Duration Analysis of Regime Changes in the Exchange Rate
Mechanism
February 2002
Preliminary version
Please do not quote without the authors’ permission
Simón Sosvilla-Rivero
(FEDEA and Universidad Complutense de Madrid)
Reyes Maroto-Illera
(FEDEA and Universidad Carlos III)
Francisco Pérez-Bermejo
(FEDEA)
ABSTRACT
This paper examines the regime changes in the Exchange Rate Mechanism (ERM),
applying the duration model approach to quarterly data of eight currencies participating in
the ERM, covering the complete EMS history. The time spells between two consecutive
changes in the ERM is studied, estimating the survival and hazard functions of such
variable.
We first make use of the nonparametric (univariate) analysis, finding that the probability of
maintaining the current regime decreases very rapidly for the short durations to register
then smoother variations as time increases. Therefore, for those regimes with high
durations, the ERM would have been relatively stable, while for the (more common)
regimes associated with short durations would have been more unstable.
Then we apply a parametric (multivariate) analysis to investigate the role of other variables
in the probability of a regime change. In this case, three alternative theoretical frameworks
are used to select potential explanatory variables: exchange-rate determination models, first
generation models of currency crisis and second generation models of currency crisis. Our
results suggest that the money supply differential with Germany would have negatively
affected the probability of change of a given regime, while credibility, price differential
with Germany, the reserves/GDP ratio, changes in reserves and the evolution of the Share
index would have positively influenced such probability.
Finally, when distinguishing between groups of currencies, we observe that those in the
core are more stable than those in the periphery. A formal test for equality of survival
functions among currencies confirms that there is evidence of heterogeneity in our sample
of currencies. As well, after including a dummy variable to control for the heterogeneity by
groups of currencies, previous findings remained unaltered.
JEL Codes: C41, F31, F33
Keywords: Duration analysis, exchange rates, European Monetary System.
1. Introduction
The European Monetary System (EMS) was initially planned as an agreement to
reduce exchange rate volatility for a Europe in transition to a closer economic integration.
Following its inception in March 1979, a group of European countries linked their
exchange rates through formal participation in the Exchange Rate Mechanism (ERM). The
ERM was an adjustable peg system in which each currency had a central rate expressed in
the European Currency Unit (ECU), predecessor of the Euro. These central rates
determined a grid of bilateral central rates vis-à-vis all other participating currencies, and
defined a band around these central rates within which the exchange rates could fluctuate
freely. Intervention to support bilateral rates where obligatory at the margins, with
unlimited amounts of credit available between central banks for this purpose through the
very short term financing facility. Following the Base-Nyborg agreement of September
1987, central banks were also empowered to intervene within margins before limits were
reached. If the participating countries decided by mutual agreement that a particular parity
could not be defended, realignments of the central rates were permitted.
The ERM is the most prominent example of a target-zone exchange rate system.
There exist an extensive literature that builds on the seminal paper by Krugman (1991)
studies the behavior of exchange rates in target-zones. The main result of the target-zone
model is that, with perfect credibility, the zone exerts a stabilizing effect (the so called
“honey-moon” effect), reducing the exchange rate sensitivity to a given change in
fundamentals. Nevertheless, in a target-zone with credibility problems, expectations of
future interventions tend to destabilize the exchange rate, making it less stable than the
underlying fundamentals (Bertola and Caballero, 1992). Therefore credibility (i.e., the
degree of confidence that the economic agents assign to the announcements made by the
policy makers) becomes a key variable. In a context of an exchange rate target-zone, like
the EMS, credibility refers to the perception of economic agents with respect to the
commitment to maintain the exchange rate around a central parity. Therefore, the
possibility for the financial authorities to change the central parity could be anticipated by
the economic agents, triggering expectations of future changes in the exchange rate that can
act as a destabilizing element of the system.
In the literature, there has been several tests of credibility based on financial
instruments that reflects these market expectations [see Svenson (1992) for a survey of
literature]. Svenson (1991), e.g., proposed an arbitrage-based test of exchange rate
credibility. This test uses the interest rate differential between the domestic and foreign
currency to show that whenever the forward exchange rate lies outside the band, one can
reject the null hypothesis that the existing exchange rate is credible. On the other hand,
Campa and Chang (1996) use option prices to derive two more arbitrage test of credibility
of an exchange rate. Furthermore, Fernández-Rodríguez, Sosvilla-Rivero and MartínGonzález (2002) develop a test for target-zone credibility that make use of nonlinear
forecastable dependencies in time series. Finally, Ledesma-González et al. (2001) study the
degree of credibility of the EMS using a battery of credibility measures.
