Macro-prudential policies in a DSGE model with nancial frictions

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1 Macro-prudenial policies in a DSGE model wih nancial fricions Paolo Gelain y Norges Bank (Cenral Bank of Norway) May 16, 211 Absrac We evaluae he meris of di eren macro-prudenial policies (ools and insrumens) in he conex of a fully- edge DSGE model incorporaing a disincive role for he banking secor, for he households secor, and heir inerlinkages. We focus on hree insrumens-policies: 1) he LTV raio, 2) he banks leverage raio, 3) a ax on he banks oal asses ransferred o he banks ne worh. Preliminary resuls show ha he LTV policy is very e ecive in reducing he variabiliy in he credi marke and in in aion. Moreover i miigaes subsinially he negaive impac on he real economy due o a shock in he housing marke. Keywords: Macro-prudenial policies, nancial fricions, DSGE Preliminary and incomplee. Commens very welcome. y Senior Economis - Norges Bank Moneary Policy - Bankplassen 2, 151 Oslo, Norway. E:mail: Paolo.Gelain@Norges-Bank.no 1

2 1 Exended Absrac The aim of he paper is o evaluae he advanages and disadvanages of di eren macro-prudenial policies boh in he case when moneary policy is aken as given by he regulaor and in he case when here is an ineracion beween he wo. In order o be able o o ha, he rs sep is o build a se up rich enough o explore a large number of policies. This is he reason why we exend a fairly sandard New Keynesian DSGE model o incorporae a nancial inermediary secor ha faces endogenous balance shee consrains along he lines of Gerler and Karadi (211). Wih he imporan di erence ha credi are given o households raher han enrepreneurs. The saring poin is he disincion beween wo ypes of households as in Iacoviello (25) The impaien households discoun he fuure more heavily han he paien households, and face a binding borrowing consrain in equilibrium. Unlike he original se up of Iacoviello (25), in which banks do no play a role and he credi marke works hrough he direc ineracion beween paien and impaien households, we will explicily model he nancial inermediaion secor beween he wo ypes of households. This exension o he Iacoviello (25) framework implies ha he assumpion of a single ineres rae, i.e. he risk-free ineres rae, will no longer hold. In order o assign a non-rivial role o banks ha ac as a nancial inermediary beween paien households - who receive a risk-free ineres rae on heir deposis - and he impaien households, he ineres rae charged o he laer households for heir borrowing should di er from he risk free ineres rae. This requires he assumpion of fricions in he nancial inermediaion process. Some recen papers ake his laer aspec ino accoun. In fac, Andrés and Arce (28) and Gerali e al. (21) assume monopolisic compeiion in he banking secor. In heir framework, paien households deposi savings in banks, receiving he risk free ineres rae as remuneraion, and banks provide loans o impaien households a a rae ha hey se o be higher han he one paid on deposis due o heir monopoly power. In he Gerler and Karadi (211) framework, he assumpion of riskless reurn from deposis is kep unchanged, bu a posiive di erence is assumed beween his risk free rae and he rae of reurn banks earn on heir asses. This posiive risk premium arises due o he presence of fricions in he inermediaion process and limis o he banks abiliy o obain funds from heir deposiors by assuming a moral hazard problem beween banks and heir deposiors. This agency problem leads o an endogenous balance shee (leverage) consrain limiing he abiliy of banks o acquire asses. Alhough fricions are inroduced beween banks and heir deposiors in he Gerler and Karadi (211) se-up, he inermediaion process beween banks and borrowing enrepreneurs is assumed o be fricionless. We herefore deviae from Gerler and Karadi (211) in wo main direcions. Firs, we assume (impaien) households obaining credi from he nancial inermediaries. Second, we subjec he inermediaion process beween impaien households and inermediaries o fricions, in order o model ineracions beween changes in households wealh and banks balance shees. 2

