CIES Discussion Paper

Transcription

1 CIES Discussion Pape No. 99/15 Univesity of Adelaide Adelaide SA 5005 Austalia A KRUGMAN-DOOLEY-SACHS THIRD GENERATION MODEL OF THE ASIAN FINANCIAL CRISIS Gego Iwin and David Vines August 1999

2 2 CENTRE FOR INTERNATIONAL ECONOMIC STUDIES The Cente was established in 1989 by the Economics Depatment of the Univesity of Adelaide to stengthen teaching and eseach in the field of intenational economics and closely elated disciplines. Its specific objectives ae: to pomote individual and goup eseach by scholas within and outside the Univesity of Adelaide to stengthen undegaduate and post-gaduate education in this field to povide shote taining pogams in Austalia and elsewhee to conduct seminas, wokshops and confeences fo academics and fo the wide community to publish and pomote eseach esults to povide specialised consulting sevices to impove public undestanding of intenational economic issues, especially among policy makes and shapes Both theoetical and empiical, policy-oiented studies ae emphasised, with a paticula focus on developments within, o of elevance to, the Asia-Pacific egion. The Cente s Diecto is Pofesso Kym Andeson ( kym.andeson@adelaide.edu.au) and Deputy Diecto, D Randy Stinge ( andy.stinge@adelaide.edu.au) Futhe details and a list of publications ae available fom: Executive Assistant Cente fo Intenational Economic Studies Univesity of Adelaide Adelaide SA 5005 AUSTRALIA Telephone: (08) Facsimile: (08) [Intenational pefix: (+61 8)] jane.ussell@adelaide.edu.au Most publications can be downloaded fom ou Home page:

3 3 CIES Discussion Pape 99/15 A KRUGMAN-DOOLEY-SACHS THIRD GENERATION MODEL OF THE ASIAN FINANCIAL CRISIS Gego Iwin and David Vines Univesity of Oxfod gego.iwin@economics.ox.ac.uk Univesity of Oxfod, Austalian National Univesity, and CEPR Institute of Economics and Statistics Mano Rd, Oxfod, OX1 3UL United Kingdom Tel: Fax: david.vines@economics.ox.ac.uk Novembe 1999 We ae gateful to Mike Dooley, Geoge Fane, Ken Kletze, Paul Masson, Macus Mille, Adian Pagan, and Hyun Shin fo helpful discussions.

4 4 ABSTRACT This pape pesents a multiple-equilibium model of the Asian financial cisis. The economy has Kugman-style ove-investment caused by weak financial egulation and implicit govenment guaantees. Following Dooley, the govenment only has a limited capacity o willingness to honou such guaantees. The model has a unique long-un equilibium, with ove-investment. But in the shot un, in which the capital stock is fixed, it also has multiple equilibia. If lendes egad lending as low-isk, then it is. But if they egad lending as highisk and chage a highe inteest ate, then the costs of honouing guaantees ises, making the lending high-isk and the isk pemium self-justifying. We ague that this model usefully captues the ideas of panic and collapse which have been populaised in Sachs discussions of the Asian cisis. Keywods: Financial Cisis, Asian Economic Cisis, Ove-Investment, Multiple Equilibium. JEL: E44, F34, O16 Contact details: David Vines Univesity of Oxfod Institute of Economics and Statistics Mano Rd, Oxfod, OX1 3UL United Kingdom Tel: Fax: david.vines@economics.ox.ac.uk Gego Iwin Univesity of Oxfod Institute of Economics and Statistics Mano Rd, Oxfod, OX1 3UL United Kingdom gego.iwin@economics.ox.ac.uk

5 A KRUGMAN-DOOLEY-SACHS THIRD GENERATION MODEL OF THE ASIAN FINANCIAL CRISIS 1. Intoduction and Summay Gego Iwin and David Vines This pape pesents a multiple-equilibium model of the Asian financial cisis. It is designed to combine insights fom Kugman (1998), Dooley (1999a, 1999b), and Sachs (1995, 1996). 1 The East Asian financial cisis has been tuly emakable in moe ways than one. Suddenly the Asian miacle became the Asian cisis. But, moe than this, the existing models of cuency cisis wee poweless to explain what had happened. This was not a fist geneation cuency cisis bought about by excess budget deficits, as in Kugman (1979). No was the cisis caused by a conflict between the austeity needed to defend a fixed exchange ate and the expansion needed to emove high unemployment, as in Bitain s foced exit fom the ERM in 1992 (Eichengeen and Wyplocz, 1993). To undestand whateve happened to Asia a new thid geneation model is needed which puts cisis in the financial system at cente-stage. In the immediate aftemath of the cisis debate aged about whethe this thid geneation cisis was a poblem of panic and collapse, esulting fom a shift fom a good equilibium to a bad one (Radelet and Sachs, 1998), o, instead, a poblem esulting fom a wosening of fundamentals (Kugman, 1998). Kugman has geneously conceded defeat: I was wong (Kugman, 1999, p. 1) But in ou view (and Kugman s) a panic-and-collapse account of the Asian cisis needs to be undepinned by a stoy about what it was in the financial system that made the bad equilibium possible. This Radelet and Sachs did not povide. The pesent pape povides one possible candidate fo that stoy. The pape is set out as follows. The next sub-section sketches the model set-up and summaises ou agument. Then a shot additional intoductoy sub-section justifies ou multipleequilibium appoach, and discusses biefly the elationship between financial cisis and cuency cisis. The oles of financial intemediaies, the govenment, and foeign banks in ou basic model ae set out in section 2. The model is solved in section 3, fist fo the long un and 1 See also Radelet and Sachs (1998)

