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Speculative attacks on the currency with uncertain monetary policy reactions
Economics Letters North-Holland
75
25 (1987) 75-78
SPECULATIVE ATTACKS ON THE CURRENCY WITH UNCERTAIN MONETARY POLICY REACTIONS Alpo WILLMAN Bank of Finland, SF-00101 Received Accepted
Helsinki,
Finland
22 May 1987 24 July 1987
We show that balance-of-payments the exchange rate is constrained
crises are accompanied by discrete shifts in the exchange rate if in the pre-crisis by set limits and there is uncertainty about monetary policy reactions.
situation
1. Introduction In the recent literature concerning balance-of-payments crises it has been assumed that, once the foreign reserves have hit some critical lower bound, the central bank will, with certainty, abandon its earlier fixed exchange rate target and withdraw from the foreign exchange market. ’ With perfect foresight about the policy rules pursued by the central bank it has been shown that an exchange rate regime shift from a fixed to a floating exchange rate regime is preceded by a speculative attack on the currency and that the exchange rate regime shift occurs smoothly. i.e., without a discrete jump in the exchange rate. However, there is nothing forcing the central bank to abandon the fixed exchange rate regime at the moment the foreign reserves have been exhausted to the critical lower bound. The central bank could equally as well change its monetary policy rule consistent with the fixed exchange rate target. In this paper we show that uncertainty about monetary policy reactions affects balance-of-payments crises, if in the pre-crisis situation the exchange rate is constrained by set limits (a target zone). In this case balance-of-payments crises are accompanied by discrete shifts in the exchange rate.
2. The model and analysis We employ the same linear continuous-time small open country model as Flood (1984) and Obstfeld (1984, 1986). By assuming full employment (exogenous production), power parity and uncovered interest rate parity the model can be written as
M( t)/.S( t) = j3 - aE,S’( t),
P, a>0,
(2)
M(t) = D(t) + R(t), See e.g.,
(1979), Flood
and Garber purchasing
and Garber
(1984).
A. Wdlman / Speculative attacks
16
on currency
where M(t) is the nominal stock of non-interest-bearing domestic high-powered money, D(t) domestic credit, R(t) the stock of foreign reserves of the central bank, valued in home currency, and S(t) the spot exchange rate. E, denotes the expectation operator conditional on the information available at time t. Eq. (1) defines the demand for domestic real money balances as a decreasing function of the expected exchange depreciation. Eq. (2) defines the supply of money. If the exchange rate is allowed to float freely and assuming that the exchange rate depends only on market fundamentals, eq. (1) implies the following solution for the exchange rate: S(t)
= 1/aim
e -P(TPt)‘a E,M( r) dr.
If, in turn, the exchange rate is fixed so that s(t)
M(t)
=
R(t) =
(3) = 5, eqs. (1) and (2) imply
ps,
(4)
pS-D(t).
(5)
Let us assume a target-zone-restricted exchange rate the upper bound of which is ?. Assume further that, as long as the foreign reserves are above a critical lower limit which we assume to be zero, the central bank causes domestic credit to evolve over time according to the rule
b(t)=p.>o.
(6)
Hence, if the exchange rate has moved to its upper limit %, eqs. (5) and (6) imply that the foreign reserves must decline at the rate ~1, i.e., A(t) = -p. Of course, this is true if the exchange rate is fixed at any other level within the zone. This implies that any finite stock of foreign reserves is depleted to zero in finite time. Hence, at the moment the foreign reserves have been exhausted to zero, the central bank is forced to abandon the target zone or to change its monetary policy rule so that the condition R(t) >, 0 is not violated. In the following we assume that prior to the occurrence of a balance-of-payments crisis the exchange rate has moved to its upper limit ,!?. It is further assumed that, providing that the monetary policy rule (6) is not changed, the exchange rate is allowed to float freely from the moment the foreign reserves have been depleted to zero. This alternative is expected to occur with the probability 7~.With probability 1 - 7r the central bank is expected to change the monetary policy rule consistent with the target zone with ,!? as an upper limit, i.e.,
b(t) = 0.
