Empirical Assessment of Target-Zone using a STAR Modelby
Ayano Sato++School of Economics
Niigata Sangyo University
Kashiwazaki, Japan
June, 2006
JEL Classification Number
F31

Foreign Exchange

C22Time Series Models

Key words: Target-zone, nonlinearity, implicit zone, STAR model
Address correspondence to : Ayano Sato,
School of Economics,
Niigata Sangyo University
4730, Karuigawa, Kashiwazaki-city,
Niigata-pref. 945-1393, JAPAN
Phone & FAX: +81-257-24-8519
E-mail:ayano_sato@econ.nsu.ac.jp

Empirical Assessment of Target-Zone using a STAR Model

June, 2006

ABSTRACTThis study is intended to investigate mean reversion and nonlinearity for exchange rates in a target
zone system using a Smooth Transition Auto Regressive (STAR) model. We estimate an implicit
target zone using daily spot French franc/Deutsche mark exchange rates. Our contribution is tosupport the exchange-rate nonlinearity, a phenomenon called the honeymoon effect, and to confirm
behavior of exchange rates differs when near or distant from the implicit central parity. The
estimated implicit band is narrower than the officially announced band, not symmetric around theannounced central parity.

11. Introduction

Since the advent of the generalized floating exchange rate system in spring, 1973, the choice of an
optimal exchange rate system has remained a central issue in modern international finance.
Traditionally, the relative advantages of the two polar cases, fixed and freely floating exchange rate
regimes, have remained theoretical and empirical focal points. Both regimes present advantages anddisadvantages; tradeoff relationships might exist between them. Therefore, eclectic regimes between
two polar regimes seem to be attractive if the exchange rate exhibits flexibility with less variability
than a freely floating system would allow. An example of such eclectic systems is proposed in an
elegant theoretical framework of a target zone system by Krugman (1991), who derives two key
predictions for exchange rate movements: to the extent that the exchange rate is determined byfundamental factors that are subject to a random walk process within a credible target zone, theexchange rate is mean-reverting. That movement is approximated by an S-shaped curve near theboundaries of the target zone. Consequently, the target zone exerts a stabilizing effect on theexchange rate according to the threat of intervention at the boundaries.
Nevertheless, few empirical tests have confirmed the main predictions for the target zone models.
Svensson (1992) and Garber and Svensson (1995) attribute the rejection to the following two
assumptions imposed by Krugman (1991). The first assumption is that perfect credibility tointervention pertains. The second is that, although central banks actually intervene in the interior of azone, the central bank is assumed to intervene only at the zone margin. For that reason, empiricalstudies need to identify intervention time periods accurately. However, because of the lack ofreliable data on actual intervention, precedent empirical studies have either failed to examine thestabilizing effect of a target zone or insufficiently tested it.
The purposes of this paper are twofold. First, we investigate mean reversion and nonlinearity forexchange rates in a target zone system using a Smooth Transition Auto Regressive (STAR) model,
which is an extension of a non-linear unit root test.
The second purpose is that we estimate an implicit target zone using the daily spot Frenchfranc/Deutsche mark exchange rates, similarly using the STAR. This model is employed as
regime-switching, to account for existence of an unobservable implicit target zone that differs fromthe announced target zone, but which is perceived by actual investors who are sensitive to2

