Federal Reserve Bank of Chicago

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1 Federal Reserve Bank of Chicago A Sequenial Bargaining Model of he Fed Funds Marke wih Excess Reserves Sam Schulhofer-Wohl and James Clouse REVISED July 2018 WP hps://doi.org/ /wp * Working papers are no edied, and all opinions and errors are he responsibiliy of he auhor(s). The views expressed do no necessarily reflec he views of he Federal Reserve Bank of Chicago or he Federal Reserve Sysem.

2 A Sequenial Bargaining Model of he Fed Funds Marke wih Excess Reserves Sam Schulhofer-Wohl and James Clouse Revised July 2018 ABSTRACT We model bargaining beween non-bank invesors and heerogeneous bank borrowers in he federal funds marke. The analysis highlighs how he federal funds rae will respond o movemens in oher money marke ineres raes in an environmen wih elevaed levels of excess reserves. The model predics ha he adminisered rae offered hrough he Federal Reserve s overnigh reverse repurchase agreemen faciliy influences he fed funds rae even when he faciliy is no used. Changes in repo raes pass hrough o he federal funds rae, bu by less han one-for-one. We calibrae he model o daa from 2017 and find in an ou-of-sample es ha he model quaniaively maches he increase in he federal funds rae in he firs four monhs of The rise in he fed funds rae in 2018 is aribued o movemens in repo raes and no o changes in he scarciy value of reserves. Schulhofer-Wohl: Federal Reserve Bank of Chicago. Clouse: Board of Governors of he Federal Reserve Sysem. The views expressed herein are hose of he auhors and no necessarily hose of he Board of Governors or he saff of he Federal Reserve Sysem or he Federal Reserve Bank of Chicago.

3 1. Inroducion The Federal Open Marke Commiee adjuss he sance of moneary policy primarily by changing is arge range for he effecive federal funds rae (EFFR). The EFFR is a marke rae on overnigh ransacions beween banks and oher insiuions ha are eligible o paricipae in he federal funds marke. The aggregae supply of reserves in he banking sysem is currenly abou $2 rillion (Board of Governors of he Federal Reserve Sysem, 2018), far in excess of wha mos observers believe o be he quaniy ha banks need o hold o mee reserve requiremens and liquidiy needs. Trading in he fed funds marke a presen is herefore largely moivaed by insiuions desire o arbirage differences beween he ineres rae ha he Fed pays on excess reserves held by deposiory insiuions and oher, lower money marke raes (Ihrig, Meade, and Weinbach, 2015). Figure 1 shows he EFFR, he ineres rae on excess reserves (IOER), and wo oher imporan ineres raes in he period since he FOMC began increasing ineres raes on December 17, The EFFR has ypically been sable a a poin parway beween IOER and he ineres rae a he Fed s overnigh reverse repurchase agreemen (ON RRP) faciliy, excep ha he EFFR spikes downward a he end of mos monhs. Meanwhile, unil 2018, marke repo raes measured in he figure by he Federal Reserve Bank of New York s Broad General Collaeral Rae (BGCR) index ypically remained close o he ON RRP rae. More recenly, marke repo raes have risen significanly above he ON RRP rae, he fed funds rae has moved up oward IOER, and he monh-end and quarer-end spikes have become smaller. In his paper, we build a simple model of how he level of he EFFR is affeced by changes in he Federal Reserve s policy ools, bank balance shee coss, and oher marke ineres raes, in an environmen wih abundan reserves. The model explains he key dynamics shown in Figure 1, including he posiion of EFFR beween IOER and ON RRP, he monh-end spikes, and he changes in hese magniudes in We calibrae he model o a subse of he daa, validae i ou of sample, and use i o assess he causes of recen rae dynamics as well as he consequences of a reducion in deposi insurance premiums ha is scheduled o ake place no laer han he end of The core of he model is a bargaining problem beween lenders and borrowers in he

4 ineres rae (%) /1/2016 7/1/2016 1/1/2017 7/1/2017 1/1/2018 ineres on excess reserves Broad General Collaeral Repo overnigh reverse repo Effecive Federal Funds Rae Figure 1: Money marke ineres raes since he sar of policy normalizaion. Source: Federal Reserve Bank of New York. BGCR daa before April 2, 2018, are indicaive hisorical values. fed funds marke, similar o Bech and Klee (2011). Because boh deposiory insiuions and governmen-sponsored enerprises (GSEs) can hold reserves bu only deposiory insiuions can earn ineres on reserves, here are gains from rade whenever a GSE lends o a deposiory insiuion, which he borrower and lender mus divide in some manner. We assume ha he paries spli he gains from rade according o generalized Nash (1950) bargaining: Each pary receives a share of he surplus proporional o is bargaining power. We exend he lieraure by modeling in more deail he gains from rade and he ouside opions of he players. Firs, whereas Bech and Klee (2011) assumed arbirage was cosless for banks, we allow for banks o have coss of expanding heir balance shees o borrow fed funds and for ha cos o vary beween domesic and foreign banks; his aspec of he model allows us o assess how a change in deposi insurance premiums would move he fed funds rae. Second, we explicily model how he ON RRP rae and repo raes affec GSEs ouside opion and 2

