No.
99/15
University of Adelaide • Adelaide • SA 5005 • AustraliaA KRUGMAN-DOOLEY-SACHS
THIRD GENERATION MODEL OF
THE ASIAN FINANCIAL CRISIS
Gregor Irwin and David Vines
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CIES Discussion Paper 99/15
A KRUGMAN-DOOLEY-SACHS
THIRD GENERATION MODEL
OF THE ASIAN FINANCIAL CRISIS
Gregor Irwin and David Vines
University of Oxford
Email: [email protected]
University of Oxford, Australian National University, and CEPR Institute of Economics and Statistics
Manor Rd, Oxford, OX1 3UL United Kingdom Tel: + 44 1865 271067 Fax: +44 1865 271094
Email: [email protected]
November 1999
We are grateful to Mike Dooley, George Fane, Ken Kletzer, Paul Masson, Marcus Miller, Adrian Pagan, and Hyun Shin for helpful discussions.
ABSTRACT
This paper presents a multiple-equilibrium model of the Asian financial crisis. The economy has Krugman-style over-investment caused by weak financial regulation and implicit government guarantees. Following Dooley, the government only has a limited capacity or willingness to honour such guarantees. The model has a unique long-run equilibrium, with over-investment. But in the short run, in which the capital stock is fixed, it also has multiple equilibria. If lenders regard lending as low-risk, then it is. But if they regard lending as high-risk and charge a higher interest rate, then the costs of honouring guarantees rises, making the lending high-risk and the risk premium self-justifying. We argue that this model usefully captures the ideas of panic and collapse which have been popularised in Sachs’ discussions of the Asian crisis.
Keywords: Financial Crisis, Asian Economic Crisis, Over-Investment, Multiple Equilibrium.
JEL: E44, F34, O16
Contact details:
David Vines Gregor Irwin
University of Oxford University of Oxford
Institute of Economics and Statistics Institute of Economics and Statistics Manor Rd, Oxford, OX1 3UL Manor Rd, Oxford, OX1 3UL United Kingdom United Kingdom
Tel: + 44 1865 271067 Fax: +44 1865 271094
OF THE ASIAN FINANCIAL CRISIS
Gregor Irwin and David Vines
1. Introduction and SummaryThis paper presents a multiple-equilibrium model of the Asian financial crisis. It is designed to combine insights from Krugman (1998), Dooley (1999a, 1999b), and Sachs (1995, 1996).1
The East Asian financial crisis has been truly remarkable in more ways than one. Suddenly the ‘Asian miracle’ became the ‘Asian crisis’. But, more than this, the existing models of currency crisis were powerless to explain what had happened. This was not a ‘first generation’ currency crisis brought about by excess budget deficits, as in Krugman (1979). Nor was the crisis caused by a conflict between the austerity needed to defend a fixed exchange rate and the expansion needed to remove high unemployment, as in Britain’s forced exit from the ERM in 1992 (Eichengreen and Wyplocz, 1993). To understand whatever happened to Asia a new ‘third generation’ model is needed which puts crisis in the financial system at centre-stage.
In the immediate aftermath of the crisis debate raged about whether this third generation crisis was a problem of panic and collapse, resulting from a shift from a ‘good’ equilibrium to a ‘bad’ one (Radelet and Sachs, 1998), or, instead, a problem resulting from a worsening of fundamentals (Krugman, 1998). Krugman has generously conceded defeat: ‘I was wrong’ (Krugman, 1999, p. 1) But in our view (and Krugman’s) a panic-and-collapse account of the Asian crisis needs to be underpinned by a story about what it was in the financial system that made the bad equilibrium possible. This Radelet and Sachs did not provide. The present paper provides one possible candidate for that story.
The paper is set out as follows. The next sub-section sketches the model set-up and summarises our argument. Then a short additional introductory sub-section justifies our multiple-equilibrium approach, and discusses briefly the relationship between financial crisis and currency crisis. The roles of financial intermediaries, the government, and foreign banks in our basic model are set out in section 2. The model is solved in section 3, first for the long run and
then for the short run, and we then consider the dynamic adjustment between the short and long run. In Section 4 we consider how such a formal model might be used as an aid to the understanding of financial crises. An extension to the basic model is outlined in section 5, and finally some concluding remarks are presented in section 6 .
1.1 The Argument Summarised
Krugman’s by-now-famous account of the failings of the Asian financial system, released on the web very early into the crisis (Krugman, 1998), presented to the world his idea of ‘Pangloss’ investment. He suggested that we think of a representative Asian country as facing a downward-sloping demand curve for capital and that we model Asian ‘crony capitalism’ as implicit government guarantees which ensure bailouts for investments that make losses. Efficient investment requires that risk neutral investors should add to the capital stock to the point where the expected marginal product of capital equals the given risk-free world interest rate. But in the presence of credible guarantees, investors would over-invest, to the point where the marginal product of capital in the best state of the world falls to the world interest rate. The reason for this is that unexploited profit opportunities would remain if investment was not pushed this far: in a bad state of the world investors would stand to lose nothing (because of the bail-out provision), but in a good state investors would make profits in excess of their interest obligations. The trouble with this story is that it is not necessarily a story of crisis: if taxpayers can be persuaded to go on paying for the bailouts then such a set-up can go on repeating itself. It certainly does not provide the basis for a story of panic and collapse.
Michael Dooley’s prescient paper, presented in late 1993 (and forthcoming as Dooley, 1999a), provides the missing link. Dooley argued that the Asian miracle, was, in effect, organised theft; and that it might well end in a crisis. Dooley suggested that Asian governments had essentially set themselves up to pay out on the kind of guarantees which Krugman later described (although he did not specify the downward-sloping demand for capital as Krugman later did). But – in the crucial addition – he suggested that the amount available for such pay-outs was limited. Adjustment costs would mean that investors could not steal the money immediately. But in the end – he thought – they would set up enough projects with negative expected returns to walk away with the state’s capacity to pay out rewards. When that happened, there would be a crisis.
