Implications of Shadow Bank Regulation for Monetary Policy at the Zero Lower Bound

Transcription

1 Implicaions of Shadow Bank Regulaion for Moneary Policy a he Zero Lower Bound Falk Mazelis 2 November 216 (Click here for he mos recen version) Absrac Empirical evidence shows ha moneary policy ighening affecs hree ypes of financial insiuions in differen ways: banks decrease lending, while shadow banks and invesmen funds increase lending. I develop an esimaed moneary DSGE model wih funding marke fricions ha is able o replicae hese empirical facs. In a counerfacual exercise I sudy how he regulaion of shadow banks affecs an economy a he zero lower bound (ZLB). Consumpion volailiy is reduced when shadow bank asses are direcly held by commercial banks. Alernaively, regulaing shadow banks like invesmen funds resuls in a milder recession during, and a quicker escape from, he ZLB. The reason is ha a recessionary demand shock ha moves he economy o he ZLB has similar effecs o a moneary ighening due o he inabiliy o reduce he policy rae below zero. Keywords: Shadow Banking, Zero Lower Bound, Bayesian Esimaion, Search Fricions JEL Classificaion: E32, E44, E2, G11 I hank Julien Alberini, Jaroslav Borovicka, Nina Boyarchenko, Markus Brunnermeier, Michael Burda, Ivan Jaccard, Peer Karadi, Laura Kodres, Perry Mehrling, Zolan Pozsar, Alber Queralo, Richard Rogerson, Lukas Schmid, Frank Schorfheide, Chris Sims, Mahias Traband, Luz Weinke and Moohiro Yogo for commens. This research was suppored by he German Research Foundaion hrough he CRC 649 Economic Risk as well as he RTG 169 Inerdependencies in he Regulaion of Markes. Insiue for Economic Theory II, Humbold Universiy Berlin and Collaboraive Research Cener 649 Economic Risk. mazelisf@hu-berlin.de 1

2 1 Inroducion The financial secor has come under increasing scruiny following he recen financial crisis. Wih he regulaory communiy planning o especially consrain he role of shadow banks 1 in aggregae credi supply (Financial Sabiliy Board, 216; Claessens e al., 212), he resuling excess credi demand will be me by commercial banks and oher non-bank financial insiuions (NBFI). The relaive size of commercial banks in he financial secor maers for moneary policy ransmission, because bank lending is considered special (Brunnermeier e al., 213; Peek and Rosengren, 213; Boivin e al., 21). A he same ime, moneary policy makers have been faced wih a reduced abiliy o lower policy raes due o he zero lower bound (ZLB). This paper sudies how differen financial secor configuraions affec he behavior of an economy a he ZLB. I ake a sandard moneary DSGE model and develop a financial secor wih commercial banks, shadow banks and invesmen funds 2 ha is able o replicae empirical impulse response funcions and key aggregae business cycle saisics ouside he ZLB. I implemen a ZLB and conduc counerfacual analyses in which shadow banks are eliminaed from he model o mimic financial regulaion. Since he fundamenals of he real economy are no affeced by he configuraion of he financial sysem, credi demand from he real secor says consan and will eiher be filled by commercial bank credi or invesmen fund credi. I argue ha a recession a he ZLB is milder and shorer lasing if he credi sysem relies more on invesmen funds raher han on commercial banks. The reason is as follows. Moneary ighening leads households o shif savings ou of bank deposis and ino higher yielding liabiliies of invesmen funds, which herefore increase lending. For commercial banks he reducion in resources leads o a decrease in lending, which is called he bank lending channel. Because he lower bound on moneary policy prevens he policy rae from falling o he level ha would be chosen wih unconsrained moneary policy, he propagaion mechanism of a ZLB-inducing demand shock resembles a moneary policy ighening: Households prefer higher yielding asses o deposis, which acivaes he bank lending channel. This mechanism is weakened and credi reducion is dampened during a downurn, if he financial secor is more relian on non-deposi funding provided by invesmen funds. I conribue o he exising lieraure in hree ways: i) by explaining and repli- 1 Shadow banks have seen a reducion in credi inermediaion by % since he financial crisis (see Figure 9 in Appendix C). I define shadow banks as ABS Issuers, Finance Companies, Funding Corporaions and Securiy Brokers and Dealers. Their fixed income privae credi inermediaion, which is defined as loans, bonds, consumer credi and commercial paper, oaled abou 3% of all credi o he economy before he 28 financial crisis. This group s common characerisic is ha hey occupy a cenral place in he inernal funcioning of financial markes beween oher financial insiuions. Households ypically do no fund shadow banks direcly. 2 Invesmen funds are muual funds and money marke funds. Before he financial crisis hese insiuions channeled abou 2% of privae credi o he real secor, and hey have grown since hen. Unlike shadow banks, invesmen funds are direcly accessible o households and herefore feaure in household savings decisions. 2