5 hence he gains from rade; his allows us o examine he relaionship beween he rise in repo raes and he rise in he fed funds rae in Third, in our model, he ouside opion when a GSE is bargaining wih one bank includes he possibiliy of bargaining wih a differen bank; his feaure allows us o explain how he rae can be influenced by insiuions ha are no paries o he ransacion. Our model views he fed funds marke as involving a small number of well-informed borrowers and lenders. We absrac from search fricions or imperfec informaion abou counerparies coss and reurns fricions ha play a key role in he search-based models of Armener and Leser (2017) and Afonso, Armener, and Leser (2018) so ha we can highligh he way ha he fed funds rae is deermined by how insiuions spli a ime-varying surplus. We view his absracion as reasonable given ha he fed funds marke is populaed by a relaively small number of insiuions ha rade wih each oher repeaedly and can easily become well informed abou he regulaions and ineres raes ha drive marginal coss and benefis of borrowing and lending. Similarly, we absrac from mos heerogeneiy beween banks in order o highligh one paricularly impacful form of heerogeneiy: he differen regulaions facing domesic and foreign banks in he U.S. marke. These simplificaions mean ha our model can explain he cenral endency of raes in he federal funds marke he official EFFR is a volume-weighed median of raes on differen ransacions bu no he heerogeneiy in ransaced raes. In addiion, he model assumes an environmen wih high levels of excess reserves and herefore, unlike Afonso, Armener, and Leser (2018), has lile o say abou he comparaive saics of changes in he supply of reserves. However, we do allow for reserves o have some scarciy value and le he daa ell us wheher his value has changed since he Fed began o shrink he supply of reserves in lae We have four key findings. Firs, we find ha insiuions and faciliies ha are no acive in he marke can noneheless significanly influence he fed funds rae. For example, in he model, he ON RRP faciliy is no used, consisen wih he very low observed volumes in his faciliy, bu is rae noneheless affecs he fed funds rae. Similarly, domesic banks balance shee coss affec he fed funds rae even hough hey are no he main borrowers in he marke away from quarer-end. Second, he model predics ha exogenous changes in 3

6 repo raes pass hrough o he fed funds rae bu by less han one-for-one. Third, he model passes our ou-of-sample es. Given parameers calibraed o mach 2017 daa, he model quaniaively maches he runup in he fed funds rae in 2018 when we feed in he observed changes in repo raes. According o he model, he rise in he fed funds rae in 2018 can be compleely explained by changes in repo raes. There is no need o assume ha he scarciy value of reserves increased as a resul of a reduced supply of reserves. Finally, we find ha a reducion in deposi insurance premiums would increase he fed funds rae, bu by only a small fracion of he change in he premium on mos days. The paper proceeds as follows. Secion 2 provides background on he evoluion of he federal funds marke over he pas decade. Secion 3 describes he model. Secion 4 uses informaion on he observed federal funds rae in 2017 and various regulaions o calibrae he model parameers and o calculae bounds on he parameers under somewha weaker assumpions. Secion 5 shows ha he model calibraed o 2017 daa succeeds in quaniaively maching he pass-hrough of an increase in repo raes o he federal funds rae in Secion 6 examines he effecs of he scheduled reducion in deposi insurance premiums. Secion 7 discusses some possible inerpreaions of he bargaining power parameers ha are a he core of he model. Secion 8 concludes. 2. Background The naure of he federal funds marke oday has changed dramaically relaive o he period prior o he financial crisis. In he pre-crisis period, he Federal Reserve did no have he auhoriy o pay ineres on reserves. As a resul, banks demand for reserves semmed largely from mandaory reserve requiremens and he desire o avoid penalies for any deficiency in meeing hese requiremens. In ha environmen, he economic value of reserves a he margin was deermined largely by he aggregae quaniy of reserves supplied by he Federal Reserve relaive o banks aggregae demand for reserves. While he aggregae quaniy of reserves supplied each day closely mached esimaes of he aggregae demand for reserves, he reserve posiions of individual banks on any given day could be srongly affeced by shocks semming from paymens inflows and ouflows on behalf of cusomers. Toward he end of he day, some banks would be lef wih larger quaniies of reserves han hey 4

7 desired, while oher banks would be lef shor of heir desired end-of-day reserve posiions. The banks ha were shor reserves hen had a srong incenive o borrow in he federal funds marke o avoid he risk of a reserve requiremen deficiency. And he banks ha were lef wih larger-han-desired end-of-day reserve posiions had a srong incenive o lend o avoid holding large quaniies of a non-ineres-bearing asse. In shor, he pre-crisis federal funds marke involved acive inerbank rading as a mechanism ha allowed banks o offse he unexpeced shocks o heir reserve posiions in an environmen where he aggregae quaniy of reserves was se close he esimaed aggregae demand for reserves a he arge federal funds rae. The curren aciviy in he federal funds marke is enirely differen. In responding o he financial crisis, he Federal Reserve engaged in a series of large scale asse purchase programs ha dramaically expanded he size of is balance shee, from less han $1 rillion in oal asses in 2007 o abou $4.5 rillion oday. Tha expansion in Federal Reserve asses was associaed wih an enormous increase in he level of reserves in he banking sysem. Prior o he crisis, he level of reserves in he banking sysem amouned o only abou $20 billion. Today, reserve balances are abou $2 rillion (Board of Governors of he Federal Reserve Sysem, 2018). In his environmen of superabundan reserves, he key facor ha led o acive inerbank rading in he funds marke in he pre-crisis period unexpeced paymens flows among banks no longer provides a srong incenive for inerbank rading. Unexpeced paymens flows are sill presen, bu mos banks hold such large quaniies of reserves ha even sizable ouflows on any given day pose essenially no risk of a reserve requiremen deficiency. Moreover, he Federal Reserve now pays ineres on reserves. As a resul, a bank ha experiences a large reserve inflow no longer has a srong incenive o lend reserves a a rae below ha i can earn by leaving balances a he Fed. As a resul, inerbank rading in he federal funds marke is now very small and idiosyncraic. The remaining volume in he federal funds marke reflecs aciviy in which banks borrow on an overnigh basis from GSEs principally he Federal Home Loan Banks (FHLBs) ha are no eligible o earn ineres on heir balances a he Federal Reserve bu ha can paricipae in he federal funds marke. In effec, he federal funds marke is now jus anoher overnigh funding source for 5