intervention1. As many studies (Svensson, 1992; Giavazzi and Giovannini, 1989; Klein and Lewis,1993) point out, intra-marginal intervention is a fact, but few studies have estimated the exchange
rate level for the implicit band directly, except for Chung and Tauchen (2001).
We can infer whether or not Krugman’s target zone model is empirically supportable under theestimated implicit band if we obtain results for our purposes. We confirm mean reversion for
exchange rates under the implicit zone measured using its adjustment speed and transition functionof the estimated STAR model to be more specific. The mean-reversion for exchange rates signifies
stability that is absent under freely floating rates and a conventional managed float system. In short,
if we confirm that exchange rates under a target zone regime follow a globally mean reverting
process, the regime would be equally preferable or more preferable to the two polar regimes.
Although the property of a target zone has been widely pointed out2, little effort has been devoted totesting their validity, except for two noteworthy studies by Anthony and MacDonald (1998, 1999).
Our first contribution is to support the nonlinearity of exchange rate, a phenomenon called thehoneymoon effect, and to confirm that behavior of the exchange rate is different between theneighborhood of and away from the implicit band: the exchange rate locally follows a diffusion
process, whereas the exchange rate globally follows a mean-reverting process. This result contrasts
sharply with that of Anthony and MacDonald (1998, 1999), who find mean-reversion without
dividing samples by a linear unit root test and variance ratio test. That is, using the same sample
period and the same French franc/Deutsche mark exchange rate as Anthony and MacDonald (1998),
we obtain different results and conclude that exchange rates behave as though under the managed
float system, not as though they are under the target zone system.
The second contribution is that the implicit band estimated by the STAR model is narrower thanthe officially announced band; moreover, it is not symmetric around the announced central parity.
This point roughly concurs with that of Chung and Tauchen (2001). They identify the exchange ratelevel of the implicit band for the same sample period and the same French franc/Deutsche markexchange rate using the efficient method of moments, whereas we specify the implicit boundaries asa range that includes the exchange rate level estimated by Chung and Tauchen (2001). This different

1

As stated in Chung and Tauchen (2001, p255), an implicit band is defined as “a situation in which market

participants do not believe the official band and instead base their decisions on a perceived unofficial band withunstated target rates.”2

See Flood, Rose and Mathieson, 1991; Lindberg and Soderlind, 1991

3

point poses a question on Krugman’s predictions or existence of an implicit target level for theexchange rate by the government.
The remainder of this paper is organized as follows: The next section briefly introduces a target
zone model and elucidates its limitations. Section 3 is dedicated to empirical examination of thetarget zone using a STAR model. Our analysis for the implicit target zone is presented in Section 4.
The last section concludes the paper.

2. Target Zone Models

After some earlier works on exchange rate target zones, recent works have been inspired by theelegant model by Krugman (1991)3.
Krugman (1991) started from the presumption that an exchange rate depends both on some current
fundamentals and an expected future change in the exchange rate.

st = ft + α

Et [dst ]dt(1)Therein, st is the logarithm of the spot exchange rate at time t, α represents the sensitivity of theexchange rate to its own expected future change, dst is the change in the exchange rate over time,and Et represents the mathematical expectation operator. Also, ft denotes the unobservable aggregate
fundamentals, which are presumed to consist of two components: velocity, which is exogenous andstochastic; and the money supply, which is inferred to be managed by a central bank.
Krugman (1991) assumes that the fundamentals conform to a Brownian motion with the constantinstantaneous standard deviation σ,

df = σ dWt ,(2)

where a random variable dWt is a standard Wiener process.
The assumption of a Brownian motion for fundamentals is plausible because it implies that the
movements of the free-float exchange rate would be closely approximated by a random walk process,3

For instance, Williamson (1985) and Dumas (1992) are exemplary earlier works.

4

which inference corresponds to those of some empirical studies4. In Krugman (1991), the exchange
rate fluctuates within a target zone around a specified central parity by central bank intervention. We
denote this band ass ≤ st ≤ s ,(3)where s and s respectively represent the lower and upper edges of the exchange rate band.
Making the zone symmetric around s=0 to simplify the algebra, we assume that s = − s . When theexchange rate strictly satisfies eq.(3), we can obtain the general solution:st ≡ G ( ft ) = f − A[exp(λ1 f ) − exp(−λ2 f )] ,where λ =

2

ασ 2

(4)

