The Perils of Credit Booms

Transcription

1 The Perils of Credi Booms Feng Dong Jianjun Miao Pengfei Wang This Version: December 215 Firs Version: February 215 Absrac Credi booms ofen cause economic expansions. Bu some credi booms end in financial crises ye ohers do no. To find ou why, his paper presens a dynamic macroeconomic model wih adverse selecion in he financial marke. Enrepreneurs can ake on shor-erm collaeralized deb and rade long-erm asses o finance invesmen. Funding liquidiy can erode marke liquidiy. High funding liquidiy discourages firms from selling heir good long-erm asses since hese good asses have o subsidize lemons when here is informaion asymmery. This can cause a liquidiy dry-up in he marke for long-erm asses and even a marke breakdown, resuling in a financial crisis. Muliple equilibria can coexis. Credi booms combined wih changes in beliefs can cause equilibrium regime shifs, leading o an economic crisis or expansion. Keywords: Adverse Selecion, Liquidiy, Collaeral, Bubbles, Credi Boom, Financial Crises, Muliple Equilibria JEL codes: E2, E44, G1, G2 We have benefied from commens by Hengjie Ai, Wei Cui, Zhen Huo, Nicolas Jacque, Yang Jiao, Benjamin Moll, Nicola Pavoni, Vincenzo Quadrini, José-Vícor Ríos-Rull, Cheng Wang, Yi Wen, Jianhuan Xu, Tao Zha, Shenghao Zhu, Fabrizio Ziliboi, as well as paricipans a he Fourh HKUST Inernaional Workshop on Macroeconomics, he 215 AFR Summer Insiue of Economics and Finance a Zhejiang Universiy, he Sockman Conference a Universiy of Rocheser, Tsinghua Universiy, Shanghai Universiy of Finance and Economics, Singapore Managemen Universiy, Remin Universiy of China, and Peking Universiy. Anai College of Economics and Managemen, Shanghai Jiao Tong Universiy, Shanghai, China. Tel: fengdong@sju.edu.cn Deparmen of Economics, Boson Universiy, 27 Bay Sae Road, Boson, MA Tel.: miaoj@bu.edu. Homepage: hp://people.bu.edu/miaoj. Deparmen of Economics, Hong Kong Universiy of Science and Technology, Clear Waer Bay, Hong Kong. Tel: pfwang@us.hk 1

2 1 Inroducion Evidence shows ha credi booms are ofen accompanied by periods of economic expansion wih rising asse prices, invesmen, and oupu. Some credi booms end in financial crises, while ohers do no. The idea ha financial crises are due o credi booms gone wrong daes back o Minsky 1977 and Kindleberger 1978 and is suppored by some empirical sudies on emerging and advanced economies McKinnon and Pill 1997, Kaminsky and Reinhar 1999, Reinhar and Rogoff 29, Gourinchas and Obsfeld 212, and Schularick and Taylor 212. However, using a sample of 61 emerging and indusrial counries over he period, Mendoza and Terrones 212 find ha he odds are abou 1 o 4 ha once a counry eners a credi boom i will end in a currency or a banking crisis, and a lile less han 1 o 4 ha i will end in a sudden sop. Goron and Ordoñez 215 find ha here are 87 credi booms in heir sample of 34 counries over , of which 33 ended in financial crises. How can a credi boom end in a crisis? Why do some credi booms end in crises, while ohers do no? The goal of his paper is o provide a heoreical model o address hese quesions by incorporaing informaion asymmery in he financial markes Akerlof 197. Our key idea is ha funding liquidiy can erode marke liquidiy. Allowing for more shorerm borrowing backed by collaeralized real asses raises funding liquidiy, which alleviaes resource misallocaion by providing more efficien firms wih more liquidiy for invesmen and producion. High funding liquidiy, however, reduces he need for liquidiy from long-erm asses and is cosly when adverse selecion exiss in he marke for long-erm asses. High funding liquidiy discourages firms from selling heir good long-erm asses since good asses have o subsidize lemons. This can cause a liquidiy dry-up in he marke for long-erm asses and even a marke breakdown, resuling in a financial crisis. To formalize our idea, we build an infinie-horizon model of producion economies in which here is a coninuum of enrepreneurs subjec o idiosyncraic invesmen efficiency shocks. Enrepreneurs are borrowing consrained and can use heir physical capial as collaeral o borrow Kiyoaki and Moore They can also rade wo ypes of long-erm asses o finance real invesmen. One ype is a lemon, which is inrinsically useless and does no deliver any payoffs. The oher is a good asse and can deliver posiive payoffs. Sellers know he qualiy of he asses bu buyers do no. In he benchmark model under symmeric informaion, equilibrium is unique and lemons are no raded. Alhough funding liquidiy compees away some marke liquidiy, he oal 2

3 liquidiy sill rises so ha a credi boom always leads o an economic expansion. By conras, when here is asymmeric informaion abou asse qualiy, hree ypes of equilibrium can arise. In a pooling equilibrium, boh good asses and lemons are raded a a posiive pooling price. In a bubbly-lemon equilibrium, lemons are raded a a posiive price and drive he good asses ou of he marke. In a frozen equilibrium, he marke for long-erm asses breaks down. These equilibria can be ranked in a decreasing order of seady-sae capial sock. We show ha in some region of he parameer space all hree ypes of equilibrium can coexis depending on people s self-fulfilling beliefs. In his region neiher he payoff fundamenals of he good asses nor he proporion of lemons can be oo high or oo low. If he fundamenals of he good asses are oo weak, holders of he good asses will prefer o sell hem o finance real invesmen when a sufficienly high invesmen efficiency shock arrives, insead of holding hem o obain low payoffs. Thus a bubbly lemon equilibrium canno exis. Bu if he fundamenals of he good asses are oo srong, holders of hese asses will prefer o hold on o hem, and hese asses will never ge raded. Thus a pooling equilibrium canno exis. On he oher hand, if he proporion of lemons is oo low, hen he pooling price of he good asses will be high enough for enrepreneurs wih high invesmen efficiency o sell hese asses o finance heir real invesmen. Thus a bubbly lemon equilibrium canno exis. By conras, if he proporion of lemons is oo high, hen he adverse selecion problem will be so severe ha sellers are unwilling o sell heir good asses a a low pooling price. Thus a pooling equilibrium canno exis. In his case inrinsically useless lemons drive he good asses ou of he marke. The mechanism for he coexisence of he hree ypes of equilibrium is as follows. When all agens opimisically believe ha he asse price is high, enrepreneurs wih sufficienly high invesmen efficiency shocks will wan o sell heir good asses o finance invesmen. This raises he proporion of good asses in he marke and hence raises he asse price, supporing he iniial opimisic belief abou he asse price. A pooling equilibrium can arise. On he oher hand, when all agens pessimisically believe ha he asse price is sufficienly low, all enrepreneurs will no sell heir good asses, bu sell lemons only. In his case he marke will consis of lemons only. Enrepreneurs wih low invesmen efficiency shocks are willing o buy lemons a a low posiive price because hey expec o sell lemons a a high posiive price in he fuure o finance invesmen when hey are hi by a sufficienly high invesmen efficiency shock. Then a bubbly lemon equilibrium can arise. In he exreme case, when all agens believe ha he asses have no value, no asses will be raded and he financial marke will break down, leading o a frozen equilibrium. 3

