Motivation. Financial crises occur periodically, Kindleberger (1993) Spirals and adverse feedback loops Spillovers

Transcription

1 Chicago, June 3 rd, 2010

2 Moivaion Financial crises occur periodically, Kindleberger (1993) Spirals and adverse feedback loops Spillovers Across financial insiuions To real economy Deflaionary pressure, Fisher (1933) Curren macro approach Many DSGE models use represenaive agens, ignore financing fricions and spillover effecs Models wih a financial secor (e.g. Bernanke-Gerler-Gilchris) log-linearize near seady sae, miss insabiliy below seady sae (due o non-linear dynamics) Moneary effecs are ofen due o price sickiness Price sabiliy vs. financial sabiliy analyzed in differen frameworks 2

3 Main messages Macro-framework wih financial secor a he cener Paper oday: Non-linear amplificaion effecs due o volailiy dynamics and precauionary moive Asse price correlaion in imes of crisis Spillover effecs Money paper: Endogenous role of money Ineracion beween ouside money and inside money Deflaionary spirals during financial crisis 3

4 Heerogeneous agens + some lieraure Producive BGG Kiyoaki-Moore He-Krishnamurhy Moll Less paien Less risk averse Garleanu-Pedersen More opimisic Geanakoplos Limied direc lending due o fricions Less producive More paien More risk averse More pessimisic 4

5 Model ouline Producive deb inside deb equiy inside deb equiy inside deb equiy deb equiy inside ouside Inermediary Monioring Diamond (1984) Holmsröm-Tirole (1997) deb shor-erm equiy inside ouside Less producive 5

6 Model ouline Producive deb inside deb equiy inside deb equiy inside deb equiy deb equiy inside ouside Inermediary Monioring Diamond (1984) Holmsröm-Tirole (1997) deb shor-erm equiy inside ouside Less producive Why shor-erm deb? Less info-sensiive Mauriy ra race Brunnermeier-Oehmke 6

7 Some Lieraure on amplificaion Bernanke-Gerler (1989) Overlapping generaions model, bu wih persisence Bad shocks erode ne worh of young enrepreneurs, who cu back on invesmens, leading o low produciviy and low ne worh of enrepreneurs in he nex period Kiyoaki-Moore (1997), BGG (1999) Infiniely-lived agens KM: Leverage bounded by margins-km; BGG: bankrupcy coss Sronger amplificaion effecs hrough prices (low ne worh reduces leveraged insiuions demand for asses, lowering prices and furher depressing ne worh) Brunnermeier-Pedersen (2009) Volailiy effec due o higher margins/haircus

8 Some Lieraure on amplificaion Bernanke-Gerler (1989) Overlapping generaions model, bu wih persisence Bad shocks erode ne worh of young enrepreneurs, who cu back on invesmens, leading o low produciviy and low ne worh of enrepreneurs in he nex period Kiyoaki-Moore (1997), BGG (1999) Infiniely-lived agens KM: Leverage bounded by margins-km; BGG: bankrupcy coss Sronger amplificaion effecs hrough prices (low ne worh reduces leveraged insiuions demand for asses, lowering prices and furher depressing ne worh) Brunnermeier-Pedersen (2009) Volailiy effec due o higher margins/haircus

9 Preview of amplificaion & exernaliies 1. Unsable dynamics away from seady sae due o (nonlinear) liquidiy spirals Fire sales Shock o Loss of ne worh Precauion + igher margins 2. Welfare: exernaliies wihin financial secor: When levering up, insiuions ignore ha heir fire-sales depress prices for ohers --- inefficien pecuniary exernaliy o real economy 3. Asse prices become more correlaed in crisis 3. Securiizaion can lead o excessive leverage volailiy price

10 Preview of he money paper As inermediaries ne worh declines Inermediaion + inside money shrinks Economic aciviy declines Value of ouside money rises - deflaion Inermediaries are doubly hi Asse side: asse values decrease Liabiliy side: real deb value increases Deflaionary spiral

11 Roadmap Moivaion and Preview Non-linear amplificaion volailiy dynamics + precauionary hoarding Money effec: deflaionary spiral Exernaliies Compeiive = social planners soluion in baseline model Wihin financial secor (Mod. 1: speculaive HH) Towards real economy (Mod. 2: labor secor) Asse pricing implicaion (Mod. 3: idio-shocks) Defaulable deb and securiizaion (Mod.4: idio-jumps)