On the other hand, another important line of research has aimed to estimate the
probability of realignment using econometric techniques. To that end, some explanatory
variables of that probability are considered, usually the interest rate differential, the
inflation differential, the current account balance, and the unemployment rate [see, e.g.,
Edin and Vredin, (1993)].
We depart from the previous papers by using duration analysis to examine the
survival of the central parities in the EMR. We have applied this approach to eight
currencies participating in the ERM, using quarterly data of exchange rates vis-á-vis the
Deustchemark for the first quarter 1979 to the fourth quarter 1998 period, covering in
practically the complete EMS history.
The paper is organized as follows. In Section 2 we present the data. Section 3
briefly describes the methodology of duration model approach, while Section 4 presents the
empirical results. Section 5 assesses the possibility of heterogeneity in the sample. Finally,
some concluding remarks are provided in Section 6.
2. Data
It is common to distinguish four different subperiods in the experience of the ERM
(see, e. g. De Grauwe, 2000). The first subperiod extended from the ERM inception, in
March 1979, to January 1987 During this subperiod, the relatively large fluctuations bands
in the EMS (compared to those in the Bretton Woods system), together with relatively
small and frequent realignments, helped to reduce the size of speculative capital
movements and stabilised the system. The second subperiod, the so-called “New ERM”,
lasted from 1987 to the end of 1991, coinciding with increasing confidence in the ERM, the
removal of capital controls, and a greater convergence in the economic fundamentals. The
third subperiod covered successive crises of September 1992 an August 1993, where the
evolution of the EMS into a truly fixed exchange rate system with almost perfect capital
mobility led to credibility losses in a context of policy conflict among EMS countries about
how to face the severe recession experienced in 1992-93. Finally, a fourth subperiod
iniciated after the crisis of 1993, when the EMS changed its nature in drastic ways: the
EMS gained credibility with the enlargement of the fluctuation bands to ±15% (reducing
the scope for large speculative gains) and with the fixed exchange rate commitment among
potential European Monetary Union (EMU) member countries. As a result, speculation
became a stabilising factor and the market rates converged closer and closer to the fixed
conversion rates, although the world was hit by a major crisis during the second half of
1998 (De Grauwe et al., 1999).
Table 1 shows the main realignments and changes in the EMS during the 1979-1999
period. As can be seen, although the fluctuation band was originally set at  2.25%, Italy
and the newcomers (Spain, the UK and Portugal) used a wider band of fluctuation (  6%)
. After almost a year of unprecedented turmoil in the history of the EMS, the fluctuation
bands of the ERM were broadened in August 1993 to  15% except for Dutch guilder and
Deutschemark, which remained with the narrow bands of  2.25%. On 1 January 1999 the
EMS ceased to exist. On the other hand, as shown in Table 1, there were nineteen
realignments in the EMS history, being twelve of them prior to the currency turmoil of the
subperiod 1992-1993.
Table 1: Main realignments and changes in the ERM (1979-1998)
13.03.1979
ERM starts to operate with the BFR, DKR, DM, FF, IRL, LIT and HFL.
They are in the narrow band (  2.25% fluctuation), except the LIT in the wide band
(  6% fluctuation).
