WPS 2-2 7
POLICY RESEARCH WORKING PAPER 2267
Do High Interest Rates No - there is no systematic
association between interest
Defend Currencies during rates and the outcome of
Speculative Attacks? speculative attacks.
Aart Kraay
The World Bank
Development Research Group
Macroeconomics and Growth U
January 2000 a
t PQmI.CY RESEARCH WORKING PAPER 2267
Summary findings
Drawing on evidence from a large sample of speculative The lack of clear empirical evidence on the effects of
attacks in industrial and developing countries, Kraay high interest rates during speculative attacks mirrors the
argues that high interest rates do not defend currencies theoretical anmbiguities on this issue.
against speculative attacks. In fact, there is a striking lack
of any systematic association between interest rates and
the outcome of speculative attacks.
This paper - a product of Macroeconomics and Growth, Develcpment Research Group - is part of a larger effort in the
group to study the causes and consequences of financial crises. Copies of the paper are available free from the World Bank,
1818 H Street,N'W, Washington, DC 20433. Please contact Rina Bonfield, room MC3-354, telephone 202-473-1248, fax
202-522-3518, email address abonfield@worldbank.org. Policy Research Working Papers are also posted on the Web a!t
www.worldbank.org/research/workingpapers. The author may be contacted at akraay@ 7* S - 2
where xt denotes the representative speculator's perception of the probability that the
currency will be devalued.16 Solving this optimization problem and aggregating over all
speculators results in a speculative demand for local currencyS(it,i) =
The monetary authority decides whether or not to devalue the currency by
weighing the costs and benefits of maintaining a fixed exchange rate. There are two
costs to fixing: the monetary authority must spend a fraction (R' of its reserves to
R
defend the exchange rate, and in order to maintain a desired level of reserves, it may
need to set domestic interest rates higher than it would otherwise do in the absence of
speculative pressures.'7 These costs are summarized in the following loss function of
the monetary authority:
(2) L(7r i, *) = 57 i 0 * g
R
where for simplicity I have assumed that the monetary authority's disutility of raising
interest rates is linear in the interest rate, with 0* measuring the strength of its aversion
to high domestic interest rates. The parameter 0* is not known to speculators, who
16 This convenient formulation of speculative behaviour is used by Drazen (1999). In the absence of such
adjustment costs, risk-neutral speculators will take infinite short (long) positions in the currency under attack
if the expected return to shorting is positive (negative). At the cost of complicating the algebra, one can
also motivate a continuous speculative demand for loans by assuming that speculators are risk averse.
17 I follow the conventional (implicit) assumption that the monetary authority dislikes reserve losses and
devalues when these losses are excessive. However, it is natural to ask why this should be the case. One
might also imagine that the monetary authority does not value reserves per se, but rather dislikes the
capital losses it suffers following a devaluation when it restores its target level of reserves by purchasing
them at the depreciated exchange rate. In this case larger reserve losses make devaluations more costly.
Moreover, raising interest rates may have the perverse effect of raising the rationally-expected probability of
a devaluation by making devaluations less costly to the monetary authority.
17
share a common belief that it is equal to i. Let ,B dienote the benefits of maintaining the
fixed exchange rate regime. These benefits are also not known to speculators, who
correctly perceive D to be uniformly distributed on the unit interval. Speculators do know
that if the costs of maintaining a fixed exchange rate exceed the benefits, the monetary
authority will devalue the currency to 1+E.
Speculators rationally form their beliefs regarding the probability that the
monetary authority will devalue, given their perceptions of the "type" of the monetary
authority, 0, and given the interest rate set by the mronetary authority. In particular,
speculators understand that 7t = Prob[L(ir,i,9) > f3], so that the rationally-perceived
devaluation probability is: 18
(3) 7 9 R . 2
R l-Ģi-F
I plot this probability as a function of the interest rates as a bold line in the top panel of
Figure 4. At low levels of the interest rate, the perceived devaluation probability is
decreasing in i. Over this range, speculation against the currency is intense, and the
marginal benefit of raising interest rates (in terms oi reducing reserve losses S)
outweighs the perceived marginal cost to the domestic economy (as measured by the
parameter i). As a result, raising interest rates lowers the monetary authority's disutility
of maintaining the fixed exchange rate, making a devaluation is less likely. In contrast,
when interest rates are high, the marginal benefit of further increases in interest rates is
smaller than the marginal cost to the domestic economy. Over this range, increases in
the interest rate raise the disutility of the fixed exchange rate regime, and so raise the
probability that the currency will be devalued.