. A is an arbitrary constant to be determined by the smooth pasting conditions,which are obtained by continuity of the exchange rate and the expected intervention5.
Krugman (1991) shows that the exchange rate would follow a nonlinear S-shaped locus and bemean-reverting within the band. In addition, Svensson (1992) suggests that the exchange rate spends
most of the time near the edges of the band and that the distribution is U-shaped．However, few
researchers have examined the first prediction except for Anthony and MacDonald (1998), and many
researchers report that empirical tests of this simple target-zone model have not confirmed thesecond prediction.
As Garber and Svensson (1995) point out, Krugman (1991) requires two crucial assumptions.
First, the exchange rate target zone is perfectly credible, in the sense that market agents believe thatthe lower and upper edges of the band will remain fixed forever, and that no realignment will occur.
However, the assumption of perfect credibility is unrealistic given the frequent realignments that are
actually observed. Second, the target zone is defended with marginal interventions only: nointervention occurs as long as the exchange rate does not hit the edges of the target zone. However,numerous empirical findings indicate that central banks in the European Monetary System (EMS)
intervened before exchange rates hit the announced edges of the target zone, i.e., intra-marginal

4

See Meese and Rogoff (1983)

5

The smooth pasting conditions hold when both marginal and intra-marginal interventions are anticipated. See Floodand Garber (1991) and Delgado and Dumas (1992).

5

intervention6.
Therefore, we attribute the failure of most empirical studies of target-zone models to be based onassumptions that the market would base decisions on the official band of central banks. In thefollowing section 3, we empirically examine the predictions of Krugman (1991) using the estimation
method, which is different from Anthony and MacDonald (1998) and Chung and Tauchen (2001).

3. Empirical Analysis

3.1 Data

At the Bremen Summit of July 1978, the European Council (EC) endorsed the creation of the
EMS, which came into existence in March of 1979. The centerpiece of the EMS was the Exchange
Rate Mechanism (ERM), which was designed to limit exchange rate fluctuations. The seven charter
members of the ERM were Belgium, Denmark, France, Germany, Ireland, Italy and the Netherlands.
The ERM was strengthened greatly in September of 1987 with the signing of the Basle-Nyborg
agreement, which effectively stabilized the ERM for nearly five years. Apart from the Lira’s
technical realignment of January 1990, no changes in central parities occurred until the summer of
1992. Notwithstanding, the speculative attack against the currency of the EMS members is wellknown to have raged in September 1992 and August 1993. Since that time, member countries of the
EMS widened the target zone from ±2.25% to ±15% around the central parity.
The purpose of our empirical investigation is to examine the mean-reverting property of theexchange rate and the existence of an S-shaped locus, given a credible target zone.
For that purpose, we select the daily spot exchange rates for French franc/Deutsche mark(FF/DM), from 12 January 1987 to 31 July 1993, simply because it has been relatively stablecompared with the other ERM exchange rates, and because it is used by Anthony and MacDonald(1999) and Chung and Tauchen (2001), among others. The central parity is officially 3.354 FF/DM,
the upper bound is 3.429, and the lower bound is 3.278 during the period. The sample is obtained
from the database provided by the University of British Columbia7. Figure 1 shows a plot of daily
observations on FF/ DM exchange rate in the sample period and Table 1shows descriptive statistics.
6

For theoretical examination on intra-marginal intervention, see Bertola and Caballero (1992).

7

The data set is available from http://fx.sauder.ubc.ca/data.html

6

The data are expressed as deviations from central parity.

***** Insert Figure 1 and Table 1 around here *****

3.2 Econometric Methodology

The standard means of evaluating the mean-reversion for target zone models, which is known as
an Argument Dickey-Fuller unit root test (ADF), is to estimate the following regression equation.

n −1∆st = κ1st −1 + ∑ κ j ∆st − j + υt

(5)

j =1

A unit root will be present in the exchange rate series if κ1=0. The null hypothesis is tested using astandard t-ratio of the estimate of κ1 to its estimated standard error. Although this will engender anon-standard distribution, one must use the percentiles tabulated by Fuller (1976) or Mackinnon(1991). Table 2 reports the results in this linear unit root test8. The nonstationarity of the FF/DM
exchange rate is apparent.

