Banks, Sovereign Risk and Unconventional Monetary Policies

Transcription

1 Banks, Sovereign Risk and Unconvenional Moneary Policies Séphane Auray Aurélien Eyquem Xiaofei Ma May 12, 2014 Absrac We develop a wo-counry model wih an explicily microfounded inerbank marke and sovereign defaul risk. Calibraed o he Euro Area, he model performs saisfacorily in maching key business cycle facs on real, financial and fiscal ime series. We hen use he model o assess he effecs of a large crisis and quanify he poenial effecs of alernaive unconvenional policies on he dynamics of GDP, sovereign defaul risk and public indebedness. We show ha quaniaive moneary easing is more efficien in simulaing GDP, while qualiaive moneary easing relieves financial ensions and sovereign risk more efficienly. In erms of welfare, in he shor run, unconvenional moneary policies bring sizable welfare gains for households, while he long erm effecs are much smaller. Keywords: Recession, Inerbank Marke, Sovereign Defaul, Moneary Policy. JEL Classificaion: E44, F34, G15. We hank Gregory Corcos, Olivier Loisel, and Pedro Teles for insighful feedback. We also appreciae helpful discussions wih Jordan Roulleau-Pasdeloup and Anoine Vaan. All errors are our own. The auhors graefully acknowledge financial suppor of he Chair ACPR/Risk Foundaion: Regulaion and Sysemic Risk. CREST-Ensai, ULCO (EQUIPPE), and CIRPÉE; sephane.auray@ensai.fr. Universié de Lyon, Universié Lumière Lyon 2, CNRS (GATE UMR 5824); aurelien.eyquem@ens-lyon.fr. CREST-Ensai and Universié de Lyon, Universié Lumière Lyon 2, CNRS (GATE UMR 5824); xiaofei.ma@ensai.fr.

2 1 Inroducion In his paper, we analyze he ineracion beween inerbank markes and defaul risk using a wo-counry dynamic general equilibrium model, wih a focus on he ransmission of he recen financial crisis and unconvenional moneary policies. Inerbank markes are a he crossroad of financial and real spheres, as hey mach credior and debor banks. Their dynamics crucially affecs he amoun of credi in he economy, wih effecs on invesmen and GDP. They are also criical in he conduc of moneary policy, as Cenral Banks implemen open marke operaions o conrol he ineres rae in he overnigh inerbank marke o affec he yield curve. As such, hey play a cenral role in he ransmission of moneary policy decisions, as well as in he ransmission of poenial financial crises. However, despie heir apparen imporance, here are few widely acceped heoreical analysis abou how he inerbank marke operaes. This gap means ha, Cenral Banks were unsure abou how o reac, when banks sopped lending o each oher. In addiion, over he las fifeen years, European banks have increasingly owned governmen bonds of member counries. In paricular, banks of he Core European counries such as France and Germany have gradually become major holders of he sovereign deb issued by Periphery counries like Greece, Ialy, Porugal and Spain. As shown by Guerrieri, Iacoviello and Minei (2012), who used combined daa from he Bank for Inernaional Selemens and he Bank of France, he raio of French banks holdings of Periphery s sovereign deb over heir holdings of French governmen deb was 56% in he las quarer of 2009, up from 19% in he firs quarer of As a consequence, European banks were significanly exposed o he sovereign defaul risk of Periphery counries. This vicious spiral of win crisis beween banks and sovereigns imposes poenial losses for banks who invesed massively in he sovereign marke, and resuled ino banks reduced abiliy and propensiy o exend lending o he marke. 1

3 The rising inerdependence beween inerbank and sovereign bonds markes was a he hear of ECB s concerns abou rising sovereign risk in he Euro Area. I was also parly exploied by ECB s unconvenional moneary policies, o release ensions on boh markes a he same ime. To capure his inerdependence, we develop a wo-counry model based on Guerrieri e al. (2012), who sudy he inernaional propagaion of sovereign deb defaul, and add an inerbank marke à la Dib (2010). We quanify he effecs of alernaive unconvenional moneary policies on financial variables (credi, lending raes), real variables (invesmen, GDP), fiscal variables (deb-o-gdp raios, sovereign spreads). We also compue welfare losses/gains from he crisis and from he various policies, disinguishing beween differen ypes of agens (banks, households, enrepreneurs). Concerning he sovereign risk channel, we differ from Guerrieri e al. (2012) and follow Corsei, Kueser, Meier and Mueller (2013), assuming ha sovereign defaul risk is increasingly and posiively relaed o a counry s deb-o-gdp raio. As in Gerler and Kiyoaki (2010), we resric aenion o a purely real model and focus on unconvenional policies only. For he banking secor, our model incorporaes an opimizing banking secor wih wo ypes of monopolisically compeiive banks in he inerbank marke: Savings Banks and Borrowing Banks, supplying differen banking services and ransacions in he inerbank marke. 1 Savings Banks are financial inermediaries ha are ne lenders (crediors) in he inerbank marke, whereas Borrowing Banks are ne borrowers (debors). Banks have monopoly power when seing real deposi and prime lending raes. Savings Banks collec deposis from workers, se real deposi raes, and opimally choose he composiion of heir porfolio (composed of governmen bonds and risky inerbank lending). Borrowing Banks borrow from Savings Banks in he inerbank marke and raise bank capial (equiy) from bankers (shareholders) in he financial marke o saisfy he capial requiremen imposed by he regulaion. 1 The wo differen banks are necessary o generae heerogeneiy, from which differen banks can inerac in he inerbank marke (see Dib (2010). 2