4 A credi boom hrough increased collaeralized borrowing can cause a regime o shif from one ype of equilibrium o anoher. For example, when he economy is iniially a a pooling equilibrium, a sufficienly large permanen credi boom can cause a large compeing effec so ha no good asses will be raded due o adverse selecion. The economy will ener a bubbly lemon equilibrium in which he inrinsically useless lemon is raded as a bubble asse a a posiive price. Since marke liquidiy has dried up, a financial crisis will arise. Even a emporary credi boom can cause a regime shif hrough changes in confidence or beliefs. In sandard models wih a unique seady sae a emporary change in parameer values will cause he economy o reurn o he original seady sae evenually. By conras, given ha hree ypes of equilibrium can coexis in our model, a change in confidence or beliefs can cause he economy o swich from he original equilibrium o anoher ype of equilibrium as discussed previously. In a numerical example, we show ha when he economy is iniially a a good pooling seady sae and when agens pessimisically believe he economy will soon swich o he bubbly lemon equilibrium in response o a emporary credi boom, marke liquidiy will drop disconinuously and he economy will ener a recession evenually. No all credi booms end in a financial crisis. When here is no regime shif, a modes credi boom can boos oal liquidiy and cause an economic expansion. If here is a regime shif, he expansion can be large. For example, when he economy is iniially a a bubbly lemon equilibrium, a permanen modes credi boom can cause he economy o swich o a pooling equilibrium. The asse price and oupu will rise o permanenly higher levels evenually. Our paper is closely relaed o he one by Goron and Ordoñez 215 who also sudy he quesion of why some credi booms resul in financial crises while ohers do no. Unlike us, hey build an overlapping-generaions model wih adverse selecion in which borrowers and lenders have asymmeric informaion abou he collaeral qualiy. Firms finance invesmen opporuniies wih shor-erm collaeralized deb. If agens do no produce informaion abou he collaeral qualiy, a credi boom develops, accommodaing firms wih lower qualiy projecs and increasing he incenives of lenders o acquire informaion abou he collaeral, evenually riggering a crisis. When he average qualiy of invesmen opporuniies also grows, he credi boom may no end in a crisis because he gradual adopion of low qualiy projecs is no srong enough for lenders o acquire informaion abou he collaeral. Our idea ha marke liquidiy can erode funding liquidiy is relaed o Malherbe 214. He builds a hree-dae adverse selecion model of liquidiy in which cash holding by some agens imposes a negaive exernaliy on ohers because i reduces fuure marke liquidiy. The 4

5 inuiion for why holding cash worsens adverse selecion is bes undersood from a buyer s poin of view: he more cash a seller is expeced o have on hand, he less likely i is ha he is rading o raise cash, and he more likely i is ha he is rying o pass on a lemon. The impac of funding liquidiy in our paper is like ha of cash holding in his paper. Brunnermeier and Pederson 29 argue ha funding liquidiy and marke liquidiy are muually reinforcing in an endowmen economy when margin requiremens are endogenously deermined by he value-a-risk conrol. Unlike our paper, hey do no consider real invesmen and shor-erm deb backed by collaeralized real asses. As in heir paper, we show ha liquidiy can be fragile because marke liquidiy can drop disconinuously due o equilibrium regime shifs. More broadly, our paper is relaed o he recen lieraure ha uses adverse selecion models o explain financial crises and business cycles. Kurla 214 provides a dynamic model wih adverse selecion in which firms are allowed o accumulae capial only and canno rade oher ypes of asses. A fracion of capial can become useless lemons. Sellers know he qualiy of capial, bu buyers do no. In his model here can be only wo ypes of equilibrium: eiher capial is raded a a posiive price or here is no rade a all. One key difference beween Kurla 214 and our paper is ha he former shus down he channel of funding liquidiy and focuses on he effec of adverse selecion on marke liquidiy, while our paper incorporaes rades in shor-erm and long-erm asses and sudies he ineracion beween funding and marke liquidiy under informaion asymmery. Bigio 215 sudies an economy where asymmeric informaion abou he qualiy of capial endogenously deermines liquidiy. He presens a heory where liquidiy-driven recessions follow from surges in he dispersion of collaeral qualiy. 1 As inrinsically useless lemons can have a posiive price in our model, our paper is relaed o he lieraure on raional bubbles. Since he seminal sudy by Sanos and Woodford 1997, i has been widely believed ha i is hard o generae raional bubbles in models wih infiniely lived agens. Recenly, here has been a growing lieraure ha inroduces borrowing consrains o sudy bubbles in infinie horizon models wih producion see Miao 214 for a survey. This lieraure does no resolve he coexisence puzzle, i.e., why bubbles like fia money can coexis wih ineres-bearing asses. In our model he inrinsically useless lemons can coexis wih good asses wih posiive payoffs in a pooling equilibrium due o adverse selecion. 2 1 Oher relaed papers include Eisifeld 24, Tomura 212, Goron and Ordoñez 214, Benhabib, Dong and Wang 214, Li and Whied 214, and House and Masalioglu 215, among ohers. 2 In he lieraure of moneary heory, Lagos 213 provides a search model o explain he coexisence of fia 5

6 2 The Model Consider a discree-ime infinie-horizon model. The economy is populaed by a coninuum of idenical workers wih a uni measure and a coninuum of ex ane idenical enrepreneurs wih a uni measure. Each enrepreneur runs a firm ha is subjec o idiosyncraic shocks o is invesmen efficiency, so enrepreneurs are ex pos heerogeneous. There is no aggregae uncerainy abou fundamenals. Assume ha a law of large numbers holds so ha aggregae variables are deerminisic. 2.1 Seup Each worker supplies one uni of labor inelasically. For simpliciy, we assume ha workers have no access o financial markes, and hus hey simply consume heir wage income in each period. Enrepreneurs are risk neural and indexed by j [, 1]. Enrepreneur j derives uiliy from a consumpion sream {C j } according o β C j, C j, 1 = where β, 1 represens he common subjecive discoun facor. He owns a consan-reurnso-scale echnology o produce oupu according o y j = Ak α jn 1 α j, α, 1, 2 where A, k j, and n j represen produciviy, capial inpu, and labor inpu, respecively. Solving he saic labor choice problem R k k j max n j Akα jnj 1 α W n j gives labor demand and he capial reurn where W is he wage rae. [ ] 1 1 α A α n j = kj, 3 R k = αa 1 α W [ 1 α W ] 1 α α, 4 money and ineres-bearing asses. 6