3 caing he empirical reacions of non-bank financial insiuions (NBFI) o moneary policy in a moneary DSGE model; ii) by likening he mechanism of a ZLB-inducing demand shock o a response o moneary ighening; and iii) by analyzing differen financial secor configuraions regarding heir effeciveness o escape he ZLB on nominal ineres raes. Including a disinc invesmen fund secor in he analysis requires some explanaion. I add hem nex o commercial banks and shadow banks for hree reasons. Firs, invesmen funds rely on equiy funding, which is sae coningen, while commercial banks rely largely on deposi funding, which is non-sae coningen. Invesmen funds herefore represen he opposie o banks in erms of funding and warran a differen ype of model fricion. Second, alhough invesmen fund regulaions are currenly being ighened, regulaory auhoriies rea hem as a necessary par of he financial sysem, while he exisence of shadow banks is more challenged. Finally, he relevance of he srucure of he financial sysem is an imporan quesion in he lieraure (see e.g., Allen and Gale, 21), which I can explore in he conex of my model. This discussion is crucial for regions currenly assessing differen financial marke srucures. For example, in he European Union he Capial Markes Union proposal suggess a move away from a bank-dependen financial sysem o a more capial markes based sysem. In Secion 2, I conduc an empirical analysis of NBFI responses o moneary policy shocks, which moivaes he analysis. Nex, I explore how a model wih hree ypes of inermediaries and he incorporaion of a savings decision by households can replicae and accoun for hese empirical observaions. Secion 4 conains he model analysis, including calibraion and Bayesian esimaion, impulse response funcions o moneary policy shocks and business cycle effecs of eliminaing shadow banking. Secion conains he ZLB analysis and reacion of he economy under differen financial secor configuraions, as well as he comparison of a demand shock a he ZLB o a moneary ighening. Secion 6 concludes. Relaed Lieraure This paper mainly connecs o four differen srands of he lieraure. Firs, here are a number of papers focusing on differen aspecs of shadow banking. 3 I do no look a crisis periods and he accompanying effecs of fire sales, bankrupcy and regime ransiion. Insead, I focus on business cycle consequences of differen financial sysem configuraions afer hey have been implemened. 3 Meeks e al. (214) analyze financial sabiliy and consider shadow banks as off-balance shee vehicles of commercial banks o unload risky loans. Verona e al. (213) sudy adverse effecs of excessively easy moneary policy and undersand shadow banks as financial inermediaries specializing in less risky loans akin o bond issuance by invesmen banks. Moreira and Savov (214) analyze he way in which shadow bank liabiliy liquidiy characerisics change over he business cycle. Goodhar e al. (212) sudy differen regulaory regimes o sop fire sales by shadow banks and ake he opposie view o Verona e al., considering shadow banks o be less risk averse, bu sill funded by he commercial banking secor, comparable o off-balance shee vehicles as in Meeks e al. Gerler e al. (216) focus on he role of wholesale banking in ransmiing crises o he real secor. 3

4 The second srand of he lieraure analyses he credi channel of moneary policy. The credi channel posis ha following moneary ighening he amoun of credi in an economy is reduced, which amplifies radiional ineres rae and asse price channels. 4 This channel is spli up in he balance shee channel and he bank lending channel. The laer has ofen been challenged in ligh of banks abiliies o subsiue o non-deposi funding. 6 However, here is a large empirical lieraure ha finds evidence for he bank lending channel. 7 This paper inroduces a mechanism ha allows he financial secor o subsiue ino oher sources of funding and herefore decrease he effeciveness of he bank lending channel. A relaed lieraure analyzes moneary policy effeciveness. Over he pas several decades unexpeced moneary policy shocks appear o have had less and less of an influence on he real economy. 8 This is someimes explained by developmens in capial and financial markes. 9 This paper adds o he undersanding of how he financial marke srucure, especially is funding via savers, influences he effeciveness of moneary policy. Third, he paper adds o he undersanding of economies ha are consrained by a ZLB. Alhough he heoreical idea has exised for some ime 1, empirical sudies were limied o he Japanese experience. Since he financial crisis of 28, several sudies have focused on how an economy can escape he ZLB via fiscal policy or unconvenional moneary policy. 11 This paper insead focuses on how he overall composiion of he financial secor faciliaes resilience o he negaive consequences of a ZLB. Lasly, he heoreical mechanism developed in his paper is relaed o he search and maching lieraure. The iniial developmen focused on explaining he dynamics of he labor marke and replicaing key saisics. 12 I has since found applicaions o oher markes, including money and credi relaionships. 13 Following Wasmer and Weil (24), I model funding marke fricions analogously o hose on he labor marke because of heir comparable characerisics of moral hazard, heerogeneiy and specificiy. However, in my model he amoun of deposis changes endogenously. 4 For a simple exposiion in he IS/LM framework, see Bernanke and Blinder (1988). See Bernanke and Gerler (199). The balance shee channel is underlying he financial acceleraor as developed in Bernanke e al. (1999) 6 Romer and Romer (199) argue ha bank loan supply is insulaed from moneary policy if banks can fricionlessly find non-deposiory funding. 7 Early suppor from aggregae daa comes from Kashyap e al. (1993). Idenificaion issues, however, necessiae more deailed daa, which were advanced by Kashyap and Sein (199). 8 For an empirical exploraion, see e.g., Primiceri (2) and Boivin and Giannoni (26). For a srucural explanaion, see Jusiniano and Primiceri (28). 9 See Jermann and Quadrini (26) and Dynan e al. (26) as well as a criique by den Haan and Serk (211). 1 See Eggersson and Woodford (23) for a heoreical reamen. 11 Chrisiano e al. (211) explain why he governmen spending muliplier a he ZLB can generally be larger han 1, while Alberini and Poirier (21) and Chrisiano e al. (216) show poenially expansionary effecs of unemploymen benefis. Gambacora e al. (214) explore he effeciveness of unconvenional moneary policy. 12 The seminal paper is Morensen and Pissarides (1994). 13 See den Haan e al. (23) and Wasmer and Weil (24) for early conribuions and Gu e al. (216) and Beaubrun-Dian and Tripier (21) for curren applicaions. 4