4 Furher, following Goodhar, Sunirand and Tsomocos (2006) and Dib (2010), we assume endogenous sraegic defaul on inerbank borrowing. Finally, we inroduce unconvenional moneary policies in he model. Borrowing Banks can receive injecions of money from he Cenral Bank o preven freezes on he inerbank marke, a policy ha we refer o as quaniaive easing. We also consider a policy by which he Cenral Bank allows Borrowing Banks o swap a fracion of risky loans for governmen bonds, hereby improving heir balance shee. We refer o his policy as qualiaive easing. We show ha quaniaive easing is more efficien in simulaing invesmen and GDP, while qualiaive easing is a more effecive opion o relieve financial ensions and sovereign defaul risk. In erms of welfare, in he shor run, unconvenional moneary policies bring welfare gains for households, while he long erm effecs are much smaller for all ypes of agens. The paper is organized as follows. Secion 2 relaes he paper o he lieraure. Secion 3 describes he model. Secion 4 presens he calibraion. Secion 5 discusses he resuls and provides he welfare analysis. Secion 6 concludes. 2 Lieraure Review There are very few sudies on he join fricions in he credi and sovereign markes. The exising sudies abou he role of banks in global economies pay lile aenion on sovereign deb problems. Devereux and Yeman (2010) sudy a wo-counry economy in which invesors hold domesic and foreign asses bu are exposed o leverage consrains. They find ha if global financial markes are highly inegraed, produciviy shocks will be propagaed hrough invesors financial porfolios, which will generae a srong oupu comovemen. Mendoza and Quadrini (2010) build a wo-counry model wih differen degrees of financial developmen. Their model analyzes he cross-counry spillover effecs of shocks o bank capial. Boh Kollmann, Enders and Muller (2011) and Kalemli-Ozcan, Papaioannou and Perri (2012) consider a wo-counry environmen wih a global banking 3

5 secor, heir models generae synchronized business flucuaions across counries. Our paper relaes o some of he recen lieraure on inerbank markes or sovereign defaul. For insance, Guerrieri e al. (2012) sudies he inernaional propagaion of sovereign deb defaul by considering a wo-counry model calibraed o Europe. They assume ha large conracionary shocks in he Periphery rigger sovereign defaul. Their model shows sizable spillover effecs of sovereign defaul from Periphery o he Core hrough he financial channel. Mendoza and Yue (2012) consruc a small open economy model of sovereign defaul and business cycles, in which hey ake defaul as a sraegic decision of he governmen, bu disregard he poenial effecs of inerbank marke freezes. Concerning he inerbank marke, Allen, Carlei and Gale (2009) build a heoreical model o analyze Cenral Bank s inervenion on he inerbank marke bu neglec he effecs of sovereign defaul risk. Dib (2010) proposes a micro-founded DSGE model which incorporaes an inerbank marke wih wo heerogeneous banks according o heir liquidiy sufficiency. By assuming monopolisic compeiion among banks, his model sudies effecs from convenional and unconvenional moneary policies. Gerler and Kiyoaki (2010) develop a comprehensive model of he financial secor, hey show ha he ne benefis from Cenral Bank s credi marke inervenions are increasing in he severiy of he crisis. Gerler and Karadi (2013) exend he model developed in Gerler and Karadi (2011) o accoun for qualiaive easing on he bond marke. However, he model absracs from sovereign risk and neglecs he endogenous response of he governmen spending during he crisis, as well as he implied effecs on deb and defaul risk. In erms of sysemic banking crisis, Boissay, Collard and Smes (2013) build a DSGE model ha feaures a non-rivial banking secor. Their model explains how banking crises break ou in he mids of credi inensive booms and bring abou paricularly deep and long-lasing recessions. So far, non of he menioned conribuions explores he impac of Cenral Bank s 4

6 policy on he sovereign defaul risk hrough he inerbank bank marke, which is he main focus of our analysis. Our paper inegraes sovereign risk, inerbank marke, and he Cenral Bank s unconvenional moneary policy, and sudies heir join ineracion during a recession. 3 Model The world economy consiss of wo counries, Core and Periphery. In each counry here are infiniely-lived households, enrepreneurs (capial good producers), final good producers, and bankers. All agens of a given ype are homogeneous. In addiion, in each counry here is a governmen ha purchases final goods financing expendiure wih deb and lump-sum axes. There is one Cenral Bank in his wo-counry model, represening he ECB. The final good is produced using labor (non-radable inernaionally) and capial. Goods markes are compeiive. The banking secor consiss of wo ypes of heerogeneous monopolisically compeiive banks. We call hem savings and borrowing banks, o indicae ha hey offer differen banking services bu inerac in he inerbank marke. The Periphery and he Core have symmeric preferences and echnology funcional forms, only he calibraion will differ. In wha follows, we concenrae on he descripion of he Periphery, and assume ha similar relaions hold in he Core counry. We assume ha he size of Periphery Counry is 1, while Core Counry has a size of n. Agens aciviies are as follows. In each period, households supply labor o enrepreneurs. Households can save by holding deposis in domesic banks. Enrepreneurs receive loans from banks and inves ino physical capial, which hey ren o final good producers. Final good producers produce he final good using labor and capial. Saving Banks receive deposis, lend o Borrowing Banks in he inerbank marke or purchase nonsae coningen governmen bonds issued by boh governmens. Borrowing Banks make loans o domesic enrepreneurs combining borrowing from he inerbank marke and bank 5

7 capial. Bank capial is held in he form of bonds issued by boh governmens. Bankers are owners of he wo ypes of banks, from which hey receive profis. They consume, save in local governmen bonds, and accumulae bank capial supplied o Borrowing banks. In our model, he deposi D 1, loan L 1, bank capial Z 1, and physical capial sock K 1 are assumed o be predeermined variables. 3.1 Households We focus on he Periphery counry and assume behavioral symmery in he Core counry. Households maximize heir expeced discouned uiliy: max {C H,N,D} E 0 =0 β H [ log ( C H ] ) χ N (N ) 1+η 1 + η (1) subjec o C H + D + T H + AC H = R D 1D 1 + W N (2) where C H represens households consumpion, N is heir labor supply, D are households holdings of deposis in domesic banks, AC H = φ D 2 ( D D 1) 2 denoes quadraic porfolio adjusmen coss paid by he household when deviaing from he seady-sae value of deposi D. In addiion, R D 1 is he gross real ineres rae on deposi beween period 1 and period. W is he wage rae, and T H is a lump sum ax imposed on households by he governmen. Firs order condiion implies ha: λ H λ H = 1 C [ H 1 + φ ( )] D D D D 1 [ ] = β H E R D +1 λ H +1 (3) (4) χ N C H (N ) η = W (5) 6