18 To simplify this calculation, I assume that L(7r,i, O) < 1, so that Prob[L(j,i, 0) > P] = L(r,i, i) . It is
straightforward to verify that this holds in equilibrium provided that the following parameter restriction is
satisfied: R -. + < 1. This restriction will hcld provided that the devaluation rate e is
small enough and/or the amount of reserves R is large enough, which together ensure that the speculative
demand for reserves is never too large.
18
The question of interest in this paper is the slope of 7c(i), i.e. whether raising
interest rates raises or lowers the probability that a speculative attack ends in a
devaluation of the currency. However, estimating Tl(i) using the data on speculative
attack episodes described in the previous sections is complicated by two factors. First,
for a given interest rate, the slope of 7r(i) will depend on episode-specific characteristics.
This nonlinearity is illustrated in the lower panel of Figure 4, which considers two
speculative attack episodes that are alike in every respect, except that in the second the
level of reserves is higher than in the first. Not surprisingly, the probability of a
devaluation is everywhere lower in the second episode than in the first, since the
monetary authority has more reserves at its disposal to defend the exchange rate. More
important, at the same level of the interest rate (indicated by the vertical line), a small
increase in interest rates in the first episode will lower the probability of a devaluation,
while in the second episode it raises the probability of a devaluation.
The second difficulty is that the monetary authority's choice of interest rates is
endogenous, and depends on the strength of speculative pressures against the
currency. In order to illustrate this endogeneity within the confines of a very simple
model, I assume that the monetary authority sets interest rates to minimize the costs of
maintaining a fixed exchange rate. In particular, I assume that the monetary authority
chooses i to minimize Equation (2), taking into account the dependence of 7E(i) as given
by Equation (3). The optimal interest rate chosen by the monetary authority is:
( ) R ( ;*
and has a very natural interpretation. Other things equal, the higher is the devaluation
rate e or the lower are reserves R, the greater is the volume of speculation and the
higher is the interest rate set by the monetary authority to deter this speculation. The
greater is the monetary authority's aversion to high interest rates (the higher is G*), the
lower is the optimal interest rate. Finally, the more speculators think the monetary
19
authority dislikes high interest rates (the higher is 0), the higher the monetary authority
needs to raise interest rates to reduce speculation.'9
The important point is of course that the inteirest rate chosen by the monetary
authority in Equation (4) depends on the same fundamentals as speculators' perceived
probability of devaluation in Equation (3). In Figure 5, I illustrate how this endogeneity
problem can either obscure or accentuate the effects of tighter monetary policy during
speculative affacks. In the top panel, I again consider two episodes that are alike in
every respect, except that in the latter the reserves of the monetary authority are higher
than in the former. At the equilibrium in the first episode at A, 7T(i) is decreasing in i, so
that a small increase in interest rates has the conventional effect of lowering the
perceived probability of a devaluation. In the high reserves case, the speculators'
rationally-perceived devaluation probabilities are lower than before (shown as a
downwards shift in n(i)), while the monetary authority reacts to these devaluation
perceptions with a lower interest rate since it has a larger "cushion" of reserves. In this
episode, the equilibrium is at B with a lower interest rate and a lower devaluation
probability. Simply comparing these two episodes, one might easily be led to the
mistaken conclusion that raising interest rates raises the probability of a devaluation,
while precisely the converse is true (since both A and B fall on the downward-sloping
portion of 7rt(i)).
Similarly, the endogeneity problem may also lead to the conclusion that raising
interest rates has the conventional effect of lowering the probability of a devaluation
when in fact the opposite is true. 11 illustrate this possibility in the bottom panel of Figure
5. 1 again consider two identical episodes, which now differ only in the monetary
authority's distaste for interest rates (0*) and speculators' beliefs regarding this
parameter (0). The dashed lines correspond to an episode where both 9* and 0 are
lower than in the episode shown irn solid lines. Not surprisingly, the monetary authority
sets a higher interest rate, and since speculators believe that the monetary authority is
"tough", the devaluation probability is lower for every interest rate i (shown as a
19 assume that the monetary authority knows speculators' perceptions regarding its type, i.e. the monetary
authority knows 0. The main point of the model regarding the endogeneity of policy is unaffected if I
instead assume that the monetary authority does not know 0 Ibut instead takes speculators' perceived
devaluation probabilities as given when minimizing Equation (2).
I0
downwards shift in 7c(i)). Comparing the equilibria A (with a high devaluation probability
and a low interest rate) and B (with a low devaluation probability and a high interest
rate), one might easily conclude that raising interest rates lowers the probability of a
devaluation when the converse is true (since both A and B fall on the upward-sloping
portion of 7c(i)).
