MODELLING CREDIT CYCLES

Transcription

1 MODELLING CREDIT CYCLES 1 JEAN-CHARLES ROCHET (UNIVERSITY OF ZÜRICH AND TOULOUSE SCHOOL OF ECONOMICS) PREPARED FOR THE IGIER 20 TH ANNIVERSARY CONFERENCE, MILAN 8-9 JUNE 2011

2 IGIER and APPLIED THEORY 2 One major achievemen of IGIER over he las 20 years has been o produce imporan conribuions o Applied Theory in many domains of Economics : Fiscal policy Moneary policy Labor markes Poliical economy Marke microsrucure, To illusrae curren challenges in Applied Theory, I have chosen a opic closer o my domain of experise, namely applicaions of conrac heory o banking regulaion.

3 INTRODUCTION In he domain of banking regulaion, Economic Theory is currenly on demand by public auhoriies, a siuaion ha is raher unusual. 3 Following he subprime crisis, new forms of public inervenion are being considered, called macroprudenial regulaions. Regulaors urn owards academics o know wheher here is a sound heoreical foundaion for such new forms of bank regulaions.

4 INTRODUCTION (2) More precisely, regulaors claim ha banks lend oo much during booms and oo lile during recessions. 4 They envisage new regulaory ools aimed a dampening hese credi cycles : e.g., counercyclical capial requiremens for banks. My focus oday: wha Economic Theory ells us abou credi cycles and possible jusificaions for public inervenion.

5 PLAN OF THE PRESENTATION I will analyze hree heoreical mechanisms ha could generae credi flucuaions: 1. Collaeral consrains 2. Credi reversals 3. Pecuniary exernaliies 4. Wrap-up and policy implicaions 5. Conclusion 5

6 1. Collaeral consrains Kiyoaki- Moore (1997) show how small, emporary produciviy shocks can generae large, persisen flucuaions in oupu and asse prices. 6 Main mechanism: dual role of durable asses (land, capial)= producion facor +collaeral for loans. When borrowers are credi consrained, a negaive shock can force hem o sell asses, provoking a deflaionary spiral.

7 1. Collaeral consrains (2) Basic model: no uncerainy. 2 goods: land (fixed oal endowmen 1), price. frui (perishable) price 1. y = ' 2 secors: farmers ak, gaherers y = G(1 k. ) Farmers wan o leverage bu canno pledge heir fuure income. Borrowing limi = discouned resale value of heir land holdings. Their budge consrain is: q k ak q k 1+ r 7 ak ( q q q = = ) k r farmer s income borrowing limi usage cos of land

8 1. Collaeral consrains (3) A equilibrium, usage cos of land equals is marginal produciviy in he gahering secor: 8 u q q 1 1+ r + = G'(1 k 1+ r ) Equilibrium dynamics of farmers land holdings: ak = k G'(1 k 1+ r 1 ) k u( k ) Unique seady sae defined by: ak* = k * u( k*)

9 1. Collaeral consrains (4) Suppose he economy has reached he seady sae k* and consider a single (unanicipaed) produciviy shock a a dae. This shock has an immediae impac on land price (a dae ) and hus on he borrowing capaciy of farmers 9 ( a + a + q * + q ) k * q * k* = u( k ) k Linearize around he seady sae k* and denoe by η he elasiciy of u : ( a and + q a k ) k* = u( k*)(1 + η) k a dae 1 = u( k*)(1 + η) k+ s for 1 + s s

10 1. Collaeral consrains (5) Thus he unanicipaed shock is persisen, and i is amplified by he change in asse prices. The mechanism is similar o he credi muliplier effec idenified by Bernanke and Gerler (1989). However: 10 The capial of banks does no play any role (here are no banks!) The resuls disappear if deb can be indexed (see laer) Finally, addiional feaures are needed o generae cycles.