8 3.2 Bankers Bankers are he owners of he wo ypes of banks, from which hey receive profis. They consume, save in domesic governmen bonds, and accumulae bank capial supplied o Borrowing Banks. Bankers hus ener he period wih Z 1 shares of bank capial. Bank capial pays a coningen real reurn R Z, also inerpreed as dividend. Bankers maximize heir discouned uiliy funcion: subjec o max {C B,Z,BB } βb log C B (6) =0 C B + B B + Z + AC B = R 1 (1 p 1 ) B B 1 + R Z Z 1 + Π sb + Π bb T B (7) where AC B = φ Z 2 ( ) 2 Z Z 1 + φ ( ) B B B 2 2 B 1 B and where C B is he consumpion of bankers, B B is he amoun of local bonds held by bankers paying R 1 wih a possibiliy of defaul p 1 in period 1. Π sb he profis of savings banks and borrowing banks, respecively, and T B paid o he governmen. Firs order condiion are and Π bb are is a lump-sum ax 1 + φ ( B B B B B 1 + φ Z Z λ B = 1 C B ) B 1 B ( ) Z Z 1 = β B E ( λ B +1 λ B ( λ B = β B E +1 R λ B +1 Z ) R (1 p ) ) (8) (9) (10) 7

9 3.3 Banks The banking secor of each counry consiss of wo ypes of heerogeneous profi-maximizing banks: he Savings Banks (SBs) and Borrowing Banks (BBs) Savings Banks Savings Banks (SBs) refer o all financial inermediaries ha are ne crediors (lenders) in inerbank marke. There is a coninuum of monopolisically compeiive, profi-maximizing SBs indexed by j (0, 1). Each SB j collecs fully insured deposis from workers D j, and pays a deposi ineres rae Rj,, D which is opimally se as a markdown over he marginal reurn of is asses. The supply of deposis is given by ( ) υd R D j, 1 D 1 (11) D j, = R D 1 where υ D > 1 is he elasiciy of subsiuion beween differen ypes of deposis and D is he oal amoun of deposis. SB j opimally allocaes a fracion s j, of deposis o lending in he domesic and foreign inerbank markes ha reurn R IB,C and R IB,P, respecively. SB j also uses he remaining fracion 1 s j, o purchase governmen bonds, boh domesic and foreign. Lending on he inerbank marke is subjec o a defaul probabiliy δ D and induces a quadraic monioring cos s j, = χ s 2 ((s j, s) D j, ) 2 (12) ha depends on deviaions of s j, from a consan arge s. The remaining fracion of deposis is allocaed o bonds and spli beween domesic bonds and foreign bonds. These ( ) ( ) asses pay R 1 P 1 p P 1 for bonds issued in he Periphery and R C 1 1 p C 1 in he Core beween period 1 and, where p P 1 and p C 1 are he percenage defaul raes, 8

10 ha can also be inerpreed as ex ane defaul probabiliies in boh counries. Changing he composiion of bonds porfolio incurs he paymen of adjusmen cos Ad B j, = φ δ B 2 ( ) 2 δ B j, δ 1 (13) B Meanwhile, changing he composiion of he porfolio of inerbank lending incurs a similar adjusmen cos: Ad IB j, = φ δ IB 2 ( ) 2 δ IB j, δ 1 (14) IB Formally, he j h saving bank s opimizaion problem is where max E 0 {s j,,rj, D,δB j,,δib j, } βbλ B =0 {[ ] } s j, R IB,SB + (1 s j, ) R B Rj, D D j, s j, (15) R B = δ B R P ( 1 p P ) + ( 1 δ B ) R C ( 1 p C ) Ad B j, (16) and R IB,SB ( = δ IB R IB,P 1 δ D,P ) + ( ) ( ) 1 δ IB R IB,C 1 δ D,C Ad IB j, (17) subjec o he consrains above. In he definiion of R B, δ B is he fracion of deposis invesed in bonds issued in he Periphery, and R P and R C are he gross reurns on bonds in he Periphery and Core counries, respecively. Similarly, in he definiion of R IB,SB, δ IB Periphery inerbank marke, R IB,P and R IB,C he Periphery and Core counries, respecively; δ D,P is he fracion of deposis invesed in he are he gross reurns of inerbank lending in and δ D,C on inerbank lending in he Periphery and Core counries, respecively. 9 are he defaul probabiliies

11 In he symmeric siuaion, where s j, = s and R D j, = R D for all > 0, he firs-order condiions of his opimizaion problem wih respec o s, R D, δ B j,, and δ IB j, are: s = s + RIB,SB 1 + υ D ( R D υ 1 ) [ = s R IB,SB + (1 s )R B 1 D δ B δ B = 1 + δb δ IB φ δ B δib = 1 + δib φ δ IB R B (18) χ s D 1 ] χ s (s s) 2 D 1 (19) [ R P ( 1 p P ) R C ( 1 p C )] [ ( R IB,P 1 δ D,P ) R IB,C ( 1 δ D,C )] (20) (21) Borrowing Banks Borrowing Banks (BBs) refer o all ne debor (borrower) banks in he inerbank marke. There is a coninuum of monopolisically compeiive BBs indexed by j (0, 1). BBs borrow from SBs in he inerbank marke and raise bank capial from bankers o saisfy he capial requiremen. We assume ha he sock of bank capial Z j, is held by he BBs as governmen bonds in a porfolio wih fracion δ BB invesed in governmen bonds issued by he Periphery 2. In addiion, BBs can receive money from he Cenral Bank, which can be inerpreed as quaniaive easing. 3 To produce loans L j, supplied o enrepreneurs, each borrowing bank j combines funds received from SBs in he inerbank marke, D IB j,, plus any excepional injecion of money by he Cenral Bank, M j, (quaniaive moneary easing). Also, if needed, BBs may swap a fracion X j, of heir risky asses (loans o enrepreneurs) for governmen bonds from he Cenral Bank (qualiaive moneary easing) 4. Through hese wo channels, he Cenral Bank can provide liquidiy o BBs in imes of financial sress. 2 Z j, = Z 1 in symmeric case. 3 Nominal money divided by he price index. 4 Quaniaive moneary easing, which is associaed wih newly creaed money, expands banks balance shees; qualiaive moneary easing (swapping banks asses for governmen bonds) changes only banks asses composiions. 10

