the asymmetrc nformaton problem may be mtgated. In an emprcal analyss of the German unsecured overnght money market, Bräunng and Fecht (2012) determne the mpact of such relatonshp lendng for banks ablty to access lqudty. The causes of a possble dry-up of the nterbank market are also analyzed by Allen, Carlett, and Gale (2009). They show that banks wll start to hoard lqudty f they are unable to hedge dosyncratc lqudty shocks. The thrd strand of lterature deals wth monetary polcy mplementaton, bank behavor, and consequences for the condtons n the overnght nterbank market. Ths lterature can be dvded nto three groups. The frst group focuses on the U.S. before the outbreak of the fnancal crss n 2007. Consderng major nsttutonal characterstcs of the federal funds market, Ho and Saunders (1985) as well as Clouse and Dow (2002) analyze banks reserve management and draw conclusons for the condtons n the nterbank market for reserves. However, the largest part of the lterature dealng wth the federal funds mar- 6
ket focuses on why the federal funds rate fals to follow a martngale wthn the reserve mantenance perod. 7 The second group of the lterature refers to the euro area n the pre-crss perod. A bulk of ths lterature deals wth the under- and overbddng behavor n the Eurosystem s man refnancng operatons whch could be observed n the frst years of the European Monetary Unon. 8 Apart from ths, there are papers analyzng the consequences of alternatve monetary polcy mplementatons. Nautz (1998) shows that the central bank can nfluence the nterbank market rate by beng more or less vague about ts future monetary polcy. Välmäk (2001) analyzes the effects of alternatve tender procedures wth respect to the Eurosystem s refnancng operatons. Neyer and Wemers (2004) refer to the collateral framework. They show that dfferences n banks opportunty costs of holdng collateral form a ratonale for the exstence of an nterbank market for reserves. Neyer (2009) demonstrates that remuneratng requred reserves n a specfc way ncreases the flexblty of monetary polcy. Pérez-Qurós and Rodríguez-Mendzábal (2006) show that the two standng facltes offered by the Eurosystem n combnaton wth ts mnmum reserve system are an effectve nstrument to stablze the nterbank market rate. Whtesell (2006), although not explctly referrng to the euro area, looks at a mnmum reserve system and standng facltes as two alternatve regmes for controllng overnght nterest rates. Also focusng on the standng facltes, Berentsen and Monnet (2008) develop a general equlbrum framework and show that changng the rates on these facltes may be used actvely as a monetary polcy nstrument. Also Goodhart (2013) ponts out that by changng the rates on the standng facltes the central bank has an addtonal nstrument at hand. Beaupan and Durré (2008) examne the nterday and ntraday dynamcs of the euro area overnght nterbank market and argue that specfc features of the Eurosystem s operatonal framework, as ts mnmum reserve system, can explan observed regular patterns. The thrd group of ths thrd strand of lterature comprses papers regardng changes n monetary polcy mplementaton n response to the fnancal crss. Esenschmdt, Hrsch, and Lnzert (2009) analyze the relatvely aggressve bddng behavor of banks n the Eurosystem s man refnancng operatons at the begnnng of the fnancal turmol. Also 7 See Hamlton (1996), Clouse and Dow (1999), Furfne (2000), and Bartoln, Bertola, and Prat (2001, 2002). 8 Under- and overbddng behavor refers to a bddng behavor n whch total bds sgnfcantly exceed or reman under the Eurosystem s benchmark allotment. Analyses wth respect to ths under- and overbddng behavor can be found n Ayuso and Repullo (2001, 2003), Ewerhart (2002), Nautz and Oechssler (2003, 2006), and Bndsel (2005). 7
referrng to the frst part of the fnancal crss (untl 2008), Cassola and Huetl (2010) assess the effectveness of monetary polcy mplementaton durng that tme. Boro and Dsyatat (2009) descrbe man characterstcs of unconventonal monetary polces adopted durng the fnancal crss. They pont out that an mportant feature of these polces s that the central bank also uses ts balance sheet to nfluence prces and condtons n the nterbank market. Cheun, von Köppen-Mertes, and Weller (2009) analyze changes to the collateral frameworks of the Eurosystem, the Federal Reserve System and the Bank of England. Lenza, Pll, and Rechln (2010) descrbe the way n whch these three central banks generally conducted monetary