In this paper we show that when Dooley’s insight is added to Krugman’s analysis, the result can be the kind of multiple equilibrium outcome which Radelet and Sachs focussed on.
To get the essential idea across, we set the story up as a series of static, one-shot games played over time. We model stochastic shocks in the environment, as Krugman implicitly suggested we need to. We do this because we think that the arrival of a negative external shock is an essential part of the story of the Asian Crisis.2 There are Krugman-style investors – financial intermediaries – who raise funds by borrowing from foreign banks. There is an unregulated financial system in which financial intermediaries can default on loans at no cost to themselves, if things go bad. There is a government which implicitly guarantees the loans that financial intermediaries receive from abroad. Without guarantees investment is efficient, even though the financial sector is unregulated, because foreign banks simply raise interest rates to cover the risk of financial intermediaries defaulting. But with credible guarantees interest rates are kept low and it is this that causes the inefficiently high level of investment. If the guarantees are fully credible the interest rate is pushed down to the risk-free world rate, and we move to a new high-debt equilibrium – this is what we call the Pangloss outcome.
In our model, as Dooley suggests, the government has a limited willingness to pay up on its guarantees if things go bad and so the guarantees may lack credibility. We model the government’s problem by assuming it pays a one-off political cost if it ever reneges. The choice for the government is between paying this cost or the taxation cost of bailing out the losses of financial intermediaries. The outcome is critically dependent on the political cost of reneging and so to generalise the model we assume foreign banks have incomplete information about this cost.
For the Pangloss outcome to be the long-run equilibrium of the system the government must be willing to bail out all of the losses which would be incurred in bad states of the world at the higher equilibrium debt level (and so the cost of reneging must be sufficiently high). Alternatively, if this implicit fiscal obligation were to become too large, rational foreign banks would still build a risk premium into the interest rate which they demanded over and above the world interest rate; as a result the long-run equilibrium of the capital stock would be less high, although still above the pre-guarantee level. In Section 3.1 of the paper we characterise the
long-run equilibrium of the system, showing how it depends on the cost of reneging and other parameters, and we show that it is unique.
In Section 3.2, and subsequently, we explore the panic-and-crisis feature of such a set-up. Even if the Pangloss outcome is the unique long-run equilibrium, multiple equilibria may exist in the short run. Because of the short-run inflexibility of the stock of capital – due to adjustment costs – there is always the following risk. The economy has at any point of time a particular stock of capital. Suppose also that there is no risk of default and that the equilibrium interest rate is equal to the world rate. Let there be a productivity shock to the economy. Then, by assumption, if the shock is a bad one, the government can afford to pay the guarantees. This is why the interest rate can be in equilibrium at the low world level. However with this set-up there is also the possibility of financial collapse. If foreign banks believe there is a range of productivity shocks that will force the government to renege they will raise the interest rate. But if they raise the interest rate sufficiently it might be that the government has no choice but to renege, and so a crisis occurs. In this set-up there is a short-run ‘bank run’ problem. With low interest rates no productivity shock can be bad enough to cause the government to renege on its guarantees. But with sufficiently high interest rates it becomes impossible for the government to pay up, thus validating the risk premium which is the reason for the high interest rate. Hence this model has a self-fulfilling crisis possibility, the reason for which is the endogeneity of the risk premium on loans to the country. This enters non-linearly into the model, in such a way as to give the possibility of multiple equilibria, in exactly the same way that expectations of exchange rate collapse enter into the multiple-equilibrium currency crisis models.
Multiple equilibria exist in the short-run, but not in the long-run. In the long-run, high interest rates mean that much less capital is invested in the country, and this effect is strong enough to mean that the costs of paying out on the guarantees in the high interest case would be no higher than in the low interest rate case, thus removing the problem. But the realistic assumption that there is a ‘short-run’ – in which risk premia can be instantly adjusted but in which the capital stock is effectively predetermined – means that the model is one which is vulnerable to an equilibrium problem.
1.2 Why Multiple Equilibria and What of Currency Crises?
2 By doing this we answer in the affirmative the question posed by Kletzer (1999) in his comment on the
It is worth conceding immediately that our multiple-equilibrium approach to the analysis of panics is a contested one. Dooley (1998) has been deeply critical of it, and so, earlier, was Krugman (1996). Dooley’s complaints are worth quoting in detail:
‘The absence of clear thinking on this issue, and the failure to develop fundamentals-based models which illuminate it, ha[s] led to the growth of a plethora multiple equilibrium models, of which there are too many, none of which are properly testable, not least because they do not “model” the data. A return to fundamentals based models really is advisable, partly in order to re-check whether any model exists which will actually fit the data. The modelling challenge now is to try to construct a new generation of “first generation” fundamentals-based models which will meet this test. Multiple equilibrium models may be mathematically interesting. However they are almost certainly unnecessary.’ (Comments by Dooley, reported in Global Economic Institutions, 1998, p. 14).
Morris and Shin (1998, 1999) are also critical:
‘the multiple equilibrium approach is vulnerable to the charge that it does not fully explain a currency attack, since the shift in beliefs which leads to the shift from one equilibrium to another is left unexplained. In short, there is an indeterminacy in the theory’ (Morris and Shin, 1999, p. 3)
As a result, these authors choose to model the panic-and-collapse issue in a different way. They focus on a particular form of strategic complementarity between speculators – the expected profitability to one speculator from selling depends positively on the number of other speculators who are selling – and argue that as a result of this there can be ‘break-points’: on one side of a particular level of the ‘fundamentals’ a system is safe, but immediately beyond this level the system spectacularly collapses.