11 2.Credi reversals 11 Myerson (2010) develops an alernaive framework, relaed o Suarez and Sussman (1997) and Masuyama(2004), where cycles appear naurally, due o credi reversals. Myerson s model (simplified): One good (grain), can be invesed or consumed. Farmers need o borrow from bankers, who mus be given he incenives o selec he farms ha have a high probabiliy α of success (moral hazard). Bankers live n=2 periods and sign conracs wih invesors, specifying he size of he bank and he paymens o he banker, as a funcion of oucomes. No discouning, universal risk neuraliy.

12 2. Credi reversals (2) 12 Uni yield of good farm (equilibrium ROA of each bank): r(i) wih probabiliy α (and zero oherwise) decreases wih he oal size I of he farming (and banking) secor. No aggregae risk. Opimal conrac for bankers born a dae : Banker is only paid a +2 if her wo successive invesmens have succeeded. Bank liquidaed a +1 if firs invesmen fails. Bank allowed o grow a +1 if firs invesmen succeeds.

13 2. Credi reversals (3) 13 Since he banker is only paid a he end, incenives can be mainained only if: 1 each successful bank is allowed o grow by a facor α each banker ha has succeeded wice receives a he end a bonus equal o B imes he (final) size of her bank. Ne expeced ROE of a bank creaed a dae : 2 r( I+ 1) α r( I ) + α [ α B ] Wih free enry and CRS a he individual level, his ROE mus be zero.

14 2. Credi reversals (4) The equilibrium condiion is, for all : 14 r ( 1 I ) + r ( I ) + = B I expresses ha oal reurn on invesmen (over he wo periods) mus be equal o he expeced bonus ha will be paid o he banker. This obviously generaes sable 2-cycles (unless he economy sars in he unique seady sae): r I ) B r( I ) = ( + 2 = + 1 r( I )

15 Source of credi reversals: 2. Credi reversals (5) Invesors sign 2 period conracs wih bankers. 15 Equilibrium condiion implies ha if hey ge a low reurn a dae, hey mus ge a high reurn a dae +1 (and vice versa). Bu hese credi reversals disappear if bankers have posiive endowmens (capial) ω.

16 When banks have capial becomes: k ω 2. Credi reversals (6) αk 16, equilibrium condiion where is he size of banks newly creaed a dae. Two cycles disappear! ω [ B r( I ) r( I + 1)] = ω = α k + [ B ri ( + ) ri ( + )] I = + 2 = I k+ 1 k (seady sae)

17 3. Pecuniary exernaliies 17 Gersbach and Roche (2011): model wih fully anicipaed (and insurable) aggregae shocks where banks indeed lend oo much during booms and oo lile during recessions. The compeiive equilibrium is (consrained) inefficien because banks do no inernalize he impac of heir invesmen decisions on asse prices, hus generaing a pecuniary exernaliy. Efficiency can be resored if banks are subjec o a conra-cyclical lending limi.

18 3. Pecuniary exernaliies (2) 18 The model: One facor (capial) in fixed oal amoun 1, one consumpion good (numéraire), 3 daes, 2 secors: Secor B: firms mus be moniored by banks, who may also shirk (moral hazard). Reurn on asses = z R ~ z= aggregae risk (H or L) R ~ =idiosyncraic risk (success or failure). Toal asses of he banking secor = K. Secor F: firms ha can direcly access financial markes. Aggregaeoupu G(1-K).

19 3. Pecuniary exernaliies (3) 19 Timing: A =0, invesors sign conracs wih bankers A =1, macro shock z observed, k(z) invesed by each bank. A =2 oupu is shared beween invesors and bankers. Raes of reurn: Invesors are risk neural and can finance he banks and/or he F-firms: same expeced reurn E[{ k( z) ω} q( z)] = E[ k( z){ zr B}] q(z) = price of capial in sae z; B =bonus paid o he banker (per uni of size). (1)