12 We assume ha BBs use he following Leonief echnology o produce loans: L j, = min { D IB j, + M j, ; κ j, (Z j, + X j, ) } Γ (22) where κ j, κ is bank j s leverage raio and κ is he maximum leverage raio imposed by regulaors. X j, is he amoun of new asses swapped by he Cenral Bank. Γ is a shock o he financial inermediaion process affecing credi supply. Leonief echnology implies perfec complemenariy beween inerbank borrowing and bank capial, and imposes he capial requiremen, which aenuaes he real effecs of differen shocks. When lending o enrepreneurs, BB j faces he following demand funcion for loans: ( ) υl R L j, 1 L 1 (23) L j, = R L 1 where υ L > 1 is he elasiciy of subsiuion beween differen ypes of loans. The BB j opimally ses he prime lending rae, R L j,, as a markup over he marginal cos of producing loans. The j h BB s leverage raio is given by κ j, = L j, Γ (Z j, +X j,, which is subjec o he ) maximum leverage raio imposed by he regulaors, κ. Whenever BBs have a lower-hanarge leverage raio, hey receive convex gains in he form of κ j, = χ κ 2 (( )) 2 κ κj, (Z j, + X j,) (24) κ Moreover, following Goodhar e al. (2006), we allow BBs o opimally defaul on a fracion of heir inerbank borrowing, δj, D > 0. The defaul on inerbank lending can be sraegic or mandaory (when banks canno afford o repay heir deb). Noneheless, i is cosly for banks o defaul on he inerbank borrowing. In his case, banks mus pay 11

13 convex penalies in he nex period. The j h bank s penaly is given by D j, = χ δ D 2 ( ) δ D j, 1 Dj, 1 IB 2 R IB 1 (25) where χ δ D is a posiive parameer deermining he seady-sae value of D j,. Furhermore, we assume ha borrowing banks bear he same adjusmen cos as SBs when hey adjus he holding of domesic and foreign governmen bonds. The j h borrowing bank s opimizaion problem is hus max {R L j,,δd j, } E 0 βbλ B =0 Rj,L L j, ( 1 δj,) D R IB Dj, IB ( R Z R B D j, + κ j, R B M j, (R L j, R B )X j, ) Zj, (26) subjec o equaions lised above. In he symmeric equilibrium, where R L j, = R L, κ j, = κ, δ D j, = δ D, for all > 0. The firs-order condiions of his opimizaion problem are: υ L 1 ( R L υ 1 ) = Ω 1 (27) L ( ) λ δ D B = E 1 (28) β B λ B +1 χ δ DD IB where Ω is he marginal producion cos of loans: [ Ω = Γ 1 (1 δ D )R IB + E β B χ δ D λ B +1 λ B (δ D ) 2 R IB D IB + χ ] κ( κ κ ) κ 2 (29) 3.4 Enrepreneurs In each counry, here is a coninuum of idenical infiniely-lived enrepreneurs who borrow from local BBs, consume, and accumulae physical capial ha depreciaes a rae δ. 12

14 Enrepreneurs maximize heir lifeime uiliy: max {C E,K,L} βe log C E (30) =0 subjec o he budge consrain: C E + K + R L L 1 + AC E = (R K, δ) K 1 + L T E (31) where AC E = φe I 2 ( ) 2 I I 1 + φe L 2 ( ) 2 L 1 (32) L 1 denoes quadraic porfolio adjusmen coss paid by he enrepreneurs o change he invesmen, and he holdings of loans. The invesmen I is defined as: I = K (1 δ)k 1 (33) In addiion, enrepreneurs are subjec o a consrain ha limis heir leverage o a consan fracion m of heir capial holdings: L = ρ E L 1 + (1 ρ E ) mk (34) where he parameer ρ E capures he elasiciy of he loan limi o he curren capial choice of he enrepreneur. Therefore, he FOCs of he program are: λ = 1 C [ E λ 1 + φe I λ [ φ E L L 1 δk ( I ) δk 1 β Eφ E I (1 δ) δk ) ] 1 ( L L 1 1 ( )] I+1 δk 1 + λ = E β E λ +1 [ φl L +1 L 2 (35) m (1 ρ E ) λ = β E E [λ +1 (R K,+1 δ)] (36) ( ) ] L+1 1 R L,+1 + β E λ+1 ρ E (37) L 13

15 where λ and λ are he Lagrange mulipliers for consrain (31) and (34). 3.5 Final Good Producers The represenaive final good producer operaes a Cobb-Douglas producion funcion given by Y = A (K 1 ) α (N ) 1 α where Y is he oupu of domesic final good, K 1 is he capial sock rened from enrepreneurs a he rae, R K,, N is he labor inpu and A is a sochasic process for produciviy. Producers make zero profis because of perfec compeiion and consan reurns o scale. Wih compeiive facor marke and profi maximizing producers, we have: W = (1 α) Y N R K, 1 = α Y K Governmens Governmen spending is financed hrough axes on households, enrepreneurs, bankers and hrough deb. The governmen budge consrain in he Periphery counry is B R 1 (1 p 1 ) B 1 = G ( T H + T B ) + T E (38) where G is exogenous governmen spending, B is he amoun of governmen bonds issued in he Periphery. Public expendiure is financed a ime by raising axes, issuing addiional deb or parially defauling on deb issued in he pas. 14

16 We assume ha governmen spending has a couner-cyclical componen seeking o sabilize he business cycle. In addiion, we impose a cu on governmen spending when he probabiliy of defaul rises: G = ρ B G 1 + (1 ρ B ) (G σ(y Y ) γ (B 1 B)) + ε g (39) 3.7 Sovereign Defaul Risk There are mainly wo srands of lieraures abou sovereign defaul. On one hand, Eaon and Gersoviz (1981), Arellano (2008) and ohers have modeled defaul as a sraegic decision of he governmen. On he oher hand, Bi (2012) considers defaul as he consequence of he governmen s inabiliy o raise funds used o honor is deb obligaions. Under boh approaches, he probabiliy of sovereign defaul is closely and non-linearly relaed o he level of public deb o GDP. We adop he approach from Corsei e al. (2013), in which he ex ane probabiliy of defaul, p, a a cerain level of sovereign indebedness, b = B / (4Y ), will be given by he cumulaive disribuion funcion of he bea disribuion: p = F bea (b /b max, α b g, β b g) (40) where b max denoes he upper end of he suppor for he deb-o-gdp raio. We focus on he ex ane probabiliy of sovereign defaul, because he ex ane defaul risk is crucial for he pricing of governmen deb. 3.8 Equilibrium We assume ha he Core counry is characerized by similar equilibrium condiions. An equilibrium is defined as a sequence of prices and quaniies such ha all agens solve heir opimizaion problems, and ha prices clear he markes: 1. Producion facor markes 15