Nevertheless, we believe (and now Krugman does too) in opposition to Morris and Shin and (on this issue) to Dooley, that the multiple equilibrium approach is important. Both Stan Fischer and Joe Stiglitz, respectively First Deputy Managing Director of the IMF and Chief Economist of the World Bank, have made multiple equilibrium models the basis of their proposals for reform of the international monetary and financial system. (Fischer, 1999; Stiglitz, 1998) As Fischer writes, expanding on the role of a crisis manager:
‘In a panic, it is necessary to find some means for dealing with the collective action
problem. A panic is the realisation of a bad equilibrium when a good equilibrium is possible, and there is a need in such situations for some agency or group of institutions to take the lead in trying to steer the economy to the good equilibrium.’ (Fischer, 1999, p. 3, italics added)
In this paper we do not have any good theory of how or why the economy might flip from the good equilibrium to the bad one (let alone any theory of what a crisis manger might do in response to this). But, in everyday life we readily admit that we have no good theory of why a particular driver ends up dead in a motorway pileup while her friend, who left home at the same time, arrives safely. To simply argue that ‘such a view runs against our theoretical scruples against indeterminacy’ (Morris and Shin, 1999, p. 3) seems to imply a very particular philosophy of science. We stick – for the present – to our view that multiple equilibrium approaches, such as the one that we present, can be illuminating, even if incomplete.3
In two related papers, one of us has presented an extensive informal account of the Asian crisis which focuses on the interconnections between financial and currency crisis, and argues that crisis became so severe because of these interconnections. (Corbett and Vines, 1999a,b) The critical extra feature resulting from this interconnection was – we argue – that the fixed exchange rate regimes pursued in Asia before the crisis induced massive unhedged borrowing in foreign currency. When the currency depreciated this raised the burden of that borrowing and led to a worsening of the financial crisis. In the present paper our purpose is more limited, focused, and formal. We put currency crises entirely to one side, and instead seek to explore formally the underpinnings of the financial crisis. We do this because we think that the story in this paper describes what happened at the onset of the crisis.
2. The Basic Model
We assume that production is Cobb-Douglas in form:
α α − = 1 L AK Y
where A~U[0,1] is a productivity shock, realised after investment decisions are made, and K
3 Our modelling strategy is thus diametrically opposed to that of Morris and Shin. Unlike Morris and Shin
we do not model quantity interactions between speculators, but instead we focus on strategic interactions between lenders (foreign banks) and the government. Also, instead of operating, as they do, in ‘quantity space’, we operate in ‘price space’: we place the risk-premium-adjusted interest-parity condition at the core of our analysis. Our problem with the Morris and Shin approach – with which we otherwise have a lot of sympathy – is that so far it has been applied only in a model with very sparsely specified economic features. Including an endogenous risk premium – which is at the centre of our treatment – within the strategic interactions of their model at present looks to be ferociously difficult. But if it could be done the resulting picture could be very useful.
and L are capital and labour inputs.
All productive capital is owned by (many) domestic financial intermediaries who finance the entire capital stock by borrowing from foreign banks. We make three key assumptions about this debt.
(i) The principal is always recoverable.
(ii) Financial intermediaries make interest 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 bankruptcy costs are zero).
(iii) Initially the government guarantees the debt of financial intermediaries by promising to make up any shortfall in the interest payment. This obligation might turn out to be extremely costly and so the guarantee may not be fully credible.
To keep the model simple we assume labour is supplied inelastically. With the labour supply normalised to one we can write:
α
AD Y =
where D is the debt stock.
In this model there are three key groups – financial intermediaries, the government, and foreign banks – each of which are examined in turn below.
2.1. Financial Intermediaries
Financial intermediaries make profits, π, when the capital share of output exceeds interest payments to foreign banks:4
rD AD −
=α α
π (1)
Because the owners of financial intermediaries suffer no penalty if their company makes a loss, there will be an incentive to continue accumulating debt as long as profits are positive in the best state of the world (A=1). We can use this investment rule to pin down the equilibrium debt stock in the long run, DLR, as a function of the interest rate:
α α − = 1 1 ) / ( r DLR (2)
We assume that adjustment costs (not modelled explicitly) prevent debt from accumulating
instantly to the long run level. Consequently, we can write the level of debt at the beginning of any period as:
1
1 ( )−
− + −
=D D D
D ϕ LR ϕ >0 (3)
The long-run debt level, given by equation (2), exceeds the efficient debt level at which the expected marginal product of capital equals the interest rate:
α α − = 1 1 * ) 2 / ( r D (4)
In Figure 1 we compare the long run value of debt which results from efficient investment, )
( *
r
D , with the debt level that results from the excessive investment in this unregulated financial system, DLR(r) (the inverse functions are shown for each). For future reference it is useful to define D' and D'' as the debt levels that would result if borrowers faced the risk-free world rate of interest, r , in each case. By substitution into (4) and (2) respectively:
α α − = 1 1 ) 2 / ( ' r D and = α 1−α 1 ) / ( ' ' r D (5) ' '
D is the debt level associated with the Pangloss outcome discussed in the introduction.
2.2. Government
Initially the government guarantees the interest payments by financial intermediaries to foreign banks. If the government honours the guarantee, it must raise sufficient funds through taxation
r ' ' D r ) ( * r D ) (r DLR Figure 1 0 r 2 ' D D
to pay for this. From (1) the taxation cost of the guarantee is:5
α
αAD rD
T = − (6)
This commitment might turn out to be extremely costly, in particular if r is high and/or A is low (a bad productivity shock). Alternatively, we assume the government can choose to renege on the guarantee, but if it does so it must pay a one-off fixed cost. As this is a one-off cost, reneging by the government absolves it of all future commitments to foreign banks.