polcy durng the fnancal crss and pont to the mportance of ther nfluence on money market spreads. Hauck and Neyer (2013) develop a theoretcal model consderng man nsttutonal features of the Eurosystem s operatonal framework whch has been n place snce September 2008 to explan several stylzed facts observed durng the fnancal crss. Our paper combnes all three strands of ths lterature by analyzng the consequences of frctons n the overnght nterbank market, n the form of broadly defned transacton costs, for the mpact of monetary polcy on bank loan supply. Wth respect to monetary polcy mplementaton, we pont out the crucal role the central bank s standng facltes play for the effectveness of monetary polcy n the presence of nterbank market frctons and uncertan lqudty needs. 3 Framework In our model, we dstngush between three types of agents. We consder a contnuum of measure one of prce-takng commercal banks wth a large number of bank customers and a central bank. Each commercal bank grants a loan volume L to ts customers at a gven nterest rate L. Ths generates net revenues of L L 1 2 λl2 (1) for bank. The second term of (1) reflects the costs of managng loans. The quadratc form of ths cost functon captures the dea that loans dffer n ther complexty so that the bank adds the least complex loans to ts portfolo frst. Bank credts the loan volume L to ts customers demand depost accounts. The bank s customers can use ths newly created money to make payments. They pay by 8
cash or by transferrng deposts. Due to the cash payments, each bank experences cash wthdrawals cl, wth the currency rato c reflectng the share of the newly created money used for cash payments. Due to the payments made by depost transfers, a share χt of the remanng deposts (1 c)l s transferred to customers of other banks. Crucal s that the net depost transfer dffers across banks. Ths s reflected by the bank ndvdual varable t. For banks facng a net depost nflow t < 0, and for those facng a net depost outflow t > 0. For a sngle bank, ts net depost transfer s uncertan as t s the realzaton of a random varable T. Across all banks, t s dstrbuted n the nterval [t mn, t max ] accordng to the densty functon g(t ) = G (t ). Note that E[T ] = t max t mn t g(t ) dt = 0. (2) The parameter χ wth χ (0, 1 t max ] s a scale parameter whch determnes the dsperson of the dstrbuton of T. 9 If χ ncreases, the dstrbuton wll exhbt a hgher dsperson. Accordngly, we wll use χ as a measure for uncertanty about a bank s net depost transfer. Consderng both, cash wthdrawals and the net depost transfer, bank s remanng deposts are gven by D = L cl (1 c)χt L. (3) Ths mples that a sngle bank may face a lqudty surplus or defct. Bank can balance ts ndvdual lqudty needs by transactng wth the central bank or n the nterbank market. However, the cash wthdrawals mply that the bankng sector as a whole faces a structural lqudty defct whch can only be covered by the central bank beng the monopoly producer of currency. To obtan lqudty from the central bank, each bank can partcpate n the central bank s refnancng operatons and borrow the amount RO at the rate RO. Moreover, t can use a lendng faclty to borrow LF at the rate LF. 10 However, t can also place an 9 As χt as a share cannot exceed one, χ s restrcted to 1 t max. 10 Generally, credt operatons wth the central bank requre adequate collateral. In our settng a bank s loan volume L serves as collateral, and therefore, lmts ts central bank borrowng. The central bank may mpose a harcut on these loans when acceptng them as collateral, lke n Bndsel and Köng (2011). In ths settng, however, we assume that such a har cut s not bndng and neglect the collateralzaton of central bank loans. See n ths context also our remarks on ths aspect made n the ntroducton. 9
amount DF of lqudty n a depost faclty offered by the central bank at the rate DF. Accordngly, transactons wth the central bank mply net costs of RO RO + LF LF DF DF. (4) The rates on the facltes form a corrdor around the rate on the refnancng operatons wth LF > RO > DF. A sngle bank can also borrow and lend lqudty n the nterbank market. Bank s poston n ths market s B. If B > 0, bank wll borrow the amount B at the rate IBM. Conversely, B < 0 ndcates that bank wll lend the amount B at ths rate. Independently of whether bank borrows or lends n the nterbank market, transacton costs γ B accrue, wth γ 0. Therefore, net costs n the nterbank market account for IBM B + γ B. (5) Consderng