Does Interbank Market Matter for Business Cycle Fluctuation? An Estimated DSGE Model with Financial Frictions for the Euro Area

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1 Does Inerbank Marke Maer for Business Cycle Flucuaion? An Esimaed DSGE Model wih Financial Fricions for he Euro Area Federico Giri Universià Poliecnica delle Marche April 20, 2016 Absrac The aim of his paper is o assess he impac of he inerbank marke on he business cycle. To do ha, we buil a DSGE model wih heerogeneous households and banks. Ne lender banks can allocae heir resources beween inerbank lending and risk free governmen bonds. This porfolio choice is affeced by an exogenous counerpar risk shock on he inerbank marke. An increase of he counerpar risk divers funds from he inerbank markes oward he governmen bonds marke. This mechanism allows us o capure he freeze of he unsecured inerbank marke and he fligh o qualiy mechanism underlying he las financial crisis. Keywords:DSGE model, financial fricions, inerbank marke, Bayesian esimaion, Moneary Policy. JEL classificaion codes:: E30, E44, E51, E52. 1 Inroducion The inerbank marke is he primary source of fundings for banks ha need o gaher liquidiy in order o creae new loans. Shocks ha inerfere wih is normal funcioning can have significan repercussions boh on he whole financial sysem and on he real side of he economy. Figure 1 shows he spread beween he hree monh Euribor and he overnigh index swap on he EONIA ineres rae. The so called OIS spread is considered one of he mos imporan indicaors o evaluae he proper funcioning of he liquidiy marke. The higher he spread, he higher is he risk perceived by he financial inermediaries ha operae on he inerbank marke. Address: Universiá Poliecnica delle Marche, Piazzale Marelli n 8 Ancona, Ialy. f.giri@univpm.i. 1

2 Figure 1: Eur3M-OIS spread, governmen bond deained by MFI Source: The OIS spread (red line, lef axis) is aken from Daasream while he saisics of governmen bonds (blue line, righ axis) are from he ECB. OIS is expressed in percenage while governmen bond are in millions of euro. Many conribuions ried o undersand he causes behind his sharp increase of he money marke spreads and he firs suspec was he increase of liquidiy risk on he inerbank marke (see Beirne (2012)) during Augus The smoking gun can be raced back o he decision of BNP Paribas o freeze hree invesmen funds. Things changed afer he collapse of Lehman Brohers in Sepember Panic spreads in he financial markes and he fear ha several financial inermediaries wouldn be able o refund heir loans caused a sudden and exended drainage of liquidiy from he unsecured inerbank marke. As a consequence he OIS spread a he end of 2008 rose by almos 100 basis poin wih respec o he beginning of he year. Banks looked for a safe heaven choosing low bu safe reurns like governmen bond (See figure 1). A liquidiy problem seemed o urn in a solvency issue (see Socio (2011) and Filipović and Trolle (2013)). From a heoreical poin of view, Heider e al. (2015) idenified he key channel behind his fligh o liquidiy mechanism in he rise of counerpar defaul risk on he inerbank marke. Their heoreical framework is able o explained several sylized facs of he las financial crisis like accumulaion of reserves by he financial inermediaries, he increased of ineres raes and he inabiliy of moneary auhoriy of resoring he normal funcioning on he money marke hrough he shor erm ineres rae. Despie he growing ineres of he lieraure on he role of inerbank marke, very few papers concenrae heir aenions on he macroeconomic and general equilibrium effecs of credi and/or liquidiy shocks on he business cycle (Radde (2014) is amongs he few excepions). The primary objecive of his paper is ry o fill his gap in order o beer undersand he role of he inerbank marke in he propagaion of he financial crisis using a Dynamic Sochasic General Equilibrium framework. The novely of our conribuion is o embed an inerbank marke like in Dib (2010) and dewalque e al. (2010) in a model like he one proposed by Gerali e al. (2010) 2

3 including a counerpar risk on he inerbank marke like Heider e al. (2015). The combinaion of such models allow us o have a very rich se up in erm of banking sysem feaures bu a he same ime flexible enough o ake he model o he daa applying he sandard Bayesian esimaion echnique, a novely wih respec wih he previous calibraed models. This hybrid model allow us o undersand he general equilibrium effecs of an increased of riskiness on he inerbank marke, wihou disenangling beween credi and liquidiy risk, and he relaive moneary policy implicaions. Our resuls show ha a) an increase of he counerpar risk on he inerbank marke can generae a credi crunch and, as a consequence, a recession, mainly driven by a drop of invesmens and house purchases, b) his shock played a non negligible role in he rise of he ineres raes in he money and credi marke afer Augus 2007, c) counerpar risk disrups he cenral bank inervenion making he conducion of moneary policy hrough he adjusmen of he shor erm ineres raes less effecive. The paper is organized as follow. Secion 2 presens he mos recen conribuions in he field of DSGE model wih an explici inerbank secor. Secion 3 explains in deail he model and he relaive equaions. Secions 3 and 4 deal wih he soluion mehods and he esimaion echniques. Secion 5 and 6 focus heir aenion on he dynamical properies of he model and he hisorical variance decomposiion of he shocks. Finally, Secion 7 summarizes he main findings and he possible exensions. 2 Lieraure review The paper proposed by Goodhar e al. (2009) is he firs aemp o include an acive inerbank marke ino a parial equilibrium model. Heerogeneiy is imposed assuming a limied paricipaion consrain in he money marke. The inerbank marke is made of a surplus bank, which obains funds from he households, and of a defici bank ha receives loans from he surplus one o finance corporae lending. The cenral bank is able o influence he ineres rae only hrough he defici bank. Many recen conribuions are based upon Goodhar e al. (2009) in order o include an inerbank marke in a general equilibrium framework. In a general equilibrium framework, dewalque e al. (2010) buil up a relaively simple RBC model ha capures some sylized facs of he ineres rae srucure and defauls rae on inerbank marke. The inerbank marke is he preferenial channel used by he cenral bank o injec or wihdraw liquidiy o reduce he differences beween inerbank funds demand and supply. The auhors used he model o invesigae he differen oucome on sabiliy and growh cased by he Basel I and he Basel II agreemens. Secondly bu more imporanly for our purpose, hey also found evidences ha he presence of defauls on he inerbank marke can amplify he effecs of a supply side shock. Dib (2010) added o DeWalque s framework he possibiliy for he ne lender bank o allocae is funds no only on he money marke bu i can also purchase risk free governmen bonds. The cenral bank can aler he composiion of he saving bank balance shee when i inervenes o sem he inflaion growh or he oupu gap. A general resul is ha he presence of a banking secor aenuaes he impac of several shocks. Boh dewalque e al. (2010) and Dib (2010) models focus heir aenion on he unsecured segmen of he inerbank marke. They boh allow he ne debor on he inerbank marke o no pay bank a fracion of heir inerbank funds inroducing counerpar risk 3