3 To summarize, we explicily model he ineracion beween he collaeralconsrained households and he leverage-consrained banking secor, herefore merging he Iacoviello (25) framework ino Gerler and Karadi (211). 1.1 Policy Applicaions The proposed framework is rsly used o compare di eren macro-prudenial policies. We focus on hree paricular policies. Along he line of he recen Basel III accords, we consider a policy looking a he banking secor. The general idea is o impose he bank a hreshold value for he capial o asses raio. In our se-up his is equivalen o impose an upper bound o he leverage raio. The second policy we consider is based on he assumpion he he poenial regulaor can se he loan-o-value raio. This is a policy which is adoped in some counries like Honk-Kong and Canada. Finally we analysis a policy based on he assumpion ha he regulaor is able o impose a ax on he asses of he bank and make a ransfer o he bank hemselves o inegrae heir ne worh. Our framework is also useful o analyze he following issues. We will use i o look ino he e ecs of sandard moneary policy (i.e. ineres rae policy) and unconvenional moneary policy (i.e. credi policy) a he zero lower bound. The aim is o quanify he welfare e ecs of credi policy when ineres rae policy becomes ine ecive a a binding zero lower bound consrain. Alhough unconvenional moneary policy may no receive a lo of suppor by criics, i migh be one of he few ools moneary policy can use in order o a ec he economy in he shor run. Therefore, sudying he e ec of unconvenional moneary policy becomes paricularly ineresing in he presence of zero lower bound. We will conras our resuls o hose provided in Gerler and Karadi (211), as he presence of a borrowing household secor will inroduce a disinc ransmission mechanism and hence can lead o oucomes no necessarily in line wih Gerler and Karadi (211). In a nex sep, we will analyze he e ecs of exernal capial requiremens, which allows for sudying he role of capial regulaory aspecs of macro prudenial policy. In paricular, we will examine he consequences of possible ineracions beween moneary and macro prudenial (capial requiremens) policy, wih or wihou he presence of a binding consrain on he zero lower bound. We will do his by compuing he cooperaive and non-cooperaive soluions and compare our ndings wih hose of Angelini e al. (211). Based on he resuls, we will be able o quanify he welfare coss and/or bene s of alernaive policy sraegies and cooperaion schemes under di eren scenarios (e.g. crisis vs. non-crisis scenarios). This will provide us wih a framework in which we will be able o make policy recommendaions under alernaive assumpions regarding he sae of he economy. 3

4 2 The Model 2.1 Households There are wo ypes of households. On he one hand here are paien households able o smooh heir consumpion ineremporally. They deposis heir savings ino he banking secor receiving he risk free ineres rae as a remuneraion. On he oher hand here are impaien households who need o borrow from he banking secor o be able o consume. The amoun hey can borrow is limied by he value of he collaeral hey use, namely heir house. Households share some common feaures. They boh ge uiliy from housing services, hence hey boh express a posiive demand for houses. Their consumpion is subjec o inernal habi formaion. They o er labuor in a compeiive labuor markes. The rs order condiions for he paien households are where % pa % pa W pa = (L pa ) ' (1) E pa pa ;+1 R +1 = 1 (2) Q h % pa = j H pa + pa Q h +1% pa +1 (3) is he marginal uiliy of consumpion and % pa = C pa h pa C pa 1 1 h pa pa E C pa +1 h pa C pa 1 pa ;+1 = %pa +1 % pa Equaion 1 is he condiion foe he supply of labour. Equaion 2 is he Euler equaion deermining he consumpion pah over ime. Equaion 3 is used o deermine he demand for houses. Impaien households are collaeral consrained and hey face he following exra consrain on he amoun hey can borrow B im = m Qh +1" h H im R h where m is he LTV raio. Impaien households pay R h on heir loans because he credi marke is no perfec due o he fac ha banks migh experience limis in heir abiliy o obain funds from he paien households and " h is a shock o he qualiy of houses. The f.o.c.s are he following % im W im = L im ' 4

5 wih 1 im R h im ;+1 R h = %im Q h j H im % im mq h +1 im % im +1Q h +1 (4) % im = C im h im C im 1 1 h im im E C+1 im h im C im 1 im ;+1 = %im +1 % im Equaion 4 express he condiion for he impaien households demand for houses and i is he resul of he combinaion wih expression for he lagrange muliplier of he borrowing consrain. 2.2 Bankers Bankers are modeled as in Gerler and Karadi (211). We assume ha hey provide loans o impaien households only, raher han o enrepreneurs as in he original se up. They funds asses using boh heir ne worh N and deposis colleced form he paien households D. The banker s balance shee is hen given by R h B im = N + D +1 (5) Given ha he banker pays he risk free ineres rae on deposis and receive on loans, he ne worh evolves as follows N +1 = R h +1B im R +1 D +1 and using equaion 5 we can re-wrie i as N +1 = R h +1 R +1 B im + R N Assuming ha he discoun facor of he banker beween and + i is pa;i pa ;+i he banker will operae in period i only if he following inequaliy will hold E pa;i pa ;+1+i R h +1+i R +1+i ; i If capial markes are perfec his equaion will always hold as an equaliy. Wih imperfec capial markes, however, he premium may be posiive due o limis on he inermediary s abiliy o obain funds. Hence, wih imperfec capial markes here is an incenive for bankers o expand heir asses inde niely by collecing more deposis from he paien households. In order o pu a limi on he expansion of he bankers asses, Gerler and Karadi (211) assume he exising of a moral hazard/cosly enforcemen problem beween bankers and heir deposiors. In he beginning of he period 5