the descrbed costs and revenues, each bank ams to maxmze ts proft Π. Banks are rsk neutral so that by combnng equatons (1), (4), and (5), the objectve functon of bank smply reads Π = L L 1 2 λl2 RO RO LF LF + DF DF IBM B γ B (6) s.t. L + DF = RO + LF + D + B, (7) where (7) descrbes bank s balance sheet constrant. The assets consst of bank s loans L and ts deposts held at the central bank DF. Its labltes comprse ts central bank borrowng, RO +LF, and ts customers deposts D. The bank s poston n the nterbank market B mght consttute an tem on the asset or labltes sde of the balance sheet, dependng on whether the bank borrows from or lends n the nterbank market. When solvng ths optmzaton problem, we have to consder the sequence of moves. Frst, bank decdes on ts optmal loan supply L and ts optmal borrowng from the central bank s refnancng operatons RO. When makng these decsons, the bank cannot observe the realzaton t of the random varable T. The bank thus faces uncertanty about ts future lqudty needs. After bank observed t so that uncertanty about ts lqudty needs s resolved, t decdes on ts transactons n the nterbank market B and on ts use of the central bank s facltes DF and LF. Ths sequence of moves mples that the optmzaton problem can be splt up nto two stages. Solvng ths optmzaton problem 10
by backward nducton, we frst nvestgate the second stage of the model and determne a bank s optmal behavor n the nterbank market and ts optmal use of the central bank s facltes. Then, we analyze the frst stage of the model and determne a bank s optmal lendng to the non-bankng sector and ts optmal borrowng from the central bank s refnancng operatons. 4 Optmal Behavor at the Second Stage At the second stage each bank learns ts respectve share of transferred deposts t and, therefore, ts actual lqudty needs. Accordngly, banks face no uncertanty at ths stage. Usng (3) we defne bank s actual ndvdual lqudty needs as N := L RO D = L (c + (1 c)χt ) RO. (8) If N 0, bank wll nhert a lqudty defct. In ths case, the bank compares margnal costs of borrowng from the nterbank market gven by IBM + γ wth those of usng the lendng faclty whch are smply LF. As the two margnal costs are constant, the bank wll cover ts total lqudty defct by borrowng from the lendng faclty f IBM +γ > LF. If IBM +γ < LF, t wll borrow from the nterbank market only. In case both margnal costs are dentcal, the bank s essentally ndfferent between nterbank borrowng and the usage of the lendng faclty. If N < 0, bank wll nhert a lqudty surplus so that the bank decdes analogously. If the margnal revenues n the nterbank market IBM γ are hgher (lower) than the margnal revenues of the central bank s depost faclty DF, t wll place ts total surplus n the nterbank market (n the depost faclty). In case margnal revenues are dentcal, the bank wll agan be ndfferent. As banks wll only trade lqudty n the nterbank market f ths s more benefcal than usng the central bank s facltes, the nterbank rate n equlbrum wll be IBM [ DF +γ, LF γ]. Whether banks prefer the nterbank market thus crucally depends on the magntude of γ. If transacton costs are too hgh, each bank wll prefer to use the central bank s facltes nstead of tradng n the nterbank market. As a result, the nterbank market breaks down. Ths wll be the case f IBM γ < DF and IBM + γ > LF,.e. f γ > LF DF 2 =: γ. (9) 11
We thus obtan Proposton 1: If γ γ, the nterbank market wll be actve and we wll have to dstngush between three cases regardng the nterbank rate: IBM = LF γ IBM [ DF + γ, LF γ ] IBM = DF + γ f RO < cl, f RO = cl, f RO > cl. (10) If γ > γ, the nterbank market wll be nactve. Proof: Omtted. The proposton states that the nterbank rate depends crucally on the aggregate lqudty poston of the bankng sector. Denotng aggregate borrowng from the refnancng operatons by RO and aggregate lendng to the non-bankng sector by L, an aggregate lqudty defct wll arse f banks cash wthdrawals cl are larger than the aggregate amount obtaned n the refnancng operatons RO. In ths case, competton for scarce lqudty brngs the nterbank rate to ts upper lmt LF γ. A hgher nterest rate would not be accepted by the lqudty defct banks, snce then they would prefer to borrow from the central bank s lendng faclty nstead. If an aggregate lqudty surplus occurs, as cash wthdrawals are lower than the aggregate amount of lqudty obtaned n the refnancng operatons, competton for lmted lendng possbltes n the nterbank market brngs the nterbank rate to ts lower lmt DF + γ. If there s nether an aggregate lqudty defct nor surplus, nether market sde possesses market power. In consequence, any rate wthn the lower and the upper lmt depcts a possble equlbrum. 5 Optmal Behavor at the Frst Stage 5.1 A Bank s Optmzaton Problem At the frst stage of the model, bank must decde on ts loan volume L and on ts borrowng from the refnancng operatons offered by the central bank RO. The decson problem of bank that ams to maxmze ts expected proft E[π ] reads max E [π ] = L L 1 L,RO 2 λl2 RO RO max { IBM γ, DF } t N g(t ) dt t mn mn { IBM + γ, LF } t max t N g(t ) dt. (11) 12