4 in heir financial marke. Carrera and Vega (2012) buil up a DSGE model wih an inerbank marke in order o analyze alernaive macroprudenial policy rule. The auhors developed a hierarchical bank sysem in which he exchanges beween he cenral bank and he reailers are managed by anoher subjec called he narrow bank. The auhors used he model in order o invesigae he behavior of he macroprudenial policy in presence of an inerbank marke finding ou ha a reserve requiremen rule can be used joinly wih he sandard Taylor rule o avoid large swings of he ineres rae. The conribuions of Hilberg and Hollmayr (2011) and Gerler and Kiyoaki (2010) concenrae heir aenion on he unconvenional moneary policy and he relaed role of inerbank marke in he ransmission of such acions by he moneary auhoriy. In Hilberg and Hollmayr (2011) model, he reail bank is subjec o a borrowing consrain (See Kiyoaki and Moore (1997) and Iacoviello (2005)) in he amoun of funds i can obain from he invesmen bank. The asse back securiies are evaluaed a marke price insead of he fundamenal price. The formaion of asse price bubble can increase he value of he collaeral, enhancing he abiliy of he reail bank of receiving funds from he invesmen bank. This mechanism gives raise o a boom and burs financial cycle. The invesmen bank is also subjec o a borrowing consrain. In his case, he unconvenional policy rule is relaed o he haircu ha he cenral bank can apply o he asses of he invesmen bank in order o provide liquidiy. In normal ime he cenral bank acceps only liquid asses like governmen bonds while during financial sress i can also buy illiquid asse back securiies like loans. The auhors find ha relaxing he haircu is an effecive ool o boos he inerbank marke lending and consequenly economic growh. Differenly from dewalque e al. (2010) and Dib (2010), Hilberg and Hollmayr (2011) focus heir aenion on he collaeralized marke leaving ou he role of defauls. Gerler and Kiyoaki (2010) buil a DSGE model wih an inerbank marke in which all banks borrow from and lend o firms. In heir model he inerbank marke arises because banks are subjec o an idiosyncraic liquidiy shock which has he effec of creaing surplus and defici inermediaries. Limied pleadgeabiliy gives place o an endogenous leverage consrain where bankers need o use heir own equiy in order o arac exernal crediors boh on he reail (deposis) and a he wholesale level (inerbank borrowing/lending). Gerler and Kiyoaki (2010) use heir model o invesigae how several differen (unconvenional) credi policies could miigae he negaive effec of a financial crisis. In erm of modeling, he innovaion of Gerler and Kiyoaki (2010) consiss of an inerbank marke ha arises endogenously an i is no imposed by a limied paricipaion consrain. The recen conribuion by Boissay e al. (2013) pushes his concep even furher. They se up a non linear DSGE model no only able o generae an endogenous inerbank marke exploiing he differen degree of bank efficiency, bu he model is also capable of generaing endogenous financial crisis capuring several sylized facs of hisorical sysemic banking crises (see Schularick and Taylor (2012)). Our modeling choices closely follow dewalque e al. (2010) and Dib (2010) in he way he inerbank marke is inroduced in our se up. This modeling choice is moivaed on he empirical evidence ha assigns a predominan role o defauls bu i also allow us o build a rich framework ha i can be easily aken o he daa and used for policy analyses. 4

5 3 The model Our model is an exension of he one proposed by Gerali e al. (2010). The whole economy is made of several represenaive agens each of hem maximizing his objecive funcion under a budge consrain. Two kind of households, paien and impaien, live in he model. Paien households have a higher ineremporal discoun facor han he impaien ones. Therefore, paien households are ne savers and hey decide how much o consume, o work and he amoun of deposis o allocae a he surplus bank. Impaien households are ne borrowers and hey choose how much o consume and o work. They finance par of heir spending obaining loans from he reail branch of he defici bank. Boh paien and impaien households sell heir work o a union ha sells a composie labor facor o he inermediae firm. Moreover, heir uiliy also depends by he amoun of he house services hey can purchase. The res of he real side of he economy is buil on Chrisiano e al. (2005) and Smes and Wouers (2007). Capial producers operae under perfec compeiion. They buy he undepreciaed capial from he inermediae producers and a fracion of final goods from he final goods producers. They combine hese wo impus o produce new capial ha hey sell a he real price o he inermediae firms. Final goods producers operae under perfec compeiion bu sicky prices. They combine he inermediae goods ino a final goods. We sricly follow Gerali e al. (2010) o model he labor marke. Two agens operae in he labor marke, unions and labor packers. Workers provide a differeniaed labor facor o unions. Moreover, a coninuum m of labor packers acquire labor from he unions and hey sell, hrough a CES aggregaor, an homogeneous labor facor o he inermediae firms. We will no develop he deailed derivaions in he paper for he real economy of his model. They can be found in he echnical appendix A. The bank sysem of he model is an exension of Gerali e al. (2010) and Dib (2010). The defici bank is modeled like in Gerali e al. (2010) and i is a ne debor on he inerbank marke. We have a reail branch ha is direcly conneced wih firms and households. The reail branches operae under monopolisic compeiion and hey could se he ineres rae on loans provided o impaien households and firms. A wholesale branch of he defici banks has o manage he capial posiion of he holding choosing he opimal balance shee of he bank group. Moreover, like in Dib (2010), defici banks could choose he opimal amoun of defaul over he inerbank. This novely allows us o inroduce he counerpar risk in our framework. In order o keep he model as simple as possible, we inroduce wo simplificaions: a) here is no disincion in he model beween credi and liquidiy risk and we will describe he exogenous shock hiing he inerbank marke as a generic counerpar shock as described in Heider e al. (2015) and b) we consider only he unsecured inerbank marke like in dewalque e al. (2010) bu differenly from Hilberg and Hollmayr (2011) where hey considered only he secure segmen of he inerbank marke. This choice is moivaed by many empirical evidences. Taylor (2009) underlines ha he urmoil on he inerbank marke was essenially moivaed by a counerpar risk crisis and no by a liquidiy issue. The surplus banks collec loans from paien households and invess par of heir deposis eiher in he inerbank marke or in governmen bond. Similar o dewalque e al. (2010), surplus banks are subjeced o a disuiliy cos ha is proporional o he inerbank exposiion. Moneary policy is conduced by he cenral bank following a Taylor rule. We close our model specifying a governmen secor ha obeys o an ineremporal budge consrain and manages he ax rae according o a feedback rule argeing he 5