12 Model deails Preferences Risk neural bu consumpion 0 for all agens Discoun rae: r for households, ρ r for expers Oupu y = a k (easily manipulaed) Capial dk = (Φ(i /k ) δ) k d + k dz =g cons-oupu Brownian macro shock (exogenous risk) Invesmen δ δ g Inernal: i posiive or negaive (parial reversibiliy= echnological liquidiy) Exernal: purchase or sell k a price p Endogenous price process for dp /p = μ p d + σ p dz 14

13 Fire-sale price w/o speculaion Less producive households face depreciaion of δ > δ and canno speculae (added laer) liquidaion value: p p p max i r a i* ( ( i*) ) :=g(p) 15

14 Capial srucures Producive k p deb inside deb equiy inside deb equiy inside deb equiy deb equiy inside ouside a E incenive for enrepreneur o exer effor Inermediary Monioring Diamond (1984) Holmsröm-Tirole (1997) deb shor-erm equiy inside a I of oal risk ouside incenive for inermediaries o monior (have o hold ouside equiy) Less producive 16

15 Microfoundaion of srucures Assumpion: value of asses p k i is conracable, k i no Agency problem of enrepreneur Can ake projecs w/npv<0, privae benefi b(m)<1 per $1 desroyed m is amoun of monioring by inermediary Incenive consrain: a E b(m), binds in equ. a E (m) Agency problem of inermediary Save monioring cos c(m) per $1 if shirking Incenive consrain: a I c(m) Solvency consrain: n 0 (implied by IC consrains) Assume c(m) + b(m) is a consan for all m enrepreneurs & inermediaries ne worh are subsiues Special case: if enrepreneurs ne worh =0, hen m s.. b(m)=0 17

16 Merging producive HH & Inermediaries Producive k p deb inside deb equiy inside deb equiy inside deb equiy deb equiy inside ouside a E Inermediary Monioring Diamond (1984) Holmsröm-Tirole (1997) deb shor-erm equiy inside a I of oal risk ouside Less producive a : a E + a I b(m) + c(m) merged expers 18

17 Merging producive HH & Inermediaries Producive k p financing inside financing equiy inside financing equiy inside financing equiy inside financing equiy 0 a E = 0 Inermediary deb shor-erm equiy inside a I =1 Less producive Producive enrepreneurs have no, a E = 0 Perfec monioring required, b(m)=0 Inermediary can issue ouside equiy, a I 19 = 1 (appropriae choice of b(m), c(m) )

18 Balance shee dynamics Producive Inermediary Less producive asses k p deb d dk /k =(Φ(i /k )-δ)d+dz dp /p = p d+ p dz equiy= neworh n a=1 20

19 Balance shee dynamics Producive Inermediary Less producive asses k p deb d dk /k =(Φ(i /k )-δ)d+dz dp /p = p d+ p dz equiy= neworh n a=1 Produc rule of Io s Lemma: d(x Y ) = dx Y + X dy + X Y d 21

20 Balance shee dynamics Producive Inermediary Less producive asses k p deb d dk /k =(Φ(i /k )-δ)d+dz dp /p = p d+ p dz equiy= neworh n d(k p ) = (Φ(i /k ) δ + p + p ) (k p )d + ( + p ) (k p )dz dd = (r d - a k + i ) d + dc dn = d(k p ) - dd = exogenous endogenous risk dn = rn d + ak d i d - k p [(Φ(i /k ) -δ + p + p ) d + ( + p ) dz ] dc 22

21 Equilibrium Aggregae variables Sae variable 1. Inernal invesmen Enrepreneur akes price p as given N, K = N /K max i p k (Φ(i /k ) δ) i FOC: p Φ(i /k ) 1 = 0 (Tobin s q) ι(p ) = i /k, rae of invesmen per uni of g(p ) := Φ(i /k ) δ = (opimized) growh rae of Noe : g(p ) = - for p < (a-i * )/(r-g): is sold o unproducive HH 2. Exernal invesmen k Given price process dp /p = p d + p dz Solvency consrain n 0 3. When o consume? dc dynamic opimizaion + marke clearing 4. Marke clearing: Toal demand = K 23

22 Inuiion main forces a work Invesmen: Scale up Scalable profiable invesmen opporuniy Higher leverage (borrow a r) Scale back Precauion: - don exploi full (GE) deb capaciy dry powder Ulimaely, say away from fire-sales a p Deb can be rolled over if d > k p (noe, price is depressed) Ways o scale back: Inernal disinvesmen, limied by Φ(.) Exernal disinvesmen, sale of asses (price impac f(ohers leverage)) Consumpion Consume early and borrow r < ρ Consume lae o overcome invesmen fricions

