Interbank Market and Macroprudential Tools in a DSGE Model

Transcription

1 BANCO CENTRAL DE RESERVA DEL ERÚ Inerbank Marke and Macroprudenial Tools in a DSGE Model César Carrera* and Hugo Vega** * Banco Cenral de Reserva del erú ** Banco Cenral de Reserva del erú and London School of Economics DT. N Serie de Documenos de Trabajo Working aper series Junio 212 Los punos de visa expresados en ese documeno de rabajo corresponden a los auores y no reflejan necesariamene la posición del Banco Cenral de Reserva del erú. The views expressed in his paper are hose of he auhors and do no reflec necessarily he posiion of he Cenral Reserve Bank of eru.

2 Inerbank Marke and Macroprudenial Tools in a DSGE Model César Carrera Banco Cenral de Reserva del erú Hugo Vega Banco Cenral de Reserva del erú London School of Economics June 212 Absrac The inerbank marke helps regulae liquidiy in he banking secor. Banks wih ousanding resources usually lend o banks ha are in needs of liquidiy. Regulaing he inerbank marke may acually benefi he policy sance of moneary policy. Inroducing an inerbank marke in a general equilibrium model may allow beer idenificaion of he final effecs of nonconvenional policy ools such as reserve requiremens. We inroduce an inerbank marke in which here are wo ypes of privae banks and a cenral bank ha has he abiliy o issue money ino a DSGE model. Then, we use he model o analyse he effecs of changes o reserve requiremens a macroprudenial ool, while he cenral bank follows a Taylor rule o se he policy ineres rae. We find ha changes o reserve requiremens have similar effecs o ineres rae hikes and ha boh moneary policy ools can be used joinly in order o avoid big swings in he policy rae ha could have an undesired effec on privae expecaions or a zero bound i.e. liquidiy rap scenarios. Keywords: reserve requiremens, collaeral, banks, inerbank marke, DSGE. JEL classificaion: E31, O42. We are graeful o Connel Fullenkamp, Lawrence Chrisiano, hillip Bacchea, Andreas Fisher, Skander Van den Heuvel, Adriana Soares Sales, Sephen Cecchei, Francesco Caselli, Romain Baeriswyl, Carlos Monoro, Daira Vega, Jorge Loyola, aul Casillo, Nikia Céspedes, and Marco Vega, and paricipans a he 3rd BIS Consulaive Council for he Americas conference on Financial sabiliy, financial regulaion and moneary policy and he research seminars a he Swiss Naional Bank, he Gerzensee Sudy Cener, and he Cenral Bank of eru for helpful commens and suggesions. Special hanks o he commens made by saff members of he Swiss Naional Bank SNB and he Bank of Inernaional Selemen BIS, a Basel. essenia Collahua provided excellen research assisance. All remaining errors are our own. address: cesar.carrera@bcrp.gob.pe address: hugo.vega@bcrp.gob.pe 1

3 1 Inroducion In his paper, we sudy he effecs of ransiory changes in reserve requiremens in a general equilibrium conex. In paricular, we are ineresed in he shorrun effecs of ransiory shocks o reserve requiremens on real and financial variables and he ransmission mechanism behind hose effecs. We also explore he ineracion of reserve requiremen shocks wih radiional, ineresrae based, moneary policy shocks. We find ha reserve requiremen shocks are qualiaively similar o radiional moneary policy shocks. They generae a shorrun fall in inflaion, oupu and asse prices while pushing up lending and deposi raes. However, reserve requiremen shocks differ from moneary policy shocks in ha hey expand inerbank lending and conrac households deposis in he model. Addiionally, we show ha changes in reserve requiremens can complemen radiional moneary policy acions such as a hike in ineres raes. Thus, our policymaker can obain he same desired impac on real aggregaes wih a smaller change in he ineres rae, provided he is willing o complemen his acions wih a change o reserve requiremens. In our model, an increase in reserve requiremens reduces he loanable funds of financial inermediaries. These insiuions will reac demanding more inerbank lending, pushing up he ineres rae charged on hose operaions due o higher monioring coss a financial fricion. Thus, banks average cos of funding will increase. This cos hike will be ransmied o lending raes and deposis raes, resuling in a slowdown of economic aciviy. When used ogeher, reserve requiremens can parly subsiue ineres rae hikes. The reason behind his is ha boh variables affec banks average cos of funding. This is paricularly relevan when he policymaker faces a siuaion where he desired response would be a very big shif in he policy rae, 1 or, even worse, he required policy acion enails geing uncomforably close o he zero lower bound. Sandard NewKeynesian models canno accommodae boh a reserve requiremen shock and moneary policy formulaed by a Taylor Rule. The reason is ha changes o reserve requiremens aler he moneary base bu he laer becomes endogenous when he moneary policy ineres rae is governed by a Taylor Rule. 2 Any reserve requiremen shocks become undone immediaely by endogenous changes o he policy rae. In spie of he heoreical conundrum exposed above, cenral banks in Lain America have been using reserve requiremens as a policy ool recenly, usually in conjuncion wih radiional, ineresrae based, policy acions. Furhermore, Tovar e al. 212 provide empirical and anecdoal evidence ha moneary and macroprudenial insrumens, including 1 Hisorically, policy makers end o be relucan o do his, possibly as an endogenous response o uncerainy. 2 This is he case in he models developed in Clarida e al and Bernanke e al. 1999, for example. 2

4 reserve requiremens, appear o have complemened each oher in recen episodes. Reserve requiremens have also been used as a macroprudenial ool in Lain America for he pas decade. As Tovar e al. 212 repor,...policy makers in Lain America have adoped a number of macroprudenial insrumens o manage he procyclicaliy of bank credi dynamics o he privae secor and conain sysemic risk. Reserve requiremens, in paricular, have been acively employed. In order o have changes in reserve requiremens ineracing wih radiional moneary policy i.e.: a Taylor Rule, we propose a NewKeynesian model incorporaing a financial sysem wih fricions, paricularly in he inerbank marke. I urns ou ha very lile work has been done in his area: sudying inerbank markes and he fricions associaed wih hem in a general equilibrium conex is a relaively new subjec. Thus, our work also conribues o he lieraure by providing a fresh ake on how o model he agens ha paricipae in his marke and heir ineracions. Inerbank markes play an imporan role in he ransmission process from moneary policy o economic aciviy because hey help allocae resources beween financial insiuions. Financial fricions usually involving credi and regulaion haircus, reserve requiremens, and collaeral consrains consiue imporan feaures of inerbank markes ha have an impac on heir effeciveness in amplifying or dampening he real effecs of moneary policy. The res of he paper is organized as follows. Secion 2 is devoed o shor review of relaed lieraure, secion 3 describes our model wih an inerbank marke. Secion 4 deails he calibraion procedure. Secion 5 presens our resuls. Finally, secion 6 concludes. 2 A Shor Lieraure Review on Reserve Requiremens and Inerbank Markes 2.1 Reserve Requiremens The lieraure on reserve requiremen shocks in general equilibrium is very scarce. Our model bears some resemblance o Edwards and Vegh 1997 and, more recenly, rada 28. The work of Edwards and Vegh 1997 shows how foreign business cycles and shocks o he banking sysem affec oupu and employmen hrough flucuaions in bank credi. In his conex, hey explore he counercyclical use of reserve requiremens and find hey can be used o insulae he economy from he world business cycle. In order o obain his resul, Edwards and Vegh 1997 assume he producion of banking services is cosly. 3

