THE TIMING OF EXCHANGE REGIME COLLAPSE ... - CiteSeerX

INTERNATIONAL ECONOMIC JOURNAL Volume 10, Number 4, Winter 1996

123

THE TIMING OF EXCHANGE REGIME COLLAPSE UNDER CAPITAL CONTROLS DAEKEUN PARK Hanyang University JEFFREY D. SACHS* Harvard University

This paper investigates the nature of balance-of-payments crises in regimes with capital controls. It extends earlier works on capital controls by assuming that households manage their consumption and asset portfolios to maximize intertemporal utility. Our main result is that capital controls are effective in delaying, but not preventing, a breakdown of a fixed exchange rate regime in the presence of moneyfinanced fiscal deficits. [F31]

1. INTRODUCTION The vast and growing literature on balance of payments crises focuses on the incompatibility of persistent budgetary deficits and fixed exchange rates. Under the standard assumption of high international capital mobility, a government that finances its deficit through domestic credit expansion and simultaneously pegs the exchange rates, will experience a simultaneous offsetting loss of foreign exchange reserves. Eventually, a minimum level of official reserve holdings will be reached, and the government will be forced to allow the exchange rate to float (assuming that there is no correction of the underlying budget deficit). The transition to floating rates typically involves a speculative attack on the central bank reserves in the “instant” (or period) just before the float begins. The assumption of internationally mobile capital is critical to the adjustment mechanism just outlined, at two points. First, the domestic credit expansion that finances the budget deficit generally leads to an immediate offset of official reserves because domestic agents are free to convert domestic currency into foreign financial assets at the pegged exchange rate. Second, the possibility of a “speculative attack,” in which there is a large, discrete loss of central bank reserves, also depends on the ability of domestic residents instantly to convert part of their money stock into foreign assets on the eve of the exchange rate collapse. It is often for these reasons that governments resort to capital controls to help to *We would like to thank Phillippe Bacchetta and two anonymous referees for helpful comments and suggestions. All remaining errors are our own.

124

D. PARK AND J. D. SACHS

maintain an exchange rate peg. By preventing the instantaneous conversion of domestic money into foreign financial assets, governments try to preserve their central bank reserves for a longer period of time, and thereby forestall the exchange rate collapse. Under tight capital controls, according to which domestic residents are not allowed to hold foreign assets, the central bank loses foreign reserves via current account deficits only. Reserves can decline only gradually, with a current account deficit, rather than in the sudden step of a speculative attack, in which part of the domestic money stock is traded for the central bank’s foreign exchange. As many governments have learned, however, the use of exchange controls does not generally prevent the collapse of the fixed rate (though in some cases it may), but rather it delays the collapse and changes the adjustment mechanism. With exchange controls and fixed rates, domestic credit expansion does lead to a rise in domestic real money balances, since the increase in money cannot be converted to foreign assets. The buildup in real money balances leads to a rise in domestic absorption and a current account deficit. The deficit, in turn, leads to reserve losses of the central bank, and the eventual collapse of the fixed rate. However, the collapse comes smoothly in this case, with reserves trickling down to the minimum permissible level, rather than being exhausted in a single stroke by a speculative attack. Moreover, the exchange rate behavior is different in the cases of free versus restricted capital mobility. With free capital mobility, the transition from the fixed to floating rate occurs without a discrete jump in the exchange rate, while in the capital control case, there is a discrete depreciation of the currency at the moment of breakdown of the exchange rate peg.1 It should be clear why an anticipated discrete depreciation is possible only in the presence of capital controls: if agents are free to swap money for foreign assets, they would always do so the moment before an anticipated depreciation, thus causing it to occur before the “anticipated” date. In equilibrium with capital mobility, the speculative attack is timed precisely so that asset markets clear continuously without any discrete anticipated exchange rate change. Despite the widespread use of capital controls to forestall exchange rate changes, there has been relatively little modelling of the effects of capital controls on the balance of payments crises. Wyplosz (1986) provides the pioneering model in this area. This paper extends that work by couching the analysis in a model in which private agents are intertemporal utility maximizers, in contrast to the Wyplosz model in which private sector behavior is not derived from utility maximization. The benefit of using the optimization approach lies with the proper modelling of the behavior of the current account, which is the sole source of foreign exchange outflow in the absence The absence of a discrete jump in the exchange rate holds strictly only in continuous time, deterministic models. In discrete time (Obstfeld, 1984), or with stochastic monetary policy (Penati and Pennachi, 1989), discrete changes in the exchange rate may occur as equilibrium outcomes in models with free capital mobility. 1