23 Exernal invesmen & consumpion Price p( ) Inermediary s value funcion f( )n linear in n dn = rn d + ak d-i d - k p [(Φ(i /k ) - δ - p + p ) d + ( + p ) dz ] dc solve for equilibrium p( ) and f( ) Bellman equaion =0 if f( )>1 f( )n = max k E[dc + d(f( )n )] = Opimal exernal invesmen/rading sraegy k (as a funcion of and n ) 26

24 Solving Bellman equaion: f( )n d = max k E[d(f( )n )] (when f()>1) E[d(f( )n )] = f n d + f( ) k p ( + p ) d + f( ) (r n + (a - ι(p )) k + k p (g(p ) - r + p + p )) FOC: (a-ι(p ))/p + g + p + p r = - f( )/f( ) (+ p ) expeced excess reurn on Using FOC, Bellman equaion simplifies o ( - r) f( ) = f Derive p, f,, p in erms of p, p, f, f o obain ODE for p() and f() risk premium from precauionary moive 27

25 Solving 1.. where 2.. from (-r) f() = f 4 boundary condiions: p(0) = p, p( * ) = 0, f( * ) = 1, f( * ) = 0 Solve for p(), p (), p (), f(), f (), f () 29 ) ''( ) ( ) ) ( ) )( ) ( )(( '( ) ( ) ( p f p p a p p g r f f r p p'( )[(r g(p ) + 2 )( p ) + a (p )]+ 1 2 ( ) 2 p''( ) p (1 p'( )) ) ( ) ( ) '( ) ( ) ( p p f f r p g p p a ) '( 1 ) ( )) '( (1 ) ( ) '( p p p p p p p

26 Equilibrium Boundary condiions: p(0) = p, p( * ) = 0, f( * ) = 1, f( * ) = 0 Bonuses paid ou seady sae 30

27 Equilibrium seady sae 31

28 Dynamics near and away from seady-sae Seady sae: expers unconsrained Bad shock leads o lower payou raher han lower demand p( * ) = 0, p ( * ) = 0 Below seady sae: expers consrained Negaive shock leads o lower demand p( * ) is high, srong amplificaion, p ( * ) is high bu when is close o 0, p p ( ), p() and p ( * ) is low Noe difference o BGG/KM Demand K Z -shock on k Loss of ne worh Precauion p p'( ) ( p ). 1 p'( ) amplificaion p p

29 Roadmap Moivaion Non-linear amplificaion volailiy dynamics + precauionary hoarding Money effec: deflaionary spiral Exernaliies Compeiive = social planners soluion in baseline model Wihin financial secor (Mod. 1: speculaive HH) Towards real economy (Mod. 2: labor secor) Asse pricing implicaion (Mod. 3: idio-shocks) Defaulable deb and securiizaion (Mod.4: idio-jumps)

30 Money random swiches More producive Less producive Limied direc lending due o fricions 34

31 Money random swiches More producive Less producive Limied direc lending due o fricions ouside money swich money for More is in producive hands Noice difference o Bewley economy Produciviy shocks vs. endowmen shocks 35 Capial is no dominaing money

32 Inermediaion + inside money Producive k p deb inside deb equiy inside deb equiy inside deb equiy deb equiy inside ouside a E incenive for enrepreneur o exer effor Inermediary Monioring Diamond (1984) Holmsröm-Tirole (1997) deb shor-erm = inside money equiy inside a I ouside incenive for inermediaries o monior (have o hold ouside equiy) Less producive i-money o-money i-money shares o-money i-money shares o-money shares 36

33 Price of Price of money Exra: Money model (wih wo ypes)

34 Roadmap Moivaion Non-linear amplificaion volailiy dynamics + precauionary hoarding Money effec: deflaionary spiral Exernaliies Compeiive = social planners soluion in baseline model Wihin financial secor (Mod. 1: speculaive HH) Towards real economy (Mod. 2: labor secor) Asse pricing implicaion (Mod. 3: idio-shocks) Defaulable deb and securiizaion (Mod.4: idio-jumps)

35 Exernaliies so far here are no exernaliies Proposiion. The compeiive equilibrium in his economy is equivalen o he opimal policy by a monopolis exper. Skech of proof. (1) Wrie Bellman equaion for monopolis. (2) Define price p = 1/ Φ(i /k ). (3) Show ha prices ec. are as in compeiive eq. Inuiion: In compeiive equilibrium expers do affec prices by heir choices (payou and invesmen), bu hey are isolaed from prices because hey don rade given equilibrium prices. 39