***** Insert Table 2 around here *****

However, as presented in section 2, Krugman (1991) suggests that the exchange rate within thetarget zone is non-linear for fundamentals. Moreover, if an exchange rate band is credible, theexchange rate within the band should be strongly mean-reverting. In addition, Meese and Rose(1983) and Bekaert and Gray (1998) also indicate the fact that linear models do not well describe
higher-frequency exchange rate dynamics. Garratt, Psaradakis and Sola (2001) find evidence oftarget-zone nonlinearities in the sample period, from 10 October 1990 to 16 September 1992.
Therefore, the results for an ADF test are incompatible with target-zone models9. We propose an

8

We also conduct unit root tests with a drift, and with drift and a time trend. Although the results are unreported,

they show the nonstationarity of the FF/DM exchange rate as well.
9

Taylor and Iannizzotto (2001) show that an ADF test has little power.

7

alternative test using a Smooth Transition Auto Regressive (STAR) model, which extends to anonlinear unit root testing procedure to evaluate target-zone models. Another advantage of using
STAR is that it can be interpreted as a regime-switching model and can consequently treat the upperand lower boundaries as unknown parameters in the case that boundaries are unobservable because
of intra-marginal intervention.
The STAR is first introduced by Tong (1990) and Granger and Terasvirta (1993); it is popularized
by Terasvirta and Anderson (1992), and others. Michael, Nobay and Peel (1997) apply an
exponential STAR (ESTAR), which is one of the STAR family, to two data sets: annual and monthly
data. They find strong support for mean-reverting dynamic process, which is varying with sizabledeviations from Purchasing Power Parity. We apply the method of Michael, Nobay and Peel (1997)
to a target zone model and assume that the exchange rate is described by the following ESTAR
model:

p−1

p−1

j =1

j =1

∆st = λ1st−1 + ∑φj ∆st − j + (λ1*st−1 + ∑φj*∆st− j )F( yt ;γ , c) + εt , εt ~ i.i.d.(0,σ 2 ) ,(6)

where F ( yt ; γ , c) is a continuous transition function and yt is a transition variable; γ denotes the
speed of transition and c indicates central parity in a target zone. In an ESTAR model, F ( yt ; γ , c) is
substituted into the following exponential function.

F ( yt ; γ , c) = 1 − exp{−γ ( yt − c) 2 }γ > 0, 0 ≤ F ≤ 1(7)Figure 2 shows that the transition function (7) switches smoothly from an inner regime to twosymmetric outer regimes, so that the ESTAR model implies a non-linear unit root test weighted by
the transition function. The inner regime corresponds to yt =c. That is, when F ( yt ; γ , c) = 0 and eq.
(6) becomes a tractable AR (p) model, thenp −1∆st = λ1st −1 + ∑ φ j ∆st − j + ε t′ .
j =1

(8)
The outer regimes correspond to yt = ±∞ when F ( yt ; γ , c) = 1 and eq. (6) becomes a different
AR (p) model:

8

p −1

∆st = (λ1 + λ1* ) st −1 + ∑ (φ j + φ *j )∆st − j + ε t′′ .

(9)

j =1

The crucial parameters are λ1 in (11) and λ1 + λ1 in (9), indicating the adjustment speed. In our*

discussion, the effect of expected intervention suggests that the larger the deviation from central
parity, the stronger the tendency to move back. This means that, whereas λ1 ≥ 0 is possible, wemust have λ1 < 0 and λ1 + λ1 < 0 . Consequently, if these sign conditions are satisfied, it implies**

that eq. (6) with eq. (7) is globally mean-reverting.

***** Insert Figure 2 around here *****

3.3 Estimation and Results

For estimation of the ESTAR model, we first need to specify a linear autoregressive model AR (p),in which p denotes the order of the lag. The order p=2 is selected from SBIC statistics10. Next, foreach linear AR (p) model for the FF/DM exchange rate, we test linearity (F test) for a certaintransition variable, yt. It is common to select a single lagged endogenous st-d (d is called a delay
parameter) as yt. We test d=1, 2, and 3 using the following auxiliary equation11.

p

st = β 00 + ∑ ( β1 j st − j + β 2 j st − j st − d + β 3 j st − j st2− d ) +ξ t
j =1

ξt ~ n.i.d (0, σ ε2 )(10)

The null hypothesis of linearity for st is

H 0 : β 2 j = β3 j = 0 .