24.09.1979
Realignment (DKR –3%, DM +2%)
30.11.1979
23.03.1981
5.10.1981
22.02.1982
14.06.1982
Realignment (DKR –5%)
Realignment (LIT –6%)
Realignment (DM +5.5%, FF –3%, HFL +5.5%, LIT –3%)
Realignment (BFR –8.5%, DKR -3%)
Realignment (DM +4.25%, FF –5.75%, HFL +4.25%, LIT –2.75%)
Realignment (BFR +1.5%, DKR +2.5%, DM +5.5%, FF –2.5%, IRL –3.5%,
HFL +3.5%, LIT –2.5%)
22.03.1983
22.07.1985
Realignment (BFR +2%, DKR +2%, DM +2%, FF +2%, IRL +2%, HFL +2%,
LIT –6%)
17.09.1992
23.11.1992
1.02.1993
14.05.1993
2.08.1993
9.01.1995
6.03.1995
14.10.1996
25.11.1996
Realignment (BFR +1%, DKR +1%, DM +3%, FF –3%, HFL +3%)
Realignment (IRL –8%)
Realignment (BFR +2%, DM +3%, HFL +3%)
The PTA joins the ERM with the wide band (  6%)
The LIT joins the narrow band (  2.25%). Realignment (LIT –3.6774%)
The UKL joins the ERM with the wide band (  6%)
The ESC joins the ERM with the wide band (  6%)
Realignment (BFR +3.5%, DKR +3.5%, DM +3.5%, ESC +3.5%, FF +3.5%, IRL +3.5%,
HFL +3.5%, LIT –3.5%, PTA +3.5%, UKL +3.5%)
The UKL and the LIT suspend their participation in the ERM. Realignment (PTA –5%)
Realignment (ESC -6%, PTA –6%)
Realignment (IRL -10%)
Realignment (ESC –6.5%, PTA –8%)
The ERM fluctuation bands are widened to  15%, except for the DM and the HFL
The ATS joins the ERM with the new wide band (  15%)
Realignment (ESC –3.5%, PTA –7%)
The FIM joins the ERM with the new wide band (  15%)
The LIT re-joins the ERM with the new wide band (  15%)
16.03.1998
Realignment (IRL +3%). The DR joins the ERM with the new wide band (  15%)
7.04.1986
4.08.1986
12.01.1987
19.06.1989
8.01.1990
8.10.1990
6.04.1992
14.09.1992
Note: ATS, BFR, DKR, DM, DR, ESC, FF, FIM, HFL, IRL, LIT, PTA and UKL denote, respectively, the
Austrian schilling, the Belgian franc, the Danish krone, the Deustchemark, the Greek drachma, the Portuguese
escudo, the French franc, the Finnish markka, the Dutch guilder, the Irish pound, the Italian lira, the Spanish
peseta and the Pound sterling.
In our study we use quarterly data of eight currencies participating in the ERM of
the EMS, these are: the French Belgian franc (FF), the Irish pound (IRL), the Belgian franc
(BFR), the Italian lira (LIT), the Dutch guilder (HFL), the Danish crown (DKR), the
Spanish peseta (PTA) and the Portuguese escudo (ESC). Given the central role of Germany
in the European Union [see Bajo-Rubio et al. (2001)], our exchange rates are expressed vis-
á-vis the Deustchemark. The sample period runs from the first quarter of 1979 to the fourth
quarter of 1998, covering in the complete history of the EMS.
Starting from this data set, we construct a dummy variable called change, taking
value one if a regime change takes place and zero otherwise. To that end, we shall consider
as a regime change each realignment, modification of fluctuations bands or entrance/exit in
the ERM. Based on the variable change, we generate the variable duration, representing the
time spell between two consecutive regime changes. These variables, duration and change,
define the survival-time data associated with each regime.
Table 2. Descriptive statistics
ALL CURRENCIES
Change
Duration
Mean
0.468
6.617
Dev. Std.
0.501
5.976
Variance
0.251
35.715
Skewness
0.130
1.004
Kurtosis
1.017
2.932
Min
0
1
Max
1
21
N. of change
Observations
72
154
The summary statistics for change and duration are presented in Table 2. As can be
seen, for all the currencies considered, we have 154 observations. The average duration of
regime changes is 6.6 quarters, being the minimum duration of 1 quarter and the maximum
of 21 quarters. The average probability of change is 47%.
Figure 1 shows the duration of the ERM regimes along the whole sample period
1979-1998. There is a high percentage of short durations (less than 5 quarters), representing
the 52% of the total sample, while long durations (greater than 15 quarters) only account
for 9%. This result shows that the regime changes are frequent in the sample, in particular
the number of changes with duration less than 5 quarters is 49.
Figure 1: Duration of regimes in the EMS, 1979-1998.
ALL CURRENCIES
.4
Fraction
.3
.2
.1
0
1
5
10
analysis time
15
20
3. Econometric methodology
In this section, we offer a brief description of the main concepts and functions used
in the duration analysis. This analysis has been mainly used in Labor Economics 1, to study
the duration of periods of employment and unemployment and the determinants of entry
and exit rates [see Kiefer (1988) for a literature review]2.