8 banks, and he volume of aciviy in he marke is deermined by he ineracion beween bank funding needs and he availabiliy of funding from nonbank lenders. Anoher imporan change in he pos-crisis environmen is ha he Federal Reserve has implemened he ON RRP faciliy, which is available o a wide array of lenders in overnigh funding markes banks, primary dealers, Federal Home Loan Banks and oher GSEs, and money marke muual funds (MMMFs). The ON RRP program allows hese eniies o place overnigh funds a he Federal Reserve a a predeermined rae currenly se 25 basis poins below he IOER rae. The ON RRP rae hus creaes a floor on he rae a which hese eniies will lend o ohers in privae funding markes. As a resul, he ON RRP program and he ON RRP rae poenially exer a srong influence over he level of he raes observed in boh secured and unsecured overnigh funding markes. These changes in he micro srucure of he federal funds marke in urn have surfaced imporan ineracions beween aciviy in he federal funds marke and he inermediaion coss faced by differen ypes of banks. In paricular, branches and agencies of foreign banks operaing in he Unied Saes make up a subsanial share of he borrowing aciviy in he federal funds marke. The volume of borrowing by domesic commercial banks, by conras, is relaively small. Moreover, here are predicable paerns in he behavior of he federal funds rae, wih he rae ypically dropping subsanially a monh-ends and quarer-ends, as Figure 1 shows. Volume in he federal funds and oher overnigh funding markes ofen falls sharply on hese days, and volume a he Federal Reserve s ON RRP faciliy ofen increases sharply. Monh-end and quarer-end changes in raes and volumes in he federal funds marke are shor lived, bu hey provide some imporan clues abou how various bank regulaory policies may be affecing bank asse-liabiliy managemen and he behavior of overnigh raes in bank funding markes. For example, domesic commercial banks generally mus mee a leverage raio requiremen based on heir average oal asses mainained over a quarer. Moreover, hese insiuions are subjec o Federal Deposi Insurance Corporaion (FDIC) deposi insurance premiums ha are also based on average oal asses mainained over a quarer. In conras, mos foreign branches are no FDIC insured and hus do no pay deposi insurance premiums. In addiion, many of hese insiuions are subjec o a leverage raio 6

9 requiremen based on monh-end or quarer-end asses raher han daily average asses. A number of papers have poined o hese differences in he regulaory reamen of domesic and foreign insiuions as a key facor explaining he curren behavior of he federal funds marke. (See, e.g., Keaing and Macchiavelli, 2017.) Because domesic banks face higher coss on mos days in he form of deposi insurance premiums and a leverage raio based on daily-average asses, hey are no able o pos bids for funds ha compee effecively wih bids from foreign branches. Wihou deposi insurance premiums or a leverage raio consrain o worry abou on mos days, even a small spread beween IOER and he federal funds rae provides a posiive reurn o a foreign branch borrowing in he funds marke bu is no enough o allow domesic banks o cover deposi insurance premiums and he implici capial coss semming from he leverage raio requiremen. On monh-ends and quarerends, foreign branches are concerned abou he size of heir balance shees and acively seek o reduce heir required capial by paring he size of heir balance shees on hose days. Bu regulaory balance shee coss are likely no he only facor deermining he federal funds rae. As discussed, foreign banks effecively have no marginal cos of borrowing reserves a mid-monh. If here were perfec compeiion among foreign banks for he opporuniy o borrow from fed funds from FHLBs, he FHLBs would drive he borrowers o heir reservaion price, IOER. In pracice, his does no happen; he fed funds rae is significanly below IOER even a mid-monh, implying ha he borrowing banks have some marke power ha allows hem o pay less han heir reservaion price. Our model provides a quaniaive framework for undersanding how he inerplay beween balance shee coss and bargaining power deermines he fed funds rae and is dynamics over ime. 3. Model This secion describes he economic environmen and he bargaining problem beween banks and a non-bank invesor, hen solves for he equilibrium federal funds rae as a funcion of banks balance shee coss, he invesor s alernaive invesmen opions, and banks bargaining power. 7

10 A. Environmen We assume he marke conains hree agens: a represenaive GSE invesor, a represenaive domesic bank, and a represenaive foreign bank. In realiy, of course, here are muliple insiuions of each of hese ypes. The model absracs from he heerogeneiy and compeiion wihin hese groups in order o highligh he role of differences across he groups, such as he differen balance shee coss of foreign vs. domesic banks. However, he model conains parameers ha, as we discuss furher in secion 6, migh be aken o reflec he srengh of compeiion wihin each group. The non-bank has reserves ha earn zero ineres if kep in is own reserve accoun, bu he non-bank can also inves hese reserves in repurchase agreemens, or repo, or can lend hem o eiher he domesic or he foreign bank in he federal funds marke. A repo can be conduced wih he Federal Reserve s overnigh reverse repurchase agreemen (ON RRP) faciliy a he annual ineres rae onrrp or wih a privae counerpary a he marke rae repo. Le repo = max {onrrp, repo} denoe he higher of hese wo raes. We ake he marke repo rae as exogenous and do no model is deerminaion. Boh domesic and foreign banks earn ineres on reserves a he annual ineres rae ioer. If reserves are abundan, his is he only reurn on reserves. We also consider he possibiliy ha reserves are no abundan and have a scarciy value z 0 associaed wih heir usefulness in meeing paymen obligaions or saisfying regulaory requiremens. A bank s oal reurn on reserves is herefore ioer + z. In mos of he analysis, we will ake z o be 0 for all banks, reflecing he curren abundance of reserves, bu i would be possible o apply he model o siuaions where z is posiive for domesic banks, foreign banks, or boh. Domesic (d) and foreign (f) banks differ in heir balance shee coss. Balance shee coss are calculaed over a regulaory ime period. In our benchmark calibraion, his ime period will be a quarer, bu i could also be a monh. The regulaory ime period has T days if he regulaory period is a quarer, T = 90, and if he regulaory period is a monh, T = 30. Each bank i {d, f} pays a per-regulaory-period cos ha depends on some combinaion of is daily average asses and is asses a he end of he period. Le A i, be he asses of bank i on day {1, 2,..., T } of he period. The balance shee cos of bank i for 8