6 he banker can choose o diver he fracion of available funds from he projec and insead ransfer hem back o he household. The cos o he banker is ha he deposiors can force he inermediary ino bankrupcy and recover he remaining fracion 1 of asses. However, i is oo cosly for he deposiors o recover he fracion of funds ha he banker divered. In his se up he following incenive consrain mus be sais ed V B im (6) where V is he banker s expeced erminal wealh. The lef side is wha he banker would lose by divering a fracion of asses. The righ side is he gain from doing so. I can be shown ha he banker s expeced erminal wealh can be wrien as wih V = l B im + N (7) l = E (1 ) pa pa ;+1 Rh +1 R +1 + pa pa ;+1 x ;+1l +1 = E (1 ) + pa pa ;+1 z ;+1 +1 where x ;+1 is he gross growh rae in asses beween and + 1, z ;+1 he gross growh rae of ne worh, and is he probabiliy for a banker o be banker also he nex period. Combining 6 wih 7 i is possible o derive he following equaion B im = l N = h N (8) where h is he raio of privaely inermediaed asses o equiy. Holding consan N, expanding B im raises he bankers incenive o diver funds. Equaion 8 limis he inermediaries leverage raio o he poin where he banker s incenive o chea is exacly balanced by he cos. In his respec he agency problem leads o an endogenous capial consrain on he inermediary s abiliy o acquire asses. 2.3 Inermediae goods producers Enrepreneurs are sandard. They produce wholesale goods according o he following producion funcion Y = A U " k K L 1 where U is he degree of capial uilizaion and " k is a shock o he qualiy of capial as in Gerler and Karadi (211). 6

7 The f.o.c.s for he demand for labuor and capial are pm Y U = bu " k K pm (1 ) Y L pa = W pa (1 ) pm (1 ) Y L im = W im The reurn on capial is deermined as follows h i pm +1 Y+1 R k " + (Q = k +1 K+1 +1 (U +1 )) 2.4 Capial producers Q " k +1 As in CEE capial producers face invesmen adjusmen coss. Hence he evoluion of invesmens is given by he following equaion Q = 1 + f (:) + I + I I 1 + I f (:) E pa ;+1 2 I+1 + I f (:) I + I where f (1) = f (1) = and f (1) >. Capial sock evolve as follows K +1 = (1 (U )) K + I 2.5 Final goods producers They produce nal goods and hey provide he demand for he inermediae goods. They are subjec o price rigidiies and hence hey deermine he evoluion of in aion over ime which is described by he New Keynesian Phillips curve. 2.6 Housing producion As for insvesmens in capial goods, he residenial invesmens are subjec o adjusmens coss. Hence he price of houses is deermined by he following equaion Q h = 1 + f (:) + Ih + I h I h 1 + Ih f (:) E pa ;+1 Ne invesmens are given by I h +1 + I h I h + I h 2 f (:) and he house sock is I h n = I h h H 7

8 2.7 Policies H +1 = h H + I h n Given he richness of our model we can focus on di eren macro prudenial policies. Speci cally, hey will be inroduced in he model in he form of policy rules. We propose here a rule cenered on he banks leverage raio, a rule considering he LTV raio, and a rule seing a ax on he banks oal asses. According o he pas proposal of Basil II, bu also along he lines of he more recen Basel III Accord, a naural candidae for he regulaor o be chosen as an insrumen is he leverage raio. In fac, a minimum capial requiremen (relaive o he asses) for banks is seen as a soluion o safeguard deposiors and oher sakeholders from he endency of he banks o excessively increase heir leverage. The model needs o be modi ed appropriaely. In fac, seing a oor for he Ne worh o asses raio means puing a ceiling o he leverage raio (being he laer he inverse of he former). The leverage raion is already endogenously deermined in our model, bu if he regulaor ses i he banks should simply adjus heir behaviour o he curren regulaion. In erms of equaions he leverage will be se according o he following rule h = h +! p p + u where h is he seady sae value of leverage, p is a macroeconomic variable which he regulaor looks a in order o decide how o se h, and! p is a parameer regulaing he inensiy of he regulaor inervenion. I can be eiher posiive or negaive on he basis of he necessiy for he regulaor o implemen a pro or couner cyclical policy. Once he regulaor se he leverage, bankers will ac on he only variable which hey really can decide on, namely he fracion of available funds ha hey can diver. As a consequence he value of ha parameer he be adjused o he leverage se by he regulaor on he basis of seady sae consideraions. More realisically, given ha h is ime varying, we can assume ha is also ime varying. As a consequence, i will be dynamically deermined by he following equaion = + h l h The second policy is based on he LTV raio. This is a policy ha is sraighforward o implemen in our se up. In fac, he only new assumpion we need for his policy is o make he LTV raio m ime varying. The second sep is o de ne a rule for ha variable m = m +! m p + u m 8