The cost of reneging on the guarantee can be regarded as political. Such an action is likely to be costly as it will reduce the credibility of the government, not just in the eyes of foreign banks, but in all policy areas. Alternatively, this cost can be regarded as resulting from the government falling out with its ‘cronies’ in the financial sector who benefit from the low interest rate that results from a credible guarantee.
To make the model more interesting we assume the foreign banks have incomplete information about the cost of reneging. For simplicity we assume the government is one of two possible types: with probability x the government is typical and the cost of reneging is equal to V (a finite number); or, with probability 1−x, the government is resolute and never reneges as the cost of doing so is infinite. As the labels suggest, we focus on situations where the government is more likely to be of the former type and so x is close to one. We will demonstrate, however, that even a low probability that the government is resolute can have interesting implications. In section 5 we discuss how alternative assumptions regarding the structure of the incomplete information affect our conclusions.
A typical government effectively faces an optimal stopping problem. Each period it can either renege and pay the one-off cost, V, or alternatively it can honour the guarantee and pay the taxation cost T. If it takes this second course of action the government incurs an additional liability equal to the expected present-value cost of the guarantee in the subsequent period. We represent the problem for the government as choosing the action which minimises the following cost function:
[
, ( , , | , )]
min ) , , ( t t t t t tG1 t 1 t 1 t 1 t t G t r D A V T EC r D A r D C = +δ + + + + (7)5 T can be regarded as a lump-sum tax on the labour force. The linear form of equation (6) has been chosen
for analytical convenience. More generally, to the extent that taxes are distortionary, higher taxation will have a negative effect on output. Also, following a low productivity shock which reduces output, raising a given level of taxation will be more difficult, as both MPL and wages fall. Both factors suggest that raising higher taxes will become progressively more difficult.
where δ is the discount factor, T is the taxation cost of honouring the guarantee (given by equation 6), and ECtG+1
( )
⋅ is the expected cost of the guarantee next period if the government honours the guarantee this period. This optimal stopping problem is extremely complicated. In this paper we simplify by assuming that δ =0. In doing so we make the analysis tractable, but at the expense of ignoring one channel through which r and D affect the behaviour of the government.6Given δ =0 a typical government will renege on its guarantee if T >V. Substituting for T, we get the result that a typical government will only fulfil the guarantee when the productivity shock is above a trigger level, A~, where,
î í ì − = − − 1 ) / ( ) / ( 0 ~ α 1 α α α D V D r A α α α α D rD V rD V D rD rD V − ≤ < < − ≥ when when when (8)
Figure 2a shows how the trigger level,A~, varies with r at any given period in time in which the value of D is given (i.e. in the short run). This trigger value for the productivity shock, A~, is (linearly) increasing in the interest rate, r, simply because higher interest rates make guarantees more costly to honour, meaning that they will be honoured in a smaller proportion of circumstances. It is also, for obvious reasons, decreasing in the political cost of reneging on the guarantee, V, and (non-linearly) increasing in the (given) debt stock, D, since a higher D means
6 The model can be solved with δ >0 if we assume the government believes r and D will remain
unchanged in future periods. In this case the government will renege on its guarantee if T >(1−δ)V . The results are qualitatively similar.
r ) ( ~ r A 0 A~ Figure 2a 1 r ) ( ~ r A 0 A~ Figure 2b 1
that a smaller proportion of guarantees can be honoured.
The dependence of A~ on r in the long run is different, however, once we allow for the fact that in the long run D depends on r. Recall that in the long run the debt stock is given by equation (2). Substituting this in (8) we get:
î í ì − = − 1 ) / )( / ( 1 0 ~ α α 1αα r V A 0 when 0 when when 1 1 1 1 1 1 ≤ < < ≥ − − − − V r V r V -α α α α α α α α (9)
This relationship is plotted in Figure 2b. Now A~ is decreasing in r; this is because in the long run higher interest rates cause financial intermediaries to reduce their debt levels, lowering the cost of guarantees, and thus meaning that a typical government can honour them in a larger proportion of circumstances.7
2.3. Foreign Banks
Foreign banks lend elastically to financial intermediaries at a mark-up over the risk-free world interest rate, r (exogenous and constant):
) 1 /( q r
r= − (10)
where 0≤q≤1 is the expected percentage default on the interest payment. This condition must hold continuously as foreign banks are assumed to be competitive and risk neutral; banks are unable to charge a higher rate, even when productivity is high, as we assume financial intermediaries can change lender at any time without cost. 8
The expected percentage default will depend both on the expected revenues of financial intermediaries and the probability that the government will honour its guarantee. Foreign banks know that if the government is resolute it always honour its guarantees. On the other hand, foreign banks will know that if the government is typical it might renege if the productivity shock is sufficiently adverse and the cost of the bail out is too high. Suppose that foreign banks believe a typical government will honour the guarantee if productivity is above a threshold
7 This relationship may be non-linear, with either a positive or negative second derivative, depending on
α. In figure 2b we show the linear intermediate case when α=1/2.
8 We also assume that there is no possibility of financial intermediaries colluding with foreign banks to
level Aˆ. Then: 9 ) 2 /( ) ˆ ( ˆ ) ( 1 2 ˆ 0 r D A x A x dA AD rD rD x q A − − = − = α α α α (11)
Equations (10) and (11) are simultaneous in r and q. Solving for r we get:
) ˆ 1 ( 2 ˆ 2 2 1 A x D A x r r − − = α α− (12)
In Figure 3a we plot how r depends on Aˆ, for a given level of D (i.e. in the short run). For
'
D
D> (we see later that this is the relevant range of interest) and with x=1 (the government is typical for sure) the relationship is upward sloping and concave, going from r to infinity as
Aˆ goes from zero to one. The reasons for this are as follows:
(i) As Aˆ rises, bailout promises will be honoured for a smaller proportion of the range
1
0≤A≤ . This means that q, and so r, will be higher. See the (linear) term in Aˆ in the
denominator of (12).
