Alberto Martin * Jaume Ventura

Transcription

1 Asse Bubbles and Sudden Sops in a Small Open Economy Albero Marin * CREI, Universia Pompeu Fabra and Barcelona GSE Jaume Venura CREI, Universia Pompeu Fabra and Barcelona GSE One of he mos sriking feaures of he world economy over he las weny-five years has been he sharp decline in he real ineres rae from approximaely 4% in he early 99s o -.5% in 23 (figure ). During his period, here have been wo waves of large capial inflows ino emerging economies (figure 2). In he firs wave, which began in he early 99s and ended wih he Asian crisis of 997, ne capial flows o hese economies wen from zero o approximaely 3.5% of heir combined GDP. The second wave sared in he early 2s and peaked in 27 as inflows reached approximaely 5% of emerging-marke GDP. Capial inflows conraced sharply during he financial crisis of 28-29, bu hey have rebounded since. A firs glance, boh pieces of evidence appear o be posiive news for emerging markes, which have enjoyed increased access o foreign financing a lower ineres raes. And ye, here is much debae regarding he desirabiliy of low ineres raes and surges in capial inflows. * The analyical framework used in his aricle was developed in our papers Managing Credi Bubbles and The Inernaional Transmission of Credi Bubbles: Theory and Policy. We refer he reader o hese papers for formal derivaions and many addiional resuls. We would like o hank Fernando Broner for useful commens and Francisco Queiros and Tom Schmiz for excellen research assisance. Marin: CREI and Universia Pompeu Fabra, amarin@crei.ca. Venura: CREI and Universia Pompeu Fabra, jvenura@crei.ca. CREI, Universia Pompeu Fabra, Ramon Trias Fargas 25-27, 85-Barcelona, Spain. We acknowledge suppor from he Spanish Minisry of Science and Innovaion (gran ECO2-2397), and he Generalia de Caalunya- AGAUR (gran 24SGR-83). In addiion, Venura acknowledges suppor from he ERC (Advanced Gran FP ABEP), and Marin he ERC (Consolidaor Gran FP MacroColl), and he IMF Research Fellowship. Global Liquidiy, Spillovers o Emerging Markes and Policy Responses, edied by Claudio Raddaz, Diego Saravia, and Jaume Venura, Saniago, Chile. 25 Cenral Bank of Chile. 35

2 36 Albero Marin and Jaume Venura Figure. World ineres raes, World long-erm real ineres rae World shor-erm real ineres rae Source: OECD. Sa. World Series are real GDP-weighed averages for he shor-and long-erm real ineres raes in he G7 counries. The series for shor-erm real ineres raes excludes, for daa availabiliy reasons, Japan from 99 o 22, while he long-erm real ineres rae series excludes Ialy from 99 o 99. Figure 2. Ne capial inflows o emerging economies 6% 5% 4% 3% 2% % % Ne privae capial inflows (percenage of emerging marke GDP, lef axis) Ne privae capial inflows (US$ billion, righ axis) Source: IMF, Balance of Paymens Saisics. Emerging economies are defined as in Cardarelli e al. (29). One of he main reasons is ha hese episodes may end in so called sudden sops, sharp reversals in capial flows ha are ypically accompanied by falling asse prices and deep recessions. This narraive is ofen invoked o explain he evens ha ranspired across many emerging markes during he 99s, in paricular, he Mexican crisis of 994 and he Eas Asian crisis of 997. As we wrie his aricle, i is also invoked o warn of he dangers ha lie ahead once he Federal Reserve decides o ighen is moneary policy and increase ineres raes in he Unied Saes, aracing par of

3 Asse Bubbles and Sudden Sops in a Small Open Economy 37 he capial flows ha are now heading o he emerging world. This preoccupaion wih he downside risks of capial inflows has been accompanied by a growing endorsemen of policy inervenion in he form of capial conrols. Bu wha is he role of capial conrols in a world of financial globalizaion and low ineres raes? How do capial flows behave in such a world, and wha are he marke failures ha should be addressed hrough inervenion? In his paper, we provide a simple framework o hink abou hese quesions. To do so, we firs develop a sandard model of a small open economy wih borrowing consrains. In our model, agens need o borrow from foreigners in order o inves. Due o weak enforcemen insiuions, however, foreign borrowing mus be backed by he value of domesic firms. Our key innovaion is o noe ha, in low ineres rae environmens, he value of firms has boh a fundamenal and bubble componen. The fundamenal componen corresponds o he capial ha is owned by he firm, i.e., i is he par of he firm s value ha is backed by expecaions of fuure producion. The bubble componen insead corresponds o he par of he firm s value ha is posiive oday only because i is expeced o be posiive omorrow, i.e., i is he par of he firm s value ha is backed by expecaions of he fuure bubble. The lieraure on capial flows in he presence of borrowing consrains has focused exclusively on he fundamenal componen of asse prices. Whenever he ineres rae is low enough, however, we show ha his view is incomplee. In his case, here is room for invesor opimism o susain bubbles ha relax he counry s borrowing consrain and fuel capial inflows. A firs conribuion of our paper is o characerize he effecs of bubbles on capial flows, invesmen and growh. By definiion, bubbles enable domesic borrowers o obain foreign credi in excess of he fundamenal value of heir firms. Inuiively, he inernaional financial marke is willing o lend in excess of his value because i anicipaes ha firms will have a bubble componen in he fuure as well. In his sense, bubbles have a crowding-in effec, which raises gross capial inflows, invesmen and growh. Bu he bubble componen has also fueled excess credi in he pas, which requires divering some of oday s resources away from invesmen o pay foreign crediors. This is he crowding-ou effec of bubbles, which raises gross capial ouflows and reduces invesmen and growh. The ne effec of bubbles depends on he relaive srengh of hese wo effecs. In paricular, we find ha he crowding-in effec dominaes during normal imes, when he small open economy faces