9 Following Chrisensen and Meh (211) we assume ha p is he log-deviaion of he amoun borrowed B im. Finally he ax policy. As in Gerler e al. (211) a ax on he banks oal asses is inroduced o nance a ransfer o he he same bank, which evenually has o be kep as a reserve. This policy has he advanage ha he ransfer increase he ne worh and hence reduce he leverage. I has he same spiri of a minimum capial requiremen policy. The balance shee of he bank (equaion 5) becomes (1 + ) B im = (1 + ) N + D +1 where is he ax rae. In equilibrium he ax is se o make he subsidy revenue neural, so ha he ne impac on bank revenues is zero. Hence he ne worh evolves as before N +1 = R h +1B im R +1 D +1 Subsiuing he balance shee and re-arranging we have N +1 = R h +1 (1 + ) R +1 B im As a consequence we can re-wrie l and as follows + (1 + ) R N l = E (1 ) pa pa ;+1 R h +1 (1 + ) R +1 + pa pa ;+1 x ;+1l +1 = E (1 ) + (1 + ) pa pa ;+1 z ;+1 +1 All he oher equaions remain unchanged. Moneary policy is described by he following Taylor rule R = R R 1 + (1 R ) R + + y log Y log Y po + " R 2.8 Aggregaion The aggregae resource consrain Y = C + I + I h + G Aggregae consumpion and houses are aggregaed as follows C = C pa + (1 ) C im H = " h H pa + (1 ) " h H im Labour is aggregaed as a Cobb-Douglas funcion L = (L pa ) L im 1 9

10 3 Analysis 3.1 The model dynamics In gure 1-4 we repor he model dynamics using he impulse response funcion. We sar wih he moneary policy shock. An increase in he ineres rae has he usual e ec of puing he economy ino a recession. Invesmens decrease rs, bringing down he demand of capial and is price. Oupu falls as a consequence. The demand for labour drops and households consume less. Also heir demand for housing service decrease, leading o a fall in he residenial invesmens and in he price of houses. Impaien households have less collaeral o o er and hey ask for less morgages. This has a direc impac on he bank balance shee. As he asses decrease banks experience a process of deleveraging. This explains he negaive response of leverage on impac. Neverheless, he fac ha banks o er less morgages has an e ecs on heir revenues. This is he reason why also heir ne worh drops, explaining also he change in he sign of he leverage afer some quarers. A negaive echnology shock is shown in gure 2. The causes of he recession are now coming from he supply side of he economy, bu he propagaion mechanism implies similar responses o he moneary policy shock. The recession explains he decrease in all he real variables and of he associaed prices. The banking secor sill experiences a conracion of he asses associaed o a deleveraging. The ne worh now increases subsanially on impac and for some quarers because he cenral bank cus he ineres rae o face he recession, allowing he bank o remunerae deposis much less, wih an increase in heir revenues. Finally he qualiy of houses shock in gure 4. The shock originaes in he housing secor wih a sudden drop in he value of houses. The abiliy of he impaien households o obain credi is drasically reduced. They need o reduce heir consumpion and heir houses demand. This has he e ec of creaing a recession for wo negaive e ecs of consumpion and residenial invesmens on oupu. In he banking secor banks su er a cu in he morgages and an even larger decrease in he ne worh. This explains he increase in he banks leverage. 3.2 The loan-o-value policy In his secion we describe he e ecs of inroducing a regulaion in he credi marke. The regulaor has he power o se he LTV raio. We have already anicipaed he funcional form of a he rule ha i uses o se is insrumen. Given ha is main aim should be o counerac he imbalances in he credi marke, as emerging from a large increase in he indebness of households, i make sense o consider a couner cyclical policy. In fac we calibrae he parameer regulaing he inensiy of he policy! m o 5. In his exercise he regulaor akes moneary policy as given. The e ecs of such a policy are repored in gures 5-7. Considering rs 1