(ii) But this effect is dampened because the expected percentage default also falls when Aˆ
rises because the interest payments that are made if there is default go up. This is captured by the (quadratic) term in Aˆ in the numerator of (11) and in the numerator of (12).
When x<1, r is finite when Aˆ =1. The reason for this is that even if Aˆ =1 there is a non-zero probability that the government is resolute and will therefore honour the guarantee, and so the expected percentage default is less than one. The value of r when Aˆ =1 is increasing in both x and D.
9 Strictly, equation (11) is only correct if rD>αAˆDα. From (8) we can determine that this is necessarily
r ) ~ (A r 0 A~ Figure 3a r 1 r r ) ~ (A r 0 A~ Figure 3b r 2 1
The dependence of r on Aˆ is different once we allow for the fact that in the long run D depends on r (equation 2). By substitution into (12):
r A x A x r ê ù ë é + − = 2 ˆ ) ˆ 1 ( 2 2 (13)
This relationship is plotted in Figure 3b. Now r increases with Aˆ. The reason for this is that D falls as Aˆ and r rise, meaning that the proportion of interest which can be recovered if there is default increases, so moderating the increase in the interest rate which is necessary as Aˆ
increases.
3. Model Solution
The model is closed with the equilibrium condition:
A
Aˆ= ~ (14)
In this section we analyse the model solution in the long run, and then the short run, before integrating the analysis in sub-section 3.3.
3.1. Long-Run Equilibrium
We have two relationships which must hold in the long-run equilibrium. First, equation (9) shows how the trigger value of a typical government, A~, changes with the interest rate. Second, equations (13) and (14) show how foreign banks set the interest rate as a function of the expected trigger value, Aˆ, which in equilibrium must equal the actual trigger value, A~. We can plot both functions on the same diagram to determine the equilibrium. An example of an interior solution is shown in figure 4 below. Although it is not possible to derive a reduced form solution we can deduce that, for all V >0, there is necessarily a unique equilibrium in which A~<1. This follows because r is increasing in A~, whilst A~ is decreasing in r, and A~(r)
is defined for all r >0. This is sufficient to ensure a unique point of intersection.
true in any equilibrium.
r ) ( ~ r A 1 ~= A unique eqm • 2r
In figure 4 we have shown an interior solution. From (13), if we have a boundary solution with
0 ~
=
A , then the interest rate, r, will equal the world interest rate, r (this makes sense as A~=0
means that the government guarantee is fully credible). From (9) we can write the following condition for a long-run boundary solution with interest rates at world levels:
α α α α − − − ≥ 1 1 1 r V (15)
The unique long-run equilibrium is therefore the Pangloss outcome if the cost to a typical government of reneging on the guarantee, V, is sufficiently high. For expositional purposes, and to sharpen our point, we assume in the rest of this paper that this condition holds.
We can now also determine the pre-guarantee equilibrium. As the government does not bail out the losses of financial intermediaries, x=1 and V =0. As a consequence of (9) and (14),
1 ~
=
A . From (13) r=2r, and so by substitution into (2) we obtain:
' ) 2 / ( 1 1 D r D= α −α =
The pre-guarantee debt level equals the efficient debt level at the world interest rate, given by
'
D in equation (5), even though the financial sector is poorly regulated and bankruptcy costs are zero. The only differences between each outcome are that the risk is transferred from one group of risk-neutral agents to another (financial intermediaries to foreign banks) and interest rates rise to equate expected pay-offs in each case.
3.2. Short-Run Equilibrium
We also have two relationships which must hold in a short-run equilibrium. First, equation (8) shows how the trigger value of a typical government changes with the interest rate. Second, equations (12) and (14) taken together show how foreign banks set the interest rate as a function of the expected trigger value, Aˆ, which in equilibrium must equal the actual trigger
value, A~.
Given condition (15) we can characterise the short-run equilibria of the model as follows. (i) When D'≤D< D there is a unique boundary-solution equilibrium with r =r and
0 ~
=
A (D is defined and discussed below).
(ii) When D≥D we have multiple equilibria: a ‘good’ boundary-solution equilibrium with r
r = and A~=0; an unstable equilibrium with r >r and 0< A~<1; and a ‘collapse’ equilibrium with r >r and A~=1.
To prove the existence of a boundary-solution with r =r it is sufficient to show that A~(r)>0
requires r>r. From equation (8) A~(r)>0 requires V ≤rD, and so a sufficient condition for the existence of a boundary solution is that V >rD. Over the range of interest, D'≤D≤D'', this condition is stronger than (15) and so we assume it holds. Given condition (15), then, there must always exist a short-run equilibrium in which the government honours the guarantee for sure (A~=0) as is the case in the unique long-run equilibrium derived in the previous section.
The possibility of multiple short-run equilibria is demonstrated in figure 5a. From (8) A~ is increasing in r. For multiple equilibria to exist, then, we require that in the limit as A~ tends to one r(A~) exceeds the minimum interest rate necessary so that A~(r)=1. If this condition is satisfied then we have three equilibrium points of intersection between the functions ~A(r) and
) ~ (A
r , as shown in figure 5a.10
If this condition fails, then we have a unique boundary solution equilibrium, as shown in figure 5b.