3.1. Non-parametric analysis
In the non-parametric, or empirical analysis, we use the information contained in the
duration variable. In our case, this variable measures the time that passes between two
consecutive regime changes in the ERM.
Those econometric models developed to analyze this type of information are called
duration models. If we define T as the discrete random variable that measures the time spell
between two consecutive ERM regime changes, the observations at our disposal consist of
1
Duration models have been also used in the field of Industrial Organization, to analyze for example the life
duration of multinational subsidiaries in the UK manufacturing industry (McCloughan and Stone, 1998), or to
analize investment decisions (Licandro O., Goicolea A. And Maroto R , 1999).
2
See also Sosvilla-Rivero and Maroto (2001) for a detailed study of the duration of exchange rates regimes
in the European Monetary System (EMS). This section borrows heavily from the section they dedicate to
duration analysis in that article.
a series of data (t1, t2,… tn) which correspond to each of the observed durations of each
regime change in our sample. The probability distribution of the duration variable can be
specified by the cumulative distribution function:
F(t)=Pr(T<t)
(1)
which indicates the probability of the random variable T being smaller than a certain value
t. The corresponding probability function is then:
P(t)=Pr (T=t)
(2)
But in duration models, two main functions are used to characterize the probability
distribution of the duration variable:
(a) The survivor function is defined as:
S(t)=Pr(T≥t)=1-F(t)
(3)
and it gives the probability of the duration being greater than or equal to t.
(b) The hazard function is defined as:
h(t)=Pr(T=t/ T≥t)
(4)
and it gives, for each duration, the probability of a regime change, given a survival up to t.
There exists a relation between both functions given by the following expression:
S (t )   s 1|t (1  h( s ))
(5)
One of the advantages of the hazard function is that it allows us to characterize the
dependence path of duration. Formally, there exists a positive duration dependence in t* if
dh(t)/dt>0, in the moment t=t*. This positive relation implies that the probability that a
regime ends in t, given that it has reached t, depends positively on the length of the period.
Thus, the longer the period, the higher the conditional probability of entering into a new
regime. Similarly, there exists negative duration dependence if dh(t)/dt<0 in t=t*. In this
case, the longer the period, the lower the conditional probability of regime change.
The non-parametric analysis is used to estimate the unconditional hazard function
which registers all the observations for which there is a change, that is, the relative
frequency of observations with T=t. For this analysis, the Kaplan-Meier estimate is widely
used (Kaplan and Meier, 1958). The hazard function is calculated as follows:
d
hˆ(t )  t
nt
(6)
where dt represents the number of changes registered in moment t, and nt is the surviving
population in moment t, before the change takes place. From the hazard function, it is
possible to obtain the cumulative hazard function with a estimation procedure proposed by
Nelson (1972) and Aalen (1978). It is given by the following expression:
t
Hˆ ( s )   hˆ( s )
(7)
s 1
The Kaplan-Meier survivor function for duration t is calculated as the product of
one minus the existing risk until period t:
nj  d j
Sˆ (t )   j|t t (
)
j
nj
(8)
3.2. Parametric analysis
The non-parametric analysis is very limited because it does not take into account
other variables, apart from duration, that can influence the probability of a regime change.
In order to address the issue of other variables determining this probability, we also include
in this paper a section dedicated to parametric analysis. In the literature, two frequently
used models for adjusting survival functions for the effects of covariates are the accelerated
failure-time (AFT) model and the multiplicative or proportional hazard rate (PH) model.
In the Proportional Hazard (PH) rate model, the covariates have a multiplicative
effect on the hazard function:
h(t , X )  h0 (t )* g ( X )
(9)
where ho(t) is the baseline hazard function that captures the dependency of data to duration,
and g(X) is a nonnegative function of individual variables. A popular choice, and the one
adopted here, is to let g(X) equal the relative risk: g(X)=exp(X´β). The function ho(t) may
either be left unspecified, yielding the Cox proportional hazard model [see Cox (1972)], or
take a specific parametric form. Two models are currently implemented as proportional
hazard (PH) models: the Exponential and Weibull models. In the second one, h0(t)=θt
θ-1
,
where θ is a parameter that has to be estimated. When θ=1, the Weibull Model is equal to
the Exponential Model, where there exists no dependency on duration. On the other hand,
when the parameter θ>1, there exists a positive dependency on duration, and a negative
dependency when θ<1. Therefore, by estimating θ, it is possible to test the hypothesis of
duration dependency of the regime changes. Note that in this proportional specification
regressors intervene re-escalating the conditional probability to leave the current regime,
not its own duration.