11 he enire regulaory period, expressed in dollars, is C i ({A i, } T =1) = τ i [ θ i 1 T ] T A i, + (1 θ i )A i,t, (1) =1 where we assume θ i [0, 1]. The parameer θ i indexes he exen o which bank i s balance shee cos depends on daily average asses vs. period-end asses. If θ i = 1, he balance shee cos depends only on daily average asses, while if θ i = 0, he balance shee coss depends only on period-end asses. The parameer τ i > 0 measures how balance shee coss respond o changes in asses. Boh θ i and τ i should be inerpreed as reflecing boh formal regulaions and less formal coss of balance shee. For example, even if a bank faces only daily-average regulaions, i sill migh be concerned abou shareholders reacion o quarer-end balance shee numbers published in financial saemens and hus have θ i < 1. Even if a bank faces only quarerend regulaions, i migh be concerned abou mid-quarer balance shee if here are coss of adjusmen no explicily included in our model and hus have θ i > 0. We assume ha banks can adjus heir asses on a daily basis. The marginal cos of expanding he balance shee by $1 on day, expressed in dollars, is herefore [ ] C i 1 = τ i A i, T θ i + (1 θ i ) 1( = T ), (2) where we define 1( = T ) o equal 1 when = T and equal 0 oherwise. I is useful o express he marginal cos as an annual ineres rae: mc i = 360 C [ ] i 1 = 360τ i A i, T θ i + (1 θ i ) 1( = T ). (3) We assume ha τ d > τ f (4) and θ d > θ f. (5) In oher words, he domesic bank has higher marginal balance shee coss, bu also balance 9

12 shee coss ha depend more on daily average asses and less on period-end asses. There are gains from rade when he invesor lends o bank i if and only if he bank s ne reurn on reserves is greaer han wha he invesor could earn in he repo marke: repo < ioer + z mc i. (6) The marke will behave differenly when here are gains from rade a boh banks han when only one bank saisfies (6). B. Bargaining Each day, he non-bank invesor bargains sequenially wih he wo banks over he ineres rae on he invesmen. Specifically, he invesor chooses one bank o bargain wih firs. If he invesor and he bank agree on an ineres rae, he invesor leaves is funds wih his bank for he nigh. If hey do no agree, he invesor can bargain wih he second bank bu if his second round of bargaining fails, i is no allowed o reurn o he firs bank and mus inves in repo. The invesor and he banks use Nash bargaining o agree on an ineres rae. Nash bargaining means ha he wo paries he invesor and one of he banks spli he surplus, if any, from heir ransacion according o a prespecified bargaining weigh. If no gains from rade are possible because (6) does no hold for he bank in quesion, no agreemen is reached and he invesor lends o a differen bank or in repo. Le s i (r) be he surplus of bank i on day if i borrows from he invesor a rae r. Likewise, le v ij (r) be he surplus of he invesor if i lends o bank i a rae r in he jh negoiaion of day (where j = 1 or 2). We will see ha he invesor s surplus depends boh on which round of bargaining i is in and which bank i is negoiaing wih, even hough i always has he ouside opion of invesing in repo. Le β i [0, 1] be he bargaining weigh of bank i when bargaining wih he invesor. Nash bargaining assumes ha, if gains from rade are possible, hen he invesor and he bank agree o a loan a he rae rij = arg max[s i (r)] β i [v ij (r)] 1 β i. (7) r 10

13 To find he equilibrium ineres rae, we need o define he surplus funcions s i (r) and v(r). If a bank reaches no agreemen, i earns nohing; if i reaches an agreemen, i earns ioer and receives he scarciy value z bu pays is balance shee cos and he rae owed o he invesor. The bank s surplus is he difference beween he profi if an agreemen is reached and he ouside opion of earning nohing so he surplus is ioer + z minus he balance shee cos minus he fed funds rae. Thus s i (r) = ioer + z mc i r. (8) Meanwhile, he surplus of he invesor is he difference beween he ineres rae i receives and wha i could ge if i abandons his negoiaion and pursues oher opions. Le r ij be he invesor s ouside opion when bargaining wih bank i in he jh negoiaion on day. The ouside opion is differen in he firs round (j = 1) han in he second round because afer he firs round, he ouside opion sill includes he possibiliy of negoiaing wih anoher bank, whereas in he second round he only ouside opion is repo. And in he firs round, he invesor s ouside opion depends on which bank is being negoiaed wih because abandoning he negoiaion wih one bank implies he opion o negoiae wih he oher bank. Wih his noaion, if bank i and he invesor are bargaining on day, if his is he invesor s jh negoiaion of he day, and if (6) holds for bank i, he ineres rae hey agree on is: rij = arg max [ioer + z mc i r] β i [r r ij ] (1 β i) r = (1 β i ) [ioer + z mc i ] + β i r ij. (9) There is an imporan disincion in his framework beween a pary s bargaining weigh and is ouside opion. The ouside opion is wha a pary can ge if i reaches no agreemen. A pary wih a beer ouside opion ges a beer deal because oherwise i will prefer no o agree. The bargaining weigh is how he paries divide he surplus, aking heir ouside opions as given. As a pary s bargaining weigh increases, i ges a larger share of he surplus, even hough here is no change in he ouside opion i will ge wihou an 11

14 agreemen. The bargaining weigh of he single represenaive bank of ype i may be aken as reflecing he amoun of compeiion among he muliple real-world banks of ha ype for example, if here are many foreign banks, we would expec each of hem o have lile bargaining power, holding fixed he ouside opion of any foreign bank. C. Soluion Three cases are possible on any given day: here may be gains from rade a neiher bank, a only one bank, or a boh banks. We consider hese possibiliies in urn. Gains from rade a neiher bank If here are no gains from rade a eiher bank on a given day, hen he invesor canno reach agreemen when bargaining wih eiher bank. The invesor uses repo, and he fed funds marke does no operae on ha day. Gains from rade a only one bank If here are gains from rade a only one bank on a given day, he invesor will bargain wih ha bank. If he negoiaion fails, he invesor will urn o repo because here is no possibiliy of an agreemen wih he oher bank. Le i be he bank where here are gains from rade. The invesor s ouside opion when bargaining wih ha bank is r i,1 = repo. The equilibrium fed funds rae is he rae ha he invesor and bank i agree on: r,1 bank = r i,1 = (1 β i )(ioer + z mc i,) + β i repo. (10) If here are gains from rade a only one bank, hen he fed funds rae depends on he bargaining power and balance shee coss of ha bank, as well as on ioer and repo, bu is no influenced by he bargaining power and balance shee coss of he bank where here are no gains from rade. The influence of ioer and repo depends on he bank s bargaining power. When he bank has high bargaining power, i drives he invesor close o he invesor s ouside opion, which is repo; hus, he passhrough of he repo rae o he fed funds rae is high, and he passhrough of ioer is low. Conversely, when he bank has low bargaining power, he invesor drives he bank close o is ouside opion, which is ioer minus marginal cos; he passhrough 12