EXCHANGE REGIME COLLAPSE

125

of international capital mobility. This approach has also been adopted by Auernheimer (1987) and Bacchetta (1990) in characterizing the dynamics of balanceof-payments crises under strict capital controls. This paper also extends these studies to find if capital controls can prevent or delay the collapse of a fixed exchange rate regime. For this purpose we use the elegant model introduced by Calvo (1987) and follow his notation closely. This paper is organized as follows. Section 2 of this paper introduces the Calvo model, and section 3 uses the model to analyze a balance of payments crisis under the standard assumption of complete capital mobility. Section 4 then repeats the analysis under the alternative assumption of zero captial mobility, and the adjustment paths and the timing of the balance-of-payments crises in the two cases are compared in some detail. Section 5 offers some conclusions and a discussion of possible extensions. 2. THE MODEL The model presented in this section is essentially the same as in Calvo (1987), which uses an intertemporal optimization approach to study balance-of-payments crises under perfect international capital mobility. For brevity, we curtail the detailed discussion of the model and refer the reader to the original paper. We consider a small open economy with perfect international mobility of goods and capital. This economy is resided by identical households of population one who derive utility from a single perishable consumption good. The world price of the consumption good and the world interest rate, denoted by r, will be assumed to be constant throughout the paper. Then, the domestic inflation rate, πt, equals the rate of exchange depreciation by purchasing power parity. The nominal domestic interest rate, which is the opportunity cost of holding money, is r + πt by interest arbitrage. Households hold real wealth, at, consisting of a real amount of domestic currency, mt, and foreign bonds, bt. The foreign bonds are consols that pay r units of the consumption good in each instant period. at evolves according to the following relation:

a˙t = y + tr b+ τ t - π t mt - t ,c

(1)

where y is the constant flow of real output (GDP), τt is real lump-sum government transfers, π tm t is the inflation tax and c t is real consumption at time t. Since households cannot borrow an infinite amount, the following no-Ponzi-game condition is imposed: Households also face a cash-in-advance constraint according to which

126


lim at e -rt ≥ 0.

(2)

t→∞

This constraint (3) will be a strict equality as long as the nominal domestic interest m t ≥ αc t , α > 0 .

(3)

rate is positive.2 Solving the households’ problem of maximizing their utility, subject to the constraints of (1), (2), and (3), we get the following first order

Ut =

∞

∫ u(c ) e t

s

-r (s - t)

ds,

3

condition: where λt is the costate variable for the dynamic constraint (1). u' (ct ) = λ t [1 +α(r +π t )] λ˙ t =

(4)

0 ,

Government transfers (τ t) and the rate of exchange depreciation (π t ) are determined by the government. The government holds foreign bonds as reserves and uses these reserves to manage the exchange rate according to a preannounced schedule. The government reserve holdings, denoted by kt, evolve according to the following equation except for the points where m jumps:4 At the points where m takes a jump of ∆m, 2 Since we are going to confine our analysis to the case of a fixed or depreciating exchange rate, this is a reasonable assumption. 3 Note that for convenience, the subjective rate of time preference is set to be equal to the world interest rate. 4 Of course, the inflation tax is not applicable under the exchange pegging. However, once the fixed exchange regime breaks down and the float begins, it becomes the major source of government revenue.


k˙t = r kt + m˙ t + π tm t - τ t .

127

(5)

Following the balance-of-payments crisis literature (e.g., Krugman, 1979), we assume

∆kt = ∆mt .