6 2 then fo the shot un, and we then conside the dynamic adjustment between the shot and long un. In Section 4 we conside how such a fomal model might be used as an aid to the undestanding of financial cises. An extension to the basic model is outlined in section 5, and finally some concluding emaks ae pesented in section The Agument Summaised Kugman s by-now-famous account of the failings of the Asian financial system, eleased on the web vey ealy into the cisis (Kugman, 1998), pesented to the wold his idea of Pangloss investment. He suggested that we think of a epesentative Asian county as facing a downwad-sloping demand cuve fo capital and that we model Asian cony capitalism as implicit govenment guaantees which ensue bailouts fo investments that make losses. Efficient investment equies that isk neutal investos should add to the capital stock to the point whee the expected maginal poduct of capital equals the given isk-fee wold inteest ate. But in the pesence of cedible guaantees, investos would ove-invest, to the point whee the maginal poduct of capital in the best state of the wold falls to the wold inteest ate. The eason fo this is that unexploited pofit oppotunities would emain if investment was not pushed this fa: in a bad state of the wold investos would stand to lose nothing (because of the bail-out povision), but in a good state investos would make pofits in excess of thei inteest obligations. The touble with this stoy is that it is not necessaily a stoy of cisis: if taxpayes can be pesuaded to go on paying fo the bailouts then such a set-up can go on epeating itself. It cetainly does not povide the basis fo a stoy of panic and collapse. Michael Dooley s pescient pape, pesented in late 1993 (and fothcoming as Dooley, 1999a), povides the missing link. Dooley agued that the Asian miacle, was, in effect, oganised theft; and that it might well end in a cisis. Dooley suggested that Asian govenments had essentially set themselves up to pay out on the kind of guaantees which Kugman late descibed (although he did not specify the downwad-sloping demand fo capital as Kugman late did). But in the cucial addition he suggested that the amount available fo such pay-outs was limited. Adjustment costs would mean that investos could not steal the money immediately. But in the end he thought they would set up enough pojects with negative expected etuns to walk away with the state s capacity to pay out ewads. When that happened, thee would be a cisis.

7 3 In this pape we show that when Dooley s insight is added to Kugman s analysis, the esult can be the kind of multiple equilibium outcome which Radelet and Sachs focussed on. To get the essential idea acoss, we set the stoy up as a seies of static, one-shot games played ove time. We model stochastic shocks in the envionment, as Kugman implicitly suggested we need to. We do this because we think that the aival of a negative extenal shock is an essential pat of the stoy of the Asian Cisis. 2 Thee ae Kugman-style investos financial intemediaies who aise funds by boowing fom foeign banks. Thee is an unegulated financial system in which financial intemediaies can default on loans at no cost to themselves, if things go bad. Thee is a govenment which implicitly guaantees the loans that financial intemediaies eceive fom aboad. Without guaantees investment is efficient, even though the financial secto is unegulated, because foeign banks simply aise inteest ates to cove the isk of financial intemediaies defaulting. But with cedible guaantees inteest ates ae kept low and it is this that causes the inefficiently high level of investment. If the guaantees ae fully cedible the inteest ate is pushed down to the isk-fee wold ate, and we move to a new high-debt equilibium this is what we call the Pangloss outcome. In ou model, as Dooley suggests, the govenment has a limited willingness to pay up on its guaantees if things go bad and so the guaantees may lack cedibility. We model the govenment s poblem by assuming it pays a one-off political cost if it eve eneges. The choice fo the govenment is between paying this cost o the taxation cost of bailing out the losses of financial intemediaies. The outcome is citically dependent on the political cost of eneging and so to genealise the model we assume foeign banks have incomplete infomation about this cost. Fo the Pangloss outcome to be the long-un equilibium of the system the govenment must be willing to bail out all of the losses which would be incued in bad states of the wold at the highe equilibium debt level (and so the cost of eneging must be sufficiently high). Altenatively, if this implicit fiscal obligation wee to become too lage, ational foeign banks would still build a isk pemium into the inteest ate which they demanded ove and above the wold inteest ate; as a esult the long-un equilibium of the capital stock would be less high, although still above the pe-guaantee level. In Section 3.1 of the pape we chaacteise the

8 4 long-un equilibium of the system, showing how it depends on the cost of eneging and othe paametes, and we show that it is unique. In Section 3.2, and subsequently, we exploe the panic-and-cisis featue of such a set-up. Even if the Pangloss outcome is the unique long-un equilibium, multiple equilibia may exist in the shot un. Because of the shot-un inflexibility of the stock of capital due to adjustment costs thee is always the following isk. The economy has at any point of time a paticula stock of capital. Suppose also that thee is no isk of default and that the equilibium inteest ate is equal to the wold ate. Let thee be a poductivity shock to the economy. Then, by assumption, if the shock is a bad one, the govenment can affod to pay the guaantees. This is why the inteest ate can be in equilibium at the low wold level. Howeve with this set-up thee is also the possibility of financial collapse. If foeign banks believe thee is a ange of poductivity shocks that will foce the govenment to enege they will aise the inteest ate. But if they aise the inteest ate sufficiently it might be that the govenment has no choice but to enege, and so a cisis occus. In this set-up thee is a shot-un bank un poblem. With low inteest ates no poductivity shock can be bad enough to cause the govenment to enege on its guaantees. But with sufficiently high inteest ates it becomes impossible fo the govenment to pay up, thus validating the isk pemium which is the eason fo the high inteest ate. Hence this model has a self-fulfilling cisis possibility, the eason fo which is the endogeneity of the isk pemium on loans to the county. This entes non-linealy into the model, in such a way as to give the possibility of multiple equilibia, in exactly the same way that expectations of exchange ate collapse ente into the multiple-equilibium cuency cisis models. Multiple equilibia exist in the shot-un, but not in the long-un. In the long-un, high inteest ates mean that much less capital is invested in the county, and this effect is stong enough to mean that the costs of paying out on the guaantees in the high inteest case would be no highe than in the low inteest ate case, thus emoving the poblem. But the ealistic assumption that thee is a shot-un in which isk pemia can be instantly adjusted but in which the capital stock is effectively pedetemined means that the model is one which is vulneable to an equilibium poblem. 1.2 Why Multiple Equilibia and What of Cuency Cises? 2 By doing this we answe in the affimative the question posed by Kletze (1999) in his comment on the Dooley pape. Kletze called fo fomalisation of the pape in ode to see if the Dooley stoy equies, fo