The frst term on the rght hand sde of (11) reflects the nterest revenues of grantng loans to the non-bankng sector. The second term expresses the management costs assocated wth these loans. The last three terms reflect expected fundng costs. Fundng costs occur as due to certan cash wthdrawals and the uncertan net depost transfer there may be a loss of non-nterest bearng deposts. The thrd term on the rght hand sde of (11) reflects the certan frst-stage fundng costs. They accrue due to bank s borrowng from the central bank s refnancng operatons. The last two terms show expected second-stage fundng costs. Fundng needs at the begnnng of the second stage are gven by (8). The currency rato c and the scale parameter χ are certan and dentcal for all banks. In addton, the amounts L and RO are certan once they are chosen at the frst stage. Therefore, the share of net depost transfer t s the only source of uncertanty of bank at the frst stage regardng ts fundng needs N. From (8) we can nfer that bank wll face nether a lqudty defct nor a surplus at the second stage,.e. N = 0, f t = RO cl (1 c)χl =: t. (12) It follows drectly from (12) that bank s crtcal share of net depost transfer t ncreases n RO and decreases n L. If (t < t ), bank faces a lqudty surplus at the begnnng of the second stage (N < 0). Consderng the dstrbuton of T, the bank s expected lqudty surplus s gven by t t mn N g(t ) dt /G(t ). The bank wll lend ts excess lqudty n the nterbank market or wll place t n the depost faclty, dependng on whch opton s more proftable. Consequently, expected revenues n case of a lqudty surplus are max { IBM γ, DF } t t N mn g(t ) dt. G(t ) Analogously, expected costs n case of a lqudty defct are mn { tmax IBM } LF t + γ, N g(t ) dt. 1 G(t ) As the former case occurs wth probablty G(t ), and the latter wth probablty 1 G(t ), the last two terms of (11) show expected second-stage fundng costs resultng from transactons n the nterbank market or from usng the central bank s facltes. Note that uncertanty wth respect to the share of net depost transfer exsts only at the ndvdual level. At the aggregate level, the net depost transfer must be zero so that E[T ] = 0 (see equaton (2)). Ths has the followng mplcatons. Frst, for any gven 13
loan volume L and any amount RO of lqudty obtaned n the refnancng operatons, each bank has the same expectatons about ts subsequent lqudty needs. Second, banks form the same expectatons about the nterbank rate that wll preval n equlbrum. The nterbank rate wll only depend on the aggregate lqudty poston n the bankng sector. Once all banks have granted ther loans and borrowed from the refnancng operatons, ths aggregate lqudty poston s certan. Ths mples that an ndvdual bank takes the aggregate lqudty needs and, therefore, also the nterbank rate as gven. Consequently, all banks face exactly the same decson problem gven by (11). The optmal ndvdual borrowng from the refnancng operatons RO opt as well as the optmal ndvdual lendng to the non-bankng sector L opt are dentcal for all banks and are, therefore, equal to the respectve aggregate values RO and L. depost transfer t opt. The same apples for the crtcal share of net 5.2 Optmal Borrowng from the Refnancng Operatons Determnng a bank s optmal behavor at the frst stage, we can restrct our attenton to the case IBM [ RO γ, RO + γ ]. Suppose IBM < RO γ. Then, no bank has an ncentve to borrow from the central bank s refnancng operatons at the frst stage snce borrowng from the nterbank market at the second stage s strctly cheaper. However, refusng to borrow from the central bank s refnancng operatons at the frst stage mples that there s no lqudty to be traded on an nterbank market so that the nterbank market s nexstent. Therefore, IBM < RO γ consttutes no possble equlbrum. If IBM > RO + γ each bank would be ncentvzed to borrow unlmtedly from the