10 We can rule out more than three equilibria as the function
) ~ (A
r is not inflective at any point over the relevant range for A~.
r ) ~ (A r ) ( ~ r A 0 A~ 1 ~ = A unique eqm • Figure 5b r r ) ~ (A r ) ( ~ r A 0 A~ 1 ~ = A unstable eqm good eqm • • Figure 5a r collapse eqm •
The value of r as Aˆ tends to one is increasing in D. This means that for low levels of D we might have a unique equilibrium, but for higher levels of D we have multiple equilibria. We define D as the minimum debt level necessary for multiple equilibria to exist. To determine D we first solve for the lowest r in (8) at which A~(r)=1. We then equate this to r in (12) with
1 ˆ =
A . From (12) we can see that when Aˆ =1 finite r requires x<1. Assuming this, after some simplification we get the following condition for D:
0 ) 2 ( 2 ) 1 ( 2 −xV − rD + −x αDα = (16)
Unfortunately, we cannot generally solve for D, but by implicit differentiation we can deduce the following: 0 < ∂ ∂ x D and ≥0 ∂ ∂ V D
From (16) we can also deduce that in the limit as x tends to one, D tends to D' (from above). When x=1, r tends to infinity when Aˆ tends to one, except in the special case where D=D', in which case r=2r. This means that when x=1 we have a unique boundary solution equilibrium when D=D', but have multiple equilibria for higher debt levels.
We do not explicitly analyse the dynamics of adjustment to the short run equilibrium, since what is depicted is an equilibrium configuration rather than an outcome of the one-shot game which depends on the realisation of the shock to A. Nevertheless it is clear from Figure 5a that the boundary solution at r is stable, in the sense that a mistaken conjecture about Aˆ would lead to an interest rate and in turn a quit point A~(r) which was closer to zero than the initial conjecture. In a similar fashion we can deduce that any ‘collapse’ equilibrium will be stable, but an interior equilibrium with 0< A~<1 will be unstable, in the sense that any interest rate above or below this equilibrium would lead to cumulative changes in A~ and r away from equilibrium. In the rest of this paper we primarily focus on the stable equilibria.
3.3. Dynamic Adjustment
towards the new long-run equilibrium once the guarantee is introduced.
Before the guarantee there is a unique long-run equilibrium with D=D' and r=2r. Once the guarantee is introduced we move to a new regime in which, providing condition (15) holds, the long-run equilibrium interest rate is r, and DLR =D''. The debt stock begins to rise towards this Pangloss long-run equilibrium.
As discussed above, immediately following the introduction of the guarantee (when D=D') we have a unique short-run equilibrium with r=r. As the debt stock rises there will be a unique boundary solution equilibrium providing D<D. For all D≥D we have multiple short-run equilibria, as indicated by the ‘good’, ‘unstable’, and ‘collapse’ short-run equilibrium loci in figure 6.
We can now give a dynamic account of the effect of introducing a guarantee. As there is a unique short-run equilibrium whenD=D', the interest rate will immediately fall so that r=r and the debt stock will begin to rise. As long as D'≤D< D the unique short run equilibrium implies r=r, but at debt levels above D the dynamics of the model are complicated by the multiple short-run equilibria. If the economy remains at the good equilibrium each period then the debt stock will gradually increase and the economy will converge to the Pangloss outcome. But at any point in time it can flip to the collapse equilibrium, which will create a financial crisis (see below). In this model we cannot say whether the economy will, at any point in time, remain at a good equilibrium or flip to the collapse equilibrium. But the probability of such a
r ' D D= D=D'' Post-guarantee LR eqm unstable SR eqm locus Pre-guarantee LR eqm
good SR eqm locus • • r r 2 D Figure 6 0 D=D collapse SR eqm locus
flip can plausibly be asserted to be non-zero at any point in time, if such a flip has not already happened.
4. Understanding Financial Crises
In this model, if the government is typical, then a financial crisis is inevitable, even if its timing is unpredictable.11 To understand this consider figure 6 once again. Immediately following the
introduction of this bailout policy the interest rate falls to r (this is the unique short-run equilibrium when D=D'). The debt stock starts to rise, driven by the lower interest rate. Given that A~=0 when r=r the government stands by its promise to bail out any losses for sure. When the debt stock rises above D, however, multiple equilibria exist. If the good equilibrium is maintained then the debt stock will continue to rise towards the long-run equilibrium level at which D=D''. Both during this transition, and at the long-run equilibrium itself, multiple short-run equilibria exist, with the possibility of a switch to the collapse equilibrium. Such a switch must inevitably happen provided only that the probability of it remains positive at any point in time.
What is a financial crisis in this model? A financial crisis occurs if a typical government is forced to renege on its commitment to bail-out financial intermediaries. This is only possible when ~A>0, and for sufficiently high V (equation 15) this is only true for the unstable and collapse equilibria. In the case of the collapse equilibrium A~=1 and a typical government will renege on the guarantee for sure.
Why does reneging precipitate a crisis? The high debt level in this economy is driven by a reduction in the interest rate as foreign banks expect a lower default rate on interest payments given the government guarantee. By assumption, if the government ever reneges, it pays a one-off political cost; subsequently the government faces no additional penalty should it not compensate foreign banks for further default by financial intermediaries. Effectively, then, we can argue that following a crisis V returns to zero and the long-run equilibrium debt stock falls to the pre-guarantee level so that DLR =D'. A lower debt stock means a lower capital stock and therefore lower output. A key characteristic of the financial crisis, then, is a collapse in output which follows from the discrete jump in the long-run equilibrium when the government
11
is forced to renege.12
Why is a crisis inevitable when the government is typical? Once the guarantee is introduced the interest rate is depressed and financial intermediaries have an incentive to take out more debt and increase investment. At higher debt levels multiple equilibria exist. Even though initially the good equilibrium may be the most likely, we can never rule out the possibility of a switch to the collapse equilibrium.13 The crisis is inevitable because as soon as the guarantee is
introduced D rises and when D≥D the multiplicity of equilibria occurs which persists until the government is forced to renege. Even if the probability of crisis at any particular time is low, a crisis must occur eventually with probability equal to one.