15 of he repo rae is low, and he passhrough of ioer is high. The scarciy value z has he same effec on he fed funds rae as ioer. Gains from rade a boh banks If here are gains from rade a boh banks on a given day, wo rounds of negoiaions become possible he invesor can urn o he second bank if negoiaions wih he firs bank fail. Consider firs wha happens in he second negoiaion of he day (j = 2), if i occurs. The invesor s ouside opion in his case is o pu he funds in repo. Therefore r i1 = repo, and [ ri2 = arg max ioer + z 1 ] β r T τ iθ i τ i (1 θ i )1( = T ) r [r repo ] (1 β i) i [ = (1 β i ) ioer + z 1 ] T τ iθ i τ i (1 θ i )1( = T ) + β i repo (11) = (1 β i )(ioer + z) + β i repo (1 β i )mc i. Now consider he firs negoiaion of he day. The invesor s ouside opion is o pursue a second negoiaion, in which case i can ge r i,2, where i is he bank ha is no negoiaed wih firs. Therefore, [ ri1 = (1 β i ) ioer + z 1 ] T τ iθ i τ i (1 θ i )1( = T ) + β i r i,2 [ = (1 β i ) ioer + z 1 ] T τ iθ i τ i (1 θ i )1( = T ) [ + β i (1 β i ) ioer + z 1 ] T τ iθ i τ i (1 θ i )1( = T ) + β i β i repo = (1 β d β f )(ioer + z) + β d β f repo (1 β i )mc i β i (1 β i )mc i,. (12) Which bank should he invesor bargain wih firs? Since (6) holds for boh banks, ri1 > ri2 so if he invesor is going o lend o bank i, i prefers o do so in he firs round of bargaining. Therefore, he invesor will maximize is profi by firs bargaining wih he bank ha has he higher ri1 (and agreeing o his bargain raher han moving o he oher bank). The difference in firs-round raes beween he foreign and domesic banks is proporional o 13

16 he difference in heir marginal coss: [ rf1 rd1 τd θ d τ f θ f = (1 β f )(1 β d ) T = (1 β f )(1 β d )(mc d mc f ). ] + [τ d (1 θ d ) τ f (1 θ f )]1( = T ) (13) Thus, he invesor lends each day o whichever bank has he lower marginal balance shee cos on ha day. Le i be his bank, and le i be he oher bank. Then he equilibrium ineres rae is r,2 banks = (1 β d β f )(ioer + z) + β d β f repo (1 β i )mc i, β i (1 β i )mc i,. (14) If here are gains from rade a boh banks, hen he fed funds rae depends on he bargaining power and balance shee coss of boh banks, even hough he invesor lends only o one of he banks he one wih he lower marginal balance shee cos. The passhrough of oher ineres raes o he fed funds rae depends on he combined bargaining power of he wo banks, β d β f : When combined bank bargaining power is high, he passhrough of repo is high, and when combined bank bargaining power is low, he passhrough of ioer is high. Jus as when here are gains from rade a only one bank, he scarciy value z has he same effec on he fed funds rae as ioer. If he bank wih he lower marginal cos has no bargaining power (β i = 0), equaion (14) reduces o r = ioer + z mc i,, (15) which is he oucome under perfec compeiion he price of inermediaion in he fed funds marke is se equal o is marginal cos, mc i,. Undersanding end-of-period rae movemens According o he model, hree facors deermine how he fed funds rae changes a he end of he regulaory period. Firs, marginal balance shee coss change a he end of he period. Second, because marginal balance shee coss change, he ideniy of he lowes-cos bank can change, and he influence of each bank s bargaining power on he fed funds rae 14

17 depends on wheher ha bank is he lowes-cos bank. Finally, if repo raes move on he las day of he period for reasons ouside he model, ha movemen will pass hrough parially o he fed funds rae. 4. Parameer values The model has eigh parameers: β d, θ d, τ d, β f, θ f, τ f, T, z. We calibrae hese parameers based on observed ineres raes and known informaion abou balance shee coss and regulaions. Beyond he calibraion, we look for bounds on possible values of he parameers given observed ineres raes. We calibrae he model o daa from 2017; laer, we will es he model s predicions ou of sample in 2018 daa. Because reserves were generally agreed o be super-abundan in 2017, we assume ha he scarciy value of reserves z was zero in ha year and search for values of he oher seven parameers. A. Calibraion Domesic banks are generally regulaed based on daily average asses, while foreign banks are generally regulaed based on eiher quarer-end or monh-end asses. This suggess ha he regulaory period should be eiher one quarer (T = 90) or one monh (T = 30). However, Figure 1, shows ha he behavior of he fed funds rae in 2017 was he same a all monh-ends, wheher hey fell a he end of a quarer or no. If we se T = 90, he model could no explain his paern because balance shee coss would be he same a mid-quarer monh-ends as on days in he middle of a monh. We herefore se T = 30. In line wih he regulaions, we assume ha domesic banks care only abou daily average asses (θ d = 1) and ha foreign banks care only abou period-end asses (θ f = 0). Balance shee coss poenially sem from leverage raio requiremens as well as FDIC assessmens. Foreign banks ypically are no subjec o FDIC assessmens, 1 while domesic banks are assessed a percenage of daily average asses. We se he domesic FDIC assessmen a an annual ineres rae of 0.07%, he average value esimaed by Banegas and Tase (2016). Foreign banks ypically have a required leverage raio he raio of equiy o oal 1 Few foreign banks apply for deposi insurance. Those ha do apply for deposi insurance are subjec o FDIC assessmens and should be reaed as having he same balance shee coss as domesic banks in our framework. 15