7 Enrepreneur j can make invesmen i j o raise his capial sock so ha he law of moion for his capial is given by k j+1 = 1 δ k j + i j ε j, 5 where δ, 1 represens he depreciaion rae and ε j is a random variable ha is independen across firms and over ime. Le he cumulaive disribuion funcion of ε j be F on [ε min, ε max ] [,. Assume ha here is no insurance marke agains he idiosyncraic invesmen shock and his shock is unobservable by oher enrepreneurs. Assume ha invesmen is irreversible a he firm level so ha i j. Enrepreneurs can rade wo ypes of asses. Firs, hey can borrow or save by rading a one-period risk-free bond wih zero ne supply. Le R f denoe he marke ineres rae. Second, hey can rade long-erm asses, which can be of high or low qualiy. The high qualiy asse, called he good asse, delivers a posiive payoff c in every period. One may inerpre his asse as a console bond wih coupon paymen c or a sock wih dividend c. The low qualiy asse, called he lemon, does no deliver any payoff. The proporion of lemons in he economy is π. Assume ha sellers know he qualiy of heir own asses, bu buyers canno disinguish beween he lemons and he good asses. Due o his informaion asymmery, hese asses are sold a he same price P. Enrepreneur j s budge consrain is given by C j + i j + b j+1 R f = R k k j + P s g j + sl j x j + ch g j + b j, 6 where s g j, sl j, hg j, x j, and b j represen he sale of he good asse, he sale of he lemon, he holdings of he good asse, he oal purchase of he wo asses, and he bond holdings respecively. When b j <, i is inerpreed as borrowing saving. Assume ha enrepreneurs are borrowing consrained. borrowing consrains in he lieraure. We adop he following: There are many differen ways o inroduce b j+1 R f µ k j, 7 where µ [, 1]. The inerpreaion is ha enrepreneur j can use a fracion of his physical capial as collaeral o borrow from oher firms Kiyoaki and Moore We allow µ o be ime varying o capure he credi marke condiion. Because buyers do no observe he qualiy of he asses, heir purchased asses may conain boh lemons and good asses. Le Θ denoe he fracion of good asses in he marke. Then 7

8 he laws of moion for he holdings of he good asse and he lemon are given by h g j+1 = h g j sg j + Θ x j, 8 h l j+1 = h l j s l j + 1 Θ x j. 9 } Enrepreneur j s problem is o choose a nonnegaive sequence of {i j, s g j, sl j, x j, C j o maximize his uiliy in 1 subjec o 5, 6, 7, 8, 9 and he shor-sales consrains 2.2 Equilibrium Definiion s g j hg j, sl j h l j. 1 Le K = k j di, I = i j dj, C = C j dj, and Y = y j dj. A compeiive equilibrium under asymmeric informaion consiss of sequences of aggregae quaniies {C, K, I, Y }, } individual quaniies {C j, i j, s g j, sl j, x j, b j, j [, 1], prices {W, P, R k, R f }, and he marke proporion of good asses {Θ } such ha: } i The sequences {C j, i j, s g j, sl j, x j, b j solve each enrepreneur j s opimizaion problem aking {W, P, R k, R f } and {Θ } as given. ii The sequences {n j, R k } saisfy 3 and 22. iii All markes clear, x j dj = s g j + sl j dj, 11 h l jdj = π, h g j dj = 1 π, b j dj =, 12 n j dj = 1, W + C + I = Y + 1 π c. 13 iv The law of moion for aggregae capial saisfies K +1 = 1 δ K + ε j i j dj. 14 v The marke proporion of good asses is consisen wih individual enrepreneurs selling decisions, Θ = 3 Symmeric Informaion Benchmark s g j dj s l j dj + s g. 15 jdj Before deriving soluions o our model wih informaion asymmery, we firs consider a benchmark wih symmeric informaion. Suppose ha boh he buyers and sellers know he qualiy of 8

9 he long-erm asses so ha here are separae prices P g and P l associaed wih he good asse and he lemon respecively. Moreover, buyers can purchase he lemon or he good asse separaely. In his case enrepreneur j s decision problem is o choose C j, i j, s g j, sl j, xg j, xl j, b { } j o maximize 1 subjec o 5, 1, and C j + i j + b j+1 R f = R k k j + P g h g j+1 = h g j sg j + xg j, h l j+1 = h l j s l j + x l j, k j+1 = 1 δ k j + ε j i j, b j+1 R f µ k j, s g j xg j + P l s l j x l j + ch g j + b j, s g j hg j, sl j h l j, C j, k j, i j, where x g j and xl j represen he purchase of he good asse and he lemon asse respecively. A compeiive equilibrium under symmeric informaion consiss of sequences of aggregae { } quaniies {C, K, I, Y }, individual quaniies C j, i j, s g j, sl j, xg j, xl j, b j, j [, 1], and prices { W, R k, R f, P g, P l } such ha: { } i The sequences C j, i j, s g j, sl j, xg j, xl j, b j solve each enrepreneur j s opimizaion problem aking { W, R k, P g, P l } as given. ii The sequences {n j, R k } saisfy 3 and 22. iii All markes clear so ha equaions x g j dj = s g j dj, 12, and 13 hold. The following proposiion characerizes he equilibrium sysem under symmeric informaion. x l jdj = iv The law of moion for aggregae capial saisfies 14. s l jdj, Proposiion 1 In a compeiive equilibrium wih symmeric informaion, le Then: ε = 1 Q ε min, ε max. 1. Firms wih ε j ε make real invesmen, sell all of heir good asses and lemons, and exhaus heir borrowing limi. 9