6 sock of real deb like in Leeper (1991). 3.1 Savers and Borrowers The real side of he model closely follow Gerali e al. (2010). In his secion we only presens he main feaures and we leave he complee derivaions o he echnical appendix Paien households Paien households choose c(i) P, h(i) P, and d(i) P (respecively, consumpion, house services, and he amoun of deposis) in order o maximize heir uiliy funcion under he budge consrain. The uiliy funcion depends posiively on consumpion and houses services and negaively on he hours worked. [ ] E 0 βp (1 a P )ɛ z log(c P (i) a P c P 1) + ɛ h log(h P (i)) lp (i) (1+φ) (1) 1 + φ =0 where β p is he ineremporal discoun facor of paien households while a p represens he exernal habi formaion in consumpion wih respec o he whole Paien households consumpion. The exogenous variables ɛ z and ɛ h are wo sochasic disurbances affecing consumpion preferences and he house services demand. The budge consrain for paien households is described by he following equaion c P (i) + q h h P (i) + d P (i) = w P (i)l P (i) + (1 + rd 1) d P π 1(i) + T r T P (2) The lef hand side is he flow of expenses. I is composed by consumpion, variaion of he marke value of housing services, where q h is he real house price, and he amoun of deposi allocaed a he surplus bank. The righ hand side of equaion 2 represens he resource owned by he paien households. w P is he hourly wage, r d is he ne ineres rae on deposis, π is he ne inflaion and T is a lump sum ax. All variables are expressed in real erms. T r are he ransfers from he economy o he paien households. We assume ha final goods producer firms are compleely owned by he paien households and hey ransfer o hem heir profis J r while he defici banks redisribue only a fracion (1 Ω) of heir profis o he households. T P is a lump sum ax used o finance governmen expendiures. Paiens households are ne savers and hey decide o allocae a fracion of heir income in bank deposis a he surplus bank Impaien Households Impaien households choose c(i) I, h(i) I, and b(i) I in order o maximize heir uiliy funcion under he budge consrain. They behave exacly like paien households, bu insead of being ne savers hey are ne borrowers due o heir lower ineremporal discoun facor. Consequenly, hey finance a fracion of heir spending by obaining loans b(i) I from he reail branch of he defici bank. [ ] E 0 βi (1 a I )ɛ z log(c I (i) a p c I 1) + ɛ h log(h I (i)) li (i) (1+φ) (3) 1 + φ =0 6

7 Their budge consrain is described by he following expression c I (i) + q h h I (i) + (1 + rbh 1) b I π 1(i) = w I (i)l I (i) + b I (i) (4) As in Iacoviello (2005), he amoun of funds he impaien households can receive from he defici bank is limied by he following borrowing consrain: (1 + r bh )b I (i) m I E [q h +1h I π +1 ] (5) The oal exposure oward he defici banks of he impaien households mus be less or equal of he expeced value of he collaerals (houses) owned by he households. m I represens he sochasic loan-o-value-raio Enrepreneurs Enrepreneurs are self employed inermediae goods producers. Enrepreneurs choose c(i) E, k(i) E, l(i) E,P, l(i) E,I, b(i) E, u(i) E, where each variable represens respecively consumpion, capial used o produce inermediae goods, labor from paien and impaien households, he amoun of loans obained by he reail branch of he defici bank and he degree of uilizaion of capial. Like impaien households, hey are ne debors on he credi marke. Differenly from paien and impaien households, he uiliy funcion depends only on enrepreneur s consumpion: E 0 βe =0 [ (1 a E )log(c E (i) a E c E 1) ] (6) The budge consrain of he enrepreneurs is described by he following expression: c E (i) + w l E,P (i) + w l E,I (i) + = ye x + b E (i) + q k (1 δ)k E 1(i) (1 + rbe 1) b E π 1(i) + q k k E + f(u (i))k E (i) We specify he funcional form of f() like in Schmi-Grohé and Uribe (2006): f(u (i)) = ξ 1 (u (i) 1) + ξ 2 2 (u (i) 1) 2 (8) The producion funcion is a classical Cobb-Douglass where, A E represens a sochasic oal facor produciviy shock. [ y E (i) = A E k E 1 (i)u (i) ] α l E (i) (1 α) (9) Enrepreneurs use a combinaion of labor supplied by paien and impaien households following he expression l E (i) = l E,P (i) µ l E,I (i) (1 µ) (10) Like he impaien households, enrepreneurs are also subjec o a borrowing consrain (1 + r be )b E (i) m E E [q k +1(1 δ)k E (i)π +1 ] (11) While impaien households use heir amoun of houses as collaeral, enrepreneurs use he expeced value of heir endowmen of physical capial. 1 Iacoviello (2005) demonsraes ha in he neighborhood of he seady sae he consrain always binds.we neglec he problem of he occasionally binding consrains. See for furher references Guerrieri and Iacoviello (2015) and Brzoza-Brzezina e al. (2013). 7 (7)