36 Modificaion 1: speculaive households So far fixed liquidaion value a p = a/(r + g) now households can sell back o expers a i* Break even for HH p r g( p) p p c-earnings depreciaion rae is δ> δ p p () qualiy when expers hold fracion ψ < 1 of asses gains/losses, E[d(k p )] In equilibrium households pick up asses when financial secor suffers losses, i.e. η becomes small Inroduce: Some households wih limied, s.. f>1 Fire sale exernaliies (wihin financial secor) when levering up, expers hur prices ha oher expers can sell o households in he even of a crisis 41

37 Speculaive vs. non-spec households a i=1, ρ=.06, r =.05, g =.04, δ=.05, σ=.1 η* = 42.6 vs p(η*) = 55.7 vs

38 p f leverage Comparaive Saic on (.025,.05,.1)

39 Modificaion 2: add labor secor Fixed labor supply L Producion Funcion: (a K γ ) k 1-γ l γ Inermediary i s payoff: (1 - γ) a L γ k a Workers wage w : γ a K L γ -1 Inermediaries choice of leverage deermines K Invesmen decisions (Bonus) payou policy Workers welfare (value funcion) depends on K 44

40 Exernaliies wih workers 45

41 Roadmap Moivaion Non-linear amplificaion volailiy dynamics + precauionary hoarding Money effec: deflaionary spiral Exernaliies Compeiive = social planners soluion in baseline model Wihin financial secor (Mod. 1: speculaive HH) Towards real economy (Mod. 2: labor secor) Asse pricing implicaion (Mod. 3: idio-shocks) Defaulable deb and securiizaion (Mod.4: idio-jumps)

42 Sochasic Discoun Facor Capial goods marke Inermediaries SDF: m 0, = e -ρ f(η )/f(η 0 ) Ouside equiy marke Households SDF: / m 0, HH = e -r Noe ha m 0, = m 0, HH, since δ > δ Derivaives marke Volailiy smirk of opions Index opions vs. sock opions ime preference agency consrain

43 Modificaion 3: asse pricing (cross secion) Correlaion increases wih σ p Exend model o many ypes j of dk j /k j = (Φ(i j /k j )-δ)d+dz aggregae shock + σ' dz j uncorrelaed shock Expers hold diversified porfolios Equilibrium looks as before, bu Volailiy of p k is σ + σ p + σ For uncorrelaed z j and z l correlaion (p j k j, p l k l ) is (σ + σ p )/(σ + σ p + σ ) which is increasing in σ p

44 Roadmap Moivaion Non-linear amplificaion volailiy dynamics + precauionary hoarding Money effec: deflaionary spiral Exernaliies Compeiive = social planners soluion in baseline model Wihin financial secor (Mod. 1: speculaive HH) Towards real economy (Mod. 2: labor secor) Asse pricing implicaion (Mod. 3: idio-shocks) Defaulable deb and securiizaion (Mod.4: idio-jumps)

45 Modificaion 4: Idiosyncraic losses dk i = g k i d + k i dz + k i dj i J i is an idiosyncraic compensaed Poisson loss process, recovery disribuion F and inensiy λ(σ p ) v = k p drops below d, cosly sae verificaion by deb

46 Review: cosly sae verificaion Developed by Townsend (1979), used in Diamond (1984), Bernanke-Gerler-Gilchris (1999) Time 0: principal provides funding I o agen Time 1: agen s profi y ~ F[0, y * ] is his privae informaion bu principal can verify y a cos Opimal conrac (wih deerminisic verificaion) is deb wih face value d: agen repors y ruhfully and pays d if y d, riggers defaul and pays y if y < d In our conex: inermediary can cause losses (reduce v for privae benefi); debholders verify if v falls below d

47 Modificaion 4: Idiosyncraic losses dk i = g k i d + k i dz + k i dj i J i is an idiosyncraic compensaed Poisson loss process, recovery disribuion F and inensiy λ(σ p ) v = k p drops below d, cosly sae verificaion by deb Debholders loss rae Verificaion cos rae ( ( ) v v Leverage bounded no only by precauionary moive, bu also by he cos of borrowing p d v p d v 0 ( d v ) v cxdf ( x) 0 C( d ) x) df( x) Asse v = k p Liabiliies d = k p n n