17 2. Loan markes 3. Bank capial markes Z P 1 = LP 1 Γ P κ P Z C 1 = LC 1 Γ C κ C X P X C 4. The goods marke Y P ( + ny C = C H,P + C B,P ) ( + C E,P + n C H,C + C B,C ( ) ( K P (1 δ) K 1 P + n K C (1 δ) K 1) C ) + C E,C + G P + G C + adjusmen/monioring coss gains from excess bank capial 5. The inerbank marke ( n 1 δ IB,C δ IB,P s P D 1 P + nδ IB,C s C D 1 C = D IB,P = LP 1 Γ P ) s C D 1 C + (1 δ IB,P )s P D 1 P = nd IB,C = n M P ( L C 1 M C Γ C ) 6. Sovereign deb markes B P = B B,P + nδ B,C B C = B B,P [ (1 s P )D 1 P + Z 1 P + X P ] + δ B,P [ (1 s C )D 1 C + Z 1 C + X C + (1 δ B,P ) [ (1 s P )D 1 P + Z 1 P + X P ] + n(1 δ B,C ) [ (1 s C )D 1 C + Z 1 C + X C ] ] 16

18 3.9 Shock Processes The economy is subjec o produciviy, governmen expendiure, inerbank ension, convenional and unconvenional moneary policy shocks. Governmen spending shock is given by equaion (39). The lef srucural shocks follow AR(1) processes: log(λ ) = (1 ρ Λ ) log(λ) + ρ Λ log(λ 1 ) + ε Λ where Λ = {A, Γ, M, X }; Λ 0 is he seady-sae value of Λ ; ρ Λ (0, 1); and ε Λ N(0, σ Λ ). 4 Calibraion We calibrae he model o he Euro Area. The ime uni is a quarer. The Periphery comprises Greece, Ialy, Porugal and Spain while he Core is made of remaining members of he moneary union. We choose he Households discoun facor, β H, o be symmeric and equal o , implying an annual real ineres rae on deposis of 1%. The inverse of he Frisch elasiciy of labor supply is η = 2. The discoun facors of bankers and enrepreneurs are se equal o and 0.99, respecively. On he producion side, he depreciaion rae δ is 0.03 and he capial share in producion α is We se invesmen adjusmen coss φ E I = 2.5 o mach he relaive volailiy (sandard deviaion) of invesmen as much as possible. Enrepreneurs also pay a convex cos for adjusing loans; we se φ E L = 0.05 as in Guerrieri e al. (2012). We se he parameer governing enrepreneurs working capial consrain ρ E = m is chosen so ha is value maches he raio of ousanding loans over capial socks. Moving o he governmen, he deb ceiling parameer b is 3.4 for he Periphery bloc and 2.4 for he Core bloc. These choices imply a deb-o-gdp raio equal o 0.85 in he 17

19 Periphery and 0.6 in he Core, in line wih daa from he IMF Economic Oulook for Seady-sae ax raes are calibraed o represen 45% of he consumpion of each ype of agen and remain consan over simulaions. In erms of sovereign defaul risk, we follow Corsei e al. (2013), and choose parameers α b g = 3.70, β b g = 0.54, b max = In he public spending process, we assume a ρ B = 0.81 persisence, he coefficien on defaul risk is γ = in he Core and γ = 0.05 in he Periphery, and he coefficien on oupu is σ = 0.25 in he Core and σ = 0 in he Periphery. Those differen coefficien are se o mach differences in cyclical paerns of public spending beween he Core and Periphery, as well as sovereign spread volailiies. Households pay a cos for adjusing deposis, we se φ D = In he banker s problem, he parameer measuring he convexiy of he adjusing cos funcion, φ B, denoe how cosly i is for he bankers o adjus domesic and foreign bonds: we se φ B = To apporion he seady-sae holdings of governmen deb o households, Periphery and Core banks, we adop he calibraion in Guerrieri e al. (2012), i.e. 41.7% he share of public deb of he Periphery is held by he Core bloc, 18.8% is held by Periphery households, and 39.5% is allocaed o Periphery banks. For he Core governmen deb, 11% of heir collecive sovereign deb is held by households in Core counries, and 70% of he oal is assigned o Core banks. In he inerbank secor, he parameer χ s deermines he raio of bank lending o oal asses held by he savings banks s. I is se so ha he seady-sae value of s is equal o 0.64 for he Periphery and 0.86 for he Core, which corresponds o he hisorical raio observed in he daa 5. The parameer χ κ is se so ha we could have a reasonable value for ν L, i.e. around 4. Based on he Basel II minimum required bank capial raio of 8%, we assume ha he 5 This is significanly smaller han in he US (0.82), which migh have helped Europe o offse he impac from he 2008 subprime crisis. 18

20 maximum imposed bank leverage, κ, is 5.36 for Periphery and 4.03 for Core 6. Similarly, we calibrae χ δd, he parameer deermining he oal cos of banks defauls on inerbank borrowing, so ha he probabiliy of defaul in he inerbank marke equals o 0.2% in annual erm. The parameers ν D and ν L, which measure he degrees of monopoly power of savings and Borrowing banks, are se o mach he hisorical averages of real deposi and loan raes, R D and R L. Table 1 summarizes he parameerizaion and shows he implied seady-sae value of key variables in he model. 6 Before Basel II, he maximum raio of bank asse/capial is he reciprocal of required capial raio, which equals o However, loans are only a par of bank asses. The leverage raio in our model equals o loans/bank capial. 19

21 Table 1: Parameer and seady-sae values Parameer values Seady-sae values Periphery Core Periphery Core β H A β B Y β E W η N m s δ s α κ ρ E κ ν D Γ ν L R D χ s R L χ κ R IB χ δd R P/C φ D R Z φ Z RE K φ B δ D φ E I D/Y φ E L T H /Y φ δ B C H /Y φ δ IB Z/Y ρ B B B /Y γ T B /Y σ C B /Y α B g Π SB /Y β B g Π BB /Y b max K E /Y size T E /Y L/Y C E /Y D IB /Y G/(sizeY ) B/(sizeY ) Simulaions In his secion we run wo ypes of exercises. Firs, we compue he business cycle momens induced by he model and compare hem o he key business cycle momens in he 20