11 he moneary policy shock we highligh ha he conercyclical LTV policy is very e ecive in limiing he drop in he morgage deb. This has he e ec of miigaing parially he e ecs of he recession, due o he fac ha he accessabiliy of households o credi is no reduced as much as i would be wihou he regulaion. Hence heir consumpion is less negaively a eced and heir demand for houses as well. This direcly re ecs on he response of oupu ha resuls less accenuaed. The same is rue for he echnology shock in gure 6. Bu wih he di erence ha he beer condiion in credi marke favoured by he LTV policy so no ransmi o he real and nominal economy. In fac basically all he oher variables seem una eced by he regulaion. Finally and no surprisingly, he regulaion has a big impac when a shock originaed in he housing secor his he economy ( gure 7). Oupu would have dropped 3 imes more wihou he regulaion, while consumpion abou wice more. I is worh sressing ha also ucuaions in in aion and house prices are smaller han oherwise. We can conclude ha regardless he shock considered, he LTV regulaion has always he meri of reducing he volailiy in he credi marke. The e ecs on he real economy are less homogenous. In general hey are no very accenuaed, excep in he case of he qualiy of houses shocks. In he laer case also he variabiliy of in aion and house price is subsanially reduced. 4 References Andrés, J., and Arce, O. (28). Banking Compeiion, Housing Prices and Macroeconomic Sabiliy. Bank of Spain Working Paper 83. Angelini, P., Neri, S., and Panea, F. (21). Moneary and Macroprudenial Policies. Banca d Ialia, mimeo Chrisensen, I., and Meh, C. (211). Counercyclical loan-o-value raios and moneary policy. Bank of Canada, mimeo. Chrisensen, I., Meh, C., and Moran, K. (21), Bank leverage regulaion and macroeconomic dynamics. Gerali, A., Neri, S., Sessa, L., and Signorei, M.F: (21). Credi and Banking in a DSGE Model of he Euro Area. Journal of Money, Credi and Banking, Supplemen o Vol. 42, No. 6. Gerler, M., and Karadi, P. (211). A Model of Unconvenional Moneary Policy. Journal of Moneary Economics, in press. Gerler, M., Kiyoaki, N, and Queralo, A. (211). Financial Crises, Bank Risk Exposure and Governmen Financial Policy Iacoviello, M. (25). House Prices, Borrowing Consrains, and Moneary Policy in he Business Cycle. American Economic Review, American Economic Associaion, vol. 95(3), pages , Rannenberg, A. (21). Asymmeric Informaion in Credi Markes and he Business Cycle. Naional Bank of Belgium, mimeo. 11

12 5 Figures.2 Oupu 1 x 1 3 Consumpion.5 Inflaion House price Houses Houses invesmens q Capial Invesmens Morgage deb Bank leverage Bank ne worh Figure 1: Moneary policy shock 12

13 Oupu Consumpion.2 Inflaion House price Houses Houses invesmens q Morgage deb 2 4 Capial Bank leverage Invesmens Bank ne worh Figure 2: Technology shock 13

14 Oupu Consumpion 2 Inflaion House price Houses Houses invesmens q Capial 2 4 Invesmens Morgage deb 2 4 Bank leverage Bank ne worh Figure 3: Qualiy of capial shock 14

15 5 x 1 3 Oupu 5 x 1 4 Consumpion 5 x 1 3 Inflaion x 1 3 House price 2 4 Houses 2 4 Houses invesmens x 1 3 q Capial x 1 3 Invesmens Morgage deb Bank leverage Bank ne worh Figure 4: Qualiy of houses shock 15

16 5 x 1 3 Oupu 2 x 1 4 Consumpion.1 Inflaion Morgage deb.1 House price.1 Huose sock No regulaion LTV regulaion Figure 5: Moneary policy shock 16

17 Oupu Consumpion.3 Inflaion Morgage deb.2 House price House sock No regulaion LTV regulaion Figure 6: Technology shock 17

18 1 x Oupu x Consumpion x Inflaion Morgage deb 1.5 x 1 3 House price.2 House sock No regulaion LTV regulaion Figure 7: Qualiy of houses shock 18