10 2. Firms wih ε j < ε do no inves. They are willing o buy any amoun of good asses and lemons and are indifferen beween borrowing and saving. 3. Q, P g, P l, R k, R f, K, I saisfy Q = β { 1 δ Q +1 + R k+1 + R k+1 + µ +1 εmax ε +1 ε ε +1 } 1 df ε,16 P g = P g +1 + c R f, 17 P l = P +1 l, 18 R f ] K +1 = 1 δ K + [R k K + πp l + 1 π P g ε max + c + µ K εdf ε, 19 I = [ 1 εmax ] ε = β 1 + R f ε ε 1 df ε, ] [R k K + 1 π P g + c + πp l + µ K [1 F ε ], 21 and he usual ransversaliy condiions. R k = αak α 1, 22 ε Here Q represens Tobin s marginal Q or he shadow price of capial. Equaion 16 is is asse pricing equaion for capial. Each firm j makes real invesmen if and only if is invesmen efficiency shock ε j exceeds an invesmen hreshold ε = 1/Q. Tha is, he firm s marginal Q exceeds he invesmen cos 1/ε j in erms of consumpion unis. Equaions 17 and 18 are he asse pricing equaions for he good asse and he lemon respecively. The lemon represens a pure bubble asse because i does no deliver any fundamenal payoffs. If agens believe i will no have value in he fuure, P+1 l =, hen i has no value oday P l =. Equaion 2 is he asse pricing equaion for he bond. In he deerminisic model he discoun raes for he good asse and he lemon are he same and equal o he ineres rae R f. The inegral erm in 16 and 2 represens he liquidiy premium because capial and bonds can help he firm relax is borrowing consrains by raising is ne worh. We focus on he inerpreaion of 2. Purchasing a uni of bonds coss 1/R f a ime. A ime +1, when he invesmen efficiency shock ε j+1 ε +1 = 1/Q +1, firm j receives one uni of he payoff from he bond and hen uses his payoff o finance real invesmen, which generaes profis ε j+1 Q The average profis are given by he inegral erm. Equaion 2 shows ha in 1

11 equilibrium he marginal cos mus be equal o he marginal benefi. Equaions 19 and 21 give he law of moion for capial and aggregae invesmen. They reflec he fac ha firms can use inernal funds, shor-erm deb, and long-erm asses o finance real invesmen. If here were no good asse in he model, hen a lemon bubble could emerge and he bubble and bonds could coexis Miao, Wang, and Zhou 214. In his case he lemon and he bond are perfec subsiues and he ne ineres rae on bonds mus be zero R f = 1 in he seady sae. However, in he presence of an asse wih posiive payoffs, a lemon bubble canno exis. To see his we sudy he seady sae and use a variable wihou a subscrip o denoe is seady sae value. We mainain he following assumpion hroughou he paper. Assumpion 1 Le [ εmax ] ε β df ε > ε min ε min This assumpion is equivalen o βe ε > ε min, which is a weak resricion. In paricular, i is saisfied when β is sufficienly close o 1. The following lemma will be repeaedly used. Lemma 1 Under Assumpion 1, here exiss a unique soluion, denoed by ε b, o ε ε min, ε max in he equaion εmax ε β 1 + ε ε 1 df ε = The following proposiion characerizes he seady sae equilibrium of he economy under symmeric informaion. Proposiion 2 Le assumpion 1 hold. seady sae equilibrium in which P l =, When µ is sufficienly small, here exiss a unique R f = R f ε 1 β [ 1 + ε max ε ε ε 1 ], df ε 25 P g c = R f ε 1, 26 1 K = K ε β 1 + δ 1 ε [ ε max ε ε ε 1 df ε ] 1 α 1 µ αa [ 1 + ε max ε ε ε 1 df ε ], 27 where ε ε b, ε max is he unique soluion o he equaion Moreover, ε µ D ε >, K µ δk ε εmax ε εdf ε αak ε α µk ε 1 π c = Y >, µ >, R f µ >, and P g µ < π c R f ε 1. 28

12 Equaion 26 shows ha he price of he good asse is equal o he discouned presen value of dividends and he discoun rae is he ineres rae. Equaion 27 gives he seadysae capial sock and is derived from equaion 16 using ε = 1/Q. Since we will show laer ha 16 also holds under asymmeric informaion, he seady-sae capial sock has he same funcional form K. The expression on he lef-hand side of 28 represens he aggregae demand D ε for ouside liquidiy from he marke for long-erm asses and he expression on he righ-hand side represens he aggregae supply S ε of such ouside liquidiy. The demand comes from he invesmen spending ne of inernal profis, shor-erm deb backed by collaeralized capial, and dividends from he good asse. The supply comes from he sale of he good asse. The exisence of an equilibrium ε can be easily proved using equaion 28 by he inermediae value heorem. For uniqueness we impose a sufficien condiion ha µ is sufficienly small so ha he demand for and he supply of ouside liquidiy are monoonic in ε. For all our numerical examples sudied laer, we choose values of µ o ensure uniqueness. Under symmeric informaion he good asse drives he bad. If he wo ypes of asses coexised in he seady sae in he sense ha P l > and P g >, equaions 17 and 18 would imply ha P g + c P g = R f, 1 = R f. These wo equaions canno hold a he same ime whenever c >. This means ha he lemon mus have no value in he seady sae, P l =. Anicipaing zero price in he long run, he marke would no value he lemon a all imes; ha is, P l = for all by equaion 18 see Miao, Wang, and Zhou 214 for a formal proof. This resul illusraes he coexisence puzzle in he lieraure on raional bubbles and in moneary heory. We can measure marke liquidiy in wo ways. Firs, Brunnermeier and Pedersen 29 define marke liquidiy as he difference beween he marke price and he fundamenal value. Alhough he fundamenal value has various differen meanings in he lieraure, hey define i as he asse value in an economy wihou fricions. According o heir definiion, marke liquidiy is given by P g βc 1 β. Since he fundamenal value is consan, we can simply use he marke price as a proxy for marke liquidiy. Second, we can use rading volume o measure marke liquidiy. Since only he good asse is raded when ε j > ε, rading volume is given by 1 π [1 F ε ]. We can show ha hese wo measures are posiively correlaed. Turning o a comparaive saics analysis in he seady sae, we consider he impac of an increase in µ, which can be inerpreed as a permanen credi boom. Proposiion 2 shows ha a permanen credi boom raises he ineres rae and drives down marke liquidiy. Even hough 12