5 Cosly banking services are presen in rada 28 as well. This auhor elaboraes on he work done by Edwards and Vegh 1997 adding NewKeynesian rigidiies o he open economy Calvo 1983 pricing, invesmen adjusmen coss in he spiri of Chrisiano e al. 25, ec.. He finds ha reserve requiremens do no have quaniaively significan effecs. Our model bears some resemblance o Edwards and Vegh 1997 because he financial fricion we impose on he inerbank marke a monioring cos is akin o heir cosly banking services. e, neiher Edwards and Vegh 1997 nor rada 28 include an inerbank marke in heir model. More imporanly, heir findings wih respec o reserve requiremens are differen from ours. Edwards and Vegh 1997 does no sudy shorrun changes in reserve requiremens and heir effec on real aggregaes nor how hey inerac wih policy raes. rada 28 dismisses reserve requiremens because his quaniaive resuls are no significan while we find ha reserve requiremens impac he economy in a similar manner han policy raes and, more imporanly, hey can be used o complemen policy rae hikes. 2.2 Inerbank Markes The financial acceleraor of Bernanke e al usually amplifies, spreads, and gives more persisence o differen ypes of shocks in he economy, paricularly shocks ha direcly affec financial inermediaries. Afer he financial crisis of 27 29, several economiss use Bernanke e al as a sepping sone for valid exensions of he original model. One of hose exensions is he inclusion of an inerbank marke. As Walsh 21 poins ou, imperfec credi markes make he policy ineres rae insufficien o characerize he moneary policy sance. Moreover, credi effecs may arise when fricions are presen in hese financial markes. Thus, one source of moivaion for recen research is he naure of he ransmission of moneary policy hrough more han one ineres rae ineres rae passhrough and he condiions of such ransmission he inerbank lending marke. The recen lieraure reviews of Carrera 212 and Roger and Vlcek 212, highligh he lack of models feauring an inerbank marke. In ha regard, he work of Gerali e al. 21, Curdia and Woodford 21, Dib 21, and Hilberg and Hollmayr 211 are among he firs on his arena. The banking secor in Gerali e al. 21 encompasses many banks each composed of wo reail branches and one wholesale uni. The firs reail branch is responsible for giving ou differeniaed loans o households and enrepreneurs; he second for raising deposis. The wholesale uni manages he capial posiion of he group. In Curdia and Woodford 21, he fricions associaed wih financial inermediaion inermediaion requires real resources and bank lending aciviies creae opporuniies for borrowers o ake ou loans wihou being made o repay deermine boh he spread beween borrowing and lending raes and he resources consumed by he inermediary secor. Dib 21 inroduces he disincion beween banks ha only raise deposis and banks ha only give ou credi, and 4

6 ses hem up in an inerbank marke in which he firs group of banks borrows from he second group. Hilberg and Hollmayr 211 ake a differen approach and separae he inerbank marke in wo ypes of banks: commercial banks and invesmen banks. Hilberg and Hollmayr noice ha only a few banks acually inerac wih he cenral bank, and hen fund he res of he banking sysem. While he capial of he banks plays an imporan role in Gerali e al. 21 and Dib 21, for Hilberg and Hollmayr 211 i is he srucure of he marke and collaeral ha maers he mos. We parially follow on he srucure of Hilberg and Hollmayr 211 see Figure 1. The hierarchical inerbank marke is a good represenaion of he srucure in he U.S. only rimary Dealers deal wih he cenral bank whereas a vas group of commercial banks is no allowed o deal direcly wih he moneary auhoriy and in Europe only 6 ou of 25 banks are allowed o paricipae in he bidding process in main refinancing operaions of he ECB and oher banks rely on inerbank funding. 3 We depar from Hilberg and Hollmayr 211 in four dimensions: i reail banks are subjec o required reserves, 4 ii narrow banks incur in moniorcredi coss, iii narrow banks obain funding from households, no he cenral bank and iv he bond marke is used by he cenral bank o implemen moneary policy in he form of open marke operaions. Dinger and Hagen 29 poin ou ha banks are paricularly good a idenifying he risk of oher banks and presen evidence of he imporance of inerbank ransacions. We add monioring coss in he same fashion as Curdia and Woodford 21. In doing his, we find ha reserve requiremens can acually complemen he effecs of he ineres rae, a resul ha helps undersand he imporance of his macroprudenial ool. 3 The Model Our model exhibis a fairly sandard real secor coupled wih he financial acceleraor mechanism of Bernanke e al aking some addiional elemens of CohenCole and Marínez García 21. On op of his, we add an inerbank marke srucure along he lines of Hilberg and Hollmayr 211, wih bank monioring coss in Curdia and Woodford 21 fashion. 3 See Walsh 21, chaper 11, for a descripion of he FED s operaing procedures, and hp:// for more informaion on he FED s rimary Dealers. 4 These can also be inerpreed as liquidiy requiremens in line wih Basel III proposals. 5

7 Figure 1: Inerbank marke srucure Cenral Bank Liquidiy Governmen bonds Narrow Banks Inerbank liquidiy monioring coss RRs Reail Banks Loans Collaeral Neworh Deposis Real Economy Even hough his model does no jusify he exisence of banks or why hey should be regulaed, i is sill flexible enough o capure he ransmission of moneary policy wih an inerbank marke operaing. In ha sense, banks are assumed o be essenial because hey provide households wih he only riskfree asse in he economy deposis and enrepreneurs can only arac exernal finance from banks. 5 There are wo financial fricions in he model: one on he liabiliy side of reail banks and one on he asse side of narrow banks. Our firs fricion akes he form of an adjusmen cos on deposi raes given imperfec compeiion in he banking secor, a la Gerali e al. 21. Our second fricion arises from convex monioring coss a la Curdia and Woodford 21 originaed by inerbank loans from narrow banks o reail banks. Finally, our model has oneperiod nominal loan conracs. Conracs are nominal by assumpion bu we consider he feaure o be realisic and i has he added benefi of allowing 5 The model absracs from bank moral hazard, bank runs, ec. as in, for example, Dib 21 in order o sress he role of he inerbank marke and is fricions. 6