22 Euro Area. Second, we run non-linear simulaions of he model o assess he impac of quaniaive and qualiaive easing policies followed by he ECB during he crisis. 7 The idea is o compare he relaive efficiency of alernaive inervenions boh on he inerbank and he sovereign deb markes. We also inroduce a scenario when he marke reas Core governmen bond as safe asse, i.e. a safe haven. The las par of he secion proceeds o a welfare analysis of each policy. 5.1 Business Cycle Momens We firs repor he business cycle properies of he economy when driven by hree ypes of shocks: produciviy shocks, financial shocks and public spending shocks. Our calibraion for hose shocks follows Dib (2010) and assumes ρ A = ρ Γ = 0.8, σ A = 0.01 and σ Γ = The public spending rule feaures a 0.81 persisence (ρ B = 0.81) and shock volailiies are adjused o mach he volailiy of pubic spending relaive o he volailiy of GDP, i.e. σ G = in he Core and σ G = 1.01 in he Periphery. The arificial ime series generaed by he linearized soluion of he model are hen HP-filered wih λ = 1600 and we repor he sandard deviaions, auocorrelaions and correlaions wih oupu. Those resuls are compared o business cycle momens compued from he daa. The resuls are repored in Table 2. Business cycle momens concerning GDP and is main componens (consumpion, invesmen and public spending) are correcly reproduced. GDP is more volaile in he Periphery han in he Core. The relaive volailiy of consumpion is less han one in he Core and close o one in he Periphery. The relaive volailiy of invesmen is higher in he Core han in he Periphery, alhough is level is a bi larger han in he daa. 8 The relaive volailiy of public spending is perfecly mached wih daa bu he laer was 7 So far, he mos imporan insrumen from ECB is he reverse ransacion (applicable on he basis of repurchase agreemens or collaeralized loans). Is influence on he economy should be a mix of he quaniaive and qualiaive moneary easing. 8 A calibraion absracing from financial shocks allows o mach hose momens almos exacly. 21

23 Table 2: Business cycle momens Daa Core Periphery Variables (x) σ ρ ρ x,y σ ρ ρ x,y Oupu a (y) Consumpion a Public spending a Invesmen a IB rae b (r ib ) Loan rae e Deposi rae e Sov. long raes d (r) Sov. Spreads d (spr) IB. Spreads d Deb o GDP d Loans o GDP c Deposis o GDP c Correlaions (ρ x,x ) r ib r spr r ib r spr Deb o GDP d Public spending a Loans o GDP c Deposis o GDP c Model Core Periphery Variables (x) σ ρ ρ x,y σ ρ ρ x,y Oupu (y) Consumpion Public spending Invesmen IB rae (r ib ) Loan rae Deposi rae Sov. long raes (r) Sov. Spreads (spr) IB. Spreads Deb o GDP Loans o GDP Deposis o GDP Correlaions (ρ x,x ) r ib r spr r ib r spr Deb o GDP Public spending Loans o GDP Deposis o GDP See Appendix for he deails of he daa. 22

24 used as a arge o calibrae public spending shocks. In erms of persisence, he model produces a lile bi less persisence han observed in he daa, especially for invesmen and consumpion. Comovemens are reproduced a leas qualiaively, alhough invesmen is less pro-cyclical han consumpion while he opposie paern characerizes he daa. Public spending is weakly couner-cyclical in he Core while weakly pro-cyclical in he Periphery, as observed in he daa. Turning o financial variables, he model maches well he volailiy of inerbank ineres raes, bu he prediced persisence are oo low and he correlaion wih GDP are negaive which is a odds wih daa. In erms of variance decomposiion, he model is mainly driven by produciviy shocks and he laer induce a negaive correlaion beween ineres raes and GDP, while sandard RBC models predic a posiive one. In he model, he collaeral consrain applied o enrepreneurs disconnecs he dynamics of capial accumulaion from is marginal produciviy, and ies he laer o he quaniy of loans. Afer a posiive produciviy shock, oupu rises, as well as deposis, so he liquidiy in inerbank markes increases as well, allowing saving banks o offer lower deposi raes. This increase in inerbank liquidiy lowers he marginal producion cos of loans, and hen he lending rae, which raises demand for loans, and hus he capial sock. This mechanism also explains why he model produces a posiive correlaion beween he loans (or deposis) o GDP raio and he inerbank ineres rae. Loans o GDP and deposis o GDP raios are slighly more volaile han oupu bu no as much as in he daa; he correlaion wih GDP is srong and negaive while weak and mixed in he daa. The negaive correlaion of ineres raes wih GDP is mainly responsible for his counerfacual cyclical behavior. Finally, momens relaed o public finance are correcly mached. The volailiies of sovereign raes and sovereign spreads are close o daa, alhough slighly more volaile 23

25 especially for sovereign spreads. 9 Volailiy of deb o GDP raio is smaller han in daa bu he model produces a more volaile raio for he Periphery, which is in line wih he daa. In erms of he correlaion wih GDP, sovereign raes and GDP are negaively correlaed in he model, which is a odds wih daa. Sovereign spreads are srongly and negaively correlaed wih GDP while his correlaion is weaker in he daa. The correlaion beween sovereign deb and GDP is negaive as in he daa. Finally, he correlaion beween loans o GDP and inerbank ineres rae is posiive, corresponding o wha we observed in he daa. Oher correlaions, especially he correlaion beween sovereign raes and deb o GDP raio (or beween sovereign raes and public spending) could arguably be beer mached. Overall, however, he model does a saisfacory job in maching so many key business cycle facs on real, financial and fiscal ime series. We consider i as reliable enough o perform addiional simulaions o quanify he effecs of he Grea recession and unconvenional moneary policies on key aggregaes and welfare. 5.2 The Grea Recession and Cenral Bank Inervenions We sar our analysis wih he benchmark scenario were a large recession is simulaed feeding he model wih negaive TFP shocks. Alhough i is clear ha he grea recession was no caused by negaive TFP shocks, he laer induce changes in macroeconomic aggregaes ha mach paricularly well he observed paerns. In addiion, according o Meza and Quinin (2007), TFP falls remarkably during financial crises, while changes in capial sock and labor hoarding are only secondary roles. We sar our simulaion from he second quarer in Shocks are adjused o 9 In he model, long erm raes are compued as he discouned sum of shor raes wih a discoun facor of 0.85 o mach he mauriy of sovereign raes from he daa (10 years or equivalenly 40 quarers). The sovereign spread is defined as he difference beween Periphery and Core long erm sovereign raes. The inerbank spread is defined as he difference beween he Core sovereign long erm rae and he long erm inerbank rae. 24