8 3.2 Banking sysem The banking sysem is buil upon Gerali e al. (2010) and Dib (2010). Boh he surplus and he defici bank are made of a wholesale and a reailer branch. The aim of he wholesale branch is o define he opimal balance shee of he bank while he reailers have o se he ineres raes on loans and deposis. The inerbank marke operaes under perfec compeiion bu he surplus bank has o face a limied enforcemen problem: he defici bank can decide (opimally) o no pay back a cerain amoun of inerbank borrowing in each periods. On he oher hand, he surplus bank can allocae is resources among risky inerbank loans and governmen bonds. To keep he model simple, we inroduce anoher simplificaion: we do no disinguish beween secure and unsecured inerbank marke bu we assume ha all he inerbank ransacions are risky. The sequence of evens in he inerbank marke sricly follow dewalque e al. (2010): a ime he defici bank receive an amoun IB from he surplus bank. A ime + 1 he defici bank decides he amoun of defauls over he inerbank marke. Since defauls are cosly, a ime + 2 he defici bank have o pay a pecuniary defaul coss Defici Banks The wholesale branch The problem he wholesale branch has o face is he maximizaion of he cash flow of he enire holding subjec o he bank s balance shee consrain: [ maxe 0 βiλ I (1 + R)B b (j) (1 + r ib )IB (j) =0 + (1 + r ib 1)(1 δ d )IB 1 (j) K b (j) Adj kb (j) Adj δ (j) where βi λi represens he sochasic discoun facor for he Wholesale branch 2, R b, and r ib are respecively he (ne) ineres rae on loans from he wholesale branch o each reailer and he (ne) ineres rae on he loans obained on he inerbank marke. B is he oal amoun of asses, which includes boh loans o impaien households and enrepreneurs. IB are he resources he defici banks borrow on he inerbank marke from he surplus ones while K b represens he bank capial. δ d represens he share of inerbank defaul ha he Defici bank could decide o no pay back. The erm Adj kb (j) = k ( ) kb K b 2 (j) 2 B (j) v b K b (j) (13) is he bank capial requiremen. The lowes is he raio beween bank capial and he oal asse he higher is he penaly cos of providing an addiional uni of loans o he reail branch. v b is fixed a 8% in order o replicae he Basel II capial requiremen consrain. The defaul opion is cosly for he banks. Similar o Dib (2010) and dewalque e al. (2010), he erm Adj δ represens a penaly cos ha he defici bank has o pay whenever i decides o defaul on inerbank borrowing. Adj δ (j) = χ db 2 ( IB 2 (j)δ d 1(j) ) 2 2 The sochasic discoun facor is equal o he marginal uiliy of consumpion of he Impaien households because we are assuming ha hey are he only owners of he bank 8 ] (12) (14)

9 Moreover, defici bank has o obey in every period o he following balance shee consrain B = IB δ d IB 1 + K b (15) Bank capial evolves according o he following law of moion K b (j)π = (1 δ b )ɛ kb K b 1(j) + ΩJ db 1(j) (16) δ b and Ω are respecively he quarerly depreciaion rae of bank capial and he share of profis used o accumulae new bank capial 3 Subsiuing he balance shee consrain ino he objecive funcion and deriving wih respec o B and δ d we ge he firs order condiions for he wholesale branch problem ( ) ( ) R b =r ib (1 β I λi +1 K δ d b λ +1) k K I kb v b b 2 + B B { } (17) β I 2 χ db E (δ+1) d 2 λ I +1 IB λ I Equaion 17 links he ineres rae on loans o inerbank marke condiions and o he adjusmen coss he bank has o face. In paricular, he wholesale ineres rae is affeced by he capial requiremen and by he expeced value of defauls. If he bank is under capialized, i has o pay a cos ha is charge by he bank over he wholesale ineres rae. Moreover, he share of expeced inerbank defauls impac posiively on he wholesale ineres rae: whenever he bank defauls, he subsequen coss are charged over he ineres rae. The defici bank can also decide he opimal amoun of inerbank defauls. ( δ d = λ I r ib 1 β I λ I +1χ db IB 1 ) ɛ δd (18) Equaion 18 describes he evoluion of he inerbank defaul over ime. Defauls increase when he ineres rae over inerbank borrowing is higher and hey shrink when he oal amoun of inerbank borrowing increases. ɛ δ is a sochasic inerbank counerpar risk shock. In he simulaion secion we will sudy he effec of an increase of such a shock and how i will affec he business cycle The reail branch The reail branch of he defici bank has he ask of providing loans o households and enrepreneurs. The reailers bankers operae under monopolisic compeiion and hey have he power o se he ineres rae on heir loans. They have o maximize he following profis funcion maxe o =0 β Iλ I [ ] r bh (j)b I (i) + r be (j)b E (i) RB b (j) Adj kn (19) 3 Consequenly, (1 Ω) is he dividend pay-off raio ha is he quaniy of bank profi disribued o he Paien households. Assuming Ω = 1, he bank is following a zero dividends policy and all profis are used o increase he bank capial. 9

10 subjec o he loans demand of impaien households and enrepreneurs which are b n (i) = The adjusmen coss are defined as Adj kn = k bn 2 ( r bn r bn (j) ) ɛ bn b I (20) ( ) r bn 2 (j) r 1(j) 1 r bn bn b n (21) Every ime he bank changes he ineres rae i has o pay a cos in erms of profi. This adjusmen cos inroduces sickiness in he seing of ineres raes on loans. We can look a he firs order condiions for he reail branch as a New Keynesian Phillips Curve for loan ineres raes (see Aslam and Sanoro (2008)). Subsiuing he loans demand ino he objecive funcion and deriving wih respec o r bh 1 Λbn Λ bn 1 + Rb r bn β I E [ λ I +1 λ I Λ bn ( r bn 1 k bn r bn ) ( r bn Λ bn ( r bn k +1 bn 1 r bn 1 +1 r bn 1 and r be ) r bn r 1 bn we obain + ) 2 ] b n +1 = 0 where n = h, e. We express he elasiciy of subsiuion beween loans provided by differen reail branches as a funcion of he mark up Λ 4. Higher values of ɛ (or equivalenly lower values of Λ ) implies a lower marke power and a lower margin of inermediaion for he bank Aggregae aciviy Profis of he enire holding are defined as he revenues coming from all he business lines of he bank minus he inra group aciviies and he adjusmen coss. We can define he variable J db as he oal profis of he defici group as b n (22) J db = r bh b I + r be b E + r g GB db r ib IB (1 δ d ) Adj db (24) Surplus banks The surplus bank collecs deposis from paien households and decides o inves hese resources eiher in he inerbank marke or purchasing governmen bonds like in Dib (2010). The balance shee of he bank is summarized by he following equaion. IB + GB sb δ d IB 1 = D P (25) Symmerically o he defici bank, he surplus bank is divided ino a reail and a wholesale branch. 4 The elasiciy of subsiuion could be expressed as a funcion of he mark up ɛ = Λ Λ 1 (23) 10