8 us o inroduce minor Fisherian deb deflaion effecs in he moneary policy ransmission mechanism. 3.1 Households We assume a coninuum of households ha have an idenical uiliy funcion. The uiliy funcion of each household is addiively separable in consumpion, C, real cash holdings, CHS /, and labor H. Thus, he household s objecive is o maximize: E β s s= C s bc s 1 1 σ 1 + χ 1 σ 1 M CSH s s 1 σ 1 M 1 σ 1 M H s 1+ϕ 1 χ H 1 + ϕ 1 where < β < 1 is he subjecive ineremporal discoun facor, b is he habi parameer in household consumpion, σ > and σ M > are he elasiciies of ineremporal subsiuion of consumpion and real cash holdings respecively, and ϕ > is he Frisch elasiciy of labor supply. We include real cash holdings in he household s uiliy funcion o generae a money demand. This money in he uiliy funcion MIU approach has been sudied exensively in he lieraure see, for example, Walsh 21. I is usually raionalized arguing ha money holdings provide ransacion services, faciliaing he acquisiion of consumpion goods by, for example, reducing he ime needed o purchase hem. I should be noed ha wihou his assumpion households would never hold cash: any asse offering a posiive reurn e.g.: deposis would be a superior subsiue. Household income is derived from rening labor o wholesale producers a compeiive nominal wages W. Given ha households own he reailers and capial goods producers, hey receive heir oal real profis Π R and Π K respecively. The unanicipaed profis of reail banks are also fully rebaed o households in each period Π RB. Turning o asses, households demand one period deposis which pay a fixed nominal ineres, inves in shares which enile hem o a proporional fracion of he narrow banks dividends DIV NB /S 1 and hold cash deposis beween periods. Available income is used o finance aggregae consumpion C, open new deposis D, inves in shares S S, hold cash CSH /, and pay he real lumpsum ax bill T S +T B. Therefore, he households budge consrain is defined as: 1 7

9 C + T S + T B + D + S S + CSH + DIV NB + S S 1S 1 S 1 = W H + R D 1 1D 1 1S S 1 + CSH Π R + Π K + Π RB 2 where R D is he nominal oneperiod ineres rae offered o deposiors by reail banks, S is he narrow bank s relaive price per share, and is he consumer price index CI, defined laer. As a convenion, D denoes real deposis from ime o + 1. Therefore, he ineres rae R D paid a + 1 is known and deermined a ime. From he household s firs order condiions we obain, C bc 1 1 σ λ = βbe [C +1 bc 1 σ ] 3 χ H H 1 φ λ = βe [ W = λ 4 ] R D 5 λ λ = βe [ λ +1 DIV NB +1 + S S S +1S ] 1 ] CSH σ M χ M λ = βe [λ where λ is he Lagrange muliplier associaed o he household s budge consrain. We solve for he Euler equaion ha links consumpion o he deposi rae and pas consumpion. [ ] MUC = βe R D 8 MUC where MUC = C bc 1 1 σ βbe [C +1 bc 1 σ Using he definiion of MUC, we also solve for he labor supply, money demand, and he demand for shares. ]. 6 7 χ H H 1 φ = MUC W 9 8

10 E [ χ M CSH MUC σ M R D = 1 MUC R D ] R D = E [MUC +1 DIV NB +1 + S S S +1S ] Wholesale roducers We assume he exisence of a represenaive wholesale producer operaing under perfec compeiion. Our wholesale producer employs enrepreneurial H E and household H labor combined wih rened capial goods K in order o produce homogeneous wholesale goods W. The echnology involved is CobbDouglas: where a is a produciviy shock. W = e a K 1 ψ ϱ H ψ H E ϱ 12 In his consan reurnsoscale echnology, he nonmanagerial and managerial labor shares in he producion funcion are deermined by he coefficiens < ϱ < 1 and < ψ < 1. As in Bernanke e al. 1999, he managerial share ϱ is assumed o be very small. The produciviy shock follows an AR1 process of he following form: a = ρ a a 1 + ε a 13 where ε a is normal i.i.d. wih zero mean and σa 2 variance and ρ a capures he degree of persisence of he shock. Wholesale producers seek o maximize heir nominal profis: Π W = W W R W K W H W E H E 14 where Π W is he real profi of he wholesale producer, W is he nominal price of he wholesale good, R W is he nominal ren paid per uni of capial o enrepreneurs, and W and W E are he nominal wages of household and enrepreneurial labor respecively. The firs order condiions for his problem resul in he usual demands for labor household and enrepreneurial and capial, R W = 1 ψ ϱ W W K 15 W = ψ W 9 W H 16

11 W E = ϱ W Wholesale producers make zero profis. Households, who own hese firms, do no receive any dividends. Enrepreneurs receive income from heir supply of managerial labor and rened capial o wholesalers. Wholesale producers ren capial from he enrepreneurs and reurn he depreciaed capial afer producion has aken place. H E W Capial Goods roducers We assume a coninuum of compeiive capial goods producers who a ime purchase a bundle of reail goods ha will be used as invesmen X and depreciaed capial 1 δk o manufacure new capial goods K +1. The producion of new capial is limied by echnological consrains. We assume ha he aggregae sock of new capial considers invesmen adjusmen coss and evolves following he law of moion: X K +1 = 1 δk + Φ X 18 X 1 where Φ is an invesmen adjusmen cos funcion. We follow Chrisiano e al. 25 and describe he echnology available o he capial good producer as: X Φ = 1.5κ X 1 2 X X 1 1 X X 1 19 X where X 1 is he invesmen growh rae and κ > regulaes he degree of concaviy of he echnological consrain. Noe ha given our funcional choice, Φ1 = 1 and Φ 1 = implying consan reurns o scale in seady sae only. 6 A represenaive capial goods producer chooses his invesmen X and depreciaed capial 1 δk demand o maximize he expeced discouned value of his profis, solving he following problem: E s= M H s {Q s K s+1 1 δq s K s X s } 2 6 This follows from he realizaion ha he marginal produc of invesmen in he producion of new capial is Φ X X X X 1 X 1 + Φ X 1, an expression ha equals uniy only in seady sae where X X 1 = 1. 1