(6)

that there is a lower bound on k , which is assumed to be zero for the sake of definiteness.5 Therefore, when the government runs out of reserves, it stops managing the exchange rate. Instead, it allows the exchange rate to float. Equation (5) tells us that in order to manage the exchange rate, π and τ should be chosen consistently so that the government can maintain a positive amount of reserves. When π is too small or τ is too large, the government runs budget deficits, which eventually run down the reserves. Calvo (1987) investigated a balance-ofpayments crisis caused by a stabilization policy which pursues an inconsistently low rate of currency devaluation. This paper, on the other hand, adopts an increase in government transfers as the source of budget deficits while assuming that the government tries to peg the exchange rate. 3. A BALANCE-OF-PAYMENTS CRISIS UNDER PERFECT MOBILITY For the sake of definiteness, we assume that up to time zero the economy has been following a stable steady-state path along which the exchange rate is fixed (πt = 0), households consume exactly the amount of their disposable income,6 and the government maintains a balanced budget. Maintenance of a balanced budget requires that the government choose the amount of transfers consistently. In particular, we assume that the amount of government transfers has been fixed at In this case, the current account of the economy is always in balance and the amount of foreign reserves is constant at 5 It is possible for the lower bound to be negative if the government borrows reserves. The lower bound can be determined endogenously in the model by optimizing behavior of the public sector. However, it is obvious that there exists a lower bound for foreign reserves as long as the government faces intertemporal solvency requirements. 6 If households consume more than their disposable income in the steady state, they violate the no-Ponzi-game constraint of (2). In addition, the assumption of nonsatiable preference precludes the possibility of households consuming less than their disposable income.

128


Suppose that at time zero there is an unexpected permanent increase in the amount of the transfer payment from τ to τ + ε and that the government finances the resulting budget deficit by creating domestic credit. Unless the additional money supply caused by the creation of domestic credit is accomodated by households, 7 t h e government keeps losing reserves as households convert the excess money holdings into foreign bonds. Eventually, the government will run out of reserves and the exchange rate will begin depreciating at a constant rate π. Since the amount of money holdings is constant from (4) and since kt = 0 after the exchange regime breakdown, if follows from equation (5) that where m is the constant amount of money holdings after the exchange rate collapse.

π =

τ +ε > 0, m

Being fully aware that the fixed exchange regime will collapse at a future time Tm and that starting from Tm the exchange rate will begin depreciating at a constant rate of π, households reallocate their consumption based on this new information. The households’ problem in this case is basically the problem of allocating consumption intertemporally when the cost of consumption is 1 + αr before Tm and 1 + α(r + π) after Tm. Calvo (1987) shows how to solve the households’ problem and characterizes the equilibrium path of the economy. For the sake of concreteness, we investigate the particular case of log utility, that is, u(c) = ln c. The following equations are derived as the equilibrium paths of consumption, bond holdings, and foreign reserve holdings during the period prior to the collapse: where is the constant amount of foreign bond holdings before time zero. After the

c t = y +b r +τ + bt = b

ε 1 + αr

αε 1 +αr

kt = k +

ε r

-

εe rt , (1 + αr )r

As long as the domestic interest rate is positive, the increased level of money supply is accomodated by households only when they need to consume more. However, it can be easily shown that such a consumption path violates the no-Ponzi-game condition of (2). 7


129

collapse, consumption and bond holdings are constant at the following levels: The timing of the exchange regime collapse can be derived as follows:

b =b +

ατ 1 + αr

c = y

αrτ + r b = by + r . 1 +αr

As is shown in Figure 1, households increase their consumption in response to

Tm =

l n (τ + ε ) - l εn . r

(7)