9 5 It is woth conceding immediately that ou multiple-equilibium appoach to the analysis of panics is a contested one. Dooley (1998) has been deeply citical of it, and so, ealie, was Kugman (1996). Dooley s complaints ae woth quoting in detail: The absence of clea thinking on this issue, and the failue to develop fundamentalsbased models which illuminate it, ha[s] led to the gowth of a plethoa multiple equilibium models, of which thee ae too many, none of which ae popely testable, not least because they do not model the data. A etun to fundamentals based models eally is advisable, patly in ode to e-check whethe any model exists which will actually fit the data. The modelling challenge now is to ty to constuct a new geneation of fist geneation fundamentals-based models which will meet this test. Multiple equilibium models may be mathematically inteesting. Howeve they ae almost cetainly unnecessay. (Comments by Dooley, epoted in Global Economic Institutions, 1998, p. 14). Mois and Shin (1998, 1999) ae also citical: the multiple equilibium appoach is vulneable to the chage that it does not fully explain a cuency attack, since the shift in beliefs which leads to the shift fom one equilibium to anothe is left unexplained. In shot, thee is an indeteminacy in the theoy (Mois and Shin, 1999, p. 3) As a esult, these authos choose to model the panic-and-collapse issue in a diffeent way. They focus on a paticula fom of stategic complementaity between speculatos the expected pofitability to one speculato fom selling depends positively on the numbe of othe speculatos who ae selling and ague that as a esult of this thee can be beak-points : on one side of a paticula level of the fundamentals a system is safe, but immediately beyond this level the system spectaculaly collapses. Nevetheless, we believe (and now Kugman does too) in opposition to Mois and Shin and (on this issue) to Dooley, that the multiple equilibium appoach is impotant. Both Stan Fische and Joe Stiglitz, espectively Fist Deputy Managing Diecto of the IMF and Chief Economist of the Wold Bank, have made multiple equilibium models the basis of thei poposals fo efom of the intenational monetay and financial system. (Fische, 1999; Stiglitz, 1998) As Fische wites, expanding on the ole of a cisis manage: In a panic, it is necessay to find some means fo dealing with the collective action completeness, to be located in a stochastic wold. We think that it does.

10 6 poblem. A panic is the ealisation of a bad equilibium when a good equilibium is possible, and thee is a need in such situations fo some agency o goup of institutions to take the lead in tying to stee the economy to the good equilibium. (Fische, 1999, p. 3, italics added) In this pape we do not have any good theoy of how o why the economy might flip fom the good equilibium to the bad one (let alone any theoy of what a cisis mange might do in esponse to this). But, in eveyday life we eadily admit that we have no good theoy of why a paticula dive ends up dead in a motoway pileup while he fiend, who left home at the same time, aives safely. To simply ague that such a view uns against ou theoetical scuples against indeteminacy (Mois and Shin, 1999, p. 3) seems to imply a vey paticula philosophy of science. We stick fo the pesent to ou view that multiple equilibium appoaches, such as the one that we pesent, can be illuminating, even if incomplete. 3 In two elated papes, one of us has pesented an extensive infomal account of the Asian cisis which focuses on the inteconnections between financial and cuency cisis, and agues that cisis became so sevee because of these inteconnections. (Cobett and Vines, 1999a,b) The citical exta featue esulting fom this inteconnection was we ague that the fixed exchange ate egimes pusued in Asia befoe the cisis induced massive unhedged boowing in foeign cuency. When the cuency depeciated this aised the buden of that boowing and led to a wosening of the financial cisis. In the pesent pape ou pupose is moe limited, focused, and fomal. We put cuency cises entiely to one side, and instead seek to exploe fomally the undepinnings of the financial cisis. We do this because we think that the stoy in this pape descibes what happened at the onset of the cisis. 2. The Basic Model We assume that poduction is Cobb-Douglas in fom: Y = AK L α 1 α whee A U[0,1] is a poductivity shock, ealised afte investment decisions ae made, and K 3 Ou modelling stategy is thus diametically opposed to that of Mois and Shin. Unlike Mois and Shin we do not model quantity inteactions between speculatos, but instead we focus on stategic inteactions between lendes (foeign banks) and the govenment. Also, instead of opeating, as they do, in quantity space, we opeate in pice space : we place the isk-pemium-adjusted inteest-paity condition at the coe of ou analysis. Ou poblem with the Mois and Shin appoach with which we othewise have a lot of sympathy is that so fa it has been applied only in a model with vey spasely specified economic featues. Including an endogenous isk pemium which is at the cente of ou teatment within the stategic inteactions of thei model at pesent looks to be feociously difficult. But if it could be done the esulting pictue could be vey useful.