11 3.2.6 The reail branch subjec o maxe 0 =0 β P λ P [ R d d b r d d P (j) k ( ) d r d 2 ] (j) 2 r 1(j) 1 r d d d P r d (26) ( ) r d P d ɛ d (j) = (j) d P (27) ha is he deposis demand of he paien households. The resuling firs order condiion is 1 + Λd Λ d 1 r r d β P E [ λ p +1 λ p ( ) Λ d r d Λ d 1 k r d d 1 + r 1 d r 1 d ) ( ) r d d p ] +1 = 0 k d ( r d +1 r d r d d p (28) Equivalen o he expression found in Gerali e al. (2010). Equivalenly o he case of he defici bank he marke power in seing he ineres rae of deposis allows us o inerpre he derivaive of he objecive funcion wih respec o r d as a New Keynesian Phillips curve for deposi ineres rae The Wholesale branch The wholesale branch maximizes he following objecive funcion. maxe 0 =0 β P λ P { (J sb (j)) Γ (j) } (29) The erm J sb is he profi of he holding and i could be defined as J sb (j) = r ib IB (j) r 1δ ib d (j)ib 1 (j) + r g GB sb (j) r d d P (j) (30) where IB represens he inerbank lending and GB he governmen bonds deained by he surplus bank. The erm Γ = Θ ( (δ d (j)ib 1 (j) δ d 2 IB)) (31) 2 is a quadraic disuiliy relaed o he possibiliy of suffering a defaul on he inerbank marke. The disuiliy erm could be inerpreed as he cos he surplus bank has o susain in case of an unexpeced level of suffered defauls such as legal or repossession coss. Moreover, he banking aciviy is subjec o he usual balance shee consrain expressed by equaion 25. Deriving and combining he opimaliy condiions wih respec o IB and GB, we obain he opimal balance shee of he surplus bank deermined by he following equaion { δ IB = E d IB + rib (1 β } p δ+1) d r g δ+1 d Θ β (32) p (δ+1) d 2 where β p = β p (λ P +1/λ P +1) is he paien households sochasic discoun facor. Two main driving forces are in moion here: on one hand, he increase of defauls push up 11

12 he inerbank ineres rae. Since he surplus bank is risk neural, higher ineres raes represen an incenive o increase he exposiion on he inerbank marke. On he oher hand, he increase of defauls negaively affec he amoun of inerbank lending hrough he disuiliy cos. A he same ime moneary policy could diver resources from he inerbank marke seering he shor erm ineres rae r g conrolling he policy rae r. 3.3 Cenral Bank The cenral bank manages he shor erm ineres raes following a non linear Taylor rule: { (π ) (1 + r ) = (1 + r) (1 φr) (1 + r 1 ) φ φπ R ( y ) φ Y π } 1 φr (1 + ɛ R r ) (33) where r is he seady sae value of he ineres rae, while φ R, φ π and φ Y are respecively he weighs assigned by he cenral bank o he pas shor erm ineres rae, he inflaion arge and he GDP growh. 3.4 The Governmen The governmen secor has o obey an ineremporal budge consrain G + GB 1 (1 + r g 1) π = GB + T (34) where G is he exogenous public expendiure and T a lump sum ax. Following Leeper (1991), governmen fixes axaion according o he following rule ( ) GB 1 sb T = T + ρ fp GBsb (35) π π In order o close he model, we assume ha he ineres rae paid by governmen bonds are equal o he ineres raes se by he cenral bank r = r g. 3.5 Marke clearing condiions and auoregressive process We close our model specifying fifeen exogenous shocks ha evolve like AR(1) process in he form log(x ) = (1 ρ) log( X) + ρ log(x 1 ) + e (36) Wih respec o he original model we add wo addiional sochasic disurbances: he public expendiure G and he counerpar shock on he inerbank marke (ɛ δd ). The resource consrain for he economy is described by he following equaion [ y =c + q k [k (1 δ)k 1 ] + k 1 ξ 1 (u 1) + ξ ] 2 2 (u 1) 2 + δ b K b 1 π + G + Adj j (37) where c is defined as c = c P + c I + c E (38) 12

13 and h = h P + h I (39) Wihou an explici supply secor for housing, we close he model fixing a posiive ne supply h = 1 of he real esae secor. Moreover, he erm Adj j includes all he adjusmen coss of he models. 4 Soluion of he model The model is log-linearized around he non-sochasic seady sae. Like in Gerali e al. (2010), cerainy equivalence holds and here is no role for uncerainy in deermining he behavior of he agens Daase We employ foureen observable variables on he Euro area from 1998 : Q1 o 2014 : Q2 in order o carry ou he esimaion. We use, invesmen, consumpion, house price, inflaion, wage inflaion, deposis, loans o households and enrepreneurs, deposi ineres rae, cenral bank ineres rae, inerbank marke ineres rae, ineres rae on households and firm loans. All variables, wih he excepion of he ineres raes, are expressed in real erms. We made all he ime series saionary applying he one side HP filer for he rending variables 6 and subracing he sample mean from he ineres raes. 4.2 Bayesian esimaion Following Gerali e al. (2010) and DARRACQ PARIES e al. (2011), we use Bayesian echniques in order o esimae only a small subse of he parameers, focusing our aenion only on hose affecing he dynamic of he sysem. The seady sae parameers are calibraed in line wih he values of Gerali e al. (2010). The complee lis of calibraed parameers can be found in able 1. We depared from he original numerical seing imposing a seady sae raio of he Basel II capial requiremen equal o 8%, fixing he depreciaion rae of bank capial close o 0.05, a slighly lower value hen he one proposed in Gerali e al. (2010). We se he defici bank defaul cos χ db close o 0.99 in order o obain a seady sae value of he defaul δ d equal o on quarerly base which implies a yearly rae of 1% of inerbank defauls. We modify he original value of he elasiciy of subsiuion o deposis and households and enrepreneurial loans in order o mach he pre crisis mean of he ineres raes. The complee lis of seady sae values implied by he model is repored in able 3 in secion C of he echnical appendix. 5 All he procedures is carried ou using DYNARE. We used DYNARE version Adjemian e al. (2011), a MATLAB and OCTAVE oolbox capable of solving and simulae DSGE model. 6 Since we used quarerly daa we assumed ha he smoohness parameers of he HP filer is se equal o Following Sock and Wason (1999), he use of he one side HP filer allows he daa o be fully compaible wih he backward looking naure of he Kalman filer used o recover he likelihood funcion of our model. We adap he MATLAB code provided by Meyer-Gohde (2010) o obain he filered series. 13