12 where M H s is a sochasic discoun facor and Q is he price of new capial for enrepreneurs which deermines he relaive cos of invesmen in unis of consumpion Tobin s Q. Since households own he capial goods producers, capial producers compue presen value using he household s sochasic discoun facor defined as: M H τ = β τ MUC +τ MUC +τ { 1 τ = = τ 1 i= 1 R D +i τ > 21 where he second equaliy can be obained using he household s Euler equaion. Given he capial goods producer s producion funcion, he marginal rae of ransformaion of depreciaed capial o new capial is uniy. Thus, i mus be he case ha, in equilibrium, depreciaed and new capial share he same price Q. Furhermore, any quaniy of depreciaed capial is profimaximizing as long as is price is he same as ha of new capial: he capial good producer s demand for depreciaed capial is perfecly elasic a price Q. Since enrepreneurs discussed laer will supply depreciaed capial inelasically, marke clearing guaranees capial goods producers acquire all he depreciaed capial sock from enrepreneurs a price Q. Thus, we ake a shorcu o his resul incorporaing 1 δq K direcly in he capial goods producer objecive funcion. The firs order condiions derived from he opimizaion process of he capial goods producers yield a sandard link beween our Tobin s Q analogue Q and invesmen X : ] X Q [Φ + Φ X X = X 1 X 1 X 1 R D [ E Q +1 Φ X+1 X ] 2 X+1 X 22 Aggregae profis for he capial goods producers are defined as: Π K = Q K +1 1 δq K X 23 Because our capial goods producers operae in a compeiive environmen, here are no profis in equilibrium. However, during he ransiion o seady sae, hese firms can generae shorerm profis or losses because X 1 is predeermined a ime implying he marginal produc of invesmen can deviae from uniy. When ransiioning from one seady sae equilibrium o anoher, he adjusmen cos canno be se o is opimal level. 11

13 3.4 Reailers There is a coninuum of reailers indexed by z [, 1] ha purchase he homogeneous good W from wholesalers and differeniae i coslessly in order o sell i o households, enrepreneurs, and capial goods producers for consumpion or invesmen. These cusomers love variey and demand a CES bundle composed by he differeniaed varieies z offered by reailers, aggregaed wih elasiciy of subsiuion θ > 1: [ 1 = ] θ z θ 1 θ 1 θ dz Sandard opimizaion of a CES uiliy defined over he reail good varieies yields a relaive demand for each variey: 24 θ z z = 25 where z is he price of variey z being charged a ime and is a price index given by: [ 1 = ] 1 z 1 θ 1 θ dz Given he opporuniy, a reailer will se is price z o maximize he expeced discouned value of is profi sream. Because of he marke srucure in which hese firms operae monopolisic compeiion, hey have he power o charge a reail markup over he price of he homogeneous good. However, heir reopimizing processes are consrained by nominal rigidiies as in Calvo A ime, an individual reailer mainains is price fixed from he previous period wih probabiliy < α < 1. Thus, i is allowed o opimally rese is price wih probabiliy 1 α. Our paper concenraes on he effecs of reserve requiremens and he incorporaion of an inerbank marke ino a relaively sandard New Keynesian DSGE framework, wihou delving ino welfare implicaions. Thus, we choose o eliminae he disorion inroduced by reailers markup pricing assuming he governmen subsidizes a fracion τ R of heir inpu coss. Therefore, he reailer pays only 1 τ R W per uni of wholesale good acquired. 7 A reailer z ha is allowed o change is price a ime will choose i o maximize: 26 E s= M H s α s { z 1 τ R W s Ỹs, z} 27 7 In his se up, i can be shown ha τ R = 1 θ is required o guaranee = W in equilibrium. 12

14 where z is he opimal price chosen a ime and Ỹs,z = z demand of good z a ime s given ha is price remains fixed a z. where The firs order condiion for his problem is: θ θ 1 E s= { Ms α H s z θ θ 1 1 τ R s W would be he reail markup wihou he governmen s subsidy. s θ s is he relaive } Ỹ s, z = 28 Since all reopimizing reailers face a symmeric problem, he aggregae CI can be expressed as a weighed geomeric average of old and new prices: = [ α 1 1 θ + 1 α ] 1 θ 1 1 θ where = z is he symmeric opimal price. Wholesale goods marke clearing requires ha aggregae reailer demand equal he oal oupu of wholesale producers: 1 29 zdz = W 3 Inroducing he individual reailer relaive demands ino his expression will resul in: 8 where = θ W 31 [ 1 ] 1 = z θ θ dz = [ α ] 1 θ θ 1 θ + 1 α is an alernaive price index inroduced o ease noaion and highligh he efficiency disorion due o sicky prices. 9 Aggregae nominal profis ransferred o he households are: 32 which implies, Π R = 1 z 1 τ R W zdz 33 8 Recall ha is a CES bundle of he individual z and generally no equal o 1 zdz. 9 Acually, and are idenical in a firsorder approximaion. 13

15 Π R = 1 τ R W W Enrepreneurs and Reail Banks The following descripion of he ineracion beween enrepreneurs and reail banks draws heavily from Bernanke e al. 1999, Chrisiano e al. 21 and Gerali e al. 21. Enrepreneurs supply one uni of managerial labor H E = 1 o wholesale producers inelasically. They accumulae real ne worh N and ake real loans L in order o buy new capial K +1 from capial goods producers a relaive price Q. Thus, an enrepreneur s balance shee can be described as: Q K +1 = L + N 35 There is risk involved in he enrepreneurial aciviy: afer he acquisiion of new capial, enrepreneurs experience a privae idiosyncraic shock ω which ransforms he capial hey acquired, K +1, ino ωk +1. In he lieraure incorporaing he financial acceleraor mechanism described in Bernanke e al. 1999, ω is usually assumed o be lognormally disribued wih parameers µ ω and σ ω. These parameers are hen picked o be consisen wih E [ω] = 1 and a paricular seady sae defaul rae on he loans. We follow his convenion. A he end of period, an individual enrepreneur receives a nominal wage, W E, and earns income from capial rened o he producers of wholesale goods, R W ωk, plus he resale value of he depreciaed capial which is sold back o he capial goods producers 1 δ Q ωk. Therefore, we can express he individual enrepreneur s nominal reurn on capial as he raio beween income received from rening capial and selling i afer depreciaion divided by is nominal cos: ωr E = ω RW K + 1 δ Q K 1 Q 1 K 36 where R E is defined implicily as he gross nominal reurn on capial of he average enrepreneur. A, our represenaive enrepreneur signs a loan conrac wih a reail bank specifying a loan amoun L and a nominal lending rae R L. Boh he enrepreneur and he reail bank undersand he loan is desined o finance par of he acquisiion of new capial, K +1. The deb has o be repaid a ime + 1. In case of defaul, reail banks can only appropriae he gross capial reurn of he enrepreneur a ha ime, i.e. ωr E +1 Q K +1. Thus, we can define he cuoff ω +1 as he paricular value of he idiosyncraic shock ω ha allows he enrepreneur o honor his deb nex period, leaving him wih zero ne 14