11 7 and L ae capital and labou inputs. All poductive capital is owned by (many) domestic financial intemediaies who finance the entie capital stock by boowing fom foeign banks. We make thee key assumptions about this debt. (i) The pincipal is always ecoveable. (ii) Financial intemediaies make inteest payments if they have the funds to do so. To the extent that they have insufficient funds they can default without cost (effectively we assume that bankuptcy costs ae zeo). (iii) Initially the govenment guaantees the debt of financial intemediaies by pomising to make up any shotfall in the inteest payment. This obligation might tun out to be extemely costly and so the guaantee may not be fully cedible. To keep the model simple we assume labou is supplied inelastically. With the labou supply nomalised to one we can wite: α Y = AD whee D is the debt stock. In this model thee ae thee key goups financial intemediaies, the govenment, and foeign banks each of which ae examined in tun below Financial Intemediaies Financial intemediaies make pofits, π, when the capital shae of output exceeds inteest payments to foeign banks: 4 α π = αad D Because the ownes of financial intemediaies suffe no penalty if thei company makes a loss, thee will be an incentive to continue accumulating debt as long as pofits ae positive in the best state of the wold ( A = 1). We can use this investment ule to pin down the equilibium debt stock in the long un, LR D, as a function of the inteest ate: (1) D LR 1 1 α = ( α / ) (2) We assume that adjustment costs (not modelled explicitly) pevent debt fom accumulating 4 In a competitive labou maket wokes eceive eal wages equal to thei maginal poduct.

12 8 instantly to the long un level. Consequently, we can wite the level of debt at the beginning of any peiod as: D = D ϕ D ϕ > 0 (3) LR 1 + ( D ) 1 The long-un debt level, given by equation (2), exceeds the efficient debt level at which the expected maginal poduct of capital equals the inteest ate: D * 1 1 α = ( α / 2) (4) 2 D * ( ) D LR () 0 Figue 1 D' D' ' D In Figue 1 we compae the long un value of debt which esults fom efficient investment, D * ( ), with the debt level that esults fom the excessive investment in this unegulated financial system, D LR () (the invese functions ae shown fo each). Fo futue efeence it is useful to define D ' and D '' as the debt levels that would esult if boowes faced the isk-fee wold ate of inteest,, in each case. By substitution into (4) and (2) espectively: 1 1 α = ( α / 2) 1 α D ' and D '' = ( α / ) (5) D '' is the debt level associated with the Pangloss outcome discussed in the intoduction Govenment Initially the govenment guaantees the inteest payments by financial intemediaies to foeign banks. If the govenment honous the guaantee, it must aise sufficient funds though taxation

13 9 to pay fo this. Fom (1) the taxation cost of the guaantee is: 5 T = D αad α This commitment might tun out to be extemely costly, in paticula if is high and/o A is low (a bad poductivity shock). Altenatively, we assume the govenment can choose to enege on the guaantee, but if it does so it must pay a one-off fixed cost. As this is a one-off cost, eneging by the govenment absolves it of all futue commitments to foeign banks. (6) The cost of eneging on the guaantee can be egaded as political. Such an action is likely to be costly as it will educe the cedibility of the govenment, not just in the eyes of foeign banks, but in all policy aeas. Altenatively, this cost can be egaded as esulting fom the govenment falling out with its conies in the financial secto who benefit fom the low inteest ate that esults fom a cedible guaantee. To make the model moe inteesting we assume the foeign banks have incomplete infomation about the cost of eneging. Fo simplicity we assume the govenment is one of two possible types: with pobability x the govenment is typical and the cost of eneging is equal to V (a finite numbe); o, with pobability 1 x, the govenment is esolute and neve eneges as the cost of doing so is infinite. As the labels suggest, we focus on situations whee the govenment is moe likely to be of the fome type and so x is close to one. We will demonstate, howeve, that even a low pobability that the govenment is esolute can have inteesting implications. In section 5 we discuss how altenative assumptions egading the stuctue of the incomplete infomation affect ou conclusions. A typical govenment effectively faces an optimal stopping poblem. Each peiod it can eithe enege and pay the one-off cost, V, o altenatively it can honou the guaantee and pay the taxation cost T. If it takes this second couse of action the govenment incus an additional liability equal to the expected pesent-value cost of the guaantee in the subsequent peiod. We epesent the poblem fo the govenment as choosing the action which minimises the following cost function: G [ V, T + E C (, D, A, D )] G C t + ( t, Dt, At ) = min t δ t t+ 1 t+ 1 t+ 1 t 1 t t (7) 5 T can be egaded as a lump-sum tax on the labou foce. The linea fom of equation (6) has been chosen fo analytical convenience. Moe geneally, to the extent that taxes ae distotionay, highe taxation will have a negative effect on output. Also, following a low poductivity shock which educes output, aising a given level of taxation will be moe difficult, as both MPL and wages fall. Both factos suggest that aising highe taxes will become pogessively moe difficult.

14 10 whee δ is the discount facto, T is the taxation cost of honouing the guaantee (given by G equation 6), and EC 1 () is the expected cost of the guaantee next peiod if the govenment t+ honous the guaantee this peiod. This optimal stopping poblem is extemely complicated. In this pape we simplify by assuming that δ = 0. In doing so we make the analysis tactable, but at the expense of ignoing one channel though which and D affect the behaviou of the govenment. 6 Given δ = 0 a typical govenment will enege on its guaantee if T > V. Substituting fo T, we get the esult that a typical govenment will only fulfil the guaantee when the poductivity shock is above a tigge level, A, whee, 0 when V D 1 α α A = ( / α) D ( V / α) D when D αd α < V < D (8) 1 when V D αd α A ( ) A ( ) 0 1 A Figue 2a 0 1 A Figue 2b Figue 2a shows how the tigge level, A, vaies with at any given peiod in time in which the value of D is given (i.e. in the shot un). This tigge value fo the poductivity shock, A, is (linealy) inceasing in the inteest ate,, simply because highe inteest ates make guaantees moe costly to honou, meaning that they will be honoued in a smalle popotion of cicumstances. It is also, fo obvious easons, deceasing in the political cost of eneging on the guaantee, V, and (non-linealy) inceasing in the (given) debt stock, D, since a highe D means 6 The model can be solved with δ > 0 if we assume the govenment believes and D will emain unchanged in futue peiods. In this case the govenment will enege on its guaantee if T > ( 1 δ ) V. The esults ae qualitatively simila.