5 2 Evidence on he reacion of financial insiuions o moneary policy shocks This secion summarizes he empirical reacion of lending by commercial banks, shadow banks and invesmen funds o moneary ighening. I follow Chrisiano e al. (1999) in he selecion of variables and he idenificaion of shocks by assuming ha he moneary policy makers choose heir arge for he federal funds rae based on heir informaion se Ω. Variables conained in Ω are conemporaneous measures for GDP, he CPI and he index of sensiive commodiy prices (comprising he firs block of variables). The remaining variables are M2 money sock, oal cenral bank reserves, non-borrowed reserves and he amoun of lending for each inermediary (comprising he second block). Policymakers observe he second se of variables only wih a lag of one period. Since I am only ineresed in he effecs of moneary policy shocks, he ordering of variables wihin heir blocks does no maer. I use he Federal Funds Rae (FFR) as a proxy for moneary policy. I use quarerly daa from 1984:1 o 26:4. I exclude daa afer 26, because of he sar of he global financial crisis, which changed he regulaion and risk percepion of he financial secor, as well as he binding zero lower bound on moneary policy (in 28), which complicaes he idenificaion of moneary policy shocks. The analysis sars in 1984, because of a likely srucural break in he conduc of moneary policy beween he pre- and pos-volcker chairmanship of he Federal Reserve, see Clarida e al. (2). For he purpose of his paper I define shadow banks as inermediaries ha are generally deb funded by oher insiuional invesors and banks. They are ABS Issuers, Securiy Brokers and Dealers, Finance Companies and Funding Corporaions. Invesmen funds are open ended funds ha issue and redeem equiy fund shares direcly. Households can generally inves in hem. Open ended funds are Muual Funds and Money Marke Funds. Banks ake deposis from households and originae loans direcly. They are U.S. Deposiory Insiuions and Credi Unions. Daa for he financial secor variables are from he Financial Accouns of he Unied Saes (see Tabel for deails). I include loans, bonds, consumer credi and commercial paper as a measure of credi. Inermediaries ypically fund subsanial amouns of securiies issued by he governmen and municipaliies, as well as deb backed by governmen-sponsored eniies (GSEs). I purposely exclude hese iems in he measure of real economy credi since securiies wih implici or explici governmenal guaranees are ofen assumed for liquidiy reasons or used as collaeral and may herefore serve a differen purpose han o profi from lending. I use four lags o capure he dynamic properies of he quarerly daase. Because of he large number of parameers, I adop an esimaion approach wih Bayesian shrinkage of VAR parameers as in Banbura e al. (21). The model is esimaed in log-levels (excep for he FFR, which is in levels). All nominal variables are ransformed ino real variables I explain he approach in more deail in Mazelis (216), where I also conduc robusness exercises regarding ime horizon, as well as selecion and ordering of variables.

6 FFR Commercial bank lending Invesmen fund lending Shadow bank lending Figure 1: Responses of inermediaries o a conracionary moneary policy shock. Noe: Empirical impulse responses of he federal funds rae and credi by commercial banks, invesmen funds and shadow banks o an unanicipaed 1 basis poin increase in he federal funds rae. The horizonal axis repors quarers since he shock. The verical axis repors percenage deviaions from he unshocked pah. Shaded regions are 32nd-68h and 1h-9h perceniles of 1 draws. The full se of variable responses are in Figure 1 in Appendix C. Source: Mazelis (216). Figure 1 shows he resuls of he srucural analysis. Following a 1bp increase in he FFR, lending by commercial banks iniially says consan, before i drops by abou 4% afer hree o four years. The lag in he reacion conrass wih he lieraure ha uses exac iming of FOMC announcemens. 1 This is poenially due o he specific ype of asse classes I focus on. Alhough banks reduce lending for he general pool of loan applicans, informal lending relaionships and formal credi commimens require banks o suppor some cliens wih addiional funding (Morgan, 1998). On ne, his migh lead o lile change in credi a firs before bank balance shees give way o funding pressures. Invesmen fund lending increases by more han % during he firs year, before i falls back o he baseline afer wo o hree years. Lending by shadow banks increases by abou 2% during he firs year. I slowly drops below baseline and booms ou afer five years. The behavior of banks is in line wih he credi channel of moneary policy: because of an increase in funding coss for borrowers and heir cusomers, profis are reduced and collaeral values drop. The increased riskiness of borrowers ranslaes ino higher ineres raes demanded by banks, which reduces credi demand in line wih he balance shee channel (Bernanke e al., 1999). A he same ime, bank crediors subsiue o higher yielding asses (Drechsler e al., 216), which reduces he amoun of resources available o banks, which corresponds o he bank lending channel. The behavior of shadow banks is ofen explained via regulaory arbirage: because commercial banks face binding leverage and capial resricions, hey channel resources via less sricly regulaed shadow banks ha hey own and conrol. Money marke funds pass on higher reurns o invesors more quickly han banks do on heir deposis and herefore receive an inflow in funding, which is passed on as addiional lending (see Mazelis, 216). 1 See, e.g., Francis e al. (211). 6

7 There are several sudies ha find complemenary evidence. Nelson e al. (21) conduc a similar analysis, bu differ in regards o he definiion of shadow banks and asse classes. 16 Their esimaion in log differences finds commercial bank asse growh dropping afer moneary ighening, while shadow bank asse growh increases. In a Facor-Augmened VAR, Igan e al. (213) sudy he effecs of moneary policy on inermediary balance shees from 199:1 o 28:2. They similarly find ha money marke funds (a ype of invesmen fund) increase asses afer moneary ighening. Securiy brokers and dealers (a ype of shadow bank) also increase asses. Pescaori and Sole (216) esimae a VAR wih banks, ABS issuers and finance companies, bu also include governmen sponsored eniies (GSEs), agency and GSE-backed morgage pools and life insurance companies. The auhors conclude ha moneary ighening decreases aggregae credi inermediaion, bu increases he relaive sizes of non-banks, hereby poenially increasing sysemic risk by pushing credi inermediaion o less regulaed secors. den Haan and Serk (211) esimae he response of morgage and consumer credi held by banks and non-banks. Bank morgages and consumer credi decline or say relaively fla, respecively, afer moneary policy ighening, while non-bank holdings increase. Nex, I explore how a moneary DSGE model wih financial fricions can replicae and explain he empirical resuls. 3 A moneary DSGE model wih hree ypes of financial insiuions Alhough he financial secor has been incorporaed ino DSGE models recenly, i is sill largely reaed as a relaively homogeneous eniy. I follow he call by Woodford (21) for a framework for macroeconomic analysis in which inermediaion plays a crucial role and [...] which also akes accoun of he fac ha he U.S. financial secor is now largely marke-based. I employ a moneary DSGE model wih sluggish price seing o generae nominal fricions, which allows shocks o he nominal moneary policy rae o affec real variables. The srucure of he shadow banking secor and is relaionship o he res of he financial secor is comparable o Meeks e al. (214) and Gerler e al. (216). Deb and equiy financing are modeled using wo differen ypes of fricions. Deb financing via he moral hazard problem as in Gerler and Kiyoaki (21) and Gerler and Karadi (211) guaranees ha as long as he inermediary does no exceed a maximum amoun of leverage per inermediary value, crediors are indifferen owards he absolue amoun of deb ha hey hold. This inroduces endogenously varying leverage in o he model. Wihou explicily modeling i, his can be undersood as deposi insurance for commercial banks and pledged, or asse backed, deb for shadow banks. 16 They look a he change in he oal size of he balance shees insead of a single asse class (fixed income holdings wih he real secor as in his paper). This is an imperfec measure when one is ineresed in he effeciveness of he credi channel, as financial inermediaries are invesed in equiy as well as governmenal and municipal deb, which are ofen held for collaeral purposes. 7