(7)
In this case too the exchange rate can equally as well be said to float freely. Before the occurrence of the policy regime shift, eq. (1) together with the alternative policy rules (6) and (7), imply the following shadow floating exchange rate S’(t):
= D( t),‘P +
~~pa/p=.
monetary
(8)
The shadow floating exchange rate at time t is the floating exchange rate expected to prevail by investors, if the target-zone-restricted exchange rate regime were to collapse at that instant, i.e., foreign reserves were to be depleted to zero. 2 The shadow floating exchange rate rises in time as D(t) grows at the rate CL.The policy regime shift occurs at the point in time when the shadow floating exchange rate equals the upper limit of the target zone, i.e., S”(T) = s, where T indicates the point in time when the policy regime shift occurs. By this condition ‘abnormal’ profit or loss opportunities are precluded [see Flood and Garber (19X4)]. Together with eq. (8) this condition implies the following relation for the timing of the policy regime shift:
T=&/p--a/P,
(9)
where R, = /3,!?- D(O), equalling the stock of foreign reserves at t = 0. is that the monetary It can be easily seen that the smaller 7~ is, i.e., the greater the probability policy rule after the policy regime shift will be (7) the later the regime shift occurs. From eq. (6) it can be easily seen that the time needed to deplete the foreign reserves to zero without a speculative attack on the currency is R,/p. Hence, if 7~= 0 there is no speculative attack on the currency. With v = 1 eq. (13) reduces to the solution given by Flood and Garber (1984), i.e., T = R,/p - a/P. This is the earliest possible point in time when the speculative attack and the policy regime shift can occur. What happens to the actual exchange rate at t = T? From that instant onwards there is no uncertainty in the model and on the basis of eq. (3),
S(t) =
l/aim epP(Tp’)/aD(
which, after integrating,
t > T,
r) dr,
can be expressed
as
s(t)=D(T)/p+p(t-T)/p+pa/,8’
if
b(t)=p,
t&T,
D(T)/‘P
if
b(t)=O,
t&T.
=
(11)
Eq. (11) implies that with no change in the monetary policy rule the exchange rate depreciates at a constant rate p/p from T on. The adoption of the monetary policy rule b(t) = 0 implies, in turn, that the exchange rate will remain fixed at the level D(T)/p from T on. ’ From eqs. (8) and (11) it can be seen that with 0 < 7~< 1 there is a discrete jump in the exchange rate at t = T. The size of the jump is S(T)-S=(l-a)~lti/P~ =
-71p’y/p2
if
b(t)=p;
t>T,
if
b(t)=O;
t>T.
(12)
The jump in the exchange rate can be upwards or downwards. The upward jump (discrete depreciation) occurs, if the central bank adheres to its earlier monetary policy rule i>(t) = p and allows the exchange to float freely. The downward jump (discrete appreciation) occurs if the monetary policy rule (7), which is consistent with the fixed exchange target, is adopted. ’ The shadow floating target zone. 3 For expositional
exchange
reasons
rate defined
we assume
by (8) is the relevant
that this level of the exchange
shadow
rate only after exceeding
the lower level of the
rate is above the lower limit of the zone.
A. Willman / Speculmoe
78
attacks on currenq
It is worth noting that, although investors foresee with certainty that there is a discrete jump in the exchange rate at t = T, the size of the expected jump is zero. This is due to the fact that there is uncertainty concerning the direction of the jump. This uncertainty, however, disappears, if the target zone within which the exchange rate is allowed to move is narrowed to zero. Under this regime of a perfectly fixed exchange rate, the preceding example is transformed as follows: with probability r the central bank is expected to permanently withdraw from the foreign exchange market, with no change in the monetary policy rule and with probability (1 - r) to change the monetary policy rule to fi( t) = 0 retaining the fixed exchange target S(t) = s. The shadow floating exchange rate is in this case a weighted average of the freely floating exchange rate with the monetary policy rule b(t) = p and the fixed exchange rate g. Hence we can write S”(t)
=
7r/alwe -P(T-r)‘a[~(t)
+,A(T-
t)] dr+
(1 -+.