18 asses of 3% under Basel III. If his is a binding consrain, if he required reurn on equiy is 10%, and if equiy mus be held for an enire monh, hen each addiional $100 of borrowing on he las day of he period coss he foreign bank $0.30/12=$ Expressed as an annual ineres rae, he cos is 9%, far in excess of he 25-basis-poin spread beween ioer and onrrp. Even very shor holding periods and near-zero required reurns on equiy do no change he basic conclusion ha an end-of-period leverage raio requiremen eliminaes all gains from rade in lending o foreign banks a he end of he regulaory period. For example, a one-monh holding period and a reurn on equiy of jus 50 basis poins implies coss of 45 basis poins a an annual ineres rae, while a wo-day holding period and a reurn on equiy of 5% implies coss of 30 basis poins a an annual ineres rae. We herefore do no choose a specific value for foreign bank balance shee coss bu simply assume ha hey are high enough o eliminae foreign borrowing a period end: 360τ f > 0.25%. The larges domesic banks can have a required leverage raio of 6% due o he supplemenary leverage raio. Bu i is no clear ha his consrain is binding. Call repor daa show ha all of he domesic banks subjec o a 6% leverage raio requiremen repored a raio well above ha hreshold as of he end of 2017 (Federal Financial Insiuions Examinaion Council, 2017). Furhermore, he same calculus as for foreign banks implies ha a binding leverage raio consrain would drive domesic banks ou of he fed funds marke for any reasonable reurn on equiy: If he 6% leverage raio were binding for domesic banks, hen any required reurn above 4.2% would produce a balance shee cos above 25 basis poins. Since in pracice he fed funds marke does no shu down a monh ends, we conclude ha he leverage raio is no a binding consrain for domesic banks and ha heir only balance shee cos relevan o our model is he FDIC assessmen. This requires mc d = 0.07% and hence τ d = 0.07% (T/360). We now use informaion on observed ineres raes o find he values of β d and β f. Since he Federal Open Marke Commiee began he process of normalizing ineres raes in December 2015, ioer has always been se 25 basis poins above onrrp. Furher, before 2018, repo raes remained very close o onrrp, and he minor differences beween marke repo raes and onrrp could have been due o deails such as he naure of he counerparies or he ime of day of he ransacions. For simpliciy, herefore, we assume ha he ON RRP faciliy was 16

19 Table 1: Disribuion of he difference beween he federal funds rae and he ineres rae on excess reserves, 12/17/2015 4/25/2018 Saisic Quarer-end Oher monh-end All oher days 12/17/ /14/2016 mean minimum maximum observaions /15/ /13/2017 mean minimum maximum observaions /14/2017 5/14/2018 mean minimum maximum observaions All values in basis poins. he bes repo opion during he calibraion period: repo = onrrp. Table 1 shows he disribuion of he effecive federal funds rae relaive o ioer during he curren ighening cycle. During he firs year afer normalizaion began, from he December 2015 FOMC meeing o he December 2016 meeing, he fed funds rae displayed some volailiy even a mid-monh, as illusraed in Figure 1. Bu in he second year, from he December 2016 o December 2017 FOMC meeings, he fed funds rae was almos exacly 16 basis poins above onrrp and 9 basis poins below ioer a mid-monh, and ypically 18 basis poins below ioer a monh- or quarer-end. We calibrae he model o mach ha second year of daa, hen ask wheher i can explain he subsanially differen paern of raes since he December 2017 FOMC meeing. Our calibraed balance shee coss imply ha here are gains from rade when he invesor lends o eiher bank a mid-monh, while a monh-end here are gains from rade only when he invesor lends o he domesic bank. Thus, he equilibrium fed funds rae saisfies (14) a mid-monh (wih i = f) and saisfies (10) a monh-end (wih i = d). 17

20 Hence we require he parameers o saisfy ioer = (1 β d β f )(ioer + z) + β d β f repo (1 β f )mc f,<t β f (1 β d )mc d,<t (16a) ioer = (1 β d )(ioer + z mc dt ) + β d repo (16b) The soluion o hese equaions is shown in Table 2, along wih he oher parameer values are. The foreign bank capures exacly half he surplus when i negoiaes wih he invesor, while he domesic bank capures slighly more han half. Inuiively, given ha he foreign bank has no balance shee cos a mid-monh, is bargaining weigh mus be 0.5 because he fed funds rae a mid-monh is halfway beween ioer and he monh-end rae, and he monh-end rae paid by domesic banks represens wha he invesor could receive if i abandoned negoiaions wih he foreign bank. The calibraed bargaining weighs have direc implicaions for he influence of repo raes on he fed funds rae. A monh end, according o (10), each basis poin change in repo moves he fed funds rae by β d, or 0.61 basis poin in our calibraion. A mid-monh, according o (14), he pass-hrough is weaker: Each basis poin change in repo moves he fed funds rae by β d β f, or 0.31 basis poin in our calibraion. B. Bounds The observed ineres raes allow us o find some bounds on he model parameers while making only minimal assumpions abou balance shee coss. If boh banks had maximal bargaining power, β d = β f = 1, he fed funds rae would be driven down o onrrp regardless of balance shee coss. Tha he rae is no driven so low gives us an upper bound on banks bargaining power. Conversely, if neiher bank had any bargaining power, β d = β f = 0, he fed funds rae would be driven up o ioer + z minus he lowes marginal balance shee cos on any given day. Tha he fed funds rae does no rise all he way o ioer shows ha banks mus have some bargaining power or balance shee coss. To make his analysis quaniaive, we assume ha he parameers saisfy several condiions. Firs, we fix T = 30, z = 0, θ d = 1, and θ f = 0. Second, we coninue o assume 18