13 -2-4 % Trading Volume % % % % Credi Expansion Figure 1: Transiion dynamics in response o a permanen credi shock under symmeric informaion when µ rises from.1 o.165 from period 1 onward. The verical axes for variables oher han ε and µ describe percenage changes. funding liquidiy erodes marke liquidiy, oal liquidiy will rise. This improves invesmen efficiency and alleviaes resource misallocaion by raising ε, leading o increased oupu and invesmen. We close his secion by analyzing he ransiion dynamics of a permanen credi boom using a numerical example. 3 We do no inend o mach daa quaniaively and se parameer values as follows: β =.97, α =.38, A = 1, δ =.15, π =.25, and c =.6. We also se F as he uniform disribuion over [, 1]. As shown in Figure 1, a credi boom hrough an increase in µ improves invesmen efficiency by raising ε, which lowers he liquidiy premium, and herefore he marke liquidiy P g decreases. Meanwhile, since people have raional expecaions abou he unique seady sae P l =, here is no belief supporing a posiive sequence for P l he ransiion dynamics. Moreover, he credi expansion drives up he oal liquidiy, which booss invesmen, oupu and consumpion in he long run. in Consumpion drops iniially because invesmen jumps on impac, bu oal oupu does no change as i is deermined by 3 We use Dynare o compue all numerical examples in he paper based on he algorihm for solving deerminisic dynamic models described in Adjemian e al

14 predeermined capial only. 4 Asymmeric Informaion When here is informaion asymmery, hree ypes of equilibrium pooling equilibrium, bubbly lemon equilibrium, and frozen equilibrium can arise. We will firs sudy an enrepreneur s decision problem and hen sudy hese equilibria. 4.1 Decision Problem Suppose ha lemons and good asses are raded a he pooling price P >. Enrepreneurs ake sequences of prices {W, P, R f } and he marke proporion of good asses {Θ } as given. The following proposiion characerizes heir decision problems. Proposiion 3 Under asymmeric informaion, in a compeiive equilibrium wih P > for all, le ε = 1 Q ε min, ε max, where { Q, p g, pl, P, R f } saisfy equaions 16, 2, and p g = ε { p g } = min ε, ε max > ε, P [ c εmax ] + βp g ε R f ε ε 1 df ε, p l = P +1 R f, 3 P = Θ p g + 1 Θ p l If ε j ε, firm j exhauss is borrowing limi o make invesmen, sells all is lemons s l j = hl j, and does no buy any asse. I sells all is good asses sg j = hg j if ε j ε, bu does no sell any good asses s g j = if ε ε j < ε. 2. If ε j < ε, firm j does no inves, does no sell any good asses s g j =, sells all is lemons, is willing o purchase any amoun of asses, and is indifferen beween saving and borrowing. 3. The opimal invesmen rule is given by { R i j = k k j + P s g j + hl j + ch g j + µ k j + b j if ε j ε oherwise. 14

15 Unlike in he symmeric informaion case, p g and pl are shadow prices of he good asse and he lemon asse respecively, which represen he holding value of he asses. They mus saisfy equilibrium resricions 29 and 3. Boh asses are raded a he common marke price P, which is a weighed average of p l and p g. The cuoff value ε = 1/Q is he invesmen hreshold as in he symmeric informaion case. Unlike in he symmeric informaion case, informaion asymmery induces firms o sell all of heir lemons for any level of efficiency shocks ε j. The reason is ha he marke price P is a leas as high as he shadow price p l of he lemon. Equaion 3 shows ha p l is equal o he fuure selling price P +1 discouned by he ineres rae R f. Because P is also no higher han he shadow price p g of he good asse, firms will no sell he good asse unless here are oher benefis from selling in addiion o he price. The exra benefis come from profis generaed by funded addiional real invesmen. The oal benefis are given by Q ε P = P ε /ε. When hese benefis exceed he shadow price p g, he firm will sell he good asse. This gives he second cuoff ε given in he proposiion. The righ-hand side of 29 reflecs dividends c and he oal benefi from selling he good asse in he nex period. Noe ha i is possible ha p g ε /P ε max or ε = ε max. In his case no firm will sell any good asse so ha no good asse will be raded in he marke. We will analyze his case in he nex subsecion. Now we analyze an enrepreneur s decision problem when he marke for long-erm asses breaks down. In his case firms can use inernal funds, shor-erm deb, and payoffs from he good asse o finance real invesmen. Since long-erm financial asses are no raded in a frozen equilibrium, h g j = hg j for all. Proposiion 4 In a compeiive equilibrium in which he marke for long-erm asses breaks down, le ε = 1 ε min, ε max, Q where Q saisfies 16. Then he opimal invesmen rule is given by i j = { Rk k j + ch g j + µk j + b j if ε j ε oherwise. 4.2 Bubbly Lemon Equilibrium Now we impose he marke-clearing condiions and derive he equilibrium sysem when only lemons are raded in he marke. This happens when ε = ε max and hence Θ = and P = p l. 15

16 Proposiion 5 The dynamical sysem for a bubbly lemon equilibrium is given by eigh equaions 16, 2, 22, ε = 1/Q, and P = P +1, R f 32 p g = βp g +1 + c, R f 33 K +1 = 1 δ K + [R k K + πp + 1 π c + µ K ] ε max ε εdf ε, 34 I = [R k K + πp + 1 π c + µ K ] [1 F ε ], 35 for eigh variables {Q, p g, P, R k, R f, K, I, ε } saisfying he resricions < P ε ε max p g, ε min < ε < ε max. 36 Once we know he eigh equilibrium variables {Q, p g, P, R k, R f, K, I, ε }, we can derive oher equilibrium variables easily. Here p g denoes he shadow price of he good asse and P is he marke price of he lemon. When P Q ε max = P ε max /ε p g, i is no profiable even for he mos efficien firm o sell he good asse o finance real invesmen. Thus he good asse is no raded in he marke. Why can he inrinsically useless lemon asse be raded a a posiive price? The reason is ha firms wih high invesmen efficiency wan o sell his asse a a posiive price o finance invesmen. Firms wih low invesmen efficiency wan o buy his asse because hey believe ha hey can sell lemons a a posiive price o finance fuure invesmen if a high invesmen efficiency shock arrives in he fuure. To derive he exisence of such an equilibrium, we firs analyze he seady sae. Define c H δk ε b εdf ε αa [K ε b ]α µk ε b, εmax ε b c L c H 1 β ε max ε, 37 b where ε b c B c H c L π, c B π c H πc H + 1 πc L 1 π, 38 is defined in Lemma 1 and K is defined in 27. Proposiion 6 Le assumpion 1 hold. If < c B π c c B π, 39 hen here exiss a unique seady-sae equilibrium wih bubbly lemons in which he invesmen hreshold is ε b ε min, ε max, he aggregae capial sock is K ε b, he ineres rae R f = 1, he shadow price of he good asse is given by p g = c 1 β, 4 16