As reported in Table 3, it is concluded that the linearity in eq. (10) is rejected strongly for d=1;
10

If the order is determined by the AIC for a finite sample, it is known that it has a positive probability of overfitting,but it is not consistent for a large sample. In contrast, it is known that the SBIC is consistent. The sample size of ourdata is relatively large. Therefore, we adopt the SBIC. We also validate the selected order of lag with the Ljung-Box(Q) statistics.
11

See Terasvirta and Anderson (1992).

9therefore, a nonlinear stochastic process is accepted in the FF/DM. This fact suggests that ahoneymoon effect exists in the exchange rates within a band12.
Taylor and Iannizzotto (2000) show that nonlinearity is present, but that it only applies in regionsthat are very close to the tangency point at the edges of the band. That is, the honeymoon effect ismuch smaller. Jong (1994) reports that no nonlinearities exist for the three currencies (Dutch guilder,
Irish punt and Italian lira) on the six EMS exchange rates. The two results seem to conflict with ourevidence at first sight, but might indeed be consistent. The reason is explained in the next section.

*****Insert Table 3 around here*****

Finally, we use a nonlinear least-squares method to estimate eq.

(6). Terasvirta (1994) points outthat the estimation of parameters might cause some problems (e.g., slow convergence,overestimation and so on) 13. We therefore follow his recommendation in scaling the argument of thetransition function F(st-d) by dividing it by the variance of st. We set γ at 1 and use zero for allparameters other than γ as the initial value. The estimation results are listed in Table 4.

*****Insert Table 4 around here*****

Terasvirta (1994) suggests that the estimate of the parameter c be within the observed range of st.
Our estimated ĉ (=0.007) satisfies this criterion for the FF/DM and is actually positive, as reported
in Table 4. The positive ĉ means that observations for the FF/DM scatter above the announced
central parity (see Fig. 1). According to Table 5, the reduction in the residual variances relative to thelinear model is 2%, as shown by the variance ratio, and the possibility of autocorrelation is low,
although we should be cautious of heteroscedasticity14.
Most of the estimated coefficients are statistically significant at the 5% level by the t test and the12

Krugman (1991) assumes that the exchange rate is non-linear for fundamentals. Nevertheless, it is impossible totest nonlinearity of the daily exchange rate for fundamentals because daily data for fundamentals are not available.
13

A precise estimate of γ by STAR estimations is well known to be difficult to obtain. However, an apparently

non-significant estimate of γ should not be interpreted as indicating the non-significance of regime switching (see,Terasvirta and Anderson (1992)).
14

For the ratio of residual variances, the best ratio is 0.766 and the worst is 0.967 in Michael, Nobay and Peel (1997),

the best ratio is 0.883 and the worst is 0.962 in Chen and Wu (2000), respectively.

10sign conditions are satisfactory. Hence, we confirm that, whereas the exchange rates around theestimated central parity (= ĉ ) mark a diffusion process, the exchange rates that are distant from theparity follow a mean-reverting process. To reinforce this, we additionally perform a test ofmean-reversion by examining the conditions from eqs. (9) and (11). The hypotheses to be tested
are formally stated as

H 0inside : λ1 = 0,and

H 0outside : λ1 + λ1* = 0.
We confirmed that the exchange rate is global stationary and is mean-reverting toward theestimated central parity. The ones near the parity follow a diffusion process using both the Wald
test and the Likelihood ratio test (see Table 6).