In the accelerated failure-time model, the natural logarithm of the survival time ln(t)
is expressed as a linear function of the covariates, yielding the linear model:
ln(t )  X ´  
(10)
where  is the error with density f(.). The distributional form of the error term determines
the regression model. If we let f(.) be the normal density, the lognormal regression model is
obtained and the associated hazard function is then given by the following expression:
1
 1

exp  2 (ln(t )  X  ) 2 
 2

h(t )  t 2
ln(t )  X 
1 (
)
(11)

where (.) is the standard normal cumulative distribution and  is an ancillary parameter to
be estimated from the data. On the other hand, when f(.) follows a three-parameter gamma
density, the generalized gamma regression is obtained. The hazard function associated with
this model depends on the ancillary parameters  and , being extremely flexible allowing
for a large number of possible shapes. In particular, if =0, we have the lognormal model,
and if =1 we obtain the Weibull model. Finally, if =1 and =1, we have the exponential
model. Therefore, the generalized gamma model is commonly used for evaluating and
selecting an appropriate parametric model from the data.
Table 3 shows the parametrization and ancillary parameters for the survival
distributions defined for both the PH and AFT models. Each of those alternative models
implies a given temporal structure in the data. For example, the Weibull distribution is
suitable for modeling data with monotone hazard rates that either increase or decrease
exponentially with time, while the exponential distribution is suitable for modeling data
with constant hazard. In contrast, the lognormal distribution is indicated for data exhibiting
nonmonotonic hazard rates, initially increasing and then decreasing. Finally, the hazard
function of the generalized gamma distribution is extremely flexible, allowing for a large
number of shapes, including an U-shape.
Table 3: Parametric survival distributions
Ancillary
parameters
Distribution
Metric
Survival function
Parametrization
Exponential
PH
exp t
  exp( X  )
Exponential
AFT
exp  t
  exp( X  )
Weibull
PH
exp (   t ) 
  exp( X  )

  exp( X  )

  X 

  X 
 ,
Weibull
AFT
Lognormal
AFT
Generalized
gamma
AFT
exp (   t )


 ln(t )   
1 

 


 ln(t )    
1  I   , exp 

   

Note: PH and AFT denote proportional hazard and accelerated failure time respectively.  ( z )
is the standard normal cumulative distribution and I  , a  is the incomplete gamma function.
4. Empirical Results
In this section we present the results obtained in the duration analysis of the
different regimes in the history of the ERM. We first report the results from the
nonparametric analysis using the Kaplan-Meier survival and hazard estimates. We then
include the covariates making use of the different parametric models introduced in the
previous section.
4.1 Nonparametric estimation
The estimate for Kaplan-Meier survival function is shown in Table 4 and Figure 2.
This function gives, for each duration spelt, the probability of maintaining the current
regime. As can be seen, these probability decreases very rapidly for the short durations (less
than 4 quarters), to register then smoother variations as time increases. This behavior
suggests that for those regimes with high duration, the ERM would be relatively stable,
while for the (more common) regimes associated with short durations the ERM would be
more unstable. For the whole sample, the probability of maintaining a certain regime is
estimated to be 0.56.
Table 4. Kaplan-Meier survivor and hazard function
Beg.
Net
Survivor Hazard
Time
Total Failure Lost
Function Function
1
154
11
22
0.93
0.07
2
121
15
4
0.81
0.12
3
102
19
6
0.66
0.19
4
77
4
0
0.63
0.05
5
73
0
2
0.63
0.00
6
71
1
12
0.62
0.01
7
58
0
2
0.62
0.00
8
56
2
0
0.60
0.04
9
54
4
7
0.55
0.07
10
43
7
0
0.46
0.16
12
36
1
8
0.45
0.03
13
27
1
5
0.43
0.04
15
21
2
5
0.39
0.10
18
14
1
4
0.36
0.07
21
9
4
5
0.20
0.44
Failure
Change
Analysis Time
Duration
Figure 2. Kaplan-Meier estimate. All currencies.