17 and he marke price of he lemon P saisfies δk ε b εdf ε αak ε b α µk ε b 1 π c = πp. 41 εmax ε b The inuiion for condiion 39 is as follows. If < c < c B π, hen he fundamenals of he good asse are oo weak so ha is shadow price or holding value is oo low. Thus i is more profiable for firms wih sufficienly high invesmen shocks o sell he good asse o finance real invesmen. This means ha he good asse will be raded in he marke and he bubbly lemon equilibrium canno exis. On he oher hand, if c > c B π, hen firms can use he payoffs c from he good asse o finance real invesmen, and here is no room for he emergence of a lemon bubble o finance real invesmen. Consider he impac of he parameer π, holding c as well as oher parameers consan. If he proporion π of lemons is oo low, hen he price of he financial asses will be high enough for firms wih high invesmen efficiency o sell heir good asses o finance heir real invesmen. Thus a bubbly lemon equilibrium canno exis and a pooling equilibrium may arise. Figure 2 illusraes he region of he parameers for he exisence of a bubbly lemon equilibrium. We can easily show ha c B π is an increasing funcion of π on [, 1] and c B = c H and lim π 1 c B π =. Bu c B π is a decreasing funcion of π on [, 1] and c B = c H and lim π 1 c B π = c L. In addiion, c B π > c B π for π, 1]. A unique bubbly lemon equilibrium exiss for parameer values of π, c in he region beween he lines c = c B π and c = c B π. 4.3 Pooling Equilibrium The following proposiion characerizes a pooling equilibrium. Proposiion 7 The dynamical sysem for a pooling equilibrium is given by 11 equaions 16, 2, 22, 29, 3, 31, ε = 1 Q, ε = pg P ε, 1 π [1 F ε ] Θ = π + 1 π [1 F ε 42 ], εmax K +1 = 1 δ K + 1 π P εdf ε + [R k K + πp + 1 π c + µ K ] ε εmax ε εdf ε 43 17

18 c c P π Frozen Pooling c B π c H Bubbly Pooling & Bubbly Pooling c L Pooling c B π O 1 π Figure 2: Three ypes of equilibrium I = [R k K + πp + 1 π c + µ K ] [1 F ε ] + 1 π P [1 F ε ], 44 for 11 variables { Q, p g, pl, P, R k, R f, Θ, K, I, ε, ε } saisfying he resricions ε min < ε < ε < ε max. 45 In a pooling equilibrium boh he good asse and he lemon are raded a he pooling price P o finance real invesmen. There is an inerior hreshold ε for selling he good asse. Thus he proporion of good asses in he marke is given by 42. Equaion 44 reveals ha aggregae invesmen is financed by inernal funds, he lemon, and he good asse. We now analyze he seady sae of a pooling equilibrium. We will firs prove he exisence of he wo seady sae hresholds ε and ε. By 29, he seady-sae shadow price of he good asse is given by p g ε, ε By he definiion of ε and ε, he pooling price is given by β 1 + ε max ε ε ε 1 df ε 1 β 1 + ε max ε ε ε 1 c. 46 df ε P ε, ε = ε ε pg ε, ε

19 1 = Φ = 1 = 2 = Figure 3: A numerical illusraion of ε = Φ ε. We se β =.97 and F ε = ε for ε [, 1]. Equaion 3 in he seady sae gives [ p l ε, ε = β 1 + εmax Equaion 31 in he seady sae implies ha where i follows from 42 ha ε ε ] ε 1 df ε P ε, ε. 48 P ε, ε = Θ ε p g ε, ε + 1 Θ ε p l ε, ε, 49 Equaions 47, 48, and 49 imply ha 1 = Θ ε ε ε Θ ε = 1 π [1 F ε ] π + 1 π [1 F ε ]. + 1 Θ ε β [ εmax ε ] 1 + ε ε 1 df ε. 5 Lemma 2 Le assumpion 1 hold. For any ε ε b, ε max, here exiss a unique soluion, denoed by ε = Φ ε, o ε ε b, ε in equaion 5. Figure 3 illusraes he funcion Φ. I is no a monoonic funcion on ε b, ε max and saisfies he propery ha lim Φ ε = ε ε ε b = lim Φ ε. b ε ε max 19

20 Now we prove he exisence of ε using a single equaion. To derive his equaion, we firs rewrie equaion 43 in he seady sae as D ε = S ε, ε εmax ε εmax εdf ε ε εdf ε 1 π P ε, ε + πp ε, ε, 51 where D ε represens he demand for ouside liquidiy defined in secion 3 and S ε, ε represens he supply of ouside liquidiy. The supply comes from he sale of he good asse and he lemon. The lemon is always sold a he price P ε, ε, bu he good asse is sold a his price wih probabiliy ε max ε εdf ε / ε max ε εdf ε. Subsiuing ε = Φ ε ino 51 and 47 yields an equaion for ε, We can also rewrie his equaion as where D Φ ε = S Φ ε, ε. Γ ε ; π = c, 52 Γ ε ; π δkφε εmax Φε εdf ε αa [K Φ ε, π] α µk Φ ε ] [ β 1+ εmax Φε 1 π + Φε ε [π + 1 π εmax ε εdf ε εmax Φε εdf ε 1 β1+ εmax ε ε df Φε,π 1 ε ε ε 1dF ε ]. 53 Proposiion 8 Le assumpion 1 hold and c H > where c H is given in 37. For a sufficienly small µ and any π, 1, here exiss a soluion, denoed by ε p, o ε ε b, ε max in equaion 52 if and only if < c < c P π, where c P π = max ε [ε,εmax]γ ε ; π. 54 b In his case a pooling seady sae equilibrium exiss and he seady sae capial sock is given by K ε p, where ε p = Φ ε p. The inuiion behind his proposiion is as follows. If c is close o zero, hen he good asse is similar o he lemon and i is hard for buyers o disinguish beween hese wo ypes of asses. Thus he adverse selecion problem is severer and boh ypes of asses can be raded a a pooling price in equilibrium. Bu if c exceeds c P π, hen he fundamenals of he good asse are oo srong. Holders of he good asse will no wan o sell i and he good asse will 2