the unexpected increase in disposable income. To transact the increased level of consumption households also increase their money holdings by selling foreign bonds to the government. As a result, there is a discrete jump in the amount of the government foreign reserve holdings at time zero. The government, however, loses the reserves over time as the economy continues to run current account deficits. Figure 1 also shows that households choose a lower level of consumption after the regime collapse. It is because the cost of consumption after the collapse is higher due to the positive inflation rate (π > 0). Since households do not hold money in excess of the amount needed to transact their consumption, they try to get rid of the excess money holdings and instead acquire foreign bonds at the moment of exchange regime collapse. This portfolio adjustment is achieved by speculative attacks on the government foreign exchange reserves, which deplete the remaining reserves in an instant. The possibility of speculative attacks under full capital mobility may motivate policy-makers to impose restrictions on capital outflows in an effort to support the fixed exchange regime. In the following section we investigate if the government can prevent or at least delay the timing of the balance-of-payments crisis by introducing restrictions on international capital mobility.

4. THE CASE OF CAPITAL CONTROLS

130



131

Suppose that in addition to increasing the amount of transfers, the government imposes restrictions on capital account transactions at time zero. Neither the capital controls nor the change in the level of transfers are expected by households. We consider a very restrictive type of capital controls which prohibits capital inflows as well as capital outflows. These controls prohibit households from changing their foreign bond holdings. Consequently, the private bond holdings will be fixed at the level starting from time zero. Since the government continues to supply foreign exchange for current account transactions including import of goods and payment of interest, it is still possible that government reserves will be eventually depleted by an accumulation of current account deficits. We also assume that the government will not remove the capital controls after the collapse.8 One direct result of imposing capital controls is that the interest parity relation between domestic and world interest rates, which holds under full capital mobility, will not hold any more because domestic and foreign bonds are no longer freely substitutable. To be able to solve for the domestic nominal interest rate, it is convenient to introduce a market for domestic bonds, with a zero net supply of bonds. Each household then demands domestic bonds in nominal amount Dt, and with the nominal interest rate it. Real domestic bond holdings are then dt = Dt / Pt, where Pt is the domestic price level. In equilibrium, we will require dt ≡ 0, and will find the equilibrium value of it consistent with domestic market clearing. Note that adding such a market under free capital mobility is superfluous. The home interest rate would simply be it = r + πt, and dt the bt would be perfect substitutes. Now, let us define at as follows: Then, at evolves according to the following equation,

at = m t + td.

(8)

except at times of a discrete jump of the exchange rate, when we have aT+ = a T- /(1 +

a˙t = t di t + y +b r +τ + ε - π t (mt + dt ) - ct

(9)

8 Actually, removal of capital controls after the collapse does not make any difference, for domestic currency is no longer convertible to foreign currency once the government runs out of reserves. However, these alternative assumptions may give different results if storable goods are introduced to the model.

132


γ), where γ is the instantaneous jump in the exchange rate. As is pointed out by Auernheimer (1987) and Bacchetta (1990), capital controls cannot prevent the collapse of a fixed exchange regime permanently. Initially, the economy is in current account balance, with When transfer payments are raised from τ to τ + ε, households do not instantaneously change the amount of consumption, since consumption at time zero is constrained by the real money stock held right before the imposition of capital controls. As a result, the level of consumption at time zero remains equal to that of consumption the instant before, and the current account remains in balance at t = 0. Since households consume less than the amount of their disposable income at time zero, they end up with increasing the amount of their money holdings which can be used to increase consumption in the next instant. Note that money is the only means of savings because of the capital controls. As consumption increases over time, the current account deficit increases. The accumulation of current account deficits gradually drives the reserves down to zero. Another important result of the capital controls is that, as was mentioned in the introduction, the exchange rate can take a discrete jump in the process of the exchange regime collapse. This is because, unlike the case under free capital mobility, speculative attack is impossible under the capital controls9 and households cannot avoid windfall losses from the jump in the exchange rate. Since the real stock of wealth, a t, is defined as the nominal stock of wealth divided by the exchange rate, the discrete jump in the exchange rate leads to a discrete jump in the real stock of wealth. Understanding that the consumer knows and takes as given the eventual jump in the exchange rate, γ, and the timing of exchange regime collapse, T, the problem of each household can be formulated as follows. Solving the problem, we can get the following first order condition.

max ct ,mt

∫

∞

0

ln ct e-rt dt

s . t . a˙t = (it - π t )at +

y τ+ + ε + br - t m i t - ct

mt ≥ αct

(10)

π t = 0 , t< T and π t = π, t ≥ T aT- = (1 +γ )aT+

9 If goods are storable, speculative attack through current account is possible. In reality, we observe accumulation of consumer durables in expectation of devaluations. However, we assume this possibility away by assuming that goods are perishable.