15 11 that a smalle popotion of guaantees can be honoued. The dependence of A on in the long un is diffeent, howeve, once we allow fo the fact that in the long un D depends on. Recall that in the long un the debt stock is given by equation (2). Substituting this in (8) we get: 0 when V α 1-α α 1 1 α α 1 α A = 1 ( V / α)( / α) when 0 < V < α 1-α α 1 1 α (9) 1 when V 0 This elationship is plotted in Figue 2b. Now A is deceasing in ; this is because in the long un highe inteest ates cause financial intemediaies to educe thei debt levels, loweing the cost of guaantees, and thus meaning that a typical govenment can honou them in a lage popotion of cicumstances Foeign Banks Foeign banks lend elastically to financial intemediaies at a mak-up ove the isk-fee wold inteest ate, (exogenous and constant): = /( 1 q) whee 0 q 1 is the expected pecentage default on the inteest payment. This condition must hold continuously as foeign banks ae assumed to be competitive and isk neutal; banks ae unable to chage a highe ate, even when poductivity is high, as we assume financial intemediaies can change lende at any time without cost. 8 (10) The expected pecentage default will depend both on the expected evenues of financial intemediaies and the pobability that the govenment will honou its guaantee. Foeign banks know that if the govenment is esolute it always honou its guaantees. On the othe hand, foeign banks will know that if the govenment is typical it might enege if the poductivity shock is sufficiently advese and the cost of the bail out is too high. Suppose that foeign banks believe a typical govenment will honou the guaantee if poductivity is above a theshold 7 This elationship may be non-linea, with eithe a positive o negative second deivative, depending on α. In figue 2b we show the linea intemediate case when α =1/ 2. 8 We also assume that thee is no possibility of financial intemediaies colluding with foeign banks to aise the inteest ate stategically so as to exploit the govenment s vulneability to paying out guaantees.

16 12 level Â. Then: 9 q = x D Aˆ 0 ( D αad ˆ ( ˆ 2 = xa xαa D α 1 α ) da ) /(2) Equations (10) and (11) ae simultaneous in and q. Solving fo we get: ˆ 2 2 xαa D = 2(1 xaˆ) α 1 (11) (12) In Figue 3a we plot how depends on Â, fo a given level of D (i.e. in the shot un). Fo D > D' (we see late that this is the elevant ange of inteest) and with x = 1 (the govenment is typical fo sue) the elationship is upwad sloping and concave, going fom to infinity as  goes fom zeo to one. The easons fo this ae as follows: (i) As  ises, bailout pomises will be honoued fo a smalle popotion of the ange 0 A 1. This means that q, and so, will be highe. See the (linea) tem in  in the denominato of (12). (ii) But this effect is dampened because the expected pecentage default also falls when  ises because the inteest payments that ae made if thee is default go up. This is captued by the (quadatic) tem in  in the numeato of (11) and in the numeato of (12). When x < 1, is finite when A ˆ = 1. The eason fo this is that even if A ˆ = 1 thee is a non-zeo pobability that the govenment is esolute and will theefoe honou the guaantee, and so the expected pecentage default is less than one. The value of when A ˆ = 1 is inceasing in both x and D. (A) (A) A 0 1 A Figue 3a Figue 3b α Stictly, equation (11) is only coect if D > αaˆ D. Fom (8) we can detemine that this is necessaily

17 13 The dependence of on  is diffeent once we allow fo the fact that in the long un D depends on (equation 2). By substitution into (12): 2 = 2(1 xaˆ) + xaˆ 2 (13) This elationship is plotted in Figue 3b. Now inceases with Â. The eason fo this is that D falls as  and ise, meaning that the popotion of inteest which can be ecoveed if thee is default inceases, so modeating the incease in the inteest ate which is necessay as  inceases. 3. Model Solution The model is closed with the equilibium condition: A ˆ A = In this section we analyse the model solution in the long un, and then the shot un, befoe integating the analysis in sub-section 3.3. (14) 3.1. Long-Run Equilibium We have two elationships which must hold in the long-un equilibium. Fist, equation (9) shows how the tigge value of a typical govenment, A, changes with the inteest ate. Second, equations (13) and (14) show how foeign banks set the inteest ate as a function of the expected tigge value, Â, which in equilibium must equal the actual tigge value, A. We can plot both functions on the same diagam to detemine the equilibium. An example of an inteio solution is shown in figue 4 below. Although it is not possible to deive a educed fom solution we can deduce that, fo all V > 0, thee is necessaily a unique equilibium in which A < 1. This follows because is inceasing in A, whilst A is deceasing in, and A( ) is defined fo all > 0. This is sufficient to ensue a unique point of intesection. =1 A A ( ) tue in any equilibium. unique eqm 2

18 14 In figue 4 we have shown an inteio solution. Fom (13), if we have a bounday solution with A = 0, then the inteest ate,, will equal the wold inteest ate, (this makes sense as A = 0 means that the govenment guaantee is fully cedible). Fom (9) we can wite the following condition fo a long-un bounday solution with inteest ates at wold levels: V α 1 1 α 1 α α The unique long-un equilibium is theefoe the Pangloss outcome if the cost to a typical govenment of eneging on the guaantee, V, is sufficiently high. Fo expositional puposes, and to shapen ou point, we assume in the est of this pape that this condition holds. (15) We can now also detemine the pe-guaantee equilibium. As the govenment does not bail out the losses of financial intemediaies, x = 1 and V = 0. As a consequence of (9) and (14), A =1. Fom (13) = 2, and so by substitution into (2) we obtain: 1 α D = ( α / 2) = D' 1 The pe-guaantee debt level equals the efficient debt level at the wold inteest ate, given by D ' in equation (5), even though the financial secto is pooly egulated and bankuptcy costs ae zeo. The only diffeences between each outcome ae that the isk is tansfeed fom one goup of isk-neutal agents to anothe (financial intemediaies to foeign banks) and inteest ates ise to equate expected pay-offs in each case Shot-Run Equilibium We also have two elationships which must hold in a shot-un equilibium. Fist, equation (8) shows how the tigge value of a typical govenment changes with the inteest ate. Second, equations (12) and (14) taken togethe show how foeign banks set the inteest ate as a function of the expected tigge value, Â, which in equilibium must equal the actual tigge