21 Γ ; Figure 4: A numerical illusraion of Γ ε ; π. We se β =.97, α =.38, A = 1, δ =.15, π =.25, and F ε = ε on [, 1]. no be raded in he marke. Thus a pooling equilibrium canno exis and a bubbly lemon equilibrium may arise. Figure 4 illusraes he funcion Γ and he deerminaion of he equilibrium hreshold ε. We can show ha lim Γ ε ; π =, ε ε b lim ε ε max Γ ε ; π = c B π. 55 The funcion Γ ε ; π may no be monoonic in ε. There may be muliple soluions for ε and hence here may exis muliple pooling equilibria, each of which corresponds o a soluion for ε. Figure 2 illusraes he exisence condiion in he parameer space of π, c. When π 1, we mus have Θ, ε ε b, and ε ε max. Thus Γ ε ; π c H so ha c P 1 = c H. On he oher hand, when π, we mus have Θ 1 so ha ε = ε. Then Γ ε ; π reaches he maximum of infiniy when ε = ε b. I follows from 54 ha cp =. A pooling equilibrium exiss for parameer values of π, c in he region below he line c = c P π. The funcion c P π is downward sloping. Holding c as well as oher parameers consan, if he proporion π of lemons is oo high, hen he adverse selecion problem will be so severe ha rading he good asse as a way o subsidize he lemon would be highly discouraged. Thus a pooling equilibrium 21

22 canno exis. 4.4 Frozen Equilibrium We finally analyze he frozen equilibrium in which agens expec he asse price o be zero. Then no sellers will wan o sell heir asses a a zero price and no asses will be raded. The marke for long-erm asses will compleely break down. The following proposiion characerizes he equilibrium sysem. Proposiion 9 The dynamical sysem for a frozen equilibrium is given by five equaions 16, 22, ε = 1/Q, and K +1 = 1 δ K + [R k K + 1 π c + µ K ] εmax ε εdf ε, 56 I = [R k K + 1 π c + µ K ] [1 F ε ], 57 for five variables {Q, R k, K, I, ε } saisfying he resricion ε ε min, ε max. The following proposiion characerizes he seady sae. Proposiion 1 There exiss a unique seady sae for he frozen equilibrium in which he seady-sae capial sock is equal o K ε a defined in 27 where ε a ε min, ε max is he unique soluion o ε ε min, ε max in he equaion D ε =, i.e., δk ε εmax ε εdf ε αak ε α µk ε 1 π c =. 58 Equaion 58 shows ha he supply of ouside liquidiy from he marke for long-erm asses is zero. 5 Seady-Sae Properies We now combine he previous analyses and presen he parameer space of π, c for he exisence of he hree ypes of equilibrium using Figure 2. Firs, we noe ha a frozen equilibrium always exiss on he whole parameer space. Nex, by 54 and 55, we have c B π c P π. Thus he curve c = c P π is always above he curve c = c B π. We highligh wo imporan regions. We can see ha a bubbly lemon equilibrium and a pooling equilibrium coexis when π, c lies in he region { π, c c B π c min c B π, c P π }. Bu in he region { π, c c P π c c B π }, he bad asse drives ou he good one in he sense ha a bubbly lemon equilibrium exiss bu a pooling equilibrium does no. 22

23 Proposiion 11 Le assumpion 1 hold. Suppose ha he parameer values are such ha he hree ypes of equilibrium under asymmeric informaion coexis. Then K ε a < K ε b < K ε p, where ε a, ε b, and ε p denoe he invesmen hresholds in he frozen equilibrium, bubbly lemon equilibrium, and pooling equilibrium, respecively. The inuiion behind Proposiion 11 is he following. As characerized previously, he demand side for ouside liquidiy from he marke for long-erm asses is he same for all ypes of equilibria. Wha differs is he supply side. The liquidiy supplied in a pooling equilibrium is larger han ha supplied in a bubbly lemon equilibrium, which in urn is larger han ha supplied in a frozen equilibrium. Thus he seady-sae capial sock is he larges in a pooling equilibrium and he smalles in a frozen equilibrium. We have so far characerized he seady saes and heir exisence condiions. We now use some numerical examples o illusrae he impac of a permanen credi boom on he seady saes. We illusrae he effec of µ on asse prices and oupu in Figure 5. For he parameer values given in Secion 3, all hree ypes of seady sae equilibria coexis for µ [,.16]. There are wo seady-sae pooling equilibria. We will focus on he good pooling seady sae wih a higher asse price and larger oupu because his seady sae is sable a saddle poin and he oher is unsable. When µ rises, funding liquidiy rises and imposes a negaive exernaliy on he marke for he long-erm asse. The asse price and marke liquidiy decline. The oal liquidiy sum of marke liquidiy and funding liquidiy may no be monoonic wih µ and hence real invesmen and oupu are no monoonic eiher. There may exis an opimal level of µ ha srikes a balance beween funding and marke liquidiy. As illusraed on he righ panel of Figure 5, he effec of µ on asse prices and oupu is indeed non-monoone and oupu is maximized a µ =.9. When µ [.16,.17], funding liquidiy is so large ha enrepreneurs have no incenive o rade good asses because good asses mus subsidize lemons due o adverse selecion. Enrepreneurs are willing o rade lemons as a bubble because he bubble can raise heir ne worh and help hem finance invesmen. In his case only he bubbly lemon seady sae exiss. Asse prices and oupu are disconinuous a µ =.16. A small change of µ near µ =.16 can cause an equilibrium regime shif and hence liquidiy can be fragile. When µ >.17, enrepreneurs no only have no incenive o sell heir good asses, bu also have no ineres in rading lemons because hey have sufficien funding liquidiy o finance 23

24 Asse Price Pooling G Pooling B Bubbly Lemon Oupu Figure 5: The impac of µ on he seady sae asse price and oupu. We se β =.97, α =.38, A = 1, δ =.15, π =.25, c =.6, and F ε = ε on [, 1]. invesmen and here is no need o rade lemons as a bubble asse. In his case neiher he pooling seady sae nor he bubbly lemon seady sae can be suppored and he marke for long-erm asses breaks down. 6 Transiion Dynamics In his secion we sudy ransiion dynamics when he economy moves from one seady sae o anoher. This ransiion can be caused by eiher shifs in beliefs or shocks o fundamenals. Alhough financial markes are ypically disruped in recessions wih rading volume and asse prices plummeing, seldom do we observe a complee marke collapse. Therefore we focus on pooling and bubbly lemon equilibria. Meanwhile, since he flucuaions of financial markes are urbulen, and even seemingly disconinuous, here may exis regime swich from one ype of equilibrium o anoher. Thus our numerical examples proceed wih he coexisence parameer space defined in he previous secion. 24