*****Insert Tables 5 and 6 around here*****

These results yield an informative suggestion into the behavior of exchange rates within thetarget zone. Krugman (1991) points out that if a target zone is credible, the exchange rate within
the zone should exhibit mean-reversion strongly, even without intervention. However, theevidence of diffusion process we find is clearly the property of free-float system or managed
float with a target central parity, rather than that of target zone, as Svensson (1992) argued.
Surprisingly, these rejections might support the two results of Anthony and MacDonald(1998). It indicates little evidence of mean reversion using the ADF test, but it confirms that theexchange rates within the target zone are mean-reverting using the variance ratio test. That is,
the two conflicting results are consistent with our findings that exchange rates are globally
mean-reverting, but which locally show diffusion. In addition, Taylor and Iannizzotto (2000)
and Jong (1994), suspecting a nonlinearity process in exchange rates, are probably compatible
with our findings, allowing for partial existence of the random walk process within the target
zone15. In other words, our findings indicate that exchange rates have nonlinearity, but Taylor
and Iannizzotto (2000) and Jong (1994) could only slightly observe the property because the15

Jong (1994) also suggests that nonlinearities be explained by the presence of an implicit band that is narrower thanthe official band.

11

mean-reversion range in exchange rates is limited. We are unable to deny that the honeymoon
effect is smaller than the supposition of Krugman (1991), as Taylor and Iannizzotto (2000)
point out.

4. Suggestion of an Implicit band by Adjustment Speed and Transition function

Rose and Svensson (1995) suggest the existence of an implicit band. Chung and Tauchen(2001) estimate that the upper band is 3.408, the lower is 3.292, and that the central parity is 3.377.
They assert that the implicit band is narrower than the official band. In contrast, Labhard and
Wypolsz (1996) report that the implicit band is slightly larger than the official band, although they
do not identify the bandwidth. Clearly, these affirmations of the implicit band are inconsistent. Does
an implicit band really exist? And what ever does the implicit band mean? During this sample period,
several studies show that the governments in fact intervene intra-marginally. However, it is
impossible for us to accurately determine when the governments intervene, the extent or degree ofthat putative intervention, and where a target level of band is, unless a government announces it.
When we define an implicit band, we are unable to identify whether the governments actuallyintervene, or investors who are sensitive to intervention sell or buy currency spontaneously without
using accurate intervention data. The actual exchange rate level of intra-marginal intervention is notalways coincident with the level of the band perceived by investors without announcement.
Therefore, we define an implicit band only as an observable band, by which we conjecture the target
level of intra-marginal intervention and the band perceived by investors.
In this paper, the estimated transition function and adjustment speed make it possible to identify
the observed implicit band. In Fig. 3, the transition function indicates that the transition from thelower outside to the inside of zone starts from around 3.317 FF/DM and arrives at 3.377. Theinterval between 3.317 and 3.377 is interpreted as a process of regime-change. Therefore, thetransition function shows that the implicit lower band must be in this interval. This means that 3.317
is definitely in the lower regime, and 3.377 is the implicit central parity, which is perfectly consistent
with the central parity estimated by Chung and Tauchen (2001). Similarly, 3.438 is definitely in theupper regime and the implicit upper band must be in between 3.377 and 3.438.