(13)
It is easy to see from (13) that with 0 < YT< 1 the point in time T, when the shadow floating exchange rate equals to 3, is independent of the size of VT.Hence, the timing of the speculative attack is the same as in the case of perfect foresight ~7= 1 studied by Flood and Garber (1984), i.e., T = R,/p a//3. This is the only point in time without either risk of discrete appreciation or risk of discrete depreciation of the exchange rate. Before that time there exists only risk of discrete appreciation and after that time only risk of discrete depreciation. If at t = T the central bank chooses the policy mix of a floating exchange rate and the monetary policy rule fi( t) = p, then the exchange rate starts depreciating from the level s just as in the case of perfect foresight 7~= 1. If, instead, the policy mix S(t) = % and b(t) = 0 is chosen, then there is an instantaneous capital inflow corresponding to the original speculative capital flight which triggered the balance-of-payments crisis. Hence, foreign reserves are rebuilt to their pre-attack level at which they will remain permanently.
References Connolly, Michael B. and Dean Taylor, 1984, The exact timing of the collapse of an exchange rate regime and its impact on the relative price of traded goods, Journal of Money, Credit, and Banking 16, May, 194-207. Flood, Robert P. and Peter M. Garber, 1984, Collapsing exchange-rate regimes: Some linear examples, Journal of International Economics 17, l-13. Grilli, Vittorio V., 1986, Buying and selling attacks on fixed exchange rate systems, Journal of International Economics 20, 143-156. Krugman, Paul. 1979, A model of balance-of-payments crises, Journal of Money, Credit, and Banking 11, Aug., 311-325. Obstfeld, Maurice, 1984, Balance-of-payments crises and devaluation, Journal of Money, Credit, and Banking 16, May, 20X-217. Obstfeld, Maurice, 1986, Rational and self-fulfilling balance-of-payments crises, American Economic Review 76, March, 72-81.
75
25 (1987) 75-78
SPECULATIVE ATTACKS ON THE CURRENCY WITH UNCERTAIN MONETARY POLICY REACTIONS Alpo WILLMAN Bank of Finland, SF-00101 Received Accepted
Helsinki,
Finland
22 May 1987 24 July 1987
We show that balance-of-payments the exchange rate is constrained
crises are accompanied by discrete shifts in the exchange rate if in the pre-crisis by set limits and there is uncertainty about monetary policy reactions.
situation
1. Introduction In the recent literature concerning balance-of-payments crises it has been assumed that, once the foreign reserves have hit some critical lower bound, the central bank will, with certainty, abandon its earlier fixed exchange rate target and withdraw from the foreign exchange market. ’ With perfect foresight about the policy rules pursued by the central bank it has been shown that an exchange rate regime shift from a fixed to a floating exchange rate regime is preceded by a speculative attack on the currency and that the exchange rate regime shift occurs smoothly. i.e., without a discrete jump in the exchange rate. However, there is nothing forcing the central bank to abandon the fixed exchange rate regime at the moment the foreign reserves have been exhausted to the critical lower bound. The central bank could equally as well change its monetary policy rule consistent with the fixed exchange rate target. In this paper we show that uncertainty about monetary policy reactions affects balance-of-payments crises, if in the pre-crisis situation the exchange rate is constrained by set limits (a target zone). In this case balance-of-payments crises are accompanied by discrete shifts in the exchange rate.
2. The model and analysis We employ the same linear continuous-time small open country model as Flood (1984) and Obstfeld (1984, 1986). By assuming full employment (exogenous production), power parity and uncovered interest rate parity the model can be written as
M( t)/.S( t) = j3 - aE,S’( t),
P, a>0,
(2)
M(t) = D(t) + R(t), See e.g.,
(1979), Flood
and Garber purchasing
and Garber
(1984).