16 income individual enrepreneurs experiencing an idiosyncraic shock ω < ω +1 defaul on heir loans: ω +1 R E +1 Q K +1 = R L L ω +1 = R L L R E +1 Q K where ω +1 R E +1 is he minimum reurn ha enrepreneurs require in order o pay back o he bank, and R L L is he paymen amoun agreed wih he bank a ime. Noe ha he cuoff ω +1 depends posiively on he lending rae R L and negaively on he enrepreneur s leverage Q K +1 /N. The loan marke is compeiive. There is a coninuum of reail banks ha offer conracs wih lending rae R L, obain deposis a rae R D j in a marke characerized by monopolisic compeiion, and ake he ineres rae on he compeiive inerbank marke R IB as given. On he liabiliy side, he represenaive reail bank has deposis D j and inerbank funds IB j ha are obained from households and narrow banks, respecively. These funds are allocaed by he reail bank ino loans L j o enrepreneurs and reserves a he cenral bank RR D j, consiuing he asse side of he reail bank s balance shee. Reserves are compulsory due o regulaion: a fracion RR of every uni of deposis received by he reail bank mus be deposied a he cenral bank. Table 1: Balance Shee of Reail Banks Asses Liabiliies Loans L Deposis D Reserves RR D Inerbank loans IB The balance shee ideniy of he reail bank is: L = 1 RR D + IB 38 When he enrepreneur s idiosyncraic shock is below he cuoff, ω < ω +1, he bank forecloses he enrepreneur. Given he privae naure of he idiosyncraic shock, he reail bank mus pay a monioring cos in order o observe ω and absorb he enrepreneur s gross capial reurn. Following convenion in he cosly sae verificaion lieraure daing back o Townsend 1979, we assume ha in his scenario, he reail bank keeps a fracion 1 µ of he enrepreneur s gross capial reurn afer paying for monioring coss and he enrepreneur walks ou empy handed. The reail bank s expeced real profis nex period are: 15

17 [ [ ] ω+1 E Π RB +1 = E R L L df ω + 1 µ ωr+1q E K +1 df ω+ ω +1 R RR RR D i R D id i κd R D 2 i 2 R 1i 1 R D D D ] R IB IB where F ω is he cumulaive densiy of he idiosyncraic shock and R RR he cenral bank pays on reserves. is he gross ineres The reail bank has hree income sources: loan repaymens from enrepreneurs ha performed well hose wih ω > ω +1, he gross capial reurn of defauling enrepreneurs wih ω < ω +1 ne of monioring coss and ineres on reserves deposied a he cenral bank. On he oher hand, reail bank expenses include deposi repaymen wih ineres R D id i, inerbank loan repaymen wih ineres R IB IB and an adjusmen cos on he deposi rae. The inclusion of an adjusmen cos on he deposi rae can be jusified heoreically using he classic menu coss argumen of he price rigidiy lieraure: reail banks incur in coss o marke heir deposi produc in he form of adverising maerial. These coss increase whenever he deposi rae changes. Deparing from Gerali e al. 21, we do no include adjusmen coss relaed o he lending or inerbank raes. The raionale behind his decision is ha lending raes usually vary on a clien o clien basis hus, here is no unique number o publicize and he inerbank marke rae is deermined on a day o day basis in a perfecly compeiive marke wih almos perfec informaion. 1 Recall ha he loan marke where reail banks and enrepreneurs inerac and he inerbank marke where narrow banks and reail banks mee are compeiive bu he deposi marke is no. Following Gerali e al. 21, monopolisic compeiion in he deposi marke implies ha every reail bank faces a paricular demand for is slighly differeniaed deposi D i. We assume he consumer loves variey and demands a bundle of deposis D consruced as a CES aggregae of he individual deposis wih elasiciy of subsiuion ɛ. Thus, he reail bank ses is deposi rae R D i aking ino accoun he consumer s relaive demand for is paricular deposi given by: R D ɛ D i = i D 4 1 From an empirical perspecive, he deposi rae adjusmen cos is mean o capure he sylized fac ha he passhrough from inerbank raes o deposi raes is small and slow while he passhrough o lending raes is much bigger and faser. 16 R D

18 where R D is a CES index of he deposi raes R D i. The reail bank s expeced real profi nex period can be simplified using is balance shee and he cuoff definiion in order o subsiue away L and R L which yields: {[ [ ] E Π RB +1 = E gω +1 R+1p E R D i R RR RR + 1 RR 1 1 RR R D ɛ i D p 1 R D N p 1 κd R D 2 i 2 R 1i 1 R D D R IB D N R D i R RR RR 1 RR ] } N where p QK +1 N is he enrepreneur s leverage and g ω +1 [ω +1 r ω > ω µ E ω ω < ω +1 r ω < ω +1 ] 42 is he fracion of he gross nominal reurn on capial of he average enrepreneur R E +1 ha is given o he reail bank in compensaion for he loan i provided a ime. g ω +1 is increasing in ω +1 given a reasonably small seady sae defaul rae and some resricions on he parameers of F ω imposed by Bernanke e al Turning back o enrepreneurs, heir aggregae profi nex period would be: ω +1 ωr E +1Q K +1 df ω R L L Noe ha only enrepreneurs ha manage o repay heir loans ω > ω +1 make a profi. Using he cuoff ω +1 and leverage p definiions o subsiue away R L and L again, resuls in a new expression for enrepreneurs profi: [E ω ω > ω +1 r ω > ω +1 ω +1 r ω > ω +1 ] R+1p E N Given a well behaved disribuion of ω e.g.: lognormal, i can be demonsraed ha fω +1 Eω ω > ω +1 rω > ω +1 ω +1 rω > ω +1, he average enrepreneur s share of R E +1, is decreasing in ω Reail banks need o offer enrepreneurs a loan conrac specifying R L and L. However, we follow common pracice in he lieraure redefining he problem in erms of ω +1 and p 11 I should be noed ha he reail bank s share and he enrepreneur s share do no add up o uniy: gω +1 + fω +1 < 1 because par of R E +1 is los due o monioring coss