Kaplan-Meier survival estimate
1.00
0.75
0.50
0.25
0.00
0
5
10
analysis time
15
20
Figure 3 shows the log-log plot for the Kaplan-Meier survival function. As can be
seen, this plot reveals convexity rather than linearity, suggesting that a non-monotonic
hazard function could be appropriate for our data. The convexity of that function implies
that the probability of regime change is an increasing function in t, conditional on duration.
This means that the longer the period of regime accumulated until t, the higher the
probability that the regime will end in moment t. The estimated hazard function, plotted in
Figure 4, enhance this intuition, since its shape indicates a positive-to-negative duration
dependence and possibly log-normality.
Figure 3. Log Negative Log survivor function
Figure 4. Kaplan-Meier hazard estimate
Kaplan-Meier hazard estimate
1
.4
-1
h(t)
Negative Log SDF
0
.2
-2
0
-3
0
1
2
3
1
5
Log of quarter
10
analysis time
15
20
4.2 Parametric estimation
Before proceeding to present the results from the parametric estimation, it is
necessary to identify and measure those variables that can influence the probability of a
regime change. To that end, we make use of three alternative theoretical frameworks:
exchange-rate determination models, first generation models of currency crisis and second
generation models of currency crisis. Each of these approaches suggests alternative
explanatory variables to be included in the parametric analysis.
Regarding the models of exchange rate determination, the flexible-price monetary
model [see Frankel (1976), Mussa (1976) and Bilson (1978a, 1978b)] suggests that the
(log) of the exchange rate is a function of the relative (logs of) money supply, relative (logs
of) real income and relative interest rates:
s=s1 + s2(m-m*) - s3( y-y*) +s4( i-i*)
(12)
where s is the (log of) exchange rate (expressed as the home currency price of a unit of
foreign exchange), m is the (log of) money supply, y is the (log of) real income, i is nominal
interest rate, and an asterisk denotes a foreign variable. On the other hand, Dornbusch
(1976)´s sticky-price model leads to the following relationship between the exchange rate
and its fundamental variables:
s=s1 + s2(m-m*) - s3( p-p*) -s4( y-y*)
(13)
where p is the (log of) price level. Given that these models were developed for floating
exchange rates, in our empirical investigation for the ERM we will also considered the role
of a credibility indicator based on the results in Ledesma-Rodríguez et al. (2001). In
particular we use their measure of marginal credibility, since it renders the best indicator to
proxy the perception of economic agents with respect to the commitment to maintain the
exchange rate around a central parity.
Therefore, we will explore the following relationships:
h=h1 + h2(m-m*) - h3( y-y*) - h4( i-i*) - h5 credibility
(14)
and
h=h1 + h2(m-m*) - h3( p-p*) - h4( y-y*) - h5 credibility
(15)
where h denotes, for each duration, the probability that a regime change occurs.
As for the first generation models of currency crisis (also called “exogenous policy”
models), they are based on the inconsistency, under fixed exchange rates, between domestic
expansionary policies (financed by expanding domestic credit) and the exchange rate. This
causes a steady loss of international reserves. The inevitable exhaustion of reserves are
foreseen by speculators so the final stage of the collapse of the fixed rate is characterised by
a speculative attack [see Krugman (1979) and Flood and Garber (1984)]. These models
focus on the financial aspects of the problem, paying special attention to nominal variables
as determinant of the currency crisis, and therefore the abandon of the fixed exchange rate.