21 Table 2: Calibraed parameer values Parameer Value Scarciy value of reserves z 0 Asse calculaion T 30 θ d 1 θ f 0 Balance shee coss τ d T/360 τ f > /360 Bargaining weighs β d β f 0.5 ha 360τ f > 0.25%, so he foreign bank never borrows a monh-end. Third, we assume domesic balance shee coss are non-negaive. We hen seek bounds on β d, β f and τ d. The foreign bank s bargaining weigh β f is sharply idenified, using he same inuiion given for our calibraed parameer values. Regardless of he domesic bank s balance shee coss and bargaining weigh, he invesor s ouside opion a mid-monh if i does no bargain wih he foreign bank is o receive he monh-end rae 18 basis poins below ioer. Since he mid-monh rae is 9 basis poins below ioer, he foreign bank s bargaining weigh mus be 0.5 regardless of he remaining parameers. The fac ha he fed funds marke operaes a monh-end gives us an upper bound on he domesic bank s balance shee coss: hey mus no be larger han he observed spread beween ioer and he fed funds rae a monh end, or 18 basis poins a an annual ineres rae. Thus τ d T/360. (17) FDIC assessmens on large banks depend on a regulaory scorecard bu a presen are never less han 6 basis poins (Federal Deposi Insurance Corporaion, 2018), which provides a 19

22 lower bound on he domesic balance shee coss: τ d T/360. (18) Applying (10) a monh end gives us a fixed relaionship beween τ d and β d given he oher parameers: β d = τ d/t τ d /T. (19) Combining (17), (18), and (19) gives us bounds on he domesic bank s bargaining power: 0 β d (20) These bounds on he domesic bank s bargaining power in urn imply bounds on he passhrough of repo raes o he fed funds rae: beween 0 and 63.2% a monh-end, and beween 0 and 31.6% a mid-monh. 5. Ou-of-sample es: ineres raes in 2018 Figure 1 shows ha, since he December 2017 FOMC meeing, boh he fed funds rae and repo raes have risen subsanially wihin he range delimied by onrrp and ioer. We ake he rise in he repo rae as exogenous marke commenary has largely aribued i o increased issuance of Treasury bills and ask wo quesions. Firs, using he 2017 parameers and he exogenous change in he repo rae, how well does he model fi he daa on he fed funds rae in 2018? Second, does he model require any change in he scarciy value of reserves o explain he rise in he fed funds rae, or can i fi he daa while mainaining a scarciy value of zero despie he roughly $200 billion decrease in reserve supply since he Fed began normalizing is balance shee? On December 14, 2017, he firs day afer he December FOMC meeing, he Broad General Collaeral Rae (BGCR) repo index sood a 1.28%, 3 basis poins above onrrp and 22 basis poins below ioer. 2 On April 25, 2018, he BGCR index had risen o 1.67%, bu onrrp had risen o only 1.50%, so he spread had increased by 14 basis poins. We ake he 2 BGCR daa before April 2, 2018, are indicaive hisorical values and no an official reference rae. 20

23 iniial 3-basis-poin spread o onrrp as reflecing he price of differen deailed characerisics of he broad repo marke relaive o he ON RRP faciliy and assume ha repo increased by 14 basis poins more han onrrp and ioer over he period. According o (14), if balance shee coss and ioer are held fixed, a 1 basis poin increase in repo relaive o ioer causes an increase of β d β f in he fed funds rae relaive o ioer. Our calibraion has β d β f = Thus, he model predics ha he rise in repo raes should have caused he fed funds rae o increase relaive o ioer by 4.3 basis poins. In he daa, as shown in Figure 1 and Table 1, he fed funds rae rose by 4 basis poins relaive o ioer, closely maching our ou-of-sample predicion. The model predics a very slighly higher fed funds rae han acually occurred. The fed funds rae in he model is increasing in he scarciy value of reserves z, so he model does no need an increase in reserve scarciy o explain he rise in he fed funds rae in If anyhing, he model suggess ha he scarciy value fell slighly. Anoher noable feaure of Figure 1 is a change in he monh-end and quarer-end behavior of he fed funds rae. A he end of boh March and April 2018, he fed funds rae fell by only 1 basis poin, compared wih drops of 9 basis poins a previous monh ends. Can he changing dynamics of repo raes help explain he differen monh-end behavior of he fed funds rae in March and April? Recall ha in he calibraed model, he pass-hrough of repo raes o he fed funds rae is differen a monh end han a mid-monh because he foreign bank is no in he marke a monh-end. In paricular, according o (10), a 1 basis poin increase in repo a monh-end causes an increase of β d in he fed funds rae relaive o ioer. Our calibraion has β d = Thus, he calibraed model predics ha a 14-basis-poin increase in repo raes would raise he monh-end fed funds rae by 8.6 basis poins, or wice as much as he prediced 4.3-basis-poin increase a mid-monh. This implies ha he generally higher level of repo raes should have resuled in a monh-end fed funds rae drop of 4.7 basis poins, significanly smaller han he 9-basis-poin drops observed in In fac, he monh-end drop was jus 1 basis poin in boh March and April, so he generally higher level of repo raes explains no quie half of he change in monh-end dynamics. Bu in addiion, repo raes rose a he end of March and April, whereas in

24 repo raes were ypically sable a monh ends. For example, on he las day of April, he BGCR rae rose by 4 basis poins compared wih he previous rading day. In he calibraed model, a 4-basis-poin increase in repo a monh end predics an addiional 2.4 basis poin increase in he fed funds rae. Thus, combining he generally higher level of repo raes and he newly observed monh-end rises in repo raes, he model predics a monh-end fed funds rae drop of 2.3 basis poins, quie close o he 1-basis-poin drop in he daa. We can use he model o esimae he scarciy value of reserves. For any day, we can solve for he value of z such ha (14) (for mid-monh) or (10) (for monh-end) holds, given observed ineres raes and he calibraed values of he oher parameers. The calculaion requires a daily value for repo, and we canno jus ake he higher of he BGCR rae or he rae a he ON RRP faciliy because marke repo may have differen liquidiy or risk characerisics han a repo invesmen wih he Fed. On mos days in 2017, he BGCR rae was 1 o 3 basis poins above he ON RRP rae and invesmens in he ON RRP faciliy exceeded $90 billion (Federal Reserve Bank of New York, 2017). We herefore assume ha a 3-basis-poin spread of BGCR over onrrp makes invesors indifferen beween he wo invesmens and se repo = max {onrrp, BGCR }. On wo Good Friday holidays when he fed funds marke was open bu he repo marke was closed, we se repo o he previous day s value, on he assumpion ha invesors could have made forward-looking decisions abou wheher o place funds in he repo marke or in fed funds over he holiday weekend. Figure 2 shows he calculaed value of z. During he period beween he December 2016 and December 2017 FOMC meeings ha we use o calibrae he model, he scarciy value is generally almos exacly zero. However, he scarciy value drops below zero on a few daes when repo raes rose bu he fed funds rae did no respond, mos noably on June 30, 2017, when he BGCR rae rose 9 basis poins above onrrp. The model inerpres a rise in repo raes wihou a corresponding rise in he fed funds rae as a decrease in he scarciy value because if he scarciy value were consan, higher repo raes would raise he fed funds rae. An alernaive inerpreaion, ouside he model, is ha he elevaed repo raes embedded some risk or liquidiy premium relaive o he ON RRP faciliy on hose daes. Consisen wih his alernaive inerpreaion, oal invesmen in he ON RRP faciliy on June 30, 22