19 o faciliae exposiion. Inuiively speaking, a higher lending rae is equivalen o a higher cuoff and a bigger loan can be inerpreed as higher leverage. Given he compeiive environmen in he loans marke, reail banks will offer enrepreneurs he mos desirable conrac possible, driving down he presen discouned value of heir profis o zero. Thus, he opimal conrac is deermined by he reail bank choosing ω +1, p and R D i o maximize he expeced presen discouned value of he enrepreneurs aggregae profi subjec o he resricion ha he expeced presen discouned value of heir own profis is nonnegaive. 12 The Lagrangian of he problem we jus described would be: [ max L = E Ms fω H +1 R E s s+1p s N s ω +1,p,R Di s= s+1 { + λ Ms H gω +1 Rs+1p E s Rs IB p s 1 s= R D ɛ + s i D s κd 2 R D s R IB N s s R D s i R D s 1i 1 1 RR s Rs D i + Rs RR RR s 2 } ] Rs D D s s N s N s s+1 45 where λ is a consan lagrangian muliplier and M H s is he households sochasic discoun facor, previously defined. The soluion o his problem yields he financial acceleraor of Bernanke [ ] e al. 1999: a posiive relaionship beween he exernal finance premium E R E +1 /R IB and enrepreneurial leverage, defined as he raio of asses o ne worh Q K +1 /N. The paricular funcional form of he relaionship depends on f, g and heir derivaives. We follow common pracice and approximae i by, [ ] E R E [ ] υ +1 Q K +1 = 46 R IB where υ is he posiive elasiciy of he exernal finance premium wih respec o leverage. This relaionship consiues he enrepreneur s demand for new capial recall ha he reail bank is maximizing enrepreneurial profi: i is inuiive ha demand for K +1 should be decreasing in Q and increasing in E [ R E +1 ] and N. Tha demand for new capial should 12 Acually, he presen discouned value of reail banks profis will have o be zero a he opimum, oherwise hey could obain a beer oucome cuing he lending rae marginally o offer enrepreneurs a more desirable conrac. 18 N

20 be decreasing in R IB is no very inuiive bu we can remedy his by poining ou ha higher R IB mus ranslae ino higher R L in order o comply wih he paricipaion consrain of he reail bank zero expeced discouned presen value of profis. I is imporan o noe ha he coslysae verificaion framework implies ha exernal funding is more expensive for he enrepreneur han inernal funding always. Thus, he enrepreneur always uses all available ne worh N plus some loans o fund he acquisiion of new capial. Given our assumpion of monopolisic compeiion in he marke for deposis a la Gerali e al. 21, he reail bank does no find i opimal o perfecly arbirage beween is sources of funding when ransiioning from one seady sae o anoher. Adjusmen coss and monopolisic compeiion imply he following relaionship beween he deposi rae R D and he ne cos of funding obained from narrow banks in he inerbank marke afer imposing he condiion ha R D i = R D for all i by symmery. κ D R D R D 1 [ R D 1 E R 1 D +1 1 ɛ + ɛ RIB κ D R D ] = 1 RR + R RR R D RR [ D+1 R D E +1 R D 1 +1 D R D R D E [ ] ] + 47 Once he opimal conrac beween enrepreneur and reail bank has been defined, all ha remains is o characerize enrepreneurial ne worh and enrepreneurial consumpion. We assume ha each period, afer seling wih he reail banks, enrepreneurs make a decision wheher o say in business or reire. In order o avoid unnecessary complicaions, we follow he lieraure and assign he value γ o he probabiliy ha a paricular enrepreneur will remain in business. Enrepreneurs choosing no o reire use all heir gross reurn on capial plus labor income o accumulae ne worh for he nex period: + W E 48 N = γfω R E 1 Q 1 K This expression provides insigh on he necessiy of enrepreneurial labor. In our se up, an individual enrepreneur ha incurs in defaul migh no choose o reire. Given ha he reail bank has appropriaed all his asses, he needs some ne worh in order o paricipae in he loan marke nex period reail banks do no lend o enrepreneurs wih zero ne worh. Enrepreneurial labor provides he ne worh seed required o sar over. We implicily assume ha credi hisory is erased every period and he enrepreneur s pas credi performance does no affec his abiliy o obain a loan from a reail bank in period in any way. 19

21 Enrepreneurs ha exi he marke reire consume heir enire gross reurn on capial in period : C E = 1 γfω R E 1 Q 1 K Narrow banks Our se up assumes he exisence of a handful of compeiive narrow banks. These financial insiuions are key in our model. Jus like reail banks, narrow banks require funding in period in order o make financial invesmens ha pay off in There is a crucial difference hough: reail banks promise a fixed reurn in exchange for funding in he form of deposis and inerbank loans whereas narrow banks offer a variable reurn on heir shares. Funds obained by issuing shares S S are used by narrow banks o inves in governmen bonds B NB, purchased in he open marke a relaive price B, and offer inerbank loans IB compeiively o reail banks. Table 2: Balance Shee of Narrow Banks Asse Liabiliies Governmen bonds B B NB Equiy S S Inerbank Loans IB Noe ha narrow bank liabiliies consis only of equiy obained by issuing shares S S, hese represen household invesmen in a financial sense in he narrow bank. Thus, he balance shee a represenaive narrow bank is he following: B B NB + IB = S S 5 aricipaion in he open marke is resriced o narrow banks only. The reason is ha our sylized open marke is mean o resemble a secondary bond marke where he cenral bank will carry ou open marke operaions repos buying and selling is own holdings of governmen bonds. Thus, paricipaion in he marke is limied due o regulaory resricions Noe ha real secor firms such as reail and capial goods producers do all heir business in and hus require no funding in a financial sense. 14 Hilberg and Hollmayr 211 argue ha a hierarchical inerbank marke is jusified by he srucure found in he U.S. where only rimary Dealers deal wih he cenral bank whereas a vas group of commercial banks is no allowed o direcly deal wih he moneary auhoriy. In Europe, only 6 ou of 25 banks are allowed o paricipae in he bidding process in main refinancing operaions of he ECB and oher banks rely on inerbank funding. 2