14 Table 1: Calibraed parameers Parameer Definiion Value β P Paien households discoun facor β I Impaien households discoun facor β E Enrepreneurs discoun facor α Capial share δ Depreciaion rae of physical capial φ Inverse of Frisch elasiciy µ Share of Paien workers m I Seady Sae value of LTV for impaien households m E Seady Sae value of LTV for Enrepreneurs π Ne Seady Sae inflaion ζ d Elasiciy of subsiuion of deposi ζ bh Elasiciy of subsiuion of households loans ζ be Elasiciy of subsiuion of enrepreneurs loans ξ 1 Coefficien associaed wih he degree of uilizaion of physical capial ξ 2 Coefficien associaed wih he degree of uilizaion of physical capial v b Basel II capial requiremen δ b Depreciaion rae of bank capial Ω Profis invesed in new bank capial χ db Defici bank defaul cos The choice of he Priors Given he similariy beween our model and Gerali e al. (2010) a very naural saring poin for he selecion of prior disribuions is o choose hose proposed in heir original work. We choose o slighly modify he original seing. We choose an Inverse Gamma for he sandard deviaions of he srucural shock. The prior mean and sandard deviaions are very close o Iacoviello (2014). This choice is moivaed by he fac of being conservaive abou he relevance of he financial shocks. The relaed auoregressive componens are se wih a mean of 0.75 and he sandard deviaions equal o 0.1 using a Bea prior disribuion. The parameer relaed o he disuily cos of he surplus bank (Θ) is he novely of our esimaion. Since we have few prior informaions abou his parameer we decide o be quie agnosic and seing a wide prior. We only assume a posiive suppor choosing a Gamma prior wih mean equal o 15 and a sandard deviaion equal o 10. We also include in he esimaion he coefficien relaed o he fiscal policy rule ρ fp. We se a Gamma disribuion wih mean 0.3, a value provide by Falagiarda and Saia (2013) in heir calibraion, and a sandard deviaion of 0.1. The deailed choice of he priors and heir disribuions can be found in Table Poserior disribuions We obained he poserior disribuion applying he classical procedure of Mone Carlo Markov Chain simulaion (See for a deailed explanaion Fernandez-Villaverde (2010)). We launched wo Markov chains each of hem composed by draws. We choose he scale facor of he variance and covariance marix of he random walk Meropolis- Hasings in order o obain an accepance rae slighly above 26%. We also check he 14

15 convergence of he chains hrough boh he CUSUM saisic 7 and he Brooks and Gelman (1998) saisics. The resuls are in line wih Gerali e al. (2010). Some parameers deserve furher discussion. The degree of persisence of habi formaion in consumpion is differen among he differen ype of agens in he model. Paien Households presen a low value a P of heir persisence in consumpion while he Impaien Households and he enrepreneurs presen higher values, 0.75 and 0.76 respecively. This resul was previously found in Iacoviello and Neri (2010). Anoher difference is relaed o he adjusmen cos of he ineres raes. In Gerali e al. (2010) he adjusmen coss of he ineres raes on loans are higher ha he deposis counerpar while i is he exac opposie in our model. One of he possible explanaion is relaed o srucure of our banking sysem: he surplus bank can gaher deposis as he only source of exernal funding while he wholesale branch designed by Gerali e al. (2010) can rely also on is own capial. This inroduce more sickiness in he deposis marke wih respec o he original framework. The disuiliy parameer Θ is quie high implying a srong negaive effec of defauls on he surplus balance shee. The counerpar shock displays a cerain degree of persisence wih an auoregressive coefficien ρ δ d close o The complee lis of esimaed parameers can be found in he secion C of he echnical appendix. Table 2: RESULTS FROM BAYESIAN ESTIMATION Parameers Definiion Prior Pos Pos Confidence Pos Confidence shape mode mean inerval 5 % Median inerval 95 % k p p. sickiness Γ[50, 20] k bh H. loans adj cos Γ[6, 2.5] k be E. loans adj cos Γ[3, 2.5] k d Dep. adj cos Γ[10, 2.5] k i Inv adj cos Γ[2.5, 1] k w w. sickiness Γ[50, 20] k kb Cap. req. adj cos Γ[15, 5] Θ Dis cos defaul Γ[15, 10] a P Habi PH B[0.6, 0.1] a I Habi IH B[0.6, 0.1] a E Habi E B[0.6, 0.1] ι w w. indexaion B[0.5, 0.15] ι p p. indexaion B[0.5, 0.15] φ R Policy rae smooh B[0.75, 0.1] φ π Inflaion arge Γ[2.2,0.15] φ y Oupu gap N [0.1, 0.15] ρ fp Fiscal rule Γ [0.3,0.1] To obain he COSUM saisics we exploi he DSGEBaseyianToolbox provid by Ambrogio Cesa Bianchi. I can be downloaded from hps://sies.google.com/sie/ambropo/dsgebayesiantoolbox.zip?aredirecs=0. The graph can be found in secion D of he echnical appendix. 15