A. Wdlman / Speculative attacks
16
on currency
where M(t) is the nominal stock of non-interest-bearing domestic high-powered money, D(t) domestic credit, R(t) the stock of foreign reserves of the central bank, valued in home currency, and S(t) the spot exchange rate. E, denotes the expectation operator conditional on the information available at time t. Eq. (1) defines the demand for domestic real money balances as a decreasing function of the expected exchange depreciation. Eq. (2) defines the supply of money. If the exchange rate is allowed to float freely and assuming that the exchange rate depends only on market fundamentals, eq. (1) implies the following solution for the exchange rate: S(t)
= 1/aim
e -P(TPt)‘a E,M( r) dr.
If, in turn, the exchange rate is fixed so that s(t)
M(t)
=
R(t) =
(3) = 5, eqs. (1) and (2) imply
ps,
(4)
pS-D(t).
(5)
Let us assume a target-zone-restricted exchange rate the upper bound of which is ?. Assume further that, as long as the foreign reserves are above a critical lower limit which we assume to be zero, the central bank causes domestic credit to evolve over time according to the rule
b(t)=p.>o.
(6)
Hence, if the exchange rate has moved to its upper limit %, eqs. (5) and (6) imply that the foreign reserves must decline at the rate ~1, i.e., A(t) = -p. Of course, this is true if the exchange rate is fixed at any other level within the zone. This implies that any finite stock of foreign reserves is depleted to zero in finite time. Hence, at the moment the foreign reserves have been exhausted to zero, the central bank is forced to abandon the target zone or to change its monetary policy rule so that the condition R(t) >, 0 is not violated. In the following we assume that prior to the occurrence of a balance-of-payments crisis the exchange rate has moved to its upper limit ,!?. It is further assumed that, providing that the monetary policy rule (6) is not changed, the exchange rate is allowed to float freely from the moment the foreign reserves have been depleted to zero. This alternative is expected to occur with the probability 7~.With probability 1 - 7r the central bank is expected to change the monetary policy rule consistent with the target zone with ,!? as an upper limit, i.e.,
b(t) = 0.
(7)
In this case too the exchange rate can equally as well be said to float freely. Before the occurrence of the policy regime shift, eq. (1) together with the alternative policy rules (6) and (7), imply the following shadow floating exchange rate S’(t):
= D( t),‘P +
~~pa/p=.
monetary
(8)
The shadow floating exchange rate at time t is the floating exchange rate expected to prevail by investors, if the target-zone-restricted exchange rate regime were to collapse at that instant, i.e., foreign reserves were to be depleted to zero. 2 The shadow floating exchange rate rises in time as D(t) grows at the rate CL.The policy regime shift occurs at the point in time when the shadow floating exchange rate equals the upper limit of the target zone, i.e., S”(T) = s, where T indicates the point in time when the policy regime shift occurs. By this condition ‘abnormal’ profit or loss opportunities are precluded [see Flood and Garber (19X4)]. Together with eq. (8) this condition implies the following relation for the timing of the policy regime shift:
T=&/p--a/P,
(9)
where R, = /3,!?- D(O), equalling the stock of foreign reserves at t = 0. is that the monetary It can be easily seen that the smaller 7~ is, i.e., the greater the probability policy rule after the policy regime shift will be (7) the later the regime shift occurs. From eq. (6) it can be easily seen that the time needed to deplete the foreign reserves to zero without a speculative attack on the currency is R,/p. Hence, if 7~= 0 there is no speculative attack on the currency. With v = 1 eq. (13) reduces to the solution given by Flood and Garber (1984), i.e., T = R,/p - a/P. This is the earliest possible point in time when the speculative attack and the policy regime shift can occur. What happens to the actual exchange rate at t = T? From that instant onwards there is no uncertainty in the model and on the basis of eq. (3),
S(t) =
l/aim epP(Tp’)/aD(
which, after integrating,
t > T,
r) dr,
can be expressed
as
s(t)=D(T)/p+p(t-T)/p+pa/,8’
if
b(t)=p,
t&T,
D(T)/‘P
if
b(t)=O,
t&T.
=
(11)
Eq. (11) implies that with no change in the monetary policy rule the exchange rate depreciates at a constant rate p/p from T on. The adoption of the monetary policy rule b(t) = 0 implies, in turn, that the exchange rate will remain fixed at the level D(T)/p from T on. ’ From eqs. (8) and (11) it can be seen that with 0 < 7~< 1 there is a discrete jump in the exchange rate at t = T. The size of the jump is S(T)-S=(l-a)~lti/P~ =
-71p’y/p2
if
b(t)=p;
t>T,
if
b(t)=O;
t>T.
(12)
The jump in the exchange rate can be upwards or downwards. The upward jump (discrete depreciation) occurs, if the central bank adheres to its earlier monetary policy rule i>(t) = p and allows the exchange to float freely. The downward jump (discrete appreciation) occurs if the monetary policy rule (7), which is consistent with the fixed exchange target, is adopted. ’ The shadow floating target zone. 3 For expositional
exchange
reasons
rate defined
we assume
by (8) is the relevant
that this level of the exchange
shadow
rate only after exceeding
the lower level of the
rate is above the lower limit of the zone.
A. Willman / Speculmoe
78
attacks on currenq
It is worth noting that, although investors foresee with certainty that there is a discrete jump in the exchange rate at t = T, the size of the expected jump is zero. This is due to the fact that there is uncertainty concerning the direction of the jump. This uncertainty, however, disappears, if the target zone within which the exchange rate is allowed to move is narrowed to zero. Under this regime of a perfectly fixed exchange rate, the preceding example is transformed as follows: with probability r the central bank is expected to permanently withdraw from the foreign exchange market, with no change in the monetary policy rule and with probability (1 - r) to change the monetary policy rule to fi( t) = 0 retaining the fixed exchange target S(t) = s. The shadow floating exchange rate is in this case a weighted average of the freely floating exchange rate with the monetary policy rule b(t) = p and the fixed exchange rate g. Hence we can write S”(t)
=
7r/alwe -P(T-r)‘a[~(t)
+,A(T-
t)] dr+
(1 -+.
(13)
It is easy to see from (13) that with 0 < YT< 1 the point in time T, when the shadow floating exchange rate equals to 3, is independent of the size of VT.Hence, the timing of the speculative attack is the same as in the case of perfect foresight ~7= 1 studied by Flood and Garber (1984), i.e., T = R,/p a//3. This is the only point in time without either risk of discrete appreciation or risk of discrete depreciation of the exchange rate. Before that time there exists only risk of discrete appreciation and after that time only risk of discrete depreciation. If at t = T the central bank chooses the policy mix of a floating exchange rate and the monetary policy rule fi( t) = p, then the exchange rate starts depreciating from the level s just as in the case of perfect foresight 7~= 1. If, instead, the policy mix S(t) = % and b(t) = 0 is chosen, then there is an instantaneous capital inflow corresponding to the original speculative capital flight which triggered the balance-of-payments crisis. Hence, foreign reserves are rebuilt to their pre-attack level at which they will remain permanently.
References Connolly, Michael B. and Dean Taylor, 1984, The exact timing of the collapse of an exchange rate regime and its impact on the relative price of traded goods, Journal of Money, Credit, and Banking 16, May, 194-207. Flood, Robert P. and Peter M. Garber, 1984, Collapsing exchange-rate regimes: Some linear examples, Journal of International Economics 17, l-13. Grilli, Vittorio V., 1986, Buying and selling attacks on fixed exchange rate systems, Journal of International Economics 20, 143-156. Krugman, Paul. 1979, A model of balance-of-payments crises, Journal of Money, Credit, and Banking 11, Aug., 311-325. Obstfeld, Maurice, 1984, Balance-of-payments crises and devaluation, Journal of Money, Credit, and Banking 16, May, 20X-217. Obstfeld, Maurice, 1986, Rational and self-fulfilling balance-of-payments crises, American Economic Review 76, March, 72-81.