In our empirical analysis we will considered the following macroeconomic indicators to
evaluate the first generation models of currency crisis: changes in international reserves
(ΔR), money supply differential (M-M*), the ratio money supply to reserves (M/R), and an
index of equity prices (E). Therefore, we will explore the following relationship3:
h= h1 - h2 (ΔR) + h3 (M-M*) + h4 (M/R) – h5 (E)
(16)
Finally, the second generation models of currency crisis (also called “endogenous
policy” models or “escape-clause” models) introduce non-linearities and the reaction of
government policies to changes in private behaviour (see Obstfield, 1986, 1996). The
commitment to the fixed exchange rate is state dependent, so the government can always
exercise an escape clause. Non-linearity is a source of multiple equilibrium, some of which
can be stable, others being unstable. Finally, second generation models can explain
speculative attacks even when fundamentals are not involved, introducing the idea of “selffulfilling” speculative attacks which can arise even when there is no inconsistency in
policy. In contrast with first generation models of currency crisis, second generation models
emphasise the role of real variables as potential causes of such crises. We will examine the
role of the following variables in explaining the ERM changes: industrial production (IPI),
current account balance over GDP (CA/GDP) and the unemployment rate (UR). Therefore,
we will explore the following relationship4:
h= h1 - h2 (IPI) + h3 (CA/GDP) + h4 (UR)
(17)
We have assembled quarterly data for these macroeconomic variables from the first
quarter of 1979 to the fourth quarter of 1998. The exact definition of the variables as well
as the data sources are detailed in the Appendix. Regarding the exchange-rate
determination models, since it is not clear which money supply measure is appropriate, we
use several candidate data sets. On the other hand, since we do not have quarterly data on
We have also considered the changes in money supply (ΔM) and the inflation differential (ΔP- ΔP*), but
they never were significant.
4
We also used gross domestic product (GDP) instead of IPI, but the results were qualitatively similar.
3
real income, we use the industrial production indices and the gross domestic product as the
indicator of current economic activity.
We have estimated the functional forms discussed in Section 2 by maximum
likelihood, using 154 observations and 72 changes of regime. In all the estimations we have
included as an additional explanatory variable the number of previous changes, but this
variable was never statistically significant. Following a “general-to-specific” modelling
methodology [see, e. g., Hendry (1995)], equations (14) to (17) were continuously
simplified and re-parameterised until a parsimonious representation of the data generation
process was arrived at. Table 5 to 7 contain the parameter estimates for the alternative
hazard function models for the ERM under the three theoretical approaches. It should be
notice that the estimate from an AFT model have the opposite algebraic sign from those
obtained from a PH model or from the semiparametric Cox estimation. Therefore, in order
to compare directly the parameter estimates and to show the impact on the hazard of each
covariates, we report the corrected coefficients for the parametric models.
As can be seen in Table 5, in the case of the fundamental variables (i. e., those
explanatory variables suggested by the exchange-rate determination models) the covariates
are significant and have the expected sign (positive for the money supply differential and
negative for the price differential, the credibility indicator and the reserves/GDP ratio) for
all the alternative specifications. It seems that the sticky price monetary model augmented
with credibility and reserves is a good approximation of the determinants of duration of
ERM regimes.
Regarding the nominal variables (i. e., those explanatory variables suggested by the
first generation models of currency crisis), Table 6 shows that changes in international
reserves and the share index are significant in four of the five cases considered, while the
money supply differential is only significant in two of the five cases. Note that all the
coefficients have the expected sign.
Finally, Table 7 reports the results for the case of real variables (i. e., those
explanatory variables suggested by the first generation models of currency crisis). As can
be seen, both the industrial production index and the CA/GDP ratio are significant and have
the expected sign.
Tables 5 to 7 also report estimates of the ancillary parameters for the last three
distributions. As shown, we find a significant positive duration dependence in the Weibull
model, since θ is greater than one (1.409 for the fundamental variables, 1.225 for the
monetary variables and 1.205 for the real variables), indicating that as time passes the
probability of a realignment increases, in contrast with the empirical hazard function
obtained using the Kaplan-Meier method (see Figure 4). Regarding the log-normal model,
changes in σ compress or stretch the hazard function and when this parameter is large, the
hazard peaks so rapidly that the function is almost indistinguishable from those like the
Weibull. In our case, we obtain an estimated value of 0.961 for the fundamental variables,
1.051 for the nominal variables and 1.145 for the real variables. Finally, the shape estimate
(κ =0.297 for the fundamental variables, -0.648 for the nominal variables and 0.757 for the
real variables) allows us to test the null hypotheses κ =0 and κ =1, to evaluate the validity
of the log-normal and Weibull models, respectively. Tables 5 to 7 offer the Wald test and
the likelihood ratio (LR) test for each of these hypotheses. The results of the Wald test
clearly suggest that for the fundamental variables and for the real variables we can reject
neither the null hypothesis κ =0 nor the hypothesis κ=1. In the case of the nominal
variables, we reject the hypothesis κ =1 but we cannot reject κ =0, what suggests that the
log-normal specification is the most appropriate one in this case5.