22 Narrow banks choose opimally heir supply of inerbank lending IB and demand of governmen bond holdings B B NB obained hrough open marke operaions. The ineres rae on inerbank loans R IB is he compeiive oucome of he profimaximizing behaviour of boh bank ypes. However, he equilibrium price of governmen bonds B will be chosen by he cenral bank ensuring consisency wih is moneary policy objecives. In order o simplify exposiion and highligh he ineracion beween narrow banks and he cenral bank, we will assume ha governmen bonds are consols issued a some undisclosed poin in he pas a relaive price B wihou a subscrip and ha hey pay a fixed nominal ineres R B perpeually. Thus, buying a governmen bond uni a ime makes he holder eligible o receive a fixed coupon paymen of R B 1 B a ime Furhermore, governmen bond supply is fixed for he duraion of our shock experimens. Narrow bank s dividends are defined as: DIV NB = R 1IB 1 1 Ξ IB R B 1 B 1 B 1 + B B 1B NB 1 S S 1 51 where Ξ IB 1 is a convex monioring cos incurred by he narrow bank when lending o a reail bank. The monioring cos capures all expenses incurred by he reail bank during he evaluaion process, followup and monioring ha akes place for he duraion of is credi relaionship wih a narrow bank. We argue ha he cenral bank is illequipped o perform he monioring ask and, herefore, does no offer loans direcly o reail banks. Laer, we will show his monioring cos consiues an imporan fricion in our inerbank marke se up. 16 The narrow bank maximizes shareholder reurn: 15 Muliplying he ineres rae R B 1 by B is necessary o ensure R B is an ineres facor expressed in nominal good unis and no bond unis, making i comparable o oher ineres raes inroduced before. In order o normalize B o uniy, R B mus be equal o he seady sae deposi rae. 16 See Curdia and Woodford 21 for more deails on his paricular formulaion of monioring coss in a conex of households borrowing from financial inermediaries. 21

23 max IB,B NB E [ DIV NB +1 + S S S +1S ] [ R IB IB +1 ΞIB = E + B B NB R B 1 B 1 + B +1 B B B NB + IB + IB B B NB Firs order condiions for his problem are: [ ] [ E R IB Ξ DIV NB +1 + S IB = E S S and R B 1 B B [ DIV NB +1 + S = E E B S S +1S +1S +1 ] ] ] implying he expeced reurn on inerbank loans and governmen bond invesmens mus equae o shareholder reurn. Eliminaing shareholder reurn from he firs order condiions yields: R B 1 B [ ] E R IB Ξ IB = E B +1 + B Thus, he ineres rae being charged o reail banks R IB depends posiively on he volume of inerbank lending IB and negaively on he price of bonds B. The cenral bank will exploi his relaionship when pursuing moneary policy, effecively urning he narrow bank s reurn on governmen bonds ino is moneary policy insrumen. In order o do his, he cenral bank will supplydemand governmen bonds in he open marke whenever i wans o conracexpand money supply, effecively seing B. 3.7 Cenral bank The cenral bank s liabiliies correspond o he componens of he moneary base: reail bank reserves RR D and household cash holdings CSH /. On he asse side, he cenral bank holds he remaining governmen bonds B B CB. Thus, he oal governmen bond supply B B mus equae o he join demand from narrow banks and he cenral bank B B CB + B B NB. 22

24 Table 3: Balance Shee of he Cenral Bank Asse Liabiliies Governmen bonds B B CB Reserves RR D Cash holdings CSH The balance shee of he cenral bank is as follows: B B CB = RR D + CSH 56 The cenral bank obains ineres and capial gains from is bond holdings. 17 These funds are used o pay some ineres on reserves R RR bu, given he fac ha par of he cenral bank s funding has zero cos cash holdings, he cenral bank makes profis in seady sae. These profis Π CB are ransferred o he governmen. Π CB = R B 1 B 1 CSH B 1 + B B 1B CB 1 R RR 1RR 1 D The cenral bank in his model conrols liquidiy by conducing open marke operaions, buying or selling bonds o he narrow bank. We assume he cenral bank s inervenions are guided by a pseudo Taylor rule: if conemporaneous inflaion is above is arge, he cenral bank sells governmen bonds in he secondary open marke o he narrow banks, pushing down heir price. The resul is a higher reurn on governmen bonds for narrow banks and a decrease of he cenral bank s moneary base. Addiionally, he cenral bank also reacs o deviaions of oupu from is long run rend in a similar fashion. I is useful o inroduce an auxiliary variable, R o help characerize radiional moneary policy: R R = R ρr [ 1 R 1 φπ Ȳ ] 1 ρr φy exp ε R where ρ R capures ineres rae rigidiy, φ π is he weigh of inflaion in he Taylor rule, φ y is he weigh of he oupugap, and ε R is our i.i.d. moneary policy shock. Auxiliary variable R is useful because i characerizes clearly he cenral bank s moneary policy sance. Given our assumpion ha he cenral bank s acual moneary policy 17 We could assume he cenral bank does no receive ineres on is bond holdings and our resuls would no be affeced. This is because he cenral bank will ransfer is profis o he governmen anyway. We choose o include ineres paymens o he cenral bank from he governmen in order o avoid confusion and ease exposiion

25 insrumen is he narrow bank s reurn on governmen bonds, our auxiliary policy rae mus be ranslaed ino a bond price: R B 1 [ ] B + E B = R B 59 his expression characerizes he cenral bank s demand for governmen bonds. The cenral bank will adjus is bond holdings B CB unil bond price B is consisen wih 59. In our se up, he cenral bank has a second, albei unconvenional, moneary policy ool: he reserve requiremen rae RR. Given our inen of sudying he pure effecs of his insrumen on he shorrun evoluion of he model economy, we do no ie i o a paricular rule: ρrr 1 + RR 1 + RR 1 = exp ε RR RR 1 + RR where ρ RR capures reserve requiremen rigidiy and ε RR is an i.i.d. shock. 3.8 Governmen We rule ou governmen demand for reail goods. Given ha our model focuses on moneary policy and he ineracions aking place in he inerbank marke, we ry o minimize he governmen s role in our model economy. The governmen s ineremporal budge consrain is: Π CB + B B + T S + T B = τ R W W + R B 1 B 1 B 1 + B B 1 61 where T B is a small lumpsum ax required o finance par of he ineres paymens on he sock of governmen bonds B 1. We make a number of simplifying assumpions o characerize governmen behaviour. Firs, we impose ha lumpsum ax T S be desined o finance he reailer subsidy exclusively: T S = τ R W W 62 Second, as explained before, we assume governmen bond supply o be fixed B = B 1 = B. Inroducing hese assumpions allows us o rewrie he governmen s budge consrain: Π CB + T B = R B 1 B B