48 Equilibrium Expers borrow a rae larger han r Rae depends on leverage, price volailiy d = diffusion process (wihou jumps) because losses cancel ou in aggregae 54

49 Securiizaion Expers can conrac on shocks Z and J i direcly among each oher, conracing coss are zero In principle, good hing (avoid verificaion coss) Equilibrium expers fully hedge idiosyncraic risks expers hold heir share (do no hedge) aggregae risk Z, marke price of risk depends on f ( + p ) wih securiizaion, expers lever up more (as a funcion of ) and pay hemselves sooner financial sysem becomes less sable 55

50 Conclusion Incorporae financial secor in macromodel Higher growh Exhibis insabiliy similar o exising models (BGG, KM) around seady sae non-linear liquidiy spirals (away from seady sae) Inside money - inermediaries are hi on boh side of balance shee: Deflaion spiral Exernaliies when leverage/payous are chosen Wihin financial secor: possible fire sales compromise ohers balance shees Towards real economy (workers) Securiizaion helps share idiosyncraic risk, bu amplifies sysemic risk 56

51 Thank you!

52 Differences o Bernanke-Gerler-Gilchris BGG 1. small aggregae shocks, loglinearizaion around seady sae 2. Price dynamics driven by idiosyncraic shocks and defaul risk Higher sae verificaion coss when exper goes down 3. exper incenives o keep dry powder (liquidiy/precauionary) are negligible leverage is limied by increase in ineres rae spread reflecing expeced verificaion coss 4. Payou/consumpion policy is exogenous 5. Counercyclical leverage Expers ake on same posiion afer drop in ne worh Leverage increases afer drop in neworh 5. Deb vs. Equiy Brunnermeier-Sannikov 1. Focus on (large) aggregae shocks (idiosyncraic shocks no essenial), explore nonlineariies using Bellman equaion 2. Asse price drops also due o fire sales 3. Exper s ren depends on sae Incenive o keep dry powder (liquidiy) 4. Payou/consumpion endogenous (unconsrain a his poin) 5. Procyclical leverage: Expers reduce posiion afer drop in ne worh Liquidiy spirals 6. Securiizaion (deb, inside + ouside equiy) 7. Fire-sale exernaliy 59

53 Differences o Kiyoaki-Moore KM (Kiyoaki version) 1. Zero-prob. emporary shock Persisen (dynamic loss spiral) Amplified hrough collaeral value 2. Always a he consrain 3. Exogenous payou policy a deah 4. Non- vs. producive (leveraged) secor 5. Dual role of durable asse 1. Producion 2. Collaeral 6. Exogenous conrac One period conrac Deb is limied by collaeral value 7. Durable asse doesn depreciaes, fully BruSan 1. Permanen shocks Volailiy effecs hrough precauionary moive Loss spiral (level effec) 2. Precauionary cushion away from consrain size varies 3. Endogenous payou/consumpion 4. Invesmen hrough leveraged financial secor 5. Dual role of durable asse 1. Producion 2. Securiizaion 6. (Parially) opimal conrac Dynamic conrac Deb is limied due idiosyncraic risk and cosly sae verificaion 7. δ-depreciaion rae 60

54 Differences o He-Krishnamurhy He-Krishnamurhy 1. Endowmen economy GDP growh is exogenously fixed No physical invesmen 2. No direc invesmen in risky asse by households Limied paricipaion model 3. Conracing Only shor-run relaionship ( o +d) Fracion of reurn, fee Asse composiion (risky vs. risk-free) is no conracable Non-effor lowers reurn by xd x is exogenous,no linked o fundamenal Privae benefi from shirking No benchmarking 4. Pricing Implicaions When expers wealh declines, heir marke power increases, and so does heir fee Price impac depends on assumpion ha household have larger discoun rae han expers 5. Procyclical Leverage 6. In H-K calibraion paper 1. No fee, households are raioned in heir invesmen 2. As exper wealh approaches 0, ineres rae can go o 3. Heerogeneous labor income for newborns of ld 4. Non-log uiliy funcion BruSan 1. Producion economy GDP growh depends on ne-wealh Physical invesmen 2. Direc invesmens by all households 3. Conracing (Poenial) long-run relaionship Fracion of reurn, fee, size of asse pool Effor increases fundamenal growh o gd Moneary benefi from shirking No benchmarking 4. Pricing Implicaion Price drop wih sae variable 5. Counercyclcial Leverage Enrepreneur ake on same posiion afer drop in neworh Leverage increases afer drop in ne-worh 61