*****Insert Table 7 around here*****

12

Figure 3 also depicts the adjustment speed for the FF/DM exchange rates, obtained from oursimulation. The adjustment speed is defined with the gradient vector, which means a convergenceprocess (mean-reversion) in the case of negative values and a diffusion process in the case of
positive ones. The adjustment speed is the most rapid at 3.377. The slowest is around 3.361 and3.394, changing from negative to positive. This relationship suggests that exchange rates tend to stayaround 3.361 and 3.394 for a long time. This fact seems to be consistent with the humped
distribution of exchange rates suggested by some preceding studies. However, 3.361 and 3.394 arenear the announced central parity, but it seems to be U-shaped for the estimated central parity, theestimated upper and lower regime. In addition, exchange rates follow a diffusion process between
3.361 and 3.394 FF/DM. This interpretation posits that investors only slightly expected agovernment to intervene between 3.361 and 3.394 FF/DM because the movement of exchange rates
is consistent with that of a free-float system in this range. On the other hand, exchange rates aremean-reverting between 3.317 and 3.361 and between 3.394 and 3.438. All investors might believe agovernment defense of an announced band in the range less than 3.317 and more than 3.438. But
investors expecting an intra-intervention might increase gradually from 3.317 to 3.361, or from3.394 to 3.438. In summary, our simulation experiment shows that, given perfect credibility, thelower boundary of the implicit zone is identified as below 3.361 and the upper boundary is identified
as above 3.394 for the FF/DM exchange rate during our sample period. Consequently, our estimatedimplicit band differs greatly from the officially announced target zone and is not symmetric aroundthe announced central parity. However, it is impossible to specify the level of implicit boundaries inour research, though it includes the estimation result of Chung and Tauchen (2001). Because therange of the exchange rate transiting a regime is very broad 16 . We suggest two plausible
interpretations for the implicit band. One is that each investor expects different target levels and sells
or buys currency because of reiteratively intra-marginal intervention without a definite target level,
as in a managed float system. The other is that even if a government intervenes intra-marginally witha definite target level and all investors fully forecast that level, exchange rates behave similar to
those of a managed float system by the presence of an implicit target zone, not as Krugman (1991)
suggests.

16

This is corresponding to the argument of Labhard and Wypolsz (1996) because our results show that the range ofthe upper boundary is above the officially announced upper boundary.

13

*****Insert Figure 3 around here*****

5. Concluding Remarks

This paper presented an empirical examination of the main predictions of Krugman (1991), whoconcluded that the exchange rate would remain, most of the time, near the edges of the band and bemean-reverting within the band under the perfect credibility for intervention. Through employmentof a more elaborate ESTAR model, we confirmed that (1) nonlinearity, (2) mean-reversion, and (3)existence of the implicit band (or intra-marginal intervention). Our salient results are summarized
briefly as follows.
First, this paper provides evidence that the FF/DM exchange rates follow a nonlinear process,which suggests the existence of the honeymoon effect. Second, the exchange rates far from theestimated central parity follow a mean-reverting process toward parity, whereas the exchange rate
near the estimated parity follows a diffusion process. This is an important result because it can
explain the failure in many empirical studies for nonlinearity and mean reversion. The failure in
nonlinearity tests might result from two kinds of movement for exchange rates within a target zone.
Furthermore, the failure in mean-reversion results from using a linear model and two different
movements. Finally, we found the existence of an implicit band that is different from the officiallyannounced target zone and which is asymmetric around the announced central parity by our
simulated transition function and the adjustment speed. Moreover, we specified the possible range ofthe implicit band. Although many precedent studies have suggested the existence of the implicit
band, to our knowledge, not one, except for Chung and Tauchen (2001), has directly calculated therange of the lower and upper boundaries for the implicit exchange rate band.
In conclusion, we demonstrated that the key predictions of Krugman (1991) are incorrect for the
FF/DM exchange rates during the sample period, even allowing for an implicit band, and exchange
rates behaved as in the managed float system, not like a target zone.
Nevertheless, it is important to recall that the exchange rate was stable during the sample period
and that the government kept the announced target zone.
After the EMS crisis, the bipolar view on the exchange rate regimes became dominant. However,the Brazilian crisis raised several questions against that view, and Frankel (1999) and Fischer (2001)
pointed out that intermediate exchange rate regimes are more likely to be appropriate for many
countries than the bipolar view.

14

If the target zone system or managed float system is more stable under some conditions, as wehave concluded, then adopting intermediate exchange rate regimes is supported.

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17

Table 1: Descriptive Statistics for the FF/DM Exchange Rates

MeanMedianMaximum

Minimum

3.382

3.387

3.426

3.323

Standard
Deviation
0.024

Skewness

Kurtosis

Observations-0.602

2.539

1658

Table 2: Augmented Dickey-Fuller Test for Unit Roots

FF/DM

κˆ1

S.E.