central bank s refnancng operatons to place ts lqudty n the nterbank market. Apparently, ths cannot be an equlbrum ether. Consderng ths and solvng the optmzaton problem (11) we obtan Lemma 1: Suppose that IBM [ RO γ, RO + γ ]. If t opt t := c (1 c)χ, then at the frst stage, bank wll borrow from the central bank s refnancng operatons accordng to: RO = max { IBM γ, DF } ( G t opt ) + mn { IBM + γ, LF } [ ( 1 G t opt )]. (13) Proof: See appendx. Optmal borrowng from the central bank s refnancng operatons requres margnal costs of ths borrowng to be equal to expected margnal revenues. Margnal costs are equal to the nterest rate on these operatons gven by the left hand sde of (13). The rght 14
hand sde of (13) reflects expected margnal revenues. Wth probablty G(t opt ), bank wll face a lqudty surplus at the second stage,.e. N < 0. In ths case, the bank wll ether lend ts excess lqudty n the nterbank market or place t n the depost faclty, dependng on whch alternatve yelds the hgher revenues. Wth probablty 1 G(t opt ), the bank wll face a lqudty defct,.e. N > 0, so that t wll borrow from the nterbank market or close ts lqudty gap by borrowng from the central bank s lendng faclty. In ths case borrowng from the central bank s refnancng operatons mples margnal revenues n the form of avoded llqudty costs. The adjustment process n the case margnal costs dffer from expected margnal revenues plays a crucal role n our analyss. Ths process can be descrbed as follows. Assume that margnal costs are hgher than expected margnal revenues. Then, the bank wll reduce ts borrowng from the refnancng operatons. Ths ncreases the probablty G(t ) of facng a lqudty defct at the second stage. 11 As margnal revenues n the case of a lqudty defct gven by mn { IBM + γ, LF } are strctly larger than those n the case of a lqudty surplus gven by max { IBM γ, DF }, expected margnal revenues wll ncrease f the bank reduces ts borrowng from the refnancng operatons. Consequently, as long as margnal costs are hgher than margnal revenues, the bank wshes to reduce RO untl expected margnal revenues equal margnal costs. However, f the non-negatvty constrant on RO becomes bndng, the bank cannot reduce RO any further. Ths wll be the case f t opt < t. 12 As a result, t opt can not be realzed by bank and RO opt = 0. Accordngly, margnal costs of borrowng from the refnancng operatons reman hgher than expected margnal revenues. 5.3 Optmal Lendng to the Non-Bankng Sector Solvng the optmzaton problem (11) wth respect to the optmal lendng L opt non-bankng sector, we obtan to the Lemma 2: If t opt t := c (1 c)χ, bank wll supply loans at the frst stage accordng to the followng frst order condton: L = λl opt + c RO + (1 c)χ max { IBM γ, DF } [ E t t < t opt [ ] [ ( )] + (1 c)χ mn { IBM + γ, LF } E t t > t opt 1 G t opt ] ( G t opt ), (14) 11 A decrease n RO reduces t, as equaton (12) reveals. 12 If RO opt = 0, then t opt = c (1 c)χ =: t. 15
wth t opt beng mplctly defned by (13). Proof: See appendx. Optmal lendng L opt to the non-bankng sector requres balancng margnal revenues wth expected margnal costs of grantng loans. Margnal revenues are equal to the nterest rate L. Expected margnal costs consst of margnal management costs λl opt and expected margnal fundng costs. The latter can be dvded nto two parts. The frst part c RO refers to the certan fundng costs due to borrowng from the central bank s refnancng operatons at the frst stage. The second part corresponds to the expected second stage margnal fundng costs. A lqudty surplus materalzes wth probablty G(t opt ) and a lqudty defct wth probablty 1 G(t opt ). If bank faces a lqudty surplus at the begnnng of the second stage as t t opt, t wll ether lend ts lqudty surplus n the nterbank market at IBM γ or place t n the depost faclty at DF. Hence, the thrd term on the rght hand sde of (14) determnes the expected (negatve) margnal fundng costs n the case of a lqudty surplus. The fourth term determnes the expected margnal fundng costs n the case of a lqudty defct. A lqudty defct wll occur f t > t opt. In ths case, bank wll borrow ether from the nterbank market at IBM + γ or from the lendng faclty at LF. Wth respect to our comparatve statc analyss, t s useful to rewrte expected second stage margnal fundng costs as follows [ ] [ ( (1 c)χe t t > t opt 1 G [ ] [ ( (1 c)χe t t > t opt 1 G t opt t opt )] 2γ f γ γ, (15) )] ( LF DF ) f γ > γ. (16) Equaton (15) and (16) reveal that expected second stage margnal fundng costs consst of the expected share per unt of loans for whch fundng costs are expected to accrue and the relevant fundng costs. For detals wth respect to a bank s expected second stage margnal fundng costs we refer the reader to Appendx A.3. 6 Equlbrum After havng clarfed the optmal behavor of an ndvdual bank, we are now n a poston to determne the equlbrum of our model. banks of unt mass. We have a contnuum of ex-ante dentcal Consequently, the bank-ndvdual optmal values L opt correspond to the respectve equlbrum aggregate levels L and RO. and RO opt 16