4 38 Albero Marin and Jaume Venura an elasic supply of funds from he inernaional financial marke. A hese imes, i is he value of domesic firms ha consrains foreign borrowing, and bubbles relax his consrain by raising he value of firms. In conras, during sudden sops, i is he supply of funds from he inernaional financial marke ha consrains foreign borrowing. A hese imes, bubbles canno raise gross capial inflows bu hey do raise gross ouflows because foreign crediors mus be repaid, and he crowding-ou effec of bubbles dominaes. Thus, he bubble ha aains he opimal level of invesmen grows during normal imes and shrinks during sudden sops. A second conribuion of our paper is o explore he role of capial conrols in his environmen. An essenial feaure of bubbles is ha hey are driven by invesor senimen or marke expecaions. Their value oday depends on marke expecaions abou heir value omorrow, which in urn depends on omorrow s marke expecaions abou heir value on he day afer, and so on. Because of his, he bubble provided by he marke may be oo small and gross capial inflows insufficien during normal imes, while i may be oo large and gross capial ouflows excessive during sudden sops. We show ha a governmen ha can impose axes and subsidies on gross capial flows can use such conrols o replicae he bubble allocaion ha maximizes oupu. To do so, i mus subsidize gross capial ouflows during normal imes bu ax hem during sudden sops. The view of capial conrols ha emerges here seems o conradic he recen lieraure on capial flows and pecuniary exernaliies, which emphasizes he precauionary naure of conrols. This may seem odd because boh frameworks are similar, bu hey differ in wo imporan respecs. Firs, we consider low ineres rae environmens in which bubbles may arise. These bubbles provide collaeral and make i possible for foreign borrowing o expand in normal imes. If he bubbles supplied by he marke are small, however, he governmen can complemen hem by subsidizing gross capial ouflows, which amouns o a public guaranee of privae. See, for insance, Caballero and Krishnamurhy (2), Mendoza (2), Bianchi (2), and Korinek (2). In mos of hese models, foreign borrowing is consrained by he value of domesic asses in erms of radable goods. When a sudden sop occurs, foreign borrowing declines for wo reasons: here is he direc effec of he shock ha gives rise o he sudden sop (e.g., increased risk aversion of inernaional invesors), bu here is also an indirec effec because asse prices fall and/or he real exchange rae depreciaes. Because domesic agens do no inernalize his las effec when hey make heir borrowing decisions, here is over-borrowing in equilibrium and prudenial capial conrols ha reduce ne inflows ha may be welfare-enhancing.

5 Asse Bubbles and Sudden Sops in a Small Open Economy 39 loans. By doing so, i relaxes he economy s borrowing consrain, and low ineres raes ensure ha he policy is susainable. A second difference wih he lieraure is ha borrowing consrains in our model depend on expeced as opposed o conemporaneous asse prices. This means ha, in our framework, a fall in asse prices during sudden sops is acually good for economic aciviy: given expeced asse prices, such a fall reduces paymens o foreigners and increases domesic resources available for invesmen. The res of he paper is srucured as follows. Secion develops a sylized model of an emerging marke ha faces borrowing consrains. Secions 2 and 3 explore bubbly equilibria in low ineres rae environmens and sudy he implicaions of bubbles for capial flows, invesmen and growh. Secion 4 inroduces a governmen and shows how capial conrols can be used o maximize invesmen. Secion 5 concludes.. A sylized model of an emerging marke We nex describe an economy ha is only a very small par of a large world. We refer o he ciizens of his economy as domesic residens, and o he ciizens of he res of he world as foreigners. Domesic residens work for domesic firms and manage hem. Foreigners canno do his. Domesic residens and foreigners inerac in he credi marke, where hey exchange consumpion goods for promises o deliver consumpion goods in he fuure. Domesic firms produce consumpion goods using capial and labor wih a sandard Cobb-Douglas echnology: α y = A k l α () wih A > and a (.) ; and y, k and l denoe oupu, he capial sock and he labor force, respecively. The capial sock evolves as follows: k = i + ( + δ ) k (2) where i is invesmenand d (.) is he depreciaion rae. The labor force is consan and equal o one. Workers are paid heir marginal produc and, as a resul, hey receive a fracion _ a of oupu. The remaining oupu is disribued o firm owners. Domesic residens rade old firms and hey can also creae new ones a zero cos. Le