16 5 Quaniaive experimen In his secion we repor he impulse response funcions of he model for hree srucural shock: echnological, moneary policy and he counerpar risk on he inerbank marke. We compare wo versions of our model like in dewalque e al. (2010): he baseline scenario wih an acive inerbank marke (endogenous defauls) and he second scenario where defauls are fixed a he seady sae value of he acive scenario. 5.1 Technological shock The impulse responses o a posiive one sandard deviaion (on annual erms) echnological shock (See Figure 2) presen several of he sandard feaures observed in he lieraure (see Smes and Wouers (2007) or Chrisiano e al. (2005)). Toal oupu, driven by an increase of invesmens, reacs posiively o an increase of echnological efficiency, while he inflaion rae decreases. The whole srucure of he ineres raes follows he policy rae and coherenly decreases. Credi demand is boosed by he consequen increased of asses price (boh q h and q k ) ha relaxes he borrowing consrain enhancing households and firms capabiliy o raise more financing. Similar o Dib (2010), posiive echnological shock increases bank leverage and decreases he amoun of inerbank defauls. The implicaions on he supply side of he credi marke are sraighforward. In fac, according o equaion 32, a reducion of defauls pushes up inerbank lending supply and as a consequence loans supply. Toal credi increases for almos six quarers confirming he evidence found by Carrera and Vega (2012). The composiion of he surplus bank s balance shee change. The share of inerbank lending over oal asses increases 8. In erms of a negaive shock, we can inerpre i as a fligh o qualiy scenario. A sudden deerioraion of he economic condiions encourages he surplus bank o shrink risky inerbank lending in favor of secure risk free governmen bonds. Finally, he model wih endogenous defauls amplifies he impac of he echnological shock on he business cycle in paricular wih respec o he financial variables consisenly wih dewalque e al. (2010). 5.2 Moneary policy shock Figure 3 represens he response o an increase of 50 basis poins of he cenral bank policy rae. The oal oupu, even in his case is driven by he drop of invesmens, and inflaion fall. The enire srucure of he ineres raes rises sharply following he increase of he policy rae. I is worh noicing ha credi ighness is no enirely ransmied o he credi marke hrough he inerbank marke channel due o he presence of sickiness in he seing mechanism of loans ineres raes. On impac, credi loans rae spike 20 basis poins less han he inerbank marke ineres rae. 8 The Share of inerbank lending over oal asses deained by he surplus bank is defined as S ib IB GB +IB. = 16

17 Figure 2: Technological shock The solid blue line refers o he model wih an acive inerbank marke. The do red line refers o he model wih fixed defauls. All he impulse response funcions are calculaed a he poserior median. The raes are absolue deviaion from he seady sae. All oher variables are compued as percenage deviaion from he seady sae. 17

18 Figure 3: Moneary policy shock The solid blue line refers o he model wih an acive inerbank marke. The do red line refers o he model wih fixed defauls. All he impulse response funcions are calculaed a he poserior median. The raes are absolue deviaion from he seady sae. All oher variables are compued as percenage deviaion from he seady sae. 18

19 Moneary policy also affecs he composiion of he banks balance shee. The increase of he policy rae divers resources from he inerbank marke o he bonds marke. The reason is ha inerbank lending is riskier, given a spike of inerbank defauls, while a he same ime he remuneraion of deaining risk free bonds is higher. The comparison beween he wo se up is much less clear han in he case of echnological shock. The impulse response funcions sugges ha endogenous defauls amplify he effec of moneary policy shock bu he ampliude of such shock is almos negligible. In fac, he increase of he policy rae is enirely ransmied o he money marke rae during normal ime. Wih no surprise, higher ineres raes on loans discourage credi demand. 5.3 Inerbank counerpar shock Figure 4 represens he impulse response funcions of he model o a one sandard deviaion (on annual erms) increase of he counerpar risk shock on he inerbank marke. We are no rying quaniaively o mach he effec of an increase in riskiness on he inerbank marke bu we are ying qualiaively o undersand he sory behind his mechanism. An increase of counerpar risk on he inerbank marke modifies he composiion of he balance shee of he surplus bank. The fligh o qualiy mechanism pushes he surplus bank o reallocae resources on he risk free marke insead of lending o he defici bank. As a consequence, he inerbank ineres rae goes up causing an increase of credi marke ineres raes. The higher ineres raes discourage credi demand, reducing he amoun of loans used o purchase new inermediae capial and housing services, resuling in a credi crunch. A his poin he recession spreads o he real economy hrough a conracion of invesmens and houses purchase. As a consequence, he shrinkage of invesmens causes an erosion of he physical capial owned by he inermediae firms and of he housing sock deained by he impaien households. The less he capial, he less is he value of he collaeral he enrepreneurs could use o obain credi from he bank, exacerbaing he crisis on he credi marke. Coherenly, facing he fall of he oupu, he cenral bank reacs cuing down he policy rae. dewalque and Pierrard (2010) found a similar resul analyzing a reurn shock of a securiy deained by he defici bank. As already poined ou by Hilberg and Hollmayr (2011), in his scenario he reducion of he ineres rae is highly ineffecive and is no sufficien o resore he normal operaion on he inerbank marke. This resul underlines a fundamenal policy message: shocks ha decouple he behavior of he policy rae wih respec o he money marke ineres raes canno be oally offse only using he radiional moneary policy ools. The nex secion invesigae furher his issue especially in relaion wih he 2007 financial crisis. 6 Hisorical variance decomposiion In his secion we focus our aenion on he hisorical decomposiion of he observable variables in order o undersand he conribuion of each shock o he business cycle especially he role of he counerpar shock. Figure 5 repors he hisorical decomposiions of six main variables. As we expeced, he inerbank marke shock seems o explain par of he rise of he ineres rae on he credi marke during and afer he 2007 financial crisis confirming 19

20 Figure 4: Counerpar risk shock on he inerbank marke All he impulse response funcions are calculaed a he poserior median. The raes are absolue deviaion from he seady sae. All oher variables are compued as percenage deviaion from he seady sae. 20