In the euro area, aggregate borrowng from the ECB s man refnancng operatons has been systematcally equal to or hgher than the ECB s benchmark allotment. 13 As n our model aggregate cash wthdrawals cl corresponds to the benchmark allotment, we focus n our analyss on equlbra n whch RO cl. These equlbra wll emerge f G(0) < 0.5 and f LF RO RO DF. The latter means that the corrdor, whch the rates on the central bank s facltes form around the man polcy rate, s symmetrc or asymmetrc n the sense that the lower dfference s smaller than the upper dfference. These two cases have been relevant n the euro area. 14 The former mples a left-skewed dstrbuton of T so that for each sngle bank the probablty of facng a net depost outflow s larger than the probablty of a net depost nflow. Due to E[T ] = 0, each ndvdual bank thus expects small outflows wth a hgh probablty and large nflows wth low probablty. To understand ths pattern, t s useful to dstngush between two types of bank customers. Frst, each bank possesses a huge number of bank customers predomnantly generatng relatvely small depost outflows, such as households who make payments for consumpton purposes. Second, each bank possesses a small number of bank customers predomnantly recevng relatvely large payments, such as frms as supplers of consumpton goods. Wth a small probablty these frms may beneft from spkes n demand for ther goods, e.g. caused by a major nnovaton. In consequence, ther respectve bank would face a large net depost nflow. Moreover, a large net depost nflow may also occur f outflows declne to a large extent. Ths s the case, f households experence a massve shock that sgnfcantly reduces ther spendng, e.g. f n a regon cash card payments are not feasble. As the probablty of such a shock s also small, banks expect a large net depost nflow wth a small probablty and small net depost outflows wth a large probablty. Combnng the results of Proposton 1, Lemma 1 and Lemma 2, we obtan Proposton 2: Assume that G(0) < 0.5 and that LF RO RO DF. Then, dependng on γ, we have to dstngush between three equlbra I : RO = cl, DF = 0, LF = 0, IBM = RO γ [1 2G (0)] f γ γ, (17) II : RO > cl, DF > 0, LF = 0, IBM = DF + γ f γ ( γ, γ], (18) III : RO > cl, DF > LF > 0 f γ > γ, (19) 13 See footnote 5 for a descrpton of the benchmark allotment. Note that n our model there are no reserve requrements and autonomous factors conssts of currency holdngs. 14 From Aprl 1999 untl November 2013 the rates on the Eurosystem s facltes generally formed a symmetrc corrdor around the rate on the man refnancng operatons. However, due to the zero lower bound, the rate on the depost faclty was not decreased n November 2013 contrary to the rates on the lendng faclty and on the man refnancng operatons. Consequently, there has been an asymmetrc nterest rate corrdor snce then. 17
wth γ := RO DF 2[1 G(0)], (20) and γ beng defned n (9). Proof: See appendx. In Equlbrum I, nterbank market transacton costs are that low that each bank borrows exactly an amount equal to ts cash wthdrawals from the central bank s refnancng operatons and balances ts lqudty needs resultng from the depost transfers of ts customers solely by usng the nterbank market. None of the facltes s used. Only ths behavor mples that the optmalty condton gven by (13) s fulflled. To see ths, suppose as a startng pont that γ = 0. If banks borrowed an amount larger than ther cash wthdrawals from the refnancng operatons, there would be an aggregate surplus at the second stage brngng the nterbank market to ts lower bound DF + γ = DF. However, ths cannot be an equlbrum, as then margnal costs of borrowng from the refnancng operatons gven by RO would exceed expected margnal revenues whch n ths case are equal to DF. 15 Consequently, banks wll have an ncentve to reduce ther borrowng from the refnancng operatons to balance margnal costs and expected margnal revenues (see the adjustment process