6 32 Albero Marin and Jaume Venura v be he marke value of all firms afer oupu has been disribued and before new invesmens have been made. Thus, v is he marke value of firms ha conain he undepreciaed capial lef afer producion, i.e. ( _ d). k. There are overlapping generaions of domesic residens ha live for wo periods. All generaions have a size of one and conain a fracion m of paien residens ha maximize expeced consumpion during old age, and a fracion _ m of impaien residens ha maximize consumpion during youh. Paien residens save, own firms and consume when old. Impaien residens consume when young and never own firms. These assumpions imply he following aggregae consumpion and invesmen: * c = ( s) y + v R f (3) i = s y + f v (4) where c is consumpion, f foreign borrowing and R * he ineres rae paid on foreign borrowing, and s µ ( α). In his economy, he impaien young and he paien old are he domesic consumers. Thus, equaion (3) says ha aggregae consumpion equals heir combined income which consiss of a fracion _ s of he economy s oupu, plus he price obained by he old when hey sell heir firms, minus heir foreign ineres paymens. In his economy, he paien young are he domesic invesors. Thus, equaion (4) says ha aggregae invesmen equals he income of he paien young, which is a fracion s of he economy s oupu, plus heir foreign borrowing less he price hey pay for heir firms. There are wo fricions ha limi foreign borrowing: one of hem originaes abroad, and he oher a home. The foreign fricion is he possibiliy of sudden sops. 2 In paricular, here are wo possible saes: z {N, S} which we refer o as normal imes and sudden sops. In normal imes, foreigners provide credi o domesic residens a an expeced reurn E R * + = r, up o a maximum of F. We hink of F as being large, which makes his assumpion inconsequenial for mos of he paper. I is noneheless useful because i ensures ha 2. From he perspecive of our economy, his is no really a fricion bu simply a descripion of he environmen in which i operaes. We refer noneheless o he assumpion ha he supply of funds is volaile as a foreign fricion because we hink ha his volailiy sems from an (unmodeled) imperfecion in he inernaional financial marke.

7 Asse Bubbles and Sudden Sops in a Small Open Economy 32 he small-open-economy assumpion is sensible by guaraneeing ha foreign borrowing is always bounded in equilibrium. During sudden sops, foreigners do no lend o domesic residens. Le s be he probabiliy of a sudden sop saring, i.e. s = Pr (z + =S/z = N); and le h be he probabiliy of a sudden sop ending h = Pr (z + = N/z = S). Domesic residens can always lend o he res of he world a he ineres rae r. The domesic fricion is insufficien collaeral. In paricular, domesic cours can seize he price ha firm owners obain when hey sell heir firms, bu no he oupu ha hese firms disribue o heir owners. As a resul, firm owners can only promise a paymen of v + o heir foreign crediors. Define he economy s collaeral as he maximum value of paymens omorrow ha can be promised oday. Since coningen conracs are possible, he economy s collaeral equals E v +. 3 Combining foreign and domesic fricions, we obain he counry s borrowing limi: f Ev = ρ + if z if z = N = S (5) In normal imes, he borrowing limi equals he discouned value of he economy s collaeral. During sudden sops, he borrowing limi drops o zero. 4 Ideally, he counry would borrow (or lend) unil he reurn on invesmen equals he borrowing rae. This is only possible, hough, if he borrowing required o achieve his does no exceed he borrowing limi. Oherwise, he counry borrows up o he limi. This implies he following dynamics for he capial sock: α α A k+ = min s A k + f v + ( δ) k, ρ+ δ α (6) 3. If cours could also seize he oupu ha firms disribue o heir owners, he economy s collaeral would be a.y + +E v +. If credi conracs could no be coningen, he economy s collaeral would be min v Equaion (5) incorporaes our assumpion ha F is arbirarily large and ha i, herefore, always exceeds he discouned value of he economy s collaeral.

8 322 Albero Marin and Jaume Venura For a given borrowing limi, equaion (6) shows ha high firm prices diver resources away from invesmen. This is he crowding-ou effec of curren firm prices, which is always presen. Bu equaion (5) shows ha high expeced firm prices expand he borrowing limi and provide addiional resources for invesmen. This is he crowding-in effec of fuure firm prices, which operaes in normal imes when foreign borrowing is consrained by he lack of domesic collaeral. To undersand he dynamics of capial accumulaion and foreign borrowing we mus herefore esablish how firm prices behave. We urn o his ask nex. 2. Asse bubbles and heir effecs I migh surprise some readers ha here exis equilibria in which he prices of firms exceed he price of he capial hese firms conain. When his is he case, we say ha here is a bubble in firm prices. In paricular, he appendix shows ha here are many equilibria in which firm prices ake he following form: v = ( _ d). k +b (7) Equaion (7) says ha he price of firms can be hough of as he sum of wo componens, which we refer o as he fundamenal and he bubble. The firs componen of he price of firms is he price of he capial ha firms conain, or fundamenal: ( _ d). k. Invesors are willing o pay his price for he capial conained in he firm since his is exacly wha i would cos hem o produce such an amoun of capial hrough invesmen. The second componen of he price of firms is an overvaluaion or bubble: b. A firs glance, he exisence of his bubble migh seem inconsisen wih maximizaion. If firms are bubbly, wouldn invesors prefer o creae new firms a zero cos and hen obain he same amoun of capial by invesing in hem? Wheher his is a preferable sraegy or no depends on how he bubble evolves over ime. If he bubble grows fas enough, invesors migh even prefer purchasing bubbly firms over creaing new ones a zero cos. The quesion is hen: how does he bubble componen evolve in equilibrium? The appendix shows ha he following bubble dynamics are consisen wih maximizaion and marke-clearing:

9 Asse Bubbles and Sudden Sops in a Small Open Economy b + ( ρ + u+ ) b + n+ if z = N = α ( α A k + + δ+ u+ ) b + n+ if z = S 323 (8) such ha E u + = and n + >. Equaion (8) says ha he bubble has wo sources of dynamics. The firs one is he growh of preexising bubbles, while he second one is he creaion of new bubbles. The firs erm of he righ-hand side of equaion (8) measures he growh rae of pre-exising bubbles. Since he reurn o he bubble is is growh, in equilibrium his growh is deermined by supply and demand. In normal imes, bubbles can be used as collaeral o borrow, and heir expeced growh mus equal he world ineres rae: r. If bubbles grew faser, he demand for bubbly firms would be unlimied, since borrowing o purchase bubbly firms would deliver a ne profi. If bubbles grew less, he demand for bubbly firms would be zero, since borrowing o purchase bubbles would produce a loss. During sudden sops, bubbles canno be used as collaeral o borrow and heir expeced growh mus equal he opporuniy cos of funds, α which is he reurn o invesmen: ( α A k+ + δ) b. The second source of bubble dynamics is he creaion of new bubbles: n +. The new se of bubbles ha are creaed or iniiaed by generaion of invesors consiue ne wealh for hem. The argumen above explains why he demand and supply for firms mach a he proposed firm prices. Bu his argumen is incomplee because we have implicily assumed ha he foreign borrowing associaed wih he bubble dynamics in equaion (8) never exceeds he maximum F. For his o be he case, he bubble process mus no explode and his requires ha r be low enough. This is a key observaion: bubbly equilibria are only possible in low ineres rae environmens. If r is high enough, here is a unique equilibria wih b = always. Using equaions (7) and (8), we can re-wrie equaions (5) and (6) as follows: A α k+ = min s A k + f b, α α (9) ρ+ δ α ( δ) s A k + En + + b if z = N f = ρ+ δ () if z = S

10 324 Albero Marin and Jaume Venura Figure 3. The law of moion for capial k + Normal imes Sudden sop k Equaions (9) and () joinly describe he law of moion of he capial sock. Figure 3 shows ha his law of moion conains hree differeniaed regions. For high levels of capial sock, he law of moion is fla and independen of wheher here is a sudden sop or no. In his range of capial socks, he borrowing limi is never binding. The economy is capial-abundan and i expors savings unil he reurn on invesmen equals he world ineres rae. Sudden sops are irrelevan because he economy does no borrow abroad. For inermediae levels of he capial sock, he law of moion is fla in normal imes bu upward-sloping during sudden sops. In his range of capial socks, he borrowing limi is binding during sudden sops only. The economy is no longer capial-abundan bu i has enough collaeral o impor savings unil he reurn on invesmen equals he world ineres rae in normal imes. During sudden sops, however, domesic invesors canno borrow abroad and invesmen equals domesic savings. As a resul, he capial sock drops and he reurn on invesmen increases above he world ineres rae. For low levels of he capial sock, he law of moion is upwardsloping boh in normal imes and during sudden sops. In his range of capial socks, he borrowing limi is always binding. The economy does no have enough collaeral o impor savings unil he reurn on invesmen equals he world ineres rae. The law of moion in normal imes is above ha of sudden sops because domesic invesors can supplemen domesic savings wih foreign savings in normal imes, bu his is no possible during sudden sops.

11 Asse Bubbles and Sudden Sops in a Small Open Economy 325 Equaions (9) and () show ha asse bubbles only affec capial accumulaion if he borrowing limi is binding. Ineresingly, he effecs of bubbles on capial accumulaion differ in normal imes and during sudden sops. In normal imes, bubble creaion provides collaeral ha raises foreign credi and invesmen. This raises capial accumulaion. During sudden sops, pre-exising bubbles diver par of he economy s savings away from invesmen. This lowers capial accumulaion. To deermine he relaive imporance of hese wo effecs, we mus look a specific equilibria. To find equilibria of his economy, we ake an iniial condiion {k, b, z } and a join sochasic process for {u, n, z } such ha Pr (z + =S/z = N) = s, Pr (z + = N/z = S)= h, E u + = and n +. If all possible sequences for {k, b, z } generaed in his way are such ha b and k, hen we have found an equilibrium of he model. I urns ou ha his simple model can give rise o a large se of equilibria. A full analysis of his se is beyond he scope of his paper, and we refer he reader o our earlier work. Here, we jus show some examples o build inuiion. 3. Examples We now consruc a se of examples o illusrae he effec of bubbles. Firs, we simplify by assuming ha h=. Tha is, sudden sops only las one period. Second, we assume a very simple bubble process. During normal imes he bubble is consan and equal o b. Bubble creaion adjuss o ensure his. During sudden sops he bubble drops by a fracion d and here is no bubble creaion In paricular, we assume he economy sars in k = k, b = b and z = N and {u, n } follows his sochasic process: n u + + σ ρ d b z N z N + if = and = σ = if z = N and z = S + α ( α A k + δ) ( ρ d) b if z = S + σ d if z = N and z = N + σ = d if z = N and z = S + if z = S

12 326 Albero Marin and Jaume Venura There are hus wo key parameers ha drive he example: he size of he bubble b, and is reacion o a sudden sop d. A higher value of b implies more bubble creaion and hus greaer borrowing and invesmen during normal imes, bu i also divers more resources away from invesmen during sudden sops. A higher value of d means ha he bubble becomes smaller during sudden sops and reduces is negaive impac on invesmen a hese imes. Based on hese observaions, we consider five differen equilibria ha are defined as follows: Size\Reacion o Sudden Sop d= d=r b= b=b L 2 3 b=b H 4 5 We analyze each equilibrium under he assumpion ha r < _ s (i.e., ha he probabiliy of experiencing a sudden sop is sufficienly low). In equilibria 2 and 4 he size of he bubble does no change during sudden sops, whereas in equilibria 3 and 5 he bubble disappears during sudden sops. We simulae each of hese equilibria by assuming ha he economy sars in he seady sae ha corresponds o normal imes and hen simulaing i forward for, periods. Table repors he parameer values used in hese simulaions. Table 2 repors he mean and he sandard deviaion of k, y, c, f, and v for each simulaion. Figure 4 plos he simulaed ime series of k, c and f during a window of 2 periods. These simulaions offer an excellen summary of he main effecs of bubbles in our economy. Table. Parameer values Parameer Value Parameer Value A δ.8 α.47 b L.25k * A μ.9 b H 2.5k * A ρ.6 σ.5 Noes: k * A sands for he seady-sae capial sock ha would prevail in auarky (ha is, k * A = (sa) α ).