26 reproduce he percenage deviaions of aggregae oupu in he Euro Area saring in 2008Q2. The model is solved using a Newon-ype, and he adjusmen of key variables is depiced in Figure 1. Figure 1: Benchmark Simulaion. Negaive TFP shocks wihou Cenral Bank Inervenion. % dev. from SS GDP % ps, dev. from SS Sovereign Spread: 100*(RP RC) % dev. from SS dev. from SS, % Loan o enrepreneurs Deb o annual GDP raio % levels Periphery Leverage raios Sovereign risk: 100 * (p p) Core In Figure 1, aggregae oupu falls by around 4.5% below is 2008 level, which is exacly wha is observed in he daa. The fall in GDP raises mechanically deb-o-gdp raios above heir seady-sae levels by more han 4pp in he Periphery and 3pp in he Core. The auomaic componen of public spending aimed a sabilizing GDP furher feeds he rise in deb o GDP raios. As a consequence defaul risk rises in boh counries, bu more markedly for he Periphery, explaining he rise in sovereign spreads. We hen consider hree possible inervenions from he Cenral Bank: 25

27 1. Quaniaive Moneary Easing. According o our definiion, quaniaive moneary easing is an opion of he Cenral Bank o provide liquidiy o banks wih difficulies o borrow from he inerbank marke. The Cenral Bank ries o release he inerbank ensions by injecing cash direcly o hose who are shor of liquidiy. Normally, cenral banks use his insrumen o deermine he overnigh ineres rae. In realiy, banks can use hese cash eiher o replenish heir ier 1 capial, or o provide loans. Considering boh possibiliies would complicae our analysis. Therefore, we assume ha banks are forced by he conrac o make loans. In oher words, cenral bank injec money o banks and le hem lend o enrepreneurs. 2. Qualiaive Moneary Easing. When banks face he deerioraion of loan qualiy, he Cenral Bank can help hem improve heir balance shee srengh by allowing hese banks o swap a fracion of risky loans for governmen bonds. In his way, banks balance shees are improved. This policy is quie differen because he ransmission mechanism does no go hrough loans direcly bu hrough bonds markes. However his policy will also affec loans hrough a variey of channels. Firs, qualiaive moneary easing will release he ensions on sovereign markes, lowering he reurn on bank capial and herefore he marginal producion cos of loans. Second, because he loan producion funcion has a Leonief echnology, producing loans requires a good capializaion of bank and good condiions on he inerbank marke. As a consequence, an inervenion of he very same size could in principle have similar effecs on GDP and oher key macroeconomic variables. 3. Qualiaive Moneary Easing wih he Exisence of a Safe Haven. As a final possibiliy, we consider an inervenion of he Cenral Bank by which banks are offered he possibiliy o change he composiion of heir porfolio in favor of safe asses, i.e. bonds from he Core governmen. Indeed, when sovereign defaul risk in counries from he Periphery soars, invesors end o choose bonds issued in he Core 26

28 counries as a safe haven. Since he fall of 2012, he ECB has conduced ourigh open marke operaions, i.e. unlimied sovereign bond purchases in secondary sovereign bond markes. In Sepember 2012 he ECB announced he echnical feaures i had decided upon for such operaions, named Ourigh Moneary Transacions (OMT). This operaion allowed banks o replace heir risky Periphery bonds by Core bonds. In our model, his scenario is modeled wih a emporary shock on δ B,P. Figure 2 and 3 repor he marginal effecs of he hree poenial moneary policies on boh counries. Figure 2: Periphery Counry: Marginal Effec of Eurozone wide 10pp GDP Quaniaive Easing, Qualiaive Easing, and Qualiaive Easing wih Safe Haven % dev. from SS GDP % ps, dev. from SS Sovereign Spread: 100*(RP RC) % dev. from SS dev. from SS, % Loan o enrepreneurs Deb o annual GDP raio levels % Leverage raios Sovereign risk: 100 * (p p) Quaniaive Qualiaive SH A quaniaive moneary easing amouning o 10% of Eurozone GDP yields a 0.5 percenage poins gain in Periphery and Core oupu afer 5 periods. Loans rise abou

29 pp above heir level wihou inervenion boh in he Periphery and he Core. Leverage raios rise as well bu moderaely. The impac on deb-o-gdp raio is also remarkable, as he laer falls by 1.8 pp in he Periphery and by 1.3 pp afer 5 periods in he Core. As a resul, sovereign defaul risk is relieved, more imporanly for he Periphery han for he Core: he probabiliy of defaul is cu by 0.05 pp in he Periphery while only by 0.01 pp in he Core. The marginal effecs of a quaniaive moneary easing are also quie persisen over ime, even when he size of inervenion is massively reduced. Indeed, wih a 0.95 persisence, he size of shock is only = afer 25 periods while he marginal effec on oupu remains above half of is iniial rise. Figure 3: Core Counry: Marginal Effec of Eurozone wide 10pp GDP Quaniaive Easing, Qualiaive Easing, and Qualiaive Easing wih Safe Haven % dev. from SS % dev. from SS dev. from SS, % GDP Loan o enrepreneurs Deb o annual GDP raio % ps, dev. from SS levels % Sovereign Spread: 100*(RP RC) Leverage raios Sovereign risk: 100 * (p p) Quaniaive Qualiaive SH 0 The effecs of a qualiaive moneary easing are very similar o hose of a quaniaive easing excep for he effec on leverage raio. The former falls persisenly under is seady- 28