descrbed n Subsecton 5.2). Analogously, f banks borrowed an amount lower than ther cash wthdrawals, there would be an aggregate lqudty defct brngng the nterbank rate to ts upper bound LF γ = LF. Ths s no equlbrum ether, as for ths nterbank rate expected margnal revenues of borrowng from the refnancng operatons, whch are equal to LF, exceed margnal costs gven by RO, so that banks wsh to ncrease ther borrowng. Consequently, for γ = 0 an equlbrum wll be reached f each bank borrows an amount equal to ts cash wthdrawals from the refnancng operatons. Ths mples that the nterbank market rate IBM equals the central bank s polcy rate RO. Let us assume next that γ becomes postve. Then, expected margnal revenues of borrowng from the central bank s refnancng operatons ncrease. If a bank faces a lqudty surplus at the second stage, ts margnal revenues from placng lqudty n the nterbank market wll decrease but ts avoded margnal llqudty costs n case of a lqudty defct wll ncrease (see Lemma 1). Due to the left-skewed dstrbuton of T, the probablty of facng a lqudty defct at the second stage wll be hgher than of facng a lqudty 15 One obtans expected margnal revenues by nsertng the equlbrum nterbank market rate nto the rght hand sde of (13). 18
surplus as long as each bank borrows an amount equal to ts cash wthdrawals from the central bank s refnancng operatons,.e. as long as RO = cl. Consequently, a bank s expected margnal revenues of borrowng from the refnancng operatons wll ncrease f γ becomes postve. To balance margnal costs and expected margnal revenues agan, each bank wll have an ncentve to ncrease ts borrowng from the refnancng operatons above cl (see the adjustment process descrbed n Subsecton 5.2). However, such an aggregate borrowng behavor wll result n excess aggregate lqudty so that the nterbank rate wll declne. Ths declne wll reduce expected margnal revenues of borrowng from the refnancng operatons. Accordngly, the ncentve to borrow more than cl becomes weaker. No bank wll borrow more than an amount equal to ts cash wthdrawals from the refnancng operatons f the nterbank rate decreases to IBM = RO γ [1 2G (0)]. As long as the nterbank rate s unrestrcted, an ncrease n expected margnal revenues due to hgher nterbank market transacton costs wll thus be offset by a decrease of the nterbank rate. The prce mechansm works. Ths mechansm ensures that banks have no ncentve to borrow more than an amount equal to ther cash wthdrawals from the central bank s refnancng operatons. Equlbrum I as descrbed by equaton (17) wll be realzed. If transacton costs exceed the crtcal level γ, further decreases of the nterbank rate wll not be possble to balance margnal costs and expected margnal revenues as the nterbank rate has reached ts lower bound DF + γ. Consequently, a further ncrease n γ mples that banks actually start to ncrease ther borrowng from the refnancng operatons. Ths wll reduce the probablty of facng a lqudty defct and, therefore, expected margnal revenues. As the prce mechansm does not functon, margnal costs and expected margnal revenues are balanced va a quantty effect. As ths behavor mples that banks ncrease ther borrowng from the refnancng operatons above the cash wthdrawals, an aggregate lqudty surplus wll materalze, RO > cl, whle the nterbank rate wll reman at ts lower lmt. The excess lqudty wll then be placed n the depost faclty. Hence, for suffcently hgh transacton costs, Equlbrum II gven n equaton (18) wll be realzed. In ths equlbrum, all banks wth a lqudty defct stll cover ther lqudty needs by usng the nterbank market. Some surplus banks have to use the depost faclty due to the aggregate excess lqudty. If transacton costs reach the crtcal level γ, the defct banks are no longer wllng to borrow ther lqudty from the nterbank market but prefer to use the central bank s lendng faclty nstead. The nterbank market breaks down. Both, the defct banks as 19