25 %.2 Θ Trading Volume % % % % Credi Expansion Figure 6: Belief-driven regime shif from he good pooling seady sae o he bubbly lemon seady sae. We se β =.97, α =.38, A = 1, δ =.15, π =.25, c =.6, and F ε = ε on [, 1]. 6.1 Belief-Driven Regime Shifs We firs consider he case where a change in beliefs can cause a regime shif wihou any shock o fundamenals. We se he parameer values as in Secion 2 and also µ =.1. There are wo pooling seady saes as shown in Figure 5. Suppose ha he economy is iniially a he good pooling seady sae. We will focus on he good pooling seady sae in all our numerical examples. Suppose ha agens pessimisically believe ha he economy will suddenly shif o a bubbly lemon equilibrium a dae 1. Figure 6 describes he ransiion dynamics from he pooling seady sae o he bubbly lemon seady sae. The figure shows ha he asse price drops disconinuously. Enrepreneurs do no rade good asses bu raher rade lemons only. Thus marke liquidiy declines. Real invesmen also drops disconinuously iniially and gradually rises o a lower bubbly lemon seady sae level. Oupu also drops gradually o a lower bubbly lemon seady sae level. This example shows ha a change in beliefs wihou any fundamenal shock can cause a liquidiy dry-up and a recession. Nex we show ha an opimisic belief shif can cause a boom 25

26 4 % Θ Trading Volume % % % % Credi Expansion Figure 7: Belief-driven regime shif from he bubbly lemon seady sae o he good pooling seady sae. wihou any fundamenal shock. Suppose ha he economy is iniially a he bubbly lemon seady sae. Bu people opimisically believe ha he economy will swich o a pooling equilibrium immediaely. Figure 7 shows he ransiion dynamics. When an enrepreneur opimisically believes ha oher enrepreneurs will rade heir good asses, he is willing o do he same. Thus marke liquidiy increases and he asse price rises. As more enrepreneurs are willing o sell heir good asses a lower ε, he average asse qualiy in he marke improves, which drives up he pooling price, and in urn jusifies he iniial opimisic belief. The favorable marke liquidiy hen booss invesmen, acceleraes capial accumulaion, and evenually raises boh oupu and consumpion. 6.2 Good or Bad Credi Booms Now we sudy he impac of a change in fundamenals hrough a change in funding liquidiy. In paricular, we consider he impac of a credi boom when µ rises. We will show ha a credi boom can cause eiher a boom in he real economy or a financial crisis depending on agens beliefs. Firs, we consider he impac of a emporary credi boom when µ rises from.1 o.9 26

27 %.2 Θ Trading Volume % % %.8 % Credi Expansion no regime shif regime shif -2-3 Figure 8: The impac of a emporary credi boom. The solid lines describe he ransiion dynamics from he good pooling seady sae o he same seady sae. The dashed lines describe he ransiion dynamics from he good pooling seady sae o he bubbly lemon seady sae. We se β =.97, α =.38, A = 1, δ =.15, π =.25, c =.6, and F ε = ε on [, 1]. iniially and lass for 16 periods and hen reurns o he original level forever. Suppose ha he economy is iniially a he good pooling seady sae. Figure 8 shows he ransiion dynamics. The solid lines describe he case where here is no regime shif and he economy will reurn o he original pooling seady sae evenually. The dashed lines describe he case where agens pessimisically believe ha he economy will shif o he bubbly lemon equilibrium. In his case he asse price drops disconinuously and gradually reurns o a lower level in he bubbly lemon seady sae. Real invesmen also drops disconinuously, rebounds slighly, and drops again wih µ. I hen gradually rises o is lower seady-sae level. Oupu also evenually decreases o a lower seady-sae level, resuling in a crisis. Second, we consider he impac of a permanen credi boom. Suppose ha he economy is iniially a he pooling seady sae. Figure 9 illusraes ha a modes credi boom can lead o a boom in he real economy while a large one can lead o an economic recession. The solid lines in he figure show he ransiion dynamics from one good pooling seady sae o anoher 27

28 %.2 Θ Trading Volume % % %.8.78 % Credi Expansion Modes Inensive Figure 9: The impac of a permanen credi boom. The solid lines describe he ransiion dynamics from he good pooling seady o anoher good pooling seady sae. The dashed lines describe he ransiion dynamics from he good pooling seady sae o he bubbly lemon seady sae. We se β =.97, α =.38, A = 1, δ =.15, π =.25, c =.6, and F ε = ε on [, 1]. pooling seady sae along a pooling equilibrium pah when µ rises immediaely from.1 o.9 and says here forever. Even hough funding liquidiy reduces marke liquidiy, he oal liquidiy rises so ha invesmen and oupu also rise slighly. When µ rises immediaely from.1 o.165, he credi boom is so large ha he pooling seady sae canno be suppored, as shown in Figure 5. Then he economy ransis o a bubbly lemon seady sae. The asse price and invesmen drop disconinuously on impac. During he ransiion pah, asse prices, invesmen, and oupu fall, leading o a recession. Wha happens if he economy is iniially a he bubbly lemon seady sae? Consider he impac of a permanen modes credi boom when µ rises immediaely from.1 o.9 and says here forever. Suppose ha he agens are opimisic and he economy swiches immediaely from a bubbly lemon seady sae equilibrium o a pooling equilibrium. The solid lines in Figure 1 show ha asse prices, invesmen, and oupu all rise, resuling in an economic expansion. By conras, if he credi boom is oo large e.g., µ increases from.1 o.165, hen a 28

29 5 % Θ Trading Volume % % % % Credi Expansion Modes Inensive Figure 1: The impac of a permanen credi boom. The solid lines describe he ransiion dynamics from he bubbly lemon seady sae o he good pooling seady sae. The dashed lines describe he ransiion dynamics from he bubbly lemon seady sae from anoher bubbly lemon seady sae. We se β =.97, α =.38, A = 1, δ =.15, π =.25, c =.6, and F ε = ε on [, 1]. pooling seady sae can no longer be suppored. Therefore a large credi boom worsens marke liquidiy by discouraging enrepreneurs from selling heir good asses in he marke, which in urn has a negaive effec on invesmen, oupu, and consumpion. Noe ha, when µ =.165, he bubbly lemon equilibrium and he frozen equilibrium coexis. We only consider he former equilibrium because rading volume is sill posiive in his case, albei reduced significanly. This is more realisic han he frozen equilibrium. Combining he insighs from he previous numerical examples in Figures 7 and 1 yields he richer dynamics in Figure 11. Suppose ha he economy is iniially a he bubbly lemon seady sae wih µ =.1. There is a modes unexpeced credi boom in ha µ increases from.1 o.9 from = 1 o = 16 and hen here is anoher unexpeced large credi boom where µ increases from.9 o.165 from = 17 on. As shown in Secion 5, a pooling seady sae equilibrium can be susained a a modes level of µ bu a large level. Suppose ha people are opimisic and hence he economy immediaely swiches o a pooling equilibrium regime ha lass unil = 16. Bu since a pooling seady sae canno be suppored a µ =.165, 29