19 15 value, A. Given condition (15) we can chaacteise the shot-un equilibia of the model as follows. (i) When D ' D < D thee is a unique bounday-solution equilibium with = and A = 0 ( D is defined and discussed below). (ii) When D D we have multiple equilibia: a good bounday-solution equilibium with = and A = 0 ; an unstable equilibium with > and 0 < A < 1 ; and a collapse equilibium with > and A = 1. To pove the existence of a bounday-solution with equies = it is sufficient to show that A( ) > 0 >. Fom equation (8) A ( ) > 0 equies V D, and so a sufficient condition fo the existence of a bounday solution is that V > D. Ove the ange of inteest, D' D D' ', this condition is stonge than (15) and so we assume it holds. Given condition (15), then, thee must always exist a shot-un equilibium in which the govenment honous the guaantee fo sue ( A = 0 ) as is the case in the unique long-un equilibium deived in the pevious section. The possibility of multiple shot-un equilibia is demonstated in figue 5a. Fom (8) A is inceasing in. Fo multiple equilibia to exist, then, we equie that in the limit as A tends to one (A) exceeds the minimum inteest ate necessay so that A ( ) = 1. If this condition is satisfied then we have thee equilibium points of intesection between the functions A ( ) and (A), as shown in figue 5a. 10 If this condition fails, then we have a unique bounday solution equilibium, as shown in figue 5b. collapse eqm =1 A =1 A A ( ) unstable eqm A ( ) good eqm (A) unique eqm (A) 10 0 We can ule out moe than thee equilibia A 0 as the function (A) is not inflective at any point ove A the Figue elevant ange 5a fo A. Figue 5b

20 16 The value of as  tends to one is inceasing in D. This means that fo low levels of D we might have a unique equilibium, but fo highe levels of D we have multiple equilibia. We define D as the minimum debt level necessay fo multiple equilibia to exist. To detemine D we fist solve fo the lowest in (8) at which A ( ) = 1. We then equate this to in (12) with A ˆ = 1. Fom (12) we can see that when A ˆ = 1 finite equies x < 1. Assuming this, afte some simplification we get the following condition fo D : α 2 (1 x) V 2D + (2 x) αd = 0 (16) Unfotunately, we cannot geneally solve fo D, but by implicit diffeentiation we can deduce the following: D x < 0 D and 0 V Fom (16) we can also deduce that in the limit as x tends to one, D tends to D ' (fom above). When x = 1, tends to infinity when  tends to one, except in the special case whee D = D', in which case equilibium when = 2. This means that when x = 1 we have a unique bounday solution D = D', but have multiple equilibia fo highe debt levels. We do not explicitly analyse the dynamics of adjustment to the shot un equilibium, since what is depicted is an equilibium configuation athe than an outcome of the one-shot game which depends on the ealisation of the shock to A. Nevetheless it is clea fom Figue 5a that the bounday solution at is stable, in the sense that a mistaken conjectue about  would lead to an inteest ate and in tun a quit point A ( ) which was close to zeo than the initial conjectue. In a simila fashion we can deduce that any collapse equilibium will be stable, but an inteio equilibium with 0 < A < 1 will be unstable, in the sense that any inteest ate above o below this equilibium would lead to cumulative changes in A and away fom equilibium. In the est of this pape we pimaily focus on the stable equilibia Dynamic Adjustment In figue 6 we show both long-un and shot-un equilibia and indicate how adjustment occus

21 17 towads the new long-un equilibium once the guaantee is intoduced. collapse SR eqm locus 2 Peguaantee LR eqm 0 D = D' D = D Figue 6 unstable SR eqm locus good SR eqm locus D = D' ' Postguaantee LR eqm D Befoe the guaantee thee is a unique long-un equilibium with D = D' and = 2. Once the guaantee is intoduced we move to a new egime in which, poviding condition (15) holds, the long-un equilibium inteest ate is, and this Pangloss long-un equilibium. D LR = D' '. The debt stock begins to ise towads As discussed above, immediately following the intoduction of the guaantee (when we have a unique shot-un equilibium with unique bounday solution equilibium poviding D = D' ) =. As the debt stock ises thee will be a D < D. Fo all D D we have multiple shot-un equilibia, as indicated by the good, unstable, and collapse shot-un equilibium loci in figue 6. We can now give a dynamic account of the effect of intoducing a guaantee. As thee is a unique shot-un equilibium when D = D', the inteest ate will immediately fall so that = and the debt stock will begin to ise. As long as D ' D < D the unique shot un equilibium implies =, but at debt levels above D the dynamics of the model ae complicated by the multiple shot-un equilibia. If the economy emains at the good equilibium each peiod then the debt stock will gadually incease and the economy will convege to the Pangloss outcome. But at any point in time it can flip to the collapse equilibium, which will ceate a financial cisis (see below). In this model we cannot say whethe the economy will, at any point in time, emain at a good equilibium o flip to the collapse equilibium. But the pobability of such a