133

where λ is the costate variable and µ is the Lagrangian multiplier for the cash-in-

1 = λ t (1 + αit ) ct µ t = λ t it λ˙ t = {r -(it - π t }) λ t

(11)

µ t (mt - αc t ) = 0µ, t ≥ 0 (1 + γ )λ T- = λ T+ ,

advance constraint. To find the optimal path, we make a conjecture on the optimal path and show that this path satisfies the first and second order conditions. Our conjecture is that the cash-in-advance constraint is always binding along the optimal consumption path, that is, mt = αct. Appendix A proves that the conjecture we made satisfies the first order condition in (11). The second order condition and the uniqueness of the solution naturally follow from the strict concavity of the log utility function and the linearity of the constraints. In equilibrium, dt = 0, and the equation (9) can be rewritten as follows: Substituting mt = αct in equation (12), we can get the following differential equation

m˙ t = y τ+ + ε + br - t c.

(12)

for ct: Solving (13), we obtain Thus, real consumption is increasing between time zero and T, but it is always less

c˙ t = -

1 1 c t + (y + τ + ε + br) α α

1 c0 = m = y + τ + b.r α 0 than the disposable income, which equals

(13)

Meanwhile, the no-Ponzi-

134


c t = y τ+ + rb + ε(1 - -t/α e ).

(14)

game condition of (2) and the nonsatiable preference restricts households to choose the following path of consumption after the collapse: Figure 2 shows the optimal consumption path under the capital controls together with the dynamic paths of other variables of interest.

c = y b+ . r

(15)

Since the cash-in-advance constraint is binding, mt also increases over time. The amount of money held by households right before the collapse is From (15) and (16) it is quite obvious that mT- > m T+. Thus, we have a discrete jump

m T- = α (y + br ) + ατ + αε (1 - e-t/ α ).

(16)

down of the real balances at the moment of the collapse. Unlike the case of free capital mobility, this jump in mt is not caused by speculative attacks on foreign reserves, for households are not allowed to exchange money for foreign bonds. Instead, it is caused by a discrete jump in the exchange rate. Thus, The reason why the exchange rate jumps is that when reserves run out, the flow

e T+ = (1 + γ )eT- =

mTe mT+ T-

(17)

supply of goods to the economy drops from The households try in vain to buy goods with a now excess level of money, and end up with depreciating the currency and raising the price level. After the collapse, the exchange rate will depreciate at the constant rate of Note that since the level of money holdings after the collapse under the capital controls is lower than that under free capital mobility, the steady state rate of depreciation is higher in the case of the capital controls.


135

136


The movement of the shadow domestic interest rate under the capital controls can be tracked by the following differential equation. dit 1 c˙ = (it + )(it - r - t ), t ≤ T dt α ct

(18)

As is discussed in the appendix, it can be easily shown that the nominal domestic interest rate remains higher than r until the time of the collapse and equals the steadystate level r + π at the moment of the collapse. As was discussed before, there is no speculative attack under the capital controls. Hence, the exchange regime will collapse when kt hits zero. Combining (5), (12) and (14), we can derive the following path of kt.

k t = k - ε(

ert - 1 rt e -t/ α - e ) r r + 1α/

(19)

Setting kT = 0, we can obtain the following equation for the timing of collapse under the capital controls (Tc).

c

e rT + αre-T

c

/α

= (1 + αr)

τ+ε ε

(20)