5. Extension
In this paper we have demonstrated how a government guarantee to underwrite losses in a poorly-regulated financial sector (zero capital requirements, zero bankruptcy costs) can lead to over-investment. When the debt stock rises sufficiently multiple short-run equilibria exist: a good equilibrium in which interest rates are low and the government honours the guarantee for sure; an unstable equilibrium with higher interest rates and a positive (perhaps high) probability that a typical government is forced to renege; and a collapse equilibrium in which a typical government is forced to renege for sure. In the last section we described how a financial crisis can occur, with a switch to the collapse equilibrium, if the government is typical. When this occurs there will be a sharp fall in the capital stock and long-run output as foreign banks withdraw their funds.
Until now we have assumed that the government is either typical with probability x or resolute with probability 1−x. Clearly, this analysis is sufficiently general to cover the complete information case where the government is known to be typical for sure (x=1). In this case
ε + =D'
D (where ε is infinitesimally small) and so multiple equilibria exist immediately after
interesting and so we rule it out. When x=1, Dis strictly less than D''.
12 This raises the question of how adjustment to the new long-run equilibrium occurs. Immediately
following the crisis there is an excess supply of capital goods. We have assumed that the debt principal is not at risk and this requires that capital goods can be resold without any loss in value. This requires that capital goods can be exported abroad, and that the economy is relatively small so that these exports do not depress the price of capital goods.
13
The good equilibrium will be more likely than the collapse equilibrium if we assume that discrete jumps in the interest rate are less likely than continuous adjustment, except following a change in government policy (such as introducing the guarantee).
the guarantee is introduced.
In this section we generalise the model further to consider the outcome when we have a less extreme form of incomplete information. Suppose we rule out the possibility that the government is resolute and instead assume the cost of reneging is finite for sure, but its exact value is unknown. Specifically, we assume V can take one of two values, HV or LV, with
LV
HV > . If this is the case it is possible that:
(i) there are five short-run equilibria, three of which are stable; and,
(ii) foreign banks might learn about the government commitment to the guarantee (as reflected in the value of V) by observing the outcome of ‘mini-crises’.
To see how this is possible consider figure 7 below. On this diagram we show how the trigger value, A~, changes with r given each possible value for V (as indicated by the subscripts). From (8) it is clear that for a given interest rate A~LV ≥ A~HV. In addition we show how r changes with both ALV
~
and AHV ~
. This second function is drawn with a discontinuity and needs to be interpreted carefully. The lower segment shows how r changes with A~LV conditional on
0 ~
=
HV
A . This runs from r when A~LV =0 (the government does not renege regardless of V and the realisation for A) to a finite value, r*, when A~LV =1. This pattern is similar to figure 5a; and we can show that r* is an increasing function of both the current debt level and the perceived probability that the true V is high. The upper segment of the function shows how r changes with AHV
~
conditional on A~LV =1. This runs from *
r when A~HV =0 to infinity in the limit as A~HV tends to one.
r ) 0 ~ | ~ (ALV AHV = r ) ( ~ r AHV 0 HV LV A A~ ,~ 1 ~ = A • • Figure 7 r • ) 1 ~ | ~ (AHV ALV = r ) ( ~ r ALV * r
From the diagram we can see it is possible that five short-run equilibria exist, three of which are stable. First, both the ‘good’ and ‘collapse’ equilibria exist as before. In the good equilibrium r =r, but in the collapse case r tends to infinity as both A~LV and A~HV tend to one. In addition, however, we have a third stable equilibrium with r =r*. In this equilibrium
0 ~
=
HV
A and A~LV =1, and so the government reneges for sure if V is low, but honours the guarantee for sure if V is high.
This third stable equilibrium presents us with the possibility that a ‘mini-crisis’ can occur. To understand this suppose V is actually high (V =HV ). Initially we might expect capital (and debt) accumulation to occur at the good equilibrium with r=r. Suppose, however, that for some reason (perhaps a panic by foreign banks) the equilibrium flips to the intermediate case with r =r*. In this situation low V would cause the government to renege, but as V is actually high the government honours the guarantee. By this action the government will demonstrate to the foreign banks that V is not low and so in this way the foreign banks learn about V. In subsequent periods, with complete information regarding V, only two stable equilibria can exist: the economy can either flip to the ‘collapse’ equilibrium precipitating a crisis, or revert to the good equilibrium, deferring a collapse to a later date. If the latter occurs then the jump in interest rates from r to *
r is quickly reversed.
6. Concluding Remarks
In this paper we have shown how an ‘Asian-style’ financial crises can occur with a collapse in investment and output. There are two key ingredients of this story. First, implicit government guarantees fuel moral-hazard driven excess investment, along the lines outlined by Krugman. Second, the government’s limited willingness or ability to honours these guarantees means that they may not be fully credible. When the guarantees are first introduced the low debt level ensures that the government has sufficient capacity to honour the guarantees. But as the debt level rises the implicit fiscal obligation may become too large if foreign banks raise interest rates because of self-fulfilling expectations that the government will renege. The multiple-equilibrium feature of the model means that any collapse will be sudden. The end result will be a sharp fall in output and the capital stock to the pre-guarantee level.
Two questions remain to be answered. First, why is it that the government introduces the implicit guarantees in the first place? In this model the pre-guarantee debt level and capital stock is efficient, but in a more general model this need not be the case if there is some sort of market failure. For example, if there are positive externalities from foreign investment, such as technological spillovers, efficiency may require a government subsidy (but not a blanket guarantee). More generally, for other forms of market failure a first-best intervention by the government might be infeasible. This may provide a rationale for some form of guarantee as a second-best solution.