22 18 flip can plausibly be asseted to be non-zeo at any point in time, if such a flip has not aleady happened. 4. Undestanding Financial Cises In this model, if the govenment is typical, then a financial cisis is inevitable, even if its timing is unpedictable. 11 To undestand this conside figue 6 once again. Immediately following the intoduction of this bailout policy the inteest ate falls to (this is the unique shot-un equilibium when D = D' ). The debt stock stats to ise, diven by the lowe inteest ate. Given that A = 0 when = the govenment stands by its pomise to bail out any losses fo sue. When the debt stock ises above D, howeve, multiple equilibia exist. If the good equilibium is maintained then the debt stock will continue to ise towads the long-un equilibium level at which D = D' '. Both duing this tansition, and at the long-un equilibium itself, multiple shot-un equilibia exist, with the possibility of a switch to the collapse equilibium. Such a switch must inevitably happen povided only that the pobability of it emains positive at any point in time. What is a financial cisis in this model? A financial cisis occus if a typical govenment is foced to enege on its commitment to bail-out financial intemediaies. This is only possible when A > 0, and fo sufficiently high V (equation 15) this is only tue fo the unstable and collapse equilibia. In the case of the collapse equilibium A = 1 and a typical govenment will enege on the guaantee fo sue. Why does eneging pecipitate a cisis? The high debt level in this economy is diven by a eduction in the inteest ate as foeign banks expect a lowe default ate on inteest payments given the govenment guaantee. By assumption, if the govenment eve eneges, it pays a oneoff political cost; subsequently the govenment faces no additional penalty should it not compensate foeign banks fo futhe default by financial intemediaies. Effectively, then, we can ague that following a cisis V etuns to zeo and the long-un equilibium debt stock falls to the pe-guaantee level so that D LR = D'. A lowe debt stock means a lowe capital stock and theefoe lowe output. A key chaacteistic of the financial cisis, then, is a collapse in output which follows fom the discete jump in the long-un equilibium when the govenment 11 Stictly, fo low x and high V a financial cisis may not be inevitable if D > D' '. This case is not

23 19 is foced to enege. 12 Why is a cisis inevitable when the govenment is typical? Once the guaantee is intoduced the inteest ate is depessed and financial intemediaies have an incentive to take out moe debt and incease investment. At highe debt levels multiple equilibia exist. Even though initially the good equilibium may be the most likely, we can neve ule out the possibility of a switch to the collapse equilibium. 13 The cisis is inevitable because as soon as the guaantee is intoduced D ises and when D D the multiplicity of equilibia occus which pesists until the govenment is foced to enege. Even if the pobability of cisis at any paticula time is low, a cisis must occu eventually with pobability equal to one. 5. Extension In this pape we have demonstated how a govenment guaantee to undewite losses in a pooly-egulated financial secto (zeo capital equiements, zeo bankuptcy costs) can lead to ove-investment. When the debt stock ises sufficiently multiple shot-un equilibia exist: a good equilibium in which inteest ates ae low and the govenment honous the guaantee fo sue; an unstable equilibium with highe inteest ates and a positive (pehaps high) pobability that a typical govenment is foced to enege; and a collapse equilibium in which a typical govenment is foced to enege fo sue. In the last section we descibed how a financial cisis can occu, with a switch to the collapse equilibium, if the govenment is typical. When this occus thee will be a shap fall in the capital stock and long-un output as foeign banks withdaw thei funds. Until now we have assumed that the govenment is eithe typical with pobability x o esolute with pobability 1 x. Clealy, this analysis is sufficiently geneal to cove the complete infomation case whee the govenment is known to be typical fo sue ( x = 1). In this case D = D'+ε (whee ε is infinitesimally small) and so multiple equilibia exist immediately afte inteesting and so we ule it out. When x = 1, D is stictly less than D ''. 12 This aises the question of how adjustment to the new long-un equilibium occus. Immediately following the cisis thee is an excess supply of capital goods. We have assumed that the debt pincipal is not at isk and this equies that capital goods can be esold without any loss in value. This equies that capital goods can be expoted aboad, and that the economy is elatively small so that these expots do not depess the pice of capital goods. 13 The good equilibium will be moe likely than the collapse equilibium if we assume that discete jumps in the inteest ate ae less likely than continuous adjustment, except following a change in govenment policy (such as intoducing the guaantee).

24 20 the guaantee is intoduced. In this section we genealise the model futhe to conside the outcome when we have a less exteme fom of incomplete infomation. Suppose we ule out the possibility that the govenment is esolute and instead assume the cost of eneging is finite fo sue, but its exact value is unknown. Specifically, we assume V can take one of two values, HV o LV, with HV > LV. If this is the case it is possible that: (i) thee ae five shot-un equilibia, thee of which ae stable; and, (ii) foeign banks might lean about the govenment commitment to the guaantee (as eflected in the value of V) by obseving the outcome of mini-cises. To see how this is possible conside figue 7 below. On this diagam we show how the tigge value, A, changes with given each possible value fo V (as indicated by the subscipts). Fom (8) it is clea that fo a given inteest ate A LV AHV. In addition we show how changes with both A LV and A HV. This second function is dawn with a discontinuity and needs to be intepeted caefully. The lowe segment shows how changes with A LV conditional on A HV = 0. This uns fom when A LV = 0 (the govenment does not enege egadless of V and the ealisation fo A) to a finite value, *, when A = 1. This patten is simila to figue 5a; and we can show that * is an inceasing function of both the cuent debt level and the peceived pobability that the tue V is high. The uppe segment of the function shows how changes with A * HV conditional on A LV = 1. This uns fom when A HV = 0 to infinity in the limit as A HV tends to one. LV A HV ( A HV A LV = 1) ( ) =1 A * A LV ( ) 0 Figue 7 ( A LV A HV = 0) A LV, A HV