Now, we demonstrate the following proposition regarding the timing of the exchange regime collapse. PROPOSITION: Let T m be the time of the regime collapse under free capital mobility as given in (7) and T c be that under capital controls as given in (20). Then, Tc > Tm. PROOF: Let us define a function f as follows:

f (t ) =

e + αre- t /α - (1 +αr)

rt

τ +ε ε


137

It is obvious from (20) that Tc is one of the zeros of f. It can be verified that for t ≥ 0, f '(t) = (re rt - -t/e α ) > 0 ,

(21)

Thus, f is continuous and monotonically increasing in this domain. Moreover,

f (0) = (1 - + αr)

τ +ε < 0 ε

lim f (t) = +∞

t→∞

Therefore, Tc is the unique solution for f(t) = 0 in the domain t ≥ 0. Since e-t/α < 1 for t > 0 and (τ + ε) / ε > 1, we can show that

f (T m ) = αr (e -T

m

/α

-

τ+ε ) < 0. ε

(22)

It follows from (21) and (22) that Tc should be greater than Tm. Q.E.D. Thus, the capital controls specified in this section do delay the timing of collapse, and they do so by eliminating the chance of speculative attacks and by restricting consumption and thus reducing the average current account deficit in the period before the collapse. The benefit of delayed balance-of-payments crisis, however, comes only at the cost of a lower level of consumption and a higher rate of exchange devaluation after the collapse. 5. EXTENSIONS This paper showed how controls on capital flows can be imposed to delay the timing of a balance of payments crisis when the crisis is inevitable. The delay in timing provides governments with some time to prepare and implement measures to rectify the fundamental causes of the balance-of-payments crises. This role of capital controls may justify the widespread use of capital controls as practical policy tools in countries experiencing balance-of-payments difficulties. An interesting extention may be to consider anticipated capital controls. Park (1989) investigates anticipated capital controls using a numerical analysis and shows that the initial objective of capital controls can be defeated by market behavior. Bacchetta (1990), on the other hand, shows that temporary capital

138


controls can be effective in maintaining exchange rate pegging even if they are anticipated. Another interesting extension may be to introduce storable goods with a positive rate of economic depreciation. Although the existence of storable goods would not change the results in the case of free capital mobility, it would make a difference under capital controls because holding them provides a hedge against depreciation of the domestic currency. The burgeoning literature on exchange rate target zones has evoked renewed interest in models of balance-of-payments crises. The techniques and models developed to investigate exchange rate target zones can be applied to the analysis of collapsing fixed exchange regimes because fixed exchange rate regimes in the real world, like target zone exchange rate regimes, typically have explicit finite bands within which exchange rates are allowed to float freely. The difference is that fixed exchange rate regimes have narrower bands. In particular, Bertola and Caballero (1992), which models realignments in target zone exchange rate regimes, can be applied with some modification to speculative attacks on fixed exchange rate regimes. Garber and Svensson (1994) surveys and compares theoretical models and empirical studies on exchange rate target zones and speculative attacks on fixed exchange rates. APPENDIX We will prove that the conjecture on the optimal path we made in section 4 is actually the solution to the problem (10). For this purpose, we define two functions H and Φ as follows: The Euler-Lagrange necessary condition of this problem is: H(a,c,m, λ ,µ ) = e-rt [lnc + λ{( i - π)a + y +τ + ε + r b - i m }- +c µ(m -αc)] Φ(aT- ,a T+ ) = v[(1 + γ )aT+ - Ta].

Using the definition of H and Φ, (A.1) can be written as follows:

∂H ∂H = = ∂c ∂m

0

∂ -rt ∂H (e λ ) = - , ∂t ∂a

(A.1) t ≠ T


139

∂Φ ∂Φ λ T- = - , λ T+ = ∂aT∂aT+ µ ≥ 0,

∂H ≥ 0, ∂µ

µ

∂H = ∂µ

0

Now, we take the proposed solution in section 4. Our objective is to show that this

1 = λ (1 + αi ) c

(A.2)

µ = λi

(A.3)

µ (m -αc) = 0 µ, ≥ 0 , m ≥ αc

(A.4)

λ˙ = [r -(i -π )]λ

(A.5)