well as the surplus banks, exclusvely use the facltes to balance ther lqudty needs at the second stage. As there s aggregate excess lqudty, t follows that DF > LF. Equlbrum III as gven n equaton (19) wll be realzed. In Proposton 2 we assume that G(0) < 0.5 and that LF RO RO DF. These assumptons mply that the equlbrum s characterzed by RO cl, whch s the stuaton observed n the euro area. However, for the sake of completeness, we wll brefly comment on the possble equlbrum RO < cl. Ths equlbrum wll emerge f the dstrbuton of T becomes suffcently rght-skewed or f the nterest rate corrdor becomes suffcently asymmetrc wth LF RO < RO DF. We start wth the mportance of the dstrbuton of T. Let us assume that T s dstrbuted symmetrcally around t = 0 and that the nterest rates on the facltes form a symmetrc corrdor around the man polcy rate. Then, the probablty of facng a net depost outflow equals the probablty of facng a net depost nflow due to customers depost transfers. In ths case, only RO = cl mples that (13) s fulflled. Transacton costs play no role as they ncrease margnal revenues of borrowng from the refnancng operatons n the case of a lqudty defct and decrease them n the case of a lqudty surplus, and for RO = cl both scenaros occur wth the same probablty gven the symmetrc dstrbuton of T. Now let us assume that the dstrbuton of T becomes rght-skewed. For RO = cl, the probablty of facng a lqudty surplus ncreases. In ths case, transacton costs mply that expected margnal revenues of borrowng from the refnancng operatons decrease. Accordngly, banks are ncentvzed to borrow less from the refnancng operatons. Analogously to the case of a left-skewed dstrbuton of T ths results n an ncrease n the nterbank market rate to balance margnal costs and expected margnal revenues of borrowng from the refnancng operatons. However, f the nterbank rate reaches ts upper bound so that t cannot ncrease further, banks start to borrow less from the refnancng operatons and RO < cl. In order to hghlght the mportance of the asymmetry of the nterest rate corrdor let us assume that net depost transfers T are dstrbuted symmetrcally around zero. If then the asymmetry of the nterest rate corrdor s, contrary to our assumpton n Proposton 2, gven by LF RO < γ < RO DF, the optmal behavor of bank wll be RO opt < cl opt : Facng relatvely hgh nterbank market transacton costs ( LF RO < γ), banks wth a lqudty defct wll only accept an nterbank rate below RO. Otherwse, they would prefer to use the lendng faclty. However, an nterbank rate below RO mples for RO = cl expected margnal revenues of borrowng from the refnancng operatons to be lower than 20
margnal costs. 16 Therefore, banks are ncentvzed to borrow less from the refnancng operatons. Generally, ths would lead to an ncrease n the nterbank rate balancng expected margnal revenues and margnal costs agan. However, such an adjustment s not possble as n case of a lqudty defct a bank would not accept a hgher nterbank rate. Therefore, all banks actually start to borrow less from the refnancng operatons to balance expected margnal revenues so that margnal costs and RO < cl. 7 Monetary Polcy and Bank Loan Supply Ths secton analyzes the mpact of monetary polcy on bank loan supply. As the strength of ths effect depends on the extent of uncertanty about the net depost transfer and nterbank market transactons costs, we wll start wth a bref look on ther drect mpact on bank loan supply. 7.1 Uncertanty and Interbank Market Frctons Uncertanty about the net depost transfer and nterbank market frctons have a negatve mpact on bank loan supply. 17 Both, uncertanty and nterbank market transacton costs, nfluence expected second stage margnal fundng costs as Lemma 2 reveals. An ncrease n uncertanty about the net depost transfer leads to an ncrease n both, the expected lqudty surplus and the expected lqudty defct per unt of loans as revealed by the equatons (15) and (16). As ths surplus or defct has to be costly balanced ether n the nterbank market or va the central bank s facltes, an ncrease n uncertanty mples hgher expected margnal fundng costs of grantng loans. Consequently, banks start to reduce ther loan supply. Obvously, a change n nterbank market transacton costs wll only have an mpact on bank loan supply f these costs are stll low enough to ensure an actve nterbank market,.e. f γ γ. In ths case, t follows from Lemma 2 that an ncrease n margnal transacton costs γ results n an ncrease n expected margnal fundng costs. Accordngly, banks wll reduce ther loan supply. 16 For RO opt = cl opt we get that t = 0 as equaton (12) shows. Ths means for a symmetrc dstrbuton of T that G( t = 0) = 0.5, so that expected margnal revenues of borrowng from the refnancng operatons are equal to the nterbank market rate as revealed by the rght hand sde of equaton (13). As margnal costs of borrowng from the refnancng operatons are gven by RO, IBM < RO mples expected margnal revenues to be lower than margnal costs. 17 We provde the respectve formal analyss n Appendx A.4. 21