13 f Mean Asse Bubbles and Sudden Sops in a Small Open Economy 327 Table 2. Summary saisics Equilibrium k Mean Sandard deviaion y Mean Sandard deviaion c Mean Sandard deviaion Sandard deviaion v Mean Sandard deviaion Firs, bubbles improve he workings of he economy in normal imes bu worsen hem during sudden sops. In normal imes, he collaeral ha bubbles provide raises foreign borrowing and invesmen; during sudden sops, hese same bubbles diver resources away from invesmen in wha could be ermed a bubble overhang effec. Thus, bubbles creae addiional volailiy. Table 2 indeed shows ha he mean values and sandard deviaions of k, y, c, f, and v are highes in equilibria 4 and 5, followed by equilibria 2 and 3 (in which b=b L ) and, finally, by equilibrium (in which b=). Figure 4 also illusraes his poin for a given subsample of he simulaion. In each panel, he solid line depics he simulaed ime series of he specific equilibrium being analyzed, whereas he dashed line depics he simulaed ime series for equilibrium. The figure shows how bubbles raise volailiy by increasing economic aciviy in normal imes and, in equilibria, by lowering i during sudden sops.

14 328 Albero Marin and Jaume Venura Figure 4. Simulaed ime series Equilibrium 2 Equilibrium 3 Equilibrium 4 Equilibrium 5 Capial Sock Foreign Borrowing Consumpion Noe: Dashed lines show he ime series for Equilibrium (no bubble). Second, all bubbles are no alike. In erms of economic aciviy, he bes bubbles are hose ha maximize invesmen in normal imes while huring i as lile as possible during sudden sops. Inuiively, hese are bubbles ha are large on average bu small during sudden sops. In our examples, we have already menioned ha he average values of k, c and y are in fac maximized in equilibria 4 and 5, in which b=b H. Among hese, equilibrium 4 displays boh a higher average and volailiy of hese variables. In paricular, even hough he values of k, c and y are subsanially higher in equilibrium 4 han in 5 during normal imes, he opposie is rue during sudden sops. The reason is ha d > in economy 5. This reduces volailiy

15 Asse Bubbles and Sudden Sops in a Small Open Economy 329 by making he bubble smaller during sudden sops, bu i also reduces invesmen and oupu by reducing bubble creaion during normal imes. This second resul is imporan o conras our conclusions wih hose obained from relaed models in he lieraure. In our model, a fall in asse prices during sudden sops is acually good for economic aciviy: given expeced asse prices, such a fall reduces paymens o foreigners and increases domesic resources available for invesmen. This follows in our seup because credi conracs are coningen and borrowing consrains depend on expeced asse prices. This is conrary o mos oher models in he lieraure, which assume ha borrowing consrains depend on conemporaneous asse prices. Thus, a fall in asse prices during sudden sops ighens borrowing consrains even furher, and leads o an even more severe drop in invesmen. A hird imporan poin illusraed by our example is ha, even hough all bubbles are differen, i is no possible o deermine wheher he marke will selec any specific one over he res. Thus, someimes he bubble susained by marke expecaions may be oo small, prevening he counry from aking advanage of foreign borrowing; a oher imes he bubble may be oo large, generaing large recessions during sudden sops. This raises he quesion of wheher policy can be used o improve upon he marke equilibrium. We now urn o his quesion, focusing on he specific role of capial conrols. 4. Managing capial flows We inroduce a governmen ha manages capial flows by inroducing capial conrols, i.e., axes and/or subsidies o foreign borrowing and/or repaymen. We hen use his modified model o ask wo key quesions: Can capial conrols be used o replicae a desired equilibrium bubble? If so, wha should hey look like? To address hese quesions, le us revisi he role played by he bubble in our economy. The bubble creaes a series of ransfers beween individuals. Curren borrowers use b of he funds borrowed oday o buy he bubble from previous borrowers, which in urn use his income o make paymens o foreigners. Bu he bubble also allows curren borrowers o increase heir foreign borrowing by Eb +, since hey will sell he bubble o fuure borrowers for a price ρ of b +, and hey will use his income o make addiional paymens o