20 3. Pecuniary exernaliies (4) Opimal conrac for financing he banks maximizes bankers surplus E[k(z)]B under consrain (1). 20 E[{ k( z) ω} q( z)] = E[ k( z){ zr B}] (1) Equilibrium price of capial in sae z saisfies q( z) = G'(1 K( z)) Aggregae credi K(z) obained by adding up individual financing consrains of banks E[{ K( z) W} q( z)] = E[ K( z){ zr B}] (2)

21 3. Pecuniary exernaliies (5) I is easy o see ha he compeiive allocaion maximizes social surplus under his consrain: 21 MaxE[ zrk( z) + G(1 K( z))] s.. E[{ K( z) W} q( z)] = E[ K( z){ zr B}] By conras, a social planner would recognize he impac on invesmen on asse prices and would maximize social surplus under a differen consrain: MaxE[ zrk( z) + G(1 K( z))] s.. E[{ K( z) W} G'(1 K( z))] = E[ K( z){ zr B}]

22 3.Pecuniary exernaliies (5) 22 If regulaion forces banks o lend less during booms, hey will lend more during recessions, increasing expeced oupu and social welfare. The compeiive equilibrium is no consrained efficien, because banks do no inernalize he impac of heir invesmen decisions on asse prices. This pecuniary exernaliy is similar o he noion of asse fire sales: if all disressed banks are forced o sell asses a he same ime, his will generae a deflaionary spiral. However he mechanism is symmeric: i also explains credi booms, wihou resoring o irraional exuberance.

23 4. Wrap-up and policy implicaions 23 Kiyoaki and Moore (1997): essenially a model of he credi muliplier, useful o explain he role of financial imperfecions in he amplificaion and persisence of real shocks, raher han credi cycles. Moreover, Krishnamurhy (2003) has shown ha if borrowers can insure hese shocks hrough coningen deb and financial derivaives, cycles disappear in he KM model. Thus he KM model applies more for small borrowers: do no have access o financial derivaives, canno pledge heir fuure income, borrowing capaciy is enirely deermined by fuure resale value of asses (see he empirical work of Monacelli (2006) on real esae prices and household borrowing capaciy).

24 4. Wrap up and policy implicaions (2) 24 As argued by Myerson (2011), borrowing capaciy of banks is (also) largely deermined by heir expeced fuure income. This feaure naurally generaes deerminisic credi cycles: equilibrium condiions imply negaive auocorrelaion of credi growh. However in he absence of real shocks, inroducing bank capial compleely eliminaes hese deerminisic cycles.

25 4. Wrap-up and policy implicaions (5) In Gersbach and Roche (2011) we inroduce real macro shocks in a banking model à la Holmsröm and Tirole (1997) 25 We find ha banks reac oo much o hese real shocks (excessive volailiy of credi growh and asse prices). In he absence of regulaion, banks amplify real flucuaions. So here are no deerminisic cycles like in KM or Myerson (2010), bu raher excessive reacions of bank lending o real shocks.

26 4.Wrap-up and Policy implicaions (5) A counercyclical capial requiremen is a useful regulaory ool, because i limis welfare decreasing pecuniary exernaliies. These exernaliies are also presen in he KM framework (Jeanne and Korinek, 2011): robus feaure of credi cycles models. 26

27 5 CONCLUSION Bernanke Gerler (1989) and Kiyoaki and Moore (1997) have had a major influence on he developmen of macro-models incorporaing financial imperfecions, in he form of collaeral consrains. These macro models are used by cenral banks for simulaing he impac of moneary policy decisions on credi and oupu. 27

28 5.CONCLUSION (2) 28 If new regulaory ools such as counercyclical capial requiremens are o be used, i is urgen o develop models allowing o simulae he impac of hese policy insrumens on credi and asse prices. In such models, he borrowing capaciy of banks should be deermined by he value of heir equiy (liabiliy) raher han by he value of heir collaeral (asse) as in KM. In any case, whaever he form of credi consrains, he presence of pecuniary exernaliies seems o be robus, jusifying some form of public inervenion.