21 Figure 5: Hisorical variance decomposiion (a) Inerbank in. rae (b) Enr loans in. rae (c) Households loans in. rae (d) Households loans (e) Enrepreneurial loans (f) Invesmens MP FS IB MS IV The dark blue bar represens he moneary policy shock, he ligh blue bar represens all he financial shocks, he green bar represens he counerpar shock, he orange bar group ogeher all he real shocks. The hisorical decomposiion are compued a he poserior median. The ineres raes are absolue deviaion from he seady sae. 21

22 ha he model is able o explain one of he ransmission mechanisms we described in he inroducion. Even afer 2008, ensions on he inerbank marke could be explained hrough he inerbank riskiness shock a leas unil he end of Afer 2008, wha really changed was he behavior of he ECB owards he prolonged recession. The ECB seered down he ineres raes on he credi marke drasically cuing he policy rae of over 300 basis poins afer 2008 pumping a considerable amoun of liquidiy in he money marke in par offseing he derimenal effec of he counerpar shock. According o figure 5, ensions on he money marke gradually decreased unil a resurgence during he 2010 sovereign deb crisis. The ineres raes are no he only variables affeced by he urmoil on he inerbank marke. The role of he inerbank shock affecs in a differen way he credi supply o households compared o he firms. The decrease of loans provided o households is explained for a significan porion by he adverse macroeconomic condiions and by a smaller, bu no negligible, fracion by he inerbank marke shock. Insead, he drop of enrepreneurial loans seems o be compleely explained by several financial facors such as a shrinkage of he loan o value raio and he inerbank marke seems o play no role on he amoun of credi available for he firms. The counerpar shock seems o work hrough wo differen channels. The inerbank marke shock raises ineres rae and decreases he quaniy of loans available o households bu on he oher hand i seems o have no role in fixing he credi supply for firms. The only acive channel for he firms passes hrough he increase of ineres raes ha discourage invesmen and he acquisiion of new capial, also amplified by he drop of he value of he collaeral. In general, like poined ou by Iacoviello (2014), afer he 2007, a significan porion of he variaions of he variables are driven by financial facors insead of real shocks. 7 Concluding remarks In his paper we highlighed he role of he inerbank marke as an imporan driver of he business cycle. We exended he model proposed by Gerali e al. (2010) including an inerbank marke like in Dib (2010) and dewalque e al. (2010). We ook i o he daa of he Euro area using Bayesian esimaion. The resuls sugges ha our model could be able o replicae some feaures of he 2007 financial crisis, especially some inerbank marke sylized facs. A counerpar shock could diver resources from he risky inerbank lending o a safer governmen bond holding, ending up wih higher ineres raes on enrepreneurial loans, less credi provided by he bank o he real economy, causing a recession driven by a fall of he invesmen. The hisorical decomposiion we presened shows how par of he rise of ineres raes during he financial crisis could be explained by he inroducion of an inerbank counerpar shock. We also invesigae he role of moneary policy and we find ou ha in normal imes he inerbank marke does no inerfere wih he ransmission of he moneary policy. The rise of he inerbank marke ineres rae couneracs he decrease of he policy rae reducing he effeciveness of he radiional ools of he moneary policy. In erms of soryelling, our model provide a framework where his kind of moneary policy can be analyzed and beer undersood. Some criical quesions remain unresolved. Our log-linearized framework is no he ideal framework o capure he sudden collapse of he inerbank marke in As suggesed by Benes e al. (2014), financial shocks affecing he balance shee of he banks are linked in a non linear way o he real economy. Capuring his non linear effec implies 22

23 a swiching from a linear se up o a non linear one making he esimaions a dauning ask bu such effor can be fundamenal o beer quaniaively assess he impac of a dysfuncional inerbank marke. Neverheless our model ells us a plausible and coheren ale abou he inerbank marke urbulences during he 2007 financial crisis. 8 Acknowledgmen The auhor would like o hank all he parecipans o he CIDE WEEE 2013 in Perugia, IFABS conference 2014 in Lisbon, he ISCEF conference 2014 in Paris and he Money, Banking and Finance workshop 2015 hosed in Pavia for useful suggesions. In paricular he auhor would like o hank Piergiorgio Alessandri (Bank of Ialy) for his useful discussion and Sefano Neri (Bank of Ialy) for his useful suggesions. The research leading o hese resuls received funding from he European Union, Sevenh Framework Programme FP7, under gran agreemen FinMaP n0 : All errors remain mine. References Adjemian, S., Basani, H., Karamé, F., Juillard, M., Maih, J., Mihoubi, F., Perendia, G., Rao, M., Villemo, S., Apr Dynare: Reference manual version 4. Dynare Working Papers 1, CEPREMAP. Aslam, A., Sanoro, E., May Bank lending, housing and spreads. Discussion Papers 08-27, Universiy of Copenhagen. Deparmen of Economics. Beirne, J., The EONIA spread before and during he crisis of : The role of liquidiy and credi risk. Journal of Inernaional Money and Finance 31 (3), Benes, J., Kumhof, M., Laxon, D., Apr Financial Crises in DSGE Models: A Prooype Model. IMF Working Papers 14/57, Inernaional Moneary Fund. Boissay, F., Collard, F., Smes, F., Feb Booms and sysemic banking crises. Working Paper Series 1514, European Cenral Bank. Brooks, S. P., Gelman, A., General mehods for monioring convergence of ieraive simulaions. Journal of Compuaional and Graphical Saisics 7 (4), Brzoza-Brzezina, M., Kolasa, M., Makarski, K., A penaly funcion approach o occasionally binding credi consrains. Tech. rep. Carrera, C., Vega, H., Jun Inerbank marke and macroprudenial ools in a dsge model. Working Papers , Banco Cenral de Reserva del Perú. Chrisiano, L. J., Eichenbaum, M., Evans, C. L., February Nominal rigidiies and he dynamic effecs of a shock o moneary policy. Journal of Poliical Economy 113 (1), DARRACQ PARIES, M., Sørensen, C. K., Rodriguez-Palenzuela, D., Macroeconomic propagaion under differen regulaory regimes: Evidence from an esimaed dsge model for he euro area. Inernaional Journal of Cenral Banking 7 (4),