30 sae level while i rises under a quaniaive moneary easing. This is clearly no a surprise as he iniial goal of he qualiaive easing is o help banks mainain he qualiy of heir capial, while quaniaive easing provides hem wih required liquidiy. Neverheless, since liquidiy and capial are boh imporan in he producion of loans, is marginal effecs on loans are posiive as well. From a quaniaive perspecive, in comparison o he quaniaive easing, he resuling increase in loans is boh less imporan and less persisen (0.3 pp in he Periphery agains 0.6 pp afer 20 periods). As a resul, he effec of qualiaive easing on capial sock and hus GDP is less imporan. On sovereign markes however, qualiaive easing does a beer job han quaniaive easing in limiing he increase in deb-o-gdp raios, reducing globally he risk of sovereign defaul and, o a lesser exen, he spread beween Periphery and Core sovereign deb. Transmission of he inervenion goes hrough a fall of sovereign ineres raes. As banks arbirae beween sovereign bonds and inerbank lending, inerbank ineres raes fall simulaneously wih governmen bond yields. Lending raes decline due o reduced cos on producing loans, which simulaes credi demand from he marke. Wih he exisence of a safe haven, he effecs of he inervenion are qualiaively idenical o he quaniaive moneary easing excep for he sovereign spread. Invesmen in he safe haven lowers Core governmen bond yield while raises he Peripheral ineres rae. As a resul, sovereign spread rises above is seady-sae level. Wih he presence of a safe haven, unconvenional policies implemened by he Cenral Bank end o be less efficien in reducing Periphery counry s sovereign risk. 5.3 Welfare Analysis From he experimens above we compue he welfare losses from he Grea Recession in comparison o a siuaion where he economy would have remained in he seady-sae, and he welfare gains from he hree unconvenional moneary policies. In each counry, 29

31 we compue he welfare gains/losses for households, bankers and enrepreneurs. The compuaion is made eiher using 30 quarers afer he beginning of he recession (for shor erm analysis), or 200 quarers afer he recession (for long erm analysis). Table 3 repors he resuls of he hree policies, for each ype of agen in boh regions of he moneary union. Table 3: Welfare gains, in percenage of seady-sae consumpion. Negaive signs indicae welfare losses. Shor run (30 quarers) Core Periphery H B E Av. H B E Av. Grea Recession Quaniaive Easing Qualiaive Easing QE wih Safe Haven Long run (200 quarers) Core Periphery H B E Av. H B E Av. Grea Recession Quaniaive Easing Qualiaive Easing QE wih Safe Haven Noes: H denoes households, B bankers and E enrepreneurs. Av. is he weighed average welfare gain/loss using seadysae consumpions o compue weighs. In he shor run, Table 3 shows ha he recession generaes large welfare losses for households (beween 0.68% and 0.86%) and very large losses for enrepreneurs (beween 10% and 12%) while welfare gains for bankers. However, given he small imporance of bankers consumpions in aggregae consumpion (only 3% of oal consumpion), he average welfare effec is around 3% of seady-sae consumpion. The welfare loss for enrepreneurs is larger in he Periphery bu he welfare loss for households is larger in he Core. The effecs of unconvenional moneary policies in he shor run are small and yield welfare gains for households in boh he Core and he Periphery. Quaniaive easing and QE wih safe haven produce imporan welfare gains for enrepreneurs in he Core (around 0.13%) bu welfare losses for bankers in boh counries. The effecs of QE wih safe haven 30

32 is very similar o a sandard quaniaive moneary easing, excep ha a he presence of safe haven, households and enrepreneurs gain more in he Core bu less in he Periphery. This is due o unbalanced invesmen in Core governmen bonds ha brings excess of welfare o he Core agens. The qualiaive moneary easing has small and mixed effecs on bankers, while brings large welfare losses o enrepreneurs in he Periphery counry (around 0.3%). The average effecs of unconvenional moneary policies is globally small (around 0.02% of seady-sae consumpion) and mosly negaive. Long run effecs are much smaller, as gaps from he seady-sae are progressively closed over ime. Qualiaively however, mos resuls applying o he shor run are preserved, excep ha quaniaive easing brings welfare losses o enrepreneurs in he Periphery, and ha qualiaive easing brings small welfare losses o households in he Periphery. In he long run, quaniaive easing and QE wih safe haven bring welfare gains o households, and welfare losses o bankers. Quaniaively however, he welfare effecs of unconvenional moneary policies in he long run remain quie small, close o negligible. 6 Conclusion Our resuls imply ha Cenral Bank s inervenion can be beneficial during a recession: boh quaniaive and qualiaive moneary easing help alleviae oupu decline, relieve financial ensions (including inerbank, credi marke, and sovereign ineres raes), and reduce sovereign defaul risk. Paricularly, quaniaive moneary easing is more efficien in simulaing oupu; and qualiaive moneary easing is a good choice o limi sovereign risk. The presence of a safe haven ends o parially neuralize he benefi of QE on Periphery s sovereign problem, due o he misleading belief in safe asses. Finally, alernaive poenial inervenions from he Cenral Bank can bring some welfare gains for households in shor run wih poenial losses for enrepreneurs and/or bankers. The long run welfare effecs are close o negligible. 31

33 References Allen, Franklin, Elena Carlei, and Douglas Gale, Inerbank Marke Liquidiy and Cenral Bank Inervenion, Journal of Moneary Economics, 2009, 56 (5), Carnegie-Rocheser Conference Series on Public Policy: Disress in Credi Markes: Theory, Empirics, and Policy November 14-15, Arellano, Crisina, Defaul Risk and Income Flucuaions in Emerging Economies, American Economic Review, 2008, 98 (3), Bi, Huixin, Sovereign Defaul Risk Premia, Fiscal Limis, and Fiscal Policy, European Economic Review, 2012, 56 (3), Boissay, Frédéric, Fabrice Collard, and Frank Smes, Booms and Banking Crises, Corsei, Giancarlo, Keih Kueser, André Meier, and Gerno J. Mueller, Sovereign Risk and Belief-driven Flucuaions in he Euro Area, Journal of Moneary Economics, forhcoming. Devereux, Michael B. and James Yeman, Leverage Consrains and he Inernaional Transmission of Shocks, Journal of Money, Credi and Banking, 2010, 42 (S1), Dib, Ali, Banks, Credi Marke Fricions, and Business Cycles, Working Papers 10-24, Bank of Canada Eaon, Jonahan and Mark Gersoviz, Deb wih Poenial Repudiaion: Theoreical and Empirical Analysis, Review of Economic Sudies, 1981, 48 (2), Gerler, Mark and Nobuhiro Kiyoaki, Financial Inermediaion and Credi Policy in Business Cycle Analysis, in B. M. Friedman and M. Woodford, eds., Handbook of Moneary Economics, Rober W. Kolb Series in Finance: Elsevier, 2010, pp