16 33 Albero Marin and Jaume Venura foreigners. Of course, his las effec is absen during a sudden sop. Thus, from he perspecive of he counry as a whole hese ransfers generae he following funds for invesmen: () Equaion () summarizes he effec of a bubble on invesmen. In normal imes, he counry as a whole is paying foreigners wih a fracion of he funds ha i s borrowing from hem. The bubble herefore raises boh gross inflows and ouflows (i.e., paymens from foreigners o domesic residens and vice-versa). The bubble also raises he difference beween he wo, i.e., he increase in ne inflows provides resources ha can be leveraged o boos invesmen. During sudden sops, he presence of he bubble does no increase foreign borrowing, bu i does mean ha he paien young mus diver par of heir resources owards purchasing he bubble from he old. Thus, equaion () resaes he main resul of our examples: he bubble raises invesmen in normal imes bu deracs from i during sudden sops. In erms of maximizing invesmen, herefore, he ideal bubble is one ha enails he mos bubble creaion during normal imes while being as small as possible during sudden sops. Of course, nohing guaranees ha he marke will deliver his bubble, and his is where capial conrols may be of help. Assume ha he governmen imposes a lump-sum ax on foreign borrowing (or gross capial inflows) equal o p, where p can be sae coningen and p < indicaes a subsidy on borrowing. We assume iniially ha hese ax revenues are ransferred o previous borrowers so ha hey can make paymens o foreigners, i.e., axes on gross capial inflows go hand-in-hand wih subsidies on gross capial ouflows. In order o esablish an analogy wih he dynamics of he bubble, we can express he evoluion of p as: p + ( ρ + e+ ) p + m+ if z = N =, α ( α A k + + δ+ e+ ) p + m+ if z = S (2) such ha E e + and m + reflecs he ne wealh ha he policy ransfers o paien individuals of generaion. To see his, consider

17 Asse Bubbles and Sudden Sops in a Small Open Economy 33 an individual of generaion ha pays a ax p when borrowing during youh bu expecs o receive a subsidy p +, o be used for he repaymen of crediors, during old age. For such an individual, he policy represens a ransfer of presen-value wealh equal o, Em + Ep + = p if z = N ρ ρ. Em + Ep + A k + = p α z S α δ α A k + if = α δ + + Alhough equaion (2) has been deliberaely wrien so ha he evoluion of p mimics he evoluion of b in equaion (8), boh processes are no subjec o he same consrains. In paricular, whereas b and n mus be non-negaive, p and m can be eiher posiive or negaive: p < means ha he policy prescribes a subsidy on gross capial inflows a ime, and E m + < means ha in expecaion he policy exracs wealh from generaion. We are now ready o analyze he main effecs of capial conrols on our economy. Firs, he expecaion of subsidies on gross capial ouflows omorrow enables paien individuals o expand heir borrowing oday, i.e., curren borrowers can pledge boh he expeced value of heir firms and he expeced value of subsidies. Taking his ino accoun, we can re-wrie equaions (5) and (6) as follows: A α k+ = min s A k + f b p, α α ρ+ δ (3) f Ev = + Ep + + ρ if z if z = N = S (4) Equaions (3) and (4) are naural generalizaions of equaions (9) and () and hey illusrae he conflicing effecs of policy on capial accumulaion. Every period, he policy imposes axes on curren borrowers and gives i o previous borrowers so ha hey can make paymens o foreigners. This is he crowding-ou effec of he policy. During normal imes, hough, he policy also has a crowdingin effec because i allows curren borrowers o expand heir foreign

18 332 Albero Marin and Jaume Venura borrowing agains he expeced subsidies ha hey will receive a he ime of repaymen Ep +, which will be funded wih he axes of ρ fuure borrowers. In he aggregae, his policy generaes he following funds for invesmen: v p Ep p z N = + + if = ρ δ ρ p if z = S (5) To find equilibria in his economy, we ake an iniial condiion {k, b, z, p } and a sochasic process for {u, n, e, m } such ha E u + =,, and n + for all. If all possible sequences for {k, b, z, p } generaed in his way are such ha b and k, hen we have found an equilibrium of he model. Wha can a governmen achieve by adoping capial conrols? A crucial resul, which follows direcly from comparing equaions (9) and () wih equaions (3) and (4), is ha axes and subsidies on gross capial flows can be used o complemen or counerac flucuaions in he bubble. If he bubble is no high enough o ake full advanage of foreign funds during normal imes, a policy ha ses E m + > by axing gross capial inflows and subsidizing gross capial ouflows helps raise foreign borrowing. Such a policy amouns o a governmen guaranee on foreign paymens and, as long as he rae of economic growh is higher han he ineres rae, i can be designed o raise he wealh of borrowers a each poin in ime. During sudden sops, if he bubble is posiive, hereby divering funds from invesmen, a policy ha ses p < and axes gross capial ouflows is also useful. By reducing foreign paymens and ransferring resources o he paien young, such a policy raises he availabiliy of domesic resources for invesmen and fuels growh. Thus, alhough capial conrols do no direcly affec he equilibrium value of he bubble, hey do enable he governmen o selec an equilibrium allocaion among hose ha are feasible. We reurn o our example wih h= o see how his can be done. In paricular, we choose a policy rule ha maximizes oupu. In normal imes, his policy injecs sufficien collaeral o allow he economy o borrow unil he reurn on invesmen equals he world ineres rae. During sudden sops, borrowing is no possible and he goal of