25 21 Fom the diagam we can see it is possible that five shot-un equilibia exist, thee of which ae stable. Fist, both the good and collapse equilibia exist as befoe. In the good equilibium =, but in the collapse case tends to infinity as both A LV and A HV tend to one. * In addition, howeve, we have a thid stable equilibium with =. In this equilibium A = 0 and A = 1, and so the govenment eneges fo sue if V is low, but honous the HV LV guaantee fo sue if V is high. This thid stable equilibium pesents us with the possibility that a mini-cisis can occu. To undestand this suppose V is actually high ( V = HV ). Initially we might expect capital (and debt) accumulation to occu at the good equilibium with =. Suppose, howeve, that fo some eason (pehaps a panic by foeign banks) the equilibium flips to the intemediate case with * =. In this situation low V would cause the govenment to enege, but as V is actually high the govenment honous the guaantee. By this action the govenment will demonstate to the foeign banks that V is not low and so in this way the foeign banks lean about V. In subsequent peiods, with complete infomation egading V, only two stable equilibia can exist: the economy can eithe flip to the collapse equilibium pecipitating a cisis, o evet to the good equilibium, defeing a collapse to a late date. If the latte occus then the jump in inteest ates fom to * is quickly evesed. 6. Concluding Remaks In this pape we have shown how an Asian-style financial cises can occu with a collapse in investment and output. Thee ae two key ingedients of this stoy. Fist, implicit govenment guaantees fuel moal-hazad diven excess investment, along the lines outlined by Kugman. Second, the govenment s limited willingness o ability to honous these guaantees means that they may not be fully cedible. When the guaantees ae fist intoduced the low debt level ensues that the govenment has sufficient capacity to honou the guaantees. But as the debt level ises the implicit fiscal obligation may become too lage if foeign banks aise inteest ates because of self-fulfilling expectations that the govenment will enege. The multipleequilibium featue of the model means that any collapse will be sudden. The end esult will be a shap fall in output and the capital stock to the pe-guaantee level.

26 22 Two questions emain to be answeed. Fist, why is it that the govenment intoduces the implicit guaantees in the fist place? In this model the pe-guaantee debt level and capital stock is efficient, but in a moe geneal model this need not be the case if thee is some sot of maket failue. Fo example, if thee ae positive extenalities fom foeign investment, such as technological spilloves, efficiency may equie a govenment subsidy (but not a blanket guaantee). Moe geneally, fo othe foms of maket failue a fist-best intevention by the govenment might be infeasible. This may povide a ationale fo some fom of guaantee as a second-best solution. Ou model suggests that the exact fom of govenment intevention must be caefully chosen as an inappopiate policy can have highly destabilising consequences. This leads to the second question: ae thee any stability ules which should estict the fom of govenment intevention? Refeences Ageno, Richad, Macus Mille, David Vines, and Axel Webe (1999) The Asian Financial Cises: Causes, Contagion, and Consequences. Cambidge: Cambidge Univesity Pess. P. Alba, A. Bahttachaya, S. Claessens, S. Ghosh, and L. Henandez (1998). The Role of Macoeconomic and Financial Secto Linkages in East Asia s Economic Cisis, fothcoming in Ageno, Mille, Webe and Vines (1999). Cobett, J. and D. Vines (1999a) Asian Cuency and Financial Cises: Lessons fom Vulneability, Cisis, and Collapse, fothcoming in Wold Economy, Januay Cobett, J. and D. Vines (1999b) The Asian Cisis as Vulneability and Collapse in the Tavese between Two Types of Capitalism fothcoming in Ageno, Mille, Webe and Vines (1999) Dooley, M. P. (1999a) Ae Recent Capital Inflows to Developing Counties a Vote fo o Against Economic Policy Refoms? Woking Pape #295 Univesity of Califonia Santa Cuz, Published in Exchange Rates, Capital Flows, and Monetay Policy in a Changing Wold Economy, William Guben, David Gould, and Calos Zaazaga, eds., Kluwe Academic Publishes, Boston, 1997, pp , and fothcoming in a evised fom in Ageno, Mille, Webe and Vines (1999) Dooley, M. P. (1999b) A Model of Cisis in Emeging Makets, Univesity Of Califonia

27 23 Santa Cuz, 1997, fothcoming. Eichengeen, B. and C. Wyplocz (1993) The Unstable EMS, Bookings Papes on Economic Activity no 1, pp Fische, S (1999) On the need fo an Intenational Lende of Last Resot. Pape pesented to the annual meetings of the Ameican Economic Association and available at Global Economic Institutions (1999) Financial Cises: Contagion and Volatility: Repot of a Confeence held in London on 8-9 May 1998, in Newslette of the Global Economic Institutions Reseach Pogamme, No 8, Octobe. London: Cente fo Economic Policy Reseach Kletze, K. (1999) Comment on Dooley (1999a), fothcoming in Ageno, Mille, Webe and Vines (1999) Kugman, (1996) P. Ae Cuency Cises Self-Fulfilling? in Benanke,-Ben-S.; Rotembeg,- Julio-J., eds. NBER Macoeconomics Annual. Cambidge and London: MIT Pess, pages Kugman, P. (1998a) Whateve Happened to Asia? Mois, S. and H. S. Shin (1998) Unique Equilibium in a Model of Self-Fulfilling Cuency Attacks Ameican Economic Review, vol 88, pp Mois, S. and H. S. Shin (1999) A Theoy of the Onset of Cuency Attacks fothcoming in Ageno, Mille, Webe and Vines (1999) Obstfeld, M.(1986) Rational and Self-Fulfilling Balance of Payments Cises ; Ameican Economic Review, Vol.76, pp (1991) The Destabilising Effects of Exchange Rate Escape Clauses ; NBER Woking Pape No (1994) The Logic of Cuency Cises ; NBER Woking Pape No (1995) Models of Cuency Cises with Self-Fulfilling Featues ; NBER Woking Pape No Ozkan, F.G. and Sutheland, A. (1993) A Model of the ERM Cisis ; Mimeo, Univesity of Yok (1994) A Cuency Cisis Model With an Optimising Govenment ; Mimeo, Univesity of Yok (1995) Policy Options fo a Cuency Cisis ; Economic Jounal; Vol.105, pp