26 Noe hen ha flucuaions in cenral bank profi Π BC or inflaion 1 / mus be compensaed by alering he governmen s lumpsum bond ax T B paid by households. 3.9 Goods and bonds marke equilibrium All ha is lef o ie up our model is o define he resource consrain. roducion of he final reail good is allocaed o privae consumpion by households and enrepreneurs, invesmen by capial goods producers, deposi rae adjusmen coss, and o cover monioring coss incurred by reail banks cosly sae verificaion and narrow banks. The resource consrain akes he following form: = C + C E + X + κd R D 2 1 R D 2 R 1 D + 1 fω gω R E 1 Q 1 K + ΞIB 1 1D Finally, bonds marke equilibrium requires: Table 4 summarizes he model. B = B CB + B NB 65 4 Calibraion Our calibraion of he model s parameers capures he key feaures of he U.S. economy. In Table 5 and 6 we repor he calibraion values and seady sae values and raios. Regarding he households, he seadysae gross domesic inflaion rae / 1 is se equal o 1.. The discoun facor, β is se o.99 o mach he hisorical averages of nominal deposi and riskfree ineres raes, R D and R. The ineremporal subsiuion parameer in workers uiliy funcions σ is se o 1. Assuming ha workers allocae one hird of heir ime o marke aciviies, we se he parameer deermining he weigh of leisure in uiliy χ H and he inverse of he elasiciy of ineremporal subsiuion of labor ϕ o 1. and.33, respecively. The habi formaion parameer, b, is se o.75, as esimaed in Chrisiano e al. 21. The capial share in aggregae oupu producion 1 ψ ϱ and he capial depreciaion rae δ are se o.33 and.25, respecively. The parameer measuring he degree of 25

27 Table 4: Flow of Resources Agen Inflow Ouflow W consumer H + RD 1D ΠR + Π K + Π RB + DIV NB + S S 1 1 S S 1 1S 1 S + CSH C + T S + T B + D + S S + CSH reailer + τ R w w Π R + w w capial good producer QK+1 Π K + 1 δqk + X wholesale producer w w W H + RW K + W E enrepreneur BS L + N QK+1 R enrepreneur reurn W K + 1 δqk RE Q 1K 1 enrepreneur BC f ω R E Q 1K 1 + W E C E + N reail bank g ω R E Q 1K 1 + RRR 1 RR 1D 1 1 ΠRB + R 1D 1 D 1 + RIB 1IB 1 1 reail bank BS D + IB 1 R B 1 B 1 + B L + RRD narrow bank R 1IB 1 IB + B 1 1B B 1 NB DIV NB + Ξ IB 1 narrow bank BS S S B B NB + IB governmen T S τ R w w more governmen T B + Π CB + B B R B 1 B 1 B 1 cenral bank R B 1 B 1 B 1 + B 1 + S S 1 + B B 1 1B B 1 CB Π CB + R 1 RR RR 1D CSH 1 1 cenral bank BS RRD + CSH B B CB resource consrain C + C E + X + 1 f ω g ω R E Q 1K 1 + Ξ IB Noes: Bond marke requires B = B NB + B CB, adjusmen coss and subscrips have been omied o improve presenaion. 26

28 monopoly power in he reailgoods marke θ is se o 6, which would have implied a 2 per cen markup. The nominal price rigidiy parameer α in he Calvo se up is assumed o be.75, implying ha he average price remains unchanged for four quarers. The probabiliy ha an enrepreneur will say in he marke he nex period is.97. In he same line, he probabiliy ha an enrepreneur does no mee he required income o avoid defaul rω < ω is.75. Turning o he narrow banks, monioring coss are capured using he funcional form ΞIB = Ξ IB η, as in Curdia and Woodford 21. Moneary policy parameer φ π is se o 1.5 while φ is se o zero as in Bernanke e al These values saisfy he Taylor principle see Taylor Following Bernanke e al. 1999, he seadysae leverage raio of enrepreneurs 1 N/K, is se o.5, maching he hisorical average. The seadysae elasiciy of he exernal finance premium υ is se o.5, he value ha is used by Bernanke e al Table 5: arameer Calibraion references β =.99 b =.75 σ = 1 χ M =.8 σ M = 1 χ H = 1 ϕ =.333 θ = 6 Technologies δ =.25 ψ =.66 ϱ =.1 κ = 8 Nominal rigidiies α =.75 Financial secor µ =.12 κ D = 1 ɛ = υ =.56 γ =.9728 Ξ =.726 η = 1 Moneary policy φ π = 1.5 ρ R =.7 Governmen τ R =.166 Exogeneous processes ρ a =.95 ρ RR =.9 27

29 Table 6: SeadySae Values and Raios Variables Definiions Values π inflaion 1. R policy rae R D deposi rae 1.97 RR reserve requiremens.6 R RR reserve requiremens remuneraion rae 1.92 C/ household s consumpion o oupu.681 C E / enrepreneur s consumpion o oupu.143 I/ invesmen o oupu.177 K/ capial sock o oupu 7.69 L/ lending o oupu D/ deposi o oupu IB/ inerbank funding o oupu.363 CSH/ cash holding o oupu.551 S S/ shares o oupu.2 5 Resuls There are imporan secondorder effecs ha appear when inroducing a change o reserve requiremens. However, we do no pursue a proper secondorder approximaion of our model 18 and, insead, choose o approximae only equaion 47 o secondorder because i is he one ha capures he muliplicaive naure of he ineracions beween he inerbank rae, deposi rae and reserve requiremens. Close inspecion of equaion 47 shows ha he marginal effec of he inerbank rae depends on he level of reserve requiremens and viceversa. Figure 2 shows he model s impulse responses o a one percen produciviy shock. Mos variables exhibi fairly sandard behaviour. Oupu reurns slowly o seady sae hanks o habi formaion, adjusmen coss associaed o invesmen, and he shock s own persisence. In addiion, inflaion and he policy rae decrease. Deb conracs are signed in nominal erms according o he conrac being offered by reail banks. Therefore, deflaion increases he real value of deb obligaions, generaing a negaive effec on enrepreneurial ne worh ha evenually ouweighs he produciviy boos. Similar o Gerali e al. 21, 18 This would require us o specify funcional forms we don really have much deail on such as f and g. 28