19 Asse Bubbles and Sudden Sops in a Small Open Economy 333 policy is o offse he bubble and ensure ha all domesic savings are used for capial accumulaion. 6 The effecs of his policy rule can be analyzed by simulaing he economy for each of he equilibria considered in secion 3. Table 3 repors he mean and he sandard deviaion of k, y, c, f, and v for hese simulaions, where as figure 5 and 6 plos he simulaed series for k, c and f, v and p over a window of 2 periods. The main resul here is ha, as figure 5 shows, he evoluion of k, c and f is he same for all equilibria. Figure 6 shows ha, o aain he policy goals, axes on gross inflows and ouflows are coningen on he evoluion of he bubble. In paricular, axes on gross capial inflows are used o complemen bubble creaion during normal imes, raising collaeral and hus foreign borrowing. Taxes on gross capial ouflows are used insead during sudden sops o reduce paymens o foreigners in an amoun equal o he size of he bubble. By doing so, hey redirec resources away from foreign crediors and owards young borrowers, enabling hem o purchase he bubble wihou reducing invesmen. This example shows how bubbles provide a new raionale for capial conrols. When foreign borrowing is limied by he demand for funds, he governmen can complemen he exising bubble wih subsidies o capial ouflows. When foreign borrowing is insead limied by he exernal supply of funds, he governmen can reduce he bubble s impac on invesmen by axing capial ouflows. Noe ha his policy can be loosely inerpreed as an insurance or couner-cyclical fund, o which paien individuals conribue during youh in he expecaion of receiving a ransfer during old age if he bubble urns ou o be low. Bu his insurance is no acuarially fair, and his is a crucial aspec of he policy. If E m + >, as our proposed policy is during normal imes, i provides ne resources o he paien individuals of generaion, hereby enabling hem o expand heir foreign borrowing. If E m + <, i exracs ne resources from he paien individuals of generaion. This policy migh seem a odds wih he ype of capial conrols usually sressed in he lieraure, which are used in a prudenial fashion o reduce capial inflows during normal imes. In hose models, as we have menioned, capial inflows are inefficienly high during normal imes and conrols can be useful o reduce hem. In our model, insead, capial inflows are inefficienly low during normal imes because he economy suffers from a consan lack of collaeral. 6. In paricular, we assume ha he economy sars in k = k, b = b and z = N, and for a given sochasic process {u,n }, we define he following policy rule:

20 334 Albero Marin and Jaume Venura Figure 5. Simulaed ime series wih capial conrols Capial sock Foreign borrowing Consumpion Noes: Dashed lines show he ime series for Equilibrium (no bubble) wihou capial conrols.

21 Figure 6. Tax on capial inflows and firm values Equilibrium 2 Equilibrium 3 Equilibrium 4 Equilibrium 5 Tax on capial inflows Firm value Noe: Dashed lines show he ime series for Equilibrium (no bubble). 2 The same low ineres rae environmen ha gives rise o bubbles, however, makes i possible for he governmen o injec collaeral during normal imes by axing gross capial inflows and subsidizing gross capial ouflows. If r was higher han one, he ax dynamics in equaion (2) would require p o explode during normal imes, and his would violae our implici assumpion ha foreign borrowing canno exceed he maximum F. A final consideraion refers o he robusness of our resuls. We have assumed hroughou ha he governmen runs a balanced budge in he sense ha subsidies on capial ouflows are fully financed by levying axes on capial inflows. Nohing depends on his assumpion, however, and i is possible o show ha all of he resuls of his secion go hrough if he governmen finances subsidies by issuing deb.

22 f Mean Albero Marin and Jaume Venura Table 3. Summary saisics Equilibrium k Mean Sandard deviaion y Mean..... Sandard deviaion c Mean Sandard deviaion Sandard deviaion v Mean Sandard deviaion Alhough we refer he reader o our earlier work for a horough reamen of his issue, he inuiion behind his resul is ha deb has he same effecs on invesmen as he bubble does. 7 During normal 7. For a full reamen of he effecs of deb in his kind of model, see Marin and Venura (24a).

23 Asse Bubbles and Sudden Sops in a Small Open Economy 337 imes, a high expeced value of deb allows borrowers o obain more financing oday, because all else being equal higher expeced deb means ha hey will receive higher subsidies during old age. This is he crowding-in effec of deb. During sudden sops, however, deb has also a crowding-ou effec: alhough foreign borrowing collapses, he exising sock of deb mus sill be purchased by he paien young and i herefore divers resources away from invesmen. 5. Concluding remarks We live in a world of financial globalizaion and hisorically low ineres raes. These ineres raes creae he condiions for bubbles o exis, which in urn affec he size and direcion of capial flows. In his paper, we have developed an analyical framework o hink abou his inerplay, wih hree main resuls. Firs, he effecs of bubbles on economic aciviy depend on he circumsances a hand. During normal imes, when he supply of funds from he inernaional financial marke is high, bubbles raise ne capial inflows, invesmen and growh. During sudden sops, when foreign funding dries up, bubbles insead have a negaive effec on ne capial inflows and economic aciviy. Second, he bubble ha aains he opimal level of invesmen should herefore be large during normal imes and small during sudden sops. Bu bubbles are driven by marke expecaions, and nohing guaranees ha he equilibrium bubble will behave in he way ha i is desired. This leads o our hird resul, which says ha he governmen can replicae he desired bubble allocaion hrough he appropriae use of capial conrols. In paricular, we show ha i can maximize invesmen by subsidizing gross capial ouflows and axing gross capial inflows during normal imes while adoping he opposie policy during sudden sops. The framework developed here is closely relaed o models of financial fricions ha have been recenly used o advocae he usefulness of capial conrols. 8 And ye, is implicaions for policy are quie differen. The lieraure sresses he use of capial conrols in a prudenial fashion o reduce capial inflows during normal imes. Our model insead suggess ha policy inervenions should be used o boos inflows even furher during normal imes. The main reason behind his difference is ha we focus on a low ineres rae 8. For a survey of his lieraure, see Korinek (2).