Also, we can use the likelihood-ratio test (LR) to test the hypothesis that κ=0 or
κ=1. All the tests have one degree of freedom, except that for the exponential model versus
the generalized gamma model, that has two degrees of freedom. The results are consistent
with the ones obtained with the previous test, indicating that the exponential model is not
5
It is interesting to note that the log-normal model is consistent with the non-monotonic empirical hazard
function depicted in Figure 4.
adequate for our data in the cases of fundamental and nominal variables. As well, there is
strong support against rejecting the Weibull model in the case of real variables.
As a conclusion, neither the Wald test nor the LR test are helpful in order to choose
one particular specification. This result can be due to the lack of power of such test in small
samples. Then, to select the particular model which better fit our data, we will use the
Akaike Information Criterion (AIC). Akaike (1974) proposes penalizing each log
likelihood to reflect the number of parameters being estimated in a particular model and
then comparing them. In our case, the AIC can be defined as:
AIC  2 * log[ likelihood ]  2(c  q  1)
(18)
where c is the number of model covariates and q the number of model-specific ancillary
parameters. As shown in tables 5 to 7, for fundamental and nominal variables the lognormal
specification is preferred by the AIC. In contrast, for the real variables we choose the
Weibull model.
Table 5: Parametric estimation for Fundamental variables.
Ln M3 - Ln M3 G
Cox
Exponential Weibull
Log-normal
Gamma
0.102**
(3.45)
-3.811**
(-2.92)
-1.557**
(-4.30)
-0.967**
(-5.06)
-
0.071**
(3.54)
-3.553**
(-2.93)
-1.444**
(-4.78)
-0.946**
(-5.29)
-0.240
(-0.85)
-
0.074**
(3.52)
-3.347**
(-2.64)
-1.419**
(-4.65)
-0.885**
(-4.16)
-0.323
(-1.04)
0.897**
(6.94)
0.297
(0.80)
282.78
(κ =0) 0.65
(κ =1) 1.29
Theta
-
0.088**
(3.32)
-3.215**
(-2.34)
-1.581**
(-4.23)
-0.853**
(-4.46)
-0.405
(-1.07)
-
Sigma
-
-
0.078**
(3.83)
-2.860**
(-2.46)
-1.330**
(-4.43)
-0.738**
(-4.43)
-0.562*
(-1.76)
1.409**
(13.95)
-
Kappa
-
-
-
0.961**
(14.10)
-
581.56
-
293.08
14.30
283.11
2.33
281.16
0.38
P. Index – P. Index G
Credibility
Reserves/GDP
Constant
AIC
LR[(df=1)]
Wald test
[(df=1)]
No. of subject
No. of failures
Absolute z-statistics in parentheses.
Robust variance-covariance matrix used
significant at 10% ; ** significant at 5%
G
refers to Germany
154
72
Table 6: Parametric estimation for Monetary variables.
Reserves
Cox
Exponential Weibull
Log-normal
Gamma
-0.800
(-2.53)
0.148
(2.67)
-0.549*
(-1.78)
-
-0.884**
(-3.15)
0.068
(1.29)
-0.671**
(-3.01)
-1.072**
(-6.08)
-
-0.890**
(-3.05)
-0.011
(-0.09)
-0.770**
(-2.56)
-0.946**
(-4.25)
1.108**
(11.77)
-0.648
(-0.74)
300.84
(κ =0) 0.54
(κ =1) 3.54
Theta
-
-0.814**
(-2.47)
0.140**
(2.41)
-0.571*
(-1.84)
-1.328**
(-5.84)
-
Sigma
-
-
-0.700**
(-2.51)
0.126**
(2.45)
-0.544*
(-1.91)
-1.347**
(-4.9)
1.225**
(15.21)
-
Kappa
-
-
-
1.051**
(13.99)
-
601.03
-
311.59
14.75
306.05
10.21
300.11
1.27
M1-M1G
Share Index
Constant
AIC
LR[(df=1)]
Wald test
[(df=1)]
No of subjects
No of failures
Absolute z-statistics in parentheses.
Robust variance-covariance matrix used
significant at 10% ; ** significant at 5%
G
refers to Germany
154
72
Table 7: Parametric estimation for Real variables.
IPI
Cox
Exponential Weibull
Log-normal
Gamma
-2.999**
(-2.