λ T- = v λ , T+ = (1 +γ )v

(A.6)

path satisfies the group of conditions (A.2) - (A.6). The most crucial part is to demonstrate the positivity of the equilibrium domestic interest rate derived from the conjecture. If i > 0, then µ > 0 from (A.2) and (A.3). Then, by virtue of the complementary slackness condition given in (A.4), the cash-in-advance constraint must be binding. To derive the path of the domestic interest rate we differentiate (A.2) with respect to time and get the following: Rearranging this equation using (A.2) and (A.5), we can derive the following

-

c˙ di ˙ 2 = λ (1 + αi ) + αλ c dt

differential equation for it:

(A.7)

140


di 1 c˙ = (i + )(i - r -) dt α c

(A.8)

In addition, we can also obtain the value of iT as follows. Since the cash-inadvance constraint holds as an equality both right before and after the collapse, we know that

c T- = αm T- , c T+ = αmT+ .

(A.9)

Combining (A.8) and the relation (1 + γ) mT+ = mT-,

(1 + γ )c T+ = Tc.

(A.10)

From (A.2),

1 = λ T- [1 +αiT- ] c T1 c T+

= λ T+[1 + αiT+ ]

(A.11)

c Tλ 1 + αiT+ = T+ . c T+ λ T- 1 + αiTSince cT- /cT+ = λT+ / λT- = 1 + γ, it is obvious that

iT- = i T+ = r +π,

(A.12)

which means that there is no jump in the nominal domestic interest rate at time T.


141

Now, we will demonstrate that it is positive for t < T. Suppose that it < r for some t < T. Then since for the proposed consumption path, di/dt should be negative. It means that it decreases and remains less than r in the next instant. We can see that it will keep decreasing and remain below r until time T. However, this contradicts the terminal condition of (A.12). Hence, it > r for t < T. Thus, the domestic interest rate should remain higher than the world interest rate r and settles down to r + π after the collapse. REFERENCES Auernheimer, Leonardo, “On the Outcome of Inconsistent Programs under Exchange Rate and Monetary Rules,” Journal of Monetary Economics, Volume 19, 1987, 279-305. Bacchetta, Philippe, “Temporary Capital Controls in a Balance-of-Payments Crisis,” Journal of International Money and Finance, March 1990, 246-256. Bertola, Giuseppe and Caballero, Ricardo J., “Target Zones and Realignments,” American Economic Review, June 1992, 520-536. Calvo, Guillermo A., “Temporary Stabilization: Predetermined Exchange Rate,” Journal of Political Economy, December 1986, 1319-29. Calvo, Guillermo A., “Balance of Payments Crises in a Cash-in-Advance Economy,” Journal of Money, Credit and Banking, February 1987, 19-32. Garber, Peter M. and Svensson, Lars E. O., “The Operation and Collapse of Fixed Exchange Rate Regimes,” NBER Working Paper 4971, December 1994. Krugman, Paul R., “A Model of Balance-of-Payments Crises,” Journal of Money, Credit and Banking, August 1979, 311-325. Obstfeld, Maurice, “Balance-of-Payments Crises and Devaluation,” Journal of Money, Credit and Banking, May 1984, 208-217. Obstfeld, Maurice, “Capital Controls, the Dual Exchange Rate and Devaluation,” Journal of International Economics, February 1986, 1-20. Park, Daekeun, “Capital Controls and Balance-of-Payments Crises,” Unpublished Ph. D Thesis, Harvard University, 1989. Penati, Alessandro and Pennacchi, George, “Optimal Portfolio Choice and the Collapse of a Fixed-Exchange Rate Regime,” Journal of International Economics, August 1989, 1-24. Wyplosz, Charles, “Capital Controls and Balance of Payments Crises,” Journal of International Money and Finance, June 1986, 167-179.

Mailing Address: Professor Daekeun Park, Department of Economics, Hanyang University, Seongdong-ku, Haengdang-dong 17, Seoul 133-791, KOREA. Mailing Address: Professor Jeffrey D. Sachs, Department of Economics, Harvard University, Cambridge, MA 02138, U.S.A.