24 338 Albero Marin and Jaume Venura environmen, in which bubbles are possible. This same assumpion guaranees ha he governmen can boos ne capial inflows, and hus foreign liabiliies, beyond heir equilibrium level. Basically, i can do so by using subsidies on gross capial ouflows o roll over foreign liabiliies during normal imes. Once he sudden sop comes, he policy is revered and gross capial ouflows are axed o raise domesic resources for invesmen. These resuls provide a rich view of he relaionship beween bubbles and capial flows, and heir implicaions for he design of policy. The framework has an imporan limiaion, however: i considers only he case of a small open economy. Relaxing his assumpion has crucial implicaions, boh from he perspecive of he economy ha we are considering and of he world as a whole. From he perspecive of our economy, abandoning his assumpion means ha i no longer faces a fully elasic supply of funds during normal imes. This means ha bubbles are unable o replicae he opimal level of invesmen even during normal imes, because hey raise he ineres rae faced by he counry so ha here is always boh a crowding-in and a crowding-ou effec. From he perspecive of he world as a whole, abandoning he small-open economy assumpion means ha capial conrols have effecs on hird counries. When an economy adops he policy analyzed here, i booss capial inflows for insance, hereby reducing he availabiliy of funds in he res of he world and raising he inernaional ineres rae. This lowers invesmen and growh in oher counries and, in a low-ineres rae environmen like he one ha we consider, i may generae severe crises in he res of he world by bursing exising bubbles. These global or sysemic issues are fundamenal. In Marin and Venura (24b), we develop a general equilibrium model of he world economy in order o address hem appropriaely.

25 Asse Bubbles and Sudden Sops in a Small Open Economy 339 Appendix Le j =,...,J be he paien young, and le l =,..., L be he paien old. The old sell heir firms o he young. The equilibrium prices of hese firms is v l and hey conain undepreciaed capial (_ d). k l. Since here is one firm per old, hey have he same index: l =,..., L. The young purchase hese firms and make addiional invesmens o build heir own firms. Since here is one firm per young, hey also have he same index: j =,...,J. L j now defined as he se of firms ha young purchases. He/she chooses i j, f j and L j so as o maximize: j K j j j Ec + = R+ k+ + Ev + ρ f (6) K α where R( + ) = α A k +. Maximizaion is subjec o hese consrains: j l j w = i + v f (7) l Lj ( ) j j l k+ = i + δ k (8) l Lj (9) These consrains are self-explanaory. We need o find a price process such ha, given his price process, maximizaion leads o marke-clearing. We propose he following one: j j j v = ( δ ) k + b (2) b j + j j j ( ρ + u + ) b + n + if z = N = K j j j ( R+ + δ + u + ) b + n+ if z = S (2) wih E u j + = and n j + >. Everybody expecs his sochasic process o drive prices. Le us see if markes clear when individuals maximize. The old are willing o sell a any price. Wha abou he young? We show nex ha hey are also willing o buy since hey are indifferen abou L j.

26 34 Albero Marin and Jaume Venura K Assume firs ha R + >r and he collaeral consrain is no binding. Then, using his price process and subsiuing consrains (7)-(9) ino he objecive funcion (6), we find ha: Wih hese prices, young j is indifferen abou L j. The old are happy o sell. K Assume nex ha R >r and he collaeral consrain is binding. + There are wo subcases here. Firs, assume we are in a sudden sop and f =. Using he price process and subsiuing consrains (7), (8) and (9) ino he objecive funcion (6), we find ha: j K l l Ec + = R+ ( w Σl L b )+( δ) ( w Σl L b j j )+ K l j j ( R + + δ) Σ l L b + En+ = ρ w + En + j Again, wih hese prices young j is indifferen abou L j. j Second, assume ha we are in normal imes and Ev + f =. ρ Using he price process and subsiuing consrains (7), (8) and (9) ino he objecive funcion (6), we find: j j K l l En Ec + = R+ w Σl L b + Σl Lb j j + ρ + = R K + w En + ρ Again, wih hese prices, young j is indifferen abou L j. Thus, we have reached he conclusion ha his price process is consisen wih maximizaion. Is his price process also consisen wih marke-clearing? I follows from he previous discussion ha demand and supply for firms mach wih his price process, bu here is a loose end in he discussion. In paricular, we have implicily assumed ha he upper limi on foreign borrowing F is never binding. To ensure his, firm prices canno grow oo much. And his, in urn, requires ha r be sufficienly low. We assume hroughou ha his is he case. Having proved now ha his price process is consisen wih boh maximizaion and marke-clearing, we can aggregae over j and l, obaining equaions (7) and (8) in he ex. j +

27 Asse Bubbles and Sudden Sops in a Small Open Economy 34 References Bianchi, J. 2. Overborrowing and Sysemic Exernaliies in he Business Cycle. American Economic Review, December 2, (7): Caballero, R. and A. Krishnamurhy. 2. Inernaional and Domesic Collaeral Consrains in a Model of Emerging Marke Crises. Journal of Moneary Economics 48(3): Cardarelli, R., S. Elekdag, and A. Kose, 29, Capial Inflows: Macroeconomic Implicaions and Policy responses, IMF Working Paper 9/4. Korinek, A. 2. The New Economics of Prudenial Capial Conrols. IMF Economic Review 59(3): Marin, A. and J. Venura. 24a. Managing Credi Bubbles. mimeo, CREI. Marin, A. and J. Venura. 24b. The Inernaional Transmission of Credi Bubbles: Theory and Policy. mimeo, CREI. Mendoza, E. 2. Sudden Sops, Financial Crises and Leverage. American Economic Review (5):