8 Equiy financing is risky. Since equiy invesors paricipae in he sae-coningen reurns of he inermediary, households are only willing o hold equiy claims ha have an underlying reurns profile ha fis ino he individual household s porfolio. An equiy reurn ha is higher han he ineres rae on deb capures his riskiness. Alhough no modeled explicily, his heerogeneiy on he micro level is capured via a search and maching mechanism: only a fracion of households agree o he erms of he poenial inermediaries ha hey mee on he equiy funding marke. This fricion inroduces an endogenously varying value for fund shares, while keeping households from invesing all of heir savings in higher yielding asses. Households herefore change he amoun of available savings for invesmen purposes depending on he sae of he business cycle. In addiion, his fricion allows me o solve he savings decision of households via a linear approximaion. Borrowers Goods Producers Inermediaries Commercial Banks Savers Households Physical Capial Loans (Banks) Loans (Shadow Banks) Loans (Funds) Shadow Banks CP Loans CP Ne Worh Loans CP Deposis Ne Worh Invesmen Funds CP Loans Fund Shares Deposis Fund Shares Figure 2: Balance shees of key agens in he economy. Noe: In addiion, he economy is populaed by capial producers and monopolisically compeiive reailers. A cenral bank is he source of moneary disurbances. CP = Commercial Paper. In addiion o he five agens shown in Figure 2, he economy is populaed by capial producers and monopolisically compeiive reailers. A cenral bank conducing moneary policy is he source of moneary disurbances and complees he model. 3.1 Households A coninuum of households of measure one exiss ha consume, save in a porfolio of asses and supply labor. They maximize discouned lifeime uiliy ( ) [ max E β i ln(c hc 1 ) χ ] {C,L,D,N IF } 1 + ϕ L1+ϕ = = i= subjec o he sequence of period budge consrains C + D e + N IF = W L + Π + R D 1 e + R IF N 1. IF The household is modeled as in Gerler and Karadi (211) (GK11 from here on) wih wo addiions: a ime varying discoun facor β and shares in invesmen funds 8

9 N IF as a savings alernaive o deposis D e. An increase in he discoun facor resuls in he reducion of curren consumpion C and a subsequen drop in oupu demand and inflaion, which lead o a reducion in he moneary policy rae, possibly reaching he ZLB. Each uni of labor L earns he real wage W. Π are profis from ownership of capial producers, reailers and financial inermediaries. The habi parameer is h, χ is he relaive uiliy weigh of labor and ϕ is he inverse Frisch elasiciy of labor supply. Household can save in deposis a commercial banks, D e, and shares in invesmen funds, N IF. I include fund shares o allow households o subsiue owards higher yielding asses in response o moneary ighening. On he micro level, when a household wans o inves ino shares, i eners he funding marke wih liquid asses D and randomly mees a poenial invesmen fund. If he invesmen fund is a good fi regarding individual porfolio characerisics, hey inves and form a mach. On he macro level, his behavior is approximaed by a search and maching mechanism: we only observe a fracion f of household savings D esablish a mach. The remaining savings are deposied in banks, wih end-of-period deposis D e = D (1 f ). The fracion f is endogenously deermined as explained in Secion Invesmen funds pay a sae-coningen ineres rae R IF, which is above he risk-less real reurn R ha banks pay on deposis. A fracion θ IF of households wihdraws heir exising fund invesmens every period, resuling in a law of moion for fund shareholdings: N IF = θ IF N IF 1ξ IF + f D. (1) Reinvesed fund shares migh be affeced by ξ IF, an auoregressive shock process of order one and uni mean. Wih ϱ denoing marginal uiliy of consumpion and µ denoing he addiional value of being invesed in fund shares, he firs order condiions are given by Consumpion C : 1 β +1 h ϱ = E. C hc 1 C +1 hc (2) Labor L : χl ϕ = ϱ W. (3) Deposis D : ϱ = (1 f )E β +1 R +1 ϱ +1 + f (µ + ϱ ). (4) Fund Shares N IF : µ + ϱ = E β +1 { R IF +1 ϱ +1 + µ +1 θ IF ξ IF +1}. () The firs order condiions for consumpion and labor are sandard. Equaion (4) reduces o he commonly known Euler condiion in he case ha fund invesmens do no exis or have no addiional value 17, i.e., he household increases savings unil he marginal uiliy of consumpion oday equals he discouned expeced marginal uiliy of consumpion omorrow. If households can inves in fund shares, bu heir abiliy o find a mach is consrained (i.e., f < 1), being invesed in an invesmen fund is valuable (i.e., µ > ). The household herefore increases savings unil he marginal uiliy of consumpion oday equals he probabiliy of consuming omorrow (1 f ) imes is value (he discouned expeced marginal uiliy of consumpion omorrow) plus he probabiliy of invesing in fund shares f imes ha value. 17 Iff µ =, Equaion (4) holds for all f. 9