25 5 scarciy value (basis poins) /1/2017 4/1/2017 7/1/ /1/2017 1/1/2018 4/1/2018 calibraion daa scarciy value repo marke closed Figure 2: Implied scarciy value of reserves. Source: Auhors calculaions. 2017, was $399 billion (Federal Reserve Bank of New York, 2017), he fourh-highes level ever observed and more han $100 billion above he amouns invesed in ON RRP on he immediae previous and subsequen days, suggesing ha invesors had some reason o prefer ON RRP o repo on ha day even hough he marke repo rae significanly exceeded he rae a he ON RRP faciliy. Afer he December 2017 FOMC meeing, he scarciy value becomes more volaile bu remains wihin a few basis poins of zero on almos all days. When he scarciy value deviaes from zero, i is almos always negaive, no posiive, and on he few days when i is posiive, i is jus 1 basis poin. Thus, he rise in repo raes is more han enough o explain he rise in he fed funds rae in A he end of December 2017 and he end of March 2018, he scarciy value spikes sharply downward because repo raes rose bu he fed funds rae did no move as much as 23

26 he model predics in response. Again, an alernaive inerpreaion is ha marke repo invesmens carried an elevaed risk or liquidiy premium a hose imes. 6. The effecs of a reducion in deposi insurance premiums The FDIC currenly collecs a surcharge of 4.5 basis poins (a an annual rae) on he asses of large domesic banks o raise money o increase is deposi insurance fund. This surcharge will end when he deposi insurance fund s asses reach a specified arge or on December 31, 2018, whichever comes firs (Federal Deposi Insurance Corporaion, 2016). We can use our model o assess how he removal of he surcharge will affec he fed funds marke and he EFFR. Under our calibraion, reducing domesic banks FDIC assessmen by 4.5 basis poins would cu heir balance shee cos o 2.5 basis poins a an annual rae. Tha cos would sill leave domesic banks as he low-cos borrower a monh-end and foreign banks as he low-cos borrower a mid-monh. However, he equilibrium ineres rae will change a monh-end because he domesic borrower s coss are lower, and a mid-monh because he ouside opion of invesing wih a domesic bank is more aracive and forces foreign banks o offer he invesor a beer deal. According o (10), a reducion of 4.5 basis poins in he domesic bank s balance shee cos raises he fed funds rae ha a domesic bank would pay which is he equilibrium rae a monh-end by (1 β d ) 4.5 basis poins, or 1.75 basis poins wih our calibraed value of β d = Turning o mid-monh, according o (14), a reducion of 4.5 basis poins in he domesic bank s balance shee cos raises he fed funds rae ha a foreign bank would pay by β f (1 β d ) 4.5 basis poins, or 0.88 basis poins wih our calibraed value of β f = 0.5. The removal of he 4.5 basis poin FDIC surcharge is hence prediced o increase he fed funds rae by a bi less han 2 basis poins a monh end and a bi less han 1 basis poin a mid-monh, all else equal. Imporanly, our calculaion assumes ha he change in he FDIC assessmen does no affec repo raes. If repo raes were o change as a resul of he removal of he surcharge, he movemen in repo raes would parially pass hrough o he fed funds rae and he oal effec of he policy change would be larger. 24

27 7. Inerpreing he bargaining power parameers The model makes i sraighforward o consider he effec of changes in bargaining power on he fed funds rae. Suppose, for example, ha he domesic bank has more bargaining power when i bargains wih he invesor: β d > β d. This direcly changes he relaionship beween he domesic bank and he invesor bu affecs he foreign bank only hrough he change in he invesor s ouside opion. Specifically, he invesor s ouside opion when bargaining wih he foreign bank is now worse. As a resul, he fed funds rae falls even when he invesor lends o he foreign bank. However, we mus be careful in considering wha consiues an increase in domesic banks bargaining power i is an increase in marke power among domesic banks. We will argue ha such an increase would likely be associaed wih a reducion in he number of domesic banks compeing in he fed funds marke. A change ha allowed more domesic banks o compee in he fed funds marke would likely be associaed wih a decrease in heir bargaining power. Thus, bargaining power is likely o be associaed wih he coss of enry ino banking (or, more specifically, ino he marke for borrowing reserves from GSEs) We formalize his argumen by supposing ha he economy conains N banks, indexed by i = 1,..., N, each wih bargaining weigh β i and marginal cos of balance shee mc i. To keep he noaion simple, we se he scarciy value o z = 0. Assume as before ha he invesor mus bargain sequenially, choosing a bank o bargain wih firs, proceeding o anoher bank if i canno reach an agreemen wih he firs bank, and so on, bu never reurning o a bank afer leaving i. Wihou loss of generaliy, we assume β i < 1 and mc i < ioer repo for all i. (If some bank had a bargaining weigh of 1, i could capure all of he surplus when i negoiaed wih he invesor, and so he invesor would never negoiae wih i. Likewise, an invesor would never negoiae wih a bank whose balance shee coss exceeded he difference beween IOER and repo raes. Thus, we can proceed as if such banks are no par of he economy.) Le i(j, ) be he ideniy of he bank ha he invesor chooses o bargain wih in round j on day. If he invesor reaches he las bank in he order, j = N, he invesor s 25