Our model suggests that the exact form of government intervention must be carefully chosen as an inappropriate policy can have highly destabilising consequences. This leads to the second question: are there any ‘stability rules’ which should restrict the form of government intervention?
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99/15 Irwin, Gregor and David Vines, "A Krugman-Dooley-Sachs Third Generation Model of the Asian Finanical Crisis", August 1999.
99/14 Anderson, Kym, Bernard Hoekman and Anna Strutt, "Agriculture and the WTO: Next Steps", August 1999.
99/13 Bird, Graham and Ramkishen S. Rajan, "Coping with and Cashing in on International Capital Volatility", August 1999.
99/12 Rajan, Ramkishen S., "Banks, Financial Liberalization and the ‘Interest Rate Premium Puzzle’ in East Asia", August 1999.
99/11 Bird, Graham and Ramkishen S. Rajan, "Would International Currency Taxation Help Stabilise Exchange Rates in Developing Countries?" July 1999.
99/10 Spahni, Pierre, "World Wine Developments in the 1990's: An Update on Trade Consequences", June 1999.
99/09 Alston, Julian, James A. Chalfant and Nicholas E Piggott "Advertising and Consumer Welfare", May 1999.
99/08 Wittwer, Glyn and Kym Anderson, “Impact of Tax Reform on the Australian Wine Industry: a CGE Analysis”, May 1999.
99/07 Pomfret, Richard, “Transition and Democracy in Mongolia”, April 1999.
99/06 James, Sallie and Kym Anderson, “Managing Health Risk in a Market-Liberalizing Environment: An Economic Approach”, March 1999. (Since published in in Plant Health in the New Global Trading Environment: Managing Exotic Insects, Weeds and Pathogens, edited by C.F. McRae. and S.M. Dempsey, Canberra: National Office of Animal and Plant Health, 1999.)
99/05 Soonthonsiripong, Nittaya, “Are Build-Transfer-Operate Regimes Justified?” March 1999. 99/04 Soonthonsiripong, Nittaya, “Factors Affecting the Installation of New Fixed Telephone
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99/03 Berger, Nicholas and Kym Anderson, “Consumer and Import Taxes in the World Wine Market: Australia in International Perspective”, February 1999. (Since published in Australian Agribusiness Review 7, June 1999.)
99/02 Hoekman, Bernard and Kym Anderson, “Developing Country Agriculture and the New Trade Agenda”, January 1999. (Forthcoming in Economic Development and Cultural Change 48(3), April 2000.)
99/01 Anderson, Kym, “Globalization, WTO and Development Strategies for Poorer
Countries”, January 1999. (Forthcoming in Local Dynamics in an Era of Globalisation, edited by S. Yusuf, S. Evenett and W. Wu, London and New York: Oxford University Press, 2000.)
98/09 Marko, Mary, “An Evaluation of the Basic Telecommunications Services Agreement”, December 1998.
98/08 Anderson, Kym, “Domestic Agricultural Policy Objectives and Trade Liberalization: Synergies and Trade-offs”, October 1998. (Preliminary version published in the Proceedings of the OECD Workshop on Emerging Trade Issues in Agriculture, 25-26 October 1998, http://www.oecd.org/agr/trade/). A revised version is forthcoming in Australian Journal of Agricultural and Resource Economics 44, 2000).
98/07 Findlay, Christopher, Paul Hooper and Tony Warren, “Resistances to and Options for Reform in International Air Transport”, September 1998.
98/06 Pomfret, Richard, “Enlargement to Include Formerly Centrally Planned Economies: ASEAN and the EU Compared”, May 1998. (Since published in The European Union and ASEAN: Trade and Investment Issues, edited by R. Snape, J. Slater and C. Molterie, London: Macmillan, 1999).
98/05 Kokko, Ari, “Managing the Transition to Free Trade: Vietnamese Trade Policy for the 21st Century”, May 1998.
98/04 Anderson, Kym, “Agricultural Trade Reforms, Research Incentives and the Environment”, April 1998. (Since published as Ch. 6 in Agriculture and the Environment: Perspectives on Sustainable Rural Development, edited by E. Lutz with the assistance of H.
Binswanger, P. Hazell and A. McCalla, Washington, D.C.: The World Bank, 1998). 98/03 Anderson, Kym, “Agriculture and the WTO into the 21st Century”, March 1998. (Since
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98/02 Stringer, Randy, “Environmental Policy and Australia’s Horticulture Sector”, March 1998. 98/01 Anderson, Kym, “The Future of the WTO”, February 1998. (Since published as Ch. 2 in
A. Melchior and V.D. Norman (eds.), From GATT to WTO, Oslo: Norwegian Institute of International Affairs, 1998 (in Norwegian).)
97/13 Bora, Bijit, “Potential for Investment Liberalization between AFTA and CER”, November 1997.
97/12 Findlay, Christopher and Tony Warren, “Potential for Services Liberalisation Between AFTA and CER”, November 1997.
97/11 van Beers, Cees, “Labour Standards and Trade Flows of OECD Countries”, October 1997. (Since published in The World Economy 21(1): 57-74, January 1998.)
97/10 Maskus, Keith E., “Implications of Regional and Multilateral Agreements for Intellectual Property Rights”, October 1997. (Since published in The World Economy 20(5): 681-94, August 1997.)
97/09 Maskus, Keith E. and Guifang Yang, “Intellectual Property Rights, Foreign Direct Investment, and Competition Issues in Developing Countries”, August 1997. (Since published in International Journal of Technology Management.)