10 The value of invesing in fund { shares is given by Equaion (). The righ-hand side can be rewrien o yield E β +1 r IF +1 ϱ +1 + (1 θ IF )ϱ +1 + θ IF (ϱ +1 + µ +1 ) }. The firs erm denoes he per period ne reurn r+1 IF from fund share invesmens ha every invesing household receives. The second erm is he fracion of households ha redeem heir fund shares and use hem for curren period consumpion. A fracion θ IF of households says invesed in fund shares and will reap he value of being invesed one period hence, expressed in he las erm. 3.2 Financial inermediaries There are hree ypes of inermediaries: commercial banks, invesmen funds and shadow banks. Commercial banks finance he real secor direcly via loans and buy shadow bank commercial paper. Invesmen funds finance loans o he real secor and commercial paper in shadow banks via fund shares, which hey sell o households. They are no able o leverage heir operaions wih deb. Shadow banks use heir funding o exend loans o he real secor Commercial banks There are infiniely many commercial banks in he economy, which are operaed by members of households. Each commercial bank can make loans S CB o he real secor ha maure in one period and yield a reurn R+1, K as in GK11. Following Meeks e al. (214), every commercial bank can also exend credi o he shadow banking secor, which is called commercial paper. Commercial paper M CB is differen from regular loans, because i denoes a claim on a pool of loans managed by he shadow bank and yields a reurn R+1 MCB. The commercial bank funds hese claims via ne worh N CB and deposis D ha i receives from oher households (excluding he household ha i is managed by). The balance shee of a commercial bank is hen Q S CB + M CB = N CB + D (6) where Q denoes he price of physical capial. The commercial bank accumulaes earnings ne of he ineres R ha i pays ou o deposiors one period hence: N CB = R K +1Q S CB + R MCB +1 M CB R +1 D. (7) Each commercial bank has a finie life ime and exis he marke wih a probabiliy θ CB each period. Once he commercial bank exis, i pays ou accumulaed lifeime earnings o he household whose member was is manager. The commercial bank herefore maximizes is expeced erminal ne worh V CB by picking is loan porfolio and funding according o V CB = max {S CB,M CB,D } = ( τ ) E β i τ= i= (1 θ CB )θ τ CBΛ,+τ N CB +τ, (8) where he sochasic discoun facor of he household is given by he marginal rae of subsiuion beween consumpion oday and omorrow Λ,+1 and he discoun 1

11 facor β. Since deposis only pay he risk free rae, a commercial bank has an incenive o keep leveraging up as long as i earns more han R on is credi claims. To moivae leverage endogenously, I inroduce he incenive consrain by GK11: Every period, a commercial bank can diver a fracion λ CB of is credi claims, which leads o he erminaion of he commercial bank. Since in such a case deposiors would lose heir claims on he commercial bank, hey force he commercial bank o limi is leverage in such a way ha moivaes he commercial bank o coninue operaions. A commercial bank is required o always mainain a value from coninuing operaions ha is a leas as high as he value i would gain from defauling: V CB λ CB [Q S CB + (1 λ ABS )M CB ]. (9) A commercial bank can diver a larger fracion of is real secor loans, which are non-sandardized, han of he commercial paper. Because commercial paper is a claim on a broad pool of loans, is sandardizaion makes i more pledgeable. This is capured in he facor (1 λ ABS ). As λ ABS approaches 1, a commercial bank can reduce is funding consrain by shifing from ourigh lending o commercial paper, hereby evading leverage resricions. This capures he regulaory arbirage moive of off-balance shee vehicles. The soluion o he commercial bank s problem is derived in Appendix A.1 and yields he balance shee relaion Q S CB + M CB (1 λ ABS ) = N CB φ CB (1) wih endogenous leverage φ CB. Since a consan fracion θ CB of commercial banks exi each period, he remaining commercial banks have a ne worh of N CB e = θ CB (R K Q 1 S 1 CB + R MCB M CB 1 R D 1 ). (11) o To make up for he ouflow, households esablish new commercial banks according N CB n = ω CB (Q S CB 1 + M CB 1) (12) wih ω CB calibraed o pin down he seady sae. The law of moion for commercial bank ne worh is he combinaion of boh exising and new ne worh N CB = Ne CB ξ CB + Nn CB. Exising commercial bank ne worh may be affeced by ξ CB, an auoregressive shock process of order one and uni mean Invesmen funds In addiion o commercial bank deposis, households may save in fund shares, which is a novel mechanism ha I inroduce ino he GK11 framework. Fund shares offer higher reurns on average in order o arac invesmens, bu are sae-coningen, since hey are equiy insrumens. Infiniely many invesmen funds offer fund shares ha differ on he micro level wih regards o characerisics like invesmen syle and fund managemen. Similarly, individual household preferences differ on he 11

12 micro level wih regard o he profile of an invesmen fund and individual porfolio preferences. Because of hese idiosyncraic differences, households need o find a suiable fund, which akes ime. Individual households and invesmen funds mee on he funding marke a random and evaluae he poenial for a mach in isolaion. I absrac from he mechanics on he micro level and approximae he behavior on he macro level via search and maching: in aggregae a fracion q of all invesmen funds searching for funding will find an invesing household. In order o paricipae in he funding marke, invesmen funds need o adverise heir operaions a a cos κ per adverisemen v. Afer forming a mach, an invesmen fund is able o inves ino eiher loans o he real secor S IF or he commercial paper of shadow banks M IF. In conras o commercial banks, invesmen funds do no face he same incenive consrain problem, since hey do no leverage heir operaions wih deb or deposis. They lend ou all acquired funding eiher o shadow banks or o he real economy. Given heir funding, hey maximize reurns subjec o consrains ha prohibi hem from invesing more han a share ψ IF of asses ino commercial paper. Since commercial paper from shadow banks pays a higher reurn han loans o he real secor (see Equaion (23)), invesmen funds generally inves ino commercial paper up o heir consrain ψ IF. Each period, invesmen funds pay ou a reurn R IF o heir invesing household. Some households will wan o wihdraw funding for consumpion or alernaive savings, while a fracion θ IF keeps heir exising fund shares. The value of an invesmen fund ha has formed a mach is V IF,M = R IF + ψ IF R MIF + (1 ψ IF )R K + θ IF E β +1 Λ,+1 V IF,M +1, (13) where R MIF is he reurn on commercial paper holdings of invesmen funds. Invesmen funds searching for funding have a value V IF,S = κ + q E β +1 Λ,+1 V IF,M +1. (14) Since operaing an esablished invesmen fund is profiable, he value of operaing an invesmen fund searching for funding may generally be profiable if he second erm in Equaion (14) is larger han he search cos κ. Addiional poenial invesmen funds searching for funding will herefore ener he funding marke, which depresses he average fund filling rae q, unil he value of a searching invesmen fund is zero. A Euler condiion for he number of fund adverisemens can be derived: κ q = E β +1 Λ,+1 { R IF + ψ IF R MIF + (1 ψ IF )R K + κ θ IF q +1 }. (1) New fund adverisemens are posed unil he cos of esablishing an invesmen fund is equal o he reurn, which consiss of he difference in ineres income and expenses, as well as he value from no having o look for funding in he nex period. The probabiliy of finding a mach is he number of realized maches m per 12