This discussion illustrates how the endogeneity of policy can bias the estimated
effects of policy in unknown directions. To the extent that the fundamentals that drive
both speculative pressures and the policy response are not fully observable, partial
correlations between policy and the outcome of speculative attacks will not correctly
identify the effects of policy. To achieve identification, I require an exogenous source of
variation in the interest rate set by the monetary authority that can be used as an
instrument for policy. In this stylized model, the monetary authority's private information
about its "type" (0*) plays this role, since changes in 0* shift the monetary authority's
reaction function without shifting speculators' rationally-perceived devaluation
probabilities. More generally, any private information of the monetary authority which
influences its choice of interest rates can in principle serve to identify the effects of
interest rates on speculators' beliefs that an attack will end in the devaluation of the
currency.
Empirical Specification
I now turn to the empirical specification motivated by this simple model. The
objective is to estimate the impact of monetary policy on probability that a speculative
attack fails. Although this probability is not observable, I do observe a binary indicator of
whether a speculative attack fails or not. I can therefore estimate the marginal effects of
policy on probability that an attack fails using a probit model, with this indicator as the
dependent variable. The first implication of the theory is that this probability will be a
non-linear function of fundamentals and the monetary policy response. Although the
simple model discussed above is too stylized to take the exact functional form implied by
Equation (3) literally, it does suggest that the explanatory variables in the probit equation
should include not only measures of policy and fundamentals, but also interactions
between the two. Accordingly, I consider the following non-linear probit specification:
21
yi =PO + l ii + P2'fj + 3' fj * ij +u
(~ ~ ~ ~~~~~ ) ,if Yj* >
yi O, ifyj* cn (F2ao -92
20-Oct-97 23-Ot-9
o ~~ ~~~~~ ~ ~ ~~~~ oOctn92 co
3 0-Oct-97
4-Nov-92
09-Nov-97 '
19-Nov-97 ~~~~~~~~~~~~~16-Nov-92
29-Nov-97 26Nv9 0.
09-Dec-97 8~~~~~~~~~~2-Dec-92 c2
19-Dec-97 18-Dec-92 :
C: (D~~~~~C
29-Dec-97 183-Dec-92 - I
0 CJ~~~~ -~~ -~~~ f~~3 ~~~) 0 WJ C rth. ui 0) -4j 0)
0 0 01 ~~ ~~~0 CO
0 0 ~~~0 0) 0 Krona/$
0Won/$0 0
Figure 2: Exchange Rates and Reserves During
Successful and Failed Speculative Attacks
Successful Attacks
120 --
115- /
110 I
0, 105-
II~ ~ ~~~~~~9
85 -
-12 -10 -8 -6 -4 -2 C 2 4 6 8 10 12
Months Since Attack
Failed Attacks
120 -
110 -
80 -
70 -
,,I , ,I , , -60 , r ,
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
Months Since Attack
Notes: This figure shows the evolution of the median nominal exchange rate and reserves during
successful and failed speculative attacks. The figures are constructed by cumulating the median (across
all episodes) growth rate of the indicated variables to a base of 100 twelve months prior to the attack.
42
Figure 3: Changes in Real Discount Rates During
Successful and Failed Speculative Attacks
0.25
Mean Change During
Successful Attacks = 0.45
0.2 - eD Successful Attacks
Mean Change During l Failed Attacks
Failed Attacks = 0.30
01
as
0
0
0.1 l
-25 -20 -15 -10 -5 0 5 10 15 20 25 >25
Percent Changes in Real Discount Rates Less Than:
Notes: This figure shows the frequency distribution of percentage changes in real discount rates during
successful and failed speculative attacks. The mean changes during successful and failed attacks are
based on changes in real discount rates less than 25% in absolute value.
43
Figure 4: Devaluation Probabilities as a Function of Interest Rates
Devaluation Probability
0.9
0.8
°0.7 - 2(i)
> 0.6 -
o 0.5
. 0.4
3
2 0.3
0.2
0.1
0-I
0 0.05 0.1 0.15 0.2 0.25 0.3
Interest Rate
Non-Linear Effects of Policy
1
0.9
0.8 -
0
70(i), Low Reserves
o 0.6 -
0.2 -
0
0.4 -
~~~~0.4 ~~~~~~~~~~ir(i), High Reserves
2 0.3-
0.2O-
0.1
0
0 0.05 0.1 0.15 0.2 0.25 0.3
Interest Rate
44
Figure 5: The Endogeneity of Policy
Case 1: Endogeneity Bias Obscures Conventional View
0.9
0.8 .
0
~0.7-
> 0.6
Q
0.5
.0
0.4
0.2-
0.1 I
0 i
0 0.05 0.1 0.15 0.2 0.25 0.3
Interest Rate
Case 2: Endogeneity Bias Exaggerates Conventional View
1
0.9
0.8
0.2
~0.
0.4 - l l l l l l
00.5 - 0 0 0 0
~0.2
Interest Rate
45
20.3 ~ ~ ~ ~ ~~4
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