SBIC

adjR2

-0.00350.001129-10.726

0.0236Log
Likelihood
8910.734(0.002)

S.E. is standard error of regression, Standard error is in parenthesis, adjR2 is adjusted coefficient of determination for degrees of freedom.
***, **，and *indicate significance at the 1，5，and 10％ level, respectively by Mackinnon(1996).

Table 3: Linearity Test
d=1

FF/DM
***, **，and *

d=2

2.30

3.55 ***

d=3

*

1.84

indicate significance at the 1，5，and 10％ level, respectively, and are determined by the critical value on the basis of the F distribution．

18

Table 4: The Coefficients for ESTAR Model

λ̂10.0132

FF/DM**(0.006)φˆλ̂ 1*-0.0287-0.0257(0.045)(0.008)φˆ****-0.243***(0.076)γˆĉ

1.13270.0073(0.839)(0.000)***Standard error is in parenthesis.
***, **，and *indicate significance at the 1，5，and 10％ level, respectively, and are determined by the critical value on the basis of the t distribution．

Note. γˆ = γˆ × σ s*

2

Table 5: Diagnostic Test

FF/DM

ARCH(4)

Q (4)

SBIC

JB

VR

178.8***

0.730-10.72

1811.2***

0.98

Log
likelihood
8911

adjR2

S.E.

0.037

0.0011JB is the Jarque and Bera (1980) normality test.
VR shows variance ratio

σ E2
2
2
, where σ E and σ L are the residual variances from the restricted ESTAR and the linear model, respectively.
2
σL

ARCH(k) is ARCH test up to order k.
Q(k) is the Ljung-Box statistics for residual autocorrelation up to order k.

19

Table 6: Target Zone Test

H 0inside
W
FF/DM

4.509

H 0outside

LR**

5.189 **

W
4.705

LR
**

9.250

***

W is the Wald test statistics, and LR is the likelihood ratio test statistics corresponding to H 0 . ***, **，and * indicate significance at the 1，5 and 10％
level, respectively, and are determined by the critical value on the basis of the χ distribution.
2

Table 7: Estimated Boundary Level
Upper boundary level

Central parity level

Lower boundary level

The Official band

3.429

3.354

3.278

Chung and Tauchen’s results

3.408

3.377

3.292

The results in this paper

between 3.377 and 3.438

3.377

between 3.317 and 3.377

Unit: FF/DM

20

Figure 1: Daily FF/DM Exchange Rate :1987-1993
3.500

3.450

3.400

3.350

3.300

3.250

92
/1
0/
12
93
/1
/2
0
93
/4
/3
0

92
/7
/4

88
/1
2/
12
89
/3
/2
2
89
/6
/3
0
89
/1
0/
8
90
/1
/1
6
90
/4
/2
6
90
/8
/4
90
/1
1/
12
91
/2
/2
0
91
/5
/3
1
91
/9
/8
91
/1
2/
17
92
/3
/2
6

88
/9
/3

87
/1
/1
2
87
/4
/2
2
87
/7
/3
1
87
/1
1/
8
88
/2
/1
6
88
/5
/2
6

3.200

The upper, middle, and lower lines are the announced upper edge (3.43FF/DM), the central parity(3.35FF/DM), and lower edge(3.28FF/DM),
respectively, of Target-zone.

21

Figure 2: Exponential Transition Function

Transition Function
The vertical axis: F(st-d)
1.20E+00

The horizontal axis: st-d

1.00E+00

c1=0,

8.00E-01
6.00E-01
4.00E-01
2.00E-01
0.00E+00
-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Transition Function

22

1

γ=20

Figure3 :Implicit Band and Adjustment Speed
1.5

Announced Upper Band

1.0

Announced Lower Band

Diffusion
0.5

0.0

3.255

3.271

3.287

3.304

3.320

3.337

3.354

3.371

3.388

Convergence

3.405

3.422

Convergence

-0.5

-1.0

-1.5

Transition function is indicated by blue line, adjustment speed is by red line.
The vertical axis: Adjustment speed (multiplied by10) and the estimated transition function.
The horizontal axis: The level of the FF/DM exchange rates.

23

3.439