13 adverisemen 18, q = m v. (16) The number of maches is deermined by he number of fund adverisemens as well as he amouns households wan o save. Since invesmen funds offer a higher reurn han deposis pay, households always prefer o hold fund shares. 19 The number of maches herefore rises wih he amoun of household deposis and is deermined via a Cobb-Douglas maching funcion wih maching efficiency s and maching elasiciy ξ Shadow banks m = sd ξ v 1 ξ (17) Shadow banks are financial inermediaries ha channel funding from commercial banks and invesmen funds o he real secor. Commercial banks inves ino shadow banks via commercial paper M CB, which is sandardized and herefore more pledgeable o he commercial bank crediors. Invesmen funds inves ino he commercial paper of shadow banks M IF because hey offer a high reurn. Accumulaed earnings in ne worh N SB reain he firs loss of securiized asses. The amoun of real secor lending S SB is Q S SB = M CB + M IF + N SB. (18) Since hey are leveraged, shadow banks maximize erminal expeced ne worh by choosing lending and funding sources according o ( τ ) V SB = max E β i (1 θ SB )θsbλ τ,+τ N+τ. SB (19) {S SB,M CB,M IF } = τ= Reained earnings N SB +1 in a shadow bank are made up of he ineres rae difference ha hey make on loans and wha hey pay on commercial paper by commercial banks and invesmen funds: i= N SB = R K Q S SB R MIF M IF R MCB M CB. (2) As in Meeks e al. (214), shadow banks srucure some of heir liabiliies o be exra safe, i.e., hey pool heir loans and aribue he safes reurns o cerain crediors. These crediors are commercial banks, which need pledgeable securiies o circumven heir regulaory capial consrains. Only a fracion ψ CB of all loans ha shadow banks gran mee his sandard. The amoun of loans ha can be financed via commercial paper held by commercial banks is herefore M CB ψ CB Q S SB. (21) 18 The rae a which households find a suiable invesmen is he invesmen finding rae f = m /D. 19 The invesmen fund reurn is solved via Nash Bargaining and is derived in Appendix A.4. 13

14 The soluion o he shadow banks problem is derived in Appendix A.2 and yields he balance shee relaion Q S SB = N SB + M IF. (22) 1 ψcb Since some loans remain unsecuriized and non-pledgeable, a porion of he shadow bank balance shees canno be funded by commercial bank holdings of commercial paper. Demand by invesmen funds for commercial paper herefore increases he lending operaions of shadow banks. In order o incenivize invesmen funds o hold commercial paper raher han gran loans hemselves, shadow banks share he profi hey receive from addiional lending via Nash bargaining according o R MIF = R K + ζ IF ψ CB 1 ψ CB (RK R MCB ), (23) where ζ IF is he bargaining power of he invesmen fund. Jus like commercial banks and invesmen funds, a consan fracion θ SB of shadow banks exi each period. The remaining shadow banks have a ne worh of N SB e = θ SB (R K Q S SB R MIF M IF R MCB M CB ). (24) To make up for he ouflow, new shadow banks are esablished according o N SB n = ω SB Q S SB 1 (2) wih ω SB calibraed o pin down he seady sae. The law of moion for shadow bank ne worh is he combinaion of boh exising and new ne worh N SB = Ne SB ξ SB + Nn SB. Exising shadow bank ne worh may be affeced by ξ SB, an auoregressive shock process of order one and uni mean. 3.3 Goods producers The inermediaries are no producive by hemselves and only derive profis from he reurn on loans o goods producers. Perfecly compeiive goods producers manufacure inermediae goods and sell hem o reailers a he relaive inermediae oupu price P m. Afer producion, non-depreciaed capial is sold o capial producers and refurbished. 2 Labor and capial for pas producion are remuneraed and decisions for new producion are aken: The firm maximizes profis by solving ( τ ) [ ] max E β i Λ,+τ Pmτ Y τ + (Q τ δ)ξ {K +1,L } τ K K τ W τ L τ R kτ K τ Q τ 1 = τ= i= wih producion oupu given by Y = A (ξ K K ) α L 1 α (26) 2 Capial producer and reailer programs are discussed in Appendix A.3. 14

15 where α is he capial share, Q is he real price of capial, δ is he depreciaion rae, W are wages, A is a oal facor produciviy shock and ξ K is a capial qualiy shock. The firs-order condiions are R K Q = P m α Y K + (Q δ)ξ K (27) P m (1 α) Y L = W. (28) Firms pay ou ex pos reurns o capial as ineres paymens, resuling in no profis sae by sae. Since hey pay he same ineres rae R K o all crediors, loans by differen inermediaries are perfec subsiues and do no ener he maximizaion problem of he firm: K +1 = S CB + S IF + S SB. (29) 3.4 Marke clearing, resources and policy The aggregae resource consrain is given by consumpion, invesmen and adjusmen coss ( ) In + I SS Y = C + I + f (I n + I SS ). (3) I n 1 + I SS Capial evolves according o K +1 = ξ K K + I n, (31) i.e., an auoregressive capial qualiy shock ξ K of order one capures he variabiliy of capial produciviy inheren in fixed capial. Following he lieraure on he imporance of marginal efficiency of invesmen (Jusiniano e al., 21), invesmen specific shocks ι affec he ransformaion of gross invesmen ino ne invesmen. Gross invesmen I n is I n I ι δξ K. (32) Moneary policy is characerized by a Taylor rule. The nominal ineres rae is given by i, wih a seady sae ineres rae of i SS, he seady sae value of oupu given by Y SS, an ineres rae smoohing parameer ρ i, he inflaion coefficien κ π and he oupu gap coefficien κ y : i = i ρ i 1 [ ( ) κy ] 1 ρi Y i SS (π ) κπ ɛ (33) Y SS The exogenous shock o moneary policy eners he nominal ineres rae as ɛ. The nominal ineres rae has an effec on he economy hrough he Fisher relaion where E π +1 is expeced fuure ne inflaion. 1 + i = R +1 E (1 + π +1 ), (34) 1

16 4 Model specificaion and analysis In his secion, I firs pin down he model parameerizaion via calibraion and Bayesian esimaion. Because I wan o assess he model s abiliy o replicae business cycle saisics, I use a Bayesian esimaion insead of minimizing he disance beween empirical and heoreical IRFs as in Chrisiano e al. (2). Disance minimizaion would be possible if empirical IRFs by he differen inermediaries for oher key macroeconomic disurbances were available. A Bayesian esimaion allows a complemenary analysis and can be undersood as a cross validaion for my empirical resuls: he model IRFs o moneary disurbances from he esimaed parameers are comparable o he empirical IRFs in Mazelis (216). Nex, I analyze how moneary policy shocks propagae hrough he economy for four differen composiions of he financial sysem. Since only he financial secor is reconfigured, bu fundamenals of he model economy are unaffeced, real secor credi demand in seady sae is unchanged. The baseline case is he financial sysem wih commercial banks, shadow banks and invesmen funds, corresponding o he siuaion before he financial crisis of 28. Since hen, shadow bank lending has declined and been replaced by commercial bank and invesmen fund lending, which is aribuable o consolidaion in he indusry and new regulaions. To show he effecs of differen financial secor composiions, I consider hree cases, one in which shadow bank lending has been aken up by commercial banks, an alernaive in which invesmen funds have aken up he credi demand, and one in which boh secors share previously inermediaed credi by shadow banks. The differen relaive sizes of commercial banks o invesmen funds are due o changes in parameer values. The affeced parameer values are he proporional ransfer o he enering bankers ω CB, he proporional ransfer o he enering shadow bankers ω SB, he fund s survival rae θ IF, he fund adverising cos κ, and he household bargaining power w.r.. funds ζ HH. The model is solved via firs order perurbaion around he deerminisic seady sae. 4.1 Parameerizaion Several newly inroduced parameers are calibraed o pre-crisis seady sae values or direcly follow from heir economic counerpars. Parameers ha govern he sochasic process as well as hose ha are no pinned down by seady sae values and ha do no have a direc economic counerpar are esimaed. Mos of he srucural parameers presen in GK11 are adoped here. The pre-crisis economy includes a fully acive shadow banking secor wih a share of lending of approximaely 3%, while commercial banks len 4%, and invesmen funds len he remaining 2% of credi. The risk-free rae as measured by Shiller (1992) wih updaed values from his websie is 3 percenage poins per year. This ranslaes ino a quarerly risk-free rae of 7 basis poins, i.e., i SS =.7 assuming zero inflaion in seady sae. In 16

17 Symbol Value Descripion Source Households β.99 Seady sae discoun rae Gerler and Karadi (211) h.81 Habi parameer Gerler and Karadi (211) χ 3.49 Relaive uiliy weigh of labor Gerler and Karadi (211) ϕ.276 Inverse Frisch elasiciy of labor supply Gerler and Karadi (211) Financial Secors i SS.7 Quarerly nominal rae Shiller (1992) ψ CB.3 Fracion of commercial bank asses invesed in commercial paper Meeks e al. (214) ψ IF.4 Fracion of invesmen fund asses invesed in commercial paper Flows of Funds λ ABS 1 Relaive diveribiliy of ABS Seady sae ζ IF.88 Fund bargaining power re shadow banks Seady sae ζ HH.86 Household bargaining power w.r.. funds Seady sae ω CB.1 Proporional ransfer o he enering bankers Seady sae ω SB.4 Proporional ransfer o he enering shadow bankers Seady sae s.32 Maching efficiency Seady sae κ.7 Search cos Seady sae Goods Producers α.33 Effecive capial share Gerler and Karadi (211) δ.2 Depreciaion rae Gerler and Karadi (211) Reail Firms ɛ Elasiciy of subsiuion Gerler and Karadi (211) γ.779 Probabiliy of keeping prices fixed Gerler and Karadi (211) γ p.241 Price indexaion Gerler and Karadi (211) Governmen κ π 1. Inflaion coefficien of Taylor rule Gerler and Karadi (211) κ y.12 Oupu gap coefficien of Taylor rule Gerler and Karadi (211) Table 1: Calibraed parameer values. Noe: seady sae refers o parameer values ha direcly follow from assumed seady sae values. The seady sae values are eiher he relaive share of he financial secor or ineres rae differenials. models feauring a convenional Euler equaion his implies a higher discoun facor han β =.99, which is used in his calibraion. However, noe ha if he addiional value from being invesed in invesmen funds, µ, is posiive, and if search fricions guaranee ha he finding rae f (, 1), hen over-saving will resul in a risk-free rae ha is lower han β 1. The fracion of commercial bank asses invesed in commercial paper by shadow banks is se a 3%, as indicaed in bank call repor daa repored in Meeks e al. (214). The corresponding fracion for invesmen fund asses is 4% pre-crisis as indicaed by Flows of Funds daa. Remaining model parameers are chosen o imply a spread for he borrowing rae R k R of 79 bp, equal o he bank prime loan rae spread over he 3-monh Treasury Bill rae beween 21 and 24. A spread of 19 bp as proxied by Moody s Seasoned Aaa Corporae Bond Yield is chosen for he commercial paper rae ha shadow banks pay o invesmen funds. I assume ha shadow banks belong o commercial banks and herefore do no pay a higher ineres rae R MCB han R. This resuls in commercial paper held by commercial banks o be pledgable wih a λ ABS = 1, i.e., commercial banks canno diver hese asses. I follows from he seady sae and parameer values ha he bargaining power of invesmen funds visa-vis shadow banks ζ IF is hen.88, since shadow banks need a buyer of remaining loan pools. The fracion of new equiy ha has o be injeced ino commercial bank and shadow bank equiy, respecively, is ω CB =.1 and ω SB =.4. The maching 17

18 efficiency s, search coss κ and household bargaining power ζ HH follows from he seady sae and parameer values. Table 1 shows he fixed srucural parameer values and heir source. Prior Poserior Symbol Name Type Mean Sd. Dev. Mean L.B. U.B. Srucural ξ Maching elasiciy Bea λ CB Commercial bank s diverible share Bea θ CB Commercial bank s survival rae Bea θ IF Invesmen fund s survival rae Bea θ SB Shadow banker s survival rae Bea Persisence parameers ρ A TFP Bea ρ i Moneary Policy Bea ρ ξ Capial Qualiy Bea ρ IS Invesmen Efficiency Bea ρ β Demand Bea ρ CB Commercial bank equiy Bea ρ IF Invesmen fund equiy Bea ρ SB Shadow bank equiy Bea Sd dev. e A TFP Inverse Gamma e i Moneary Policy Inverse Gamma e ξ Capial Qualiy Inverse Gamma e IS Invesmen Efficiency Inverse Gamma e β Demand Inverse Gamma e CB Commercial bank equiy Inverse Gamma e IF Invesmen fund equiy Inverse Gamma e SB Shadow bank equiy Inverse Gamma Table 2: Priors and poseriors of esimaed parameers. Noe: L.B. is he lower bound of he 9% highes poserior densiy inerval. U.B. is he upper bound of he 9% highes poserior densiy inerval. The remaining parameers, including hose governing he shock processes, are esimaed using Bayesian mehods. Commercial banks, invesmen funds and shadow banks are defined as in Mazelis (216): Commercial banks are US Deposiory Insiuions and Credi Unions. Shadow banks are ABS Issuers, Securiy Brokers and Dealers, Finance Companies and Funding Corporaions. Invesmen funds are Muual Funds and Money Marke Funds. As a measure of credi I include loans, bonds, consumer credi and commercial paper. The macroeconomic ime series underlying he daa for observables are: real GDP, he consumer price index, he federal funds rae, fixed capial, household consumpion, and credi by commercial banks, invesmen funds and shadow banks (see Table in Appendix C for deails on he daa sources). Since he model is expressed in log-deviaions from seady sae, for esimaion purposes I ake he log difference from he one-sided HP filered rend (smoohing parameer is se o 16) for all variables excep inflaion and he federal funds rae, which are depiced in Figure 12 in Appendix C.3. The daa have a quarerly frequency and range from 1984:I o 26:IV. The priors for all persisence parameers are relaively uninformaive Bea disribuions wih a mean of. and a sandard deviaion of.2. The priors for he whie noise processes on he innovaions are Inverse Gamma disribuions wih means.1 18

19 sandard deviaions of.. The shock processes are a priori independen. The prior disribuions for he srucural parameers are bea disribuions. The inerval for he maching elasiciy allows all parameers beween and 1. The commercial bank s diverible share λ CB is cenered on he GK11 value of.381 and bound from below and bound from above o limi commercial bank leverage. The inervals for survival raes are beween (., 1.). I run 2 Mone Carlo Markov Chains wih 1. draws each over he full sample period. Convergence is reached afer abou 2. draws and I drop he firs % of esimaed values. Table 2 shows he resuls. The poseriors of he shock processes are informaive (see Appendix C.3). In order o illuminae he dynamics of he maching fricion, I conduc a robusness analysis of he maching elasiciy ξ in Appendix B. 4.2 Response o a moneary policy shock Figure 3 shows impulse response funcions for key variables afer unexpeced moneary policy ighening for he case of i) he original GK11 economy, and ii) he baseline case wih invesmen funds and shadow banks. Two addiional cases describe wha happens afer eliminaion of he shadow banking sysem. In he case of iii) he loans previously held by shadow banks are now inermediaed by commercial banks (bank dependen), and iv) he shadow bank loans are inermediaed by funds (fund dependen). The hird case corresponds o commercial banks graning 7% of all loans o he real economy, while he las case has commercial banks inermediaing a oal of 4% of credi. Invesmen funds inermediae he remaining share in he laer wo cases. Firs, consider he original GK11 economy. Afer an unexpeced moneary ighening of abou 1 basis poins in he firs period, ineres raes on commercial bank deposis increase o encourage deposiors o keep heir savings wih commercial banks insead of shifing hem ino oher asses. Because households have a higher incenive o save, consumpion drops. The reducion in consumpion demand ranslaes ino lower oupu and a reducion in he demand for physical capial by firms, which also lowers he price for physical capial. Lower oupu and capial prices iniially diminish he reurn on capial for he firm, see Equaion (27). Since firms pass his reurn on as he borrowing cos o he inermediary, exising commercial bank profis are hi. In he second period, he borrowing rae increases, because he price for physical capial slowly rises from is iniial low. Since he risk-free rae does no increase by as much as he borrowing rae, he exernal finance premium (EFP) rises. Equaion (A.2) increases as he EFP rises, indicaing gains from expanding asses for commercial banks. This means ha he reducion in lending is no jus due o he balance shee channel, which would necessiae a drop in credi demand. Banks are unable o quickly raise equiy and soliciing more deposis from households would cu ino heir margin. Credi o he real secor herefore drops. The baseline case feaures shadow banks and invesmen funds. Afer a moneary policy increase, he iniial reacion in he economy is he same. However, commercial banks now have he abiliy o leverage up on heir exising ne wealh by increasing heir invesmens ino shadow banks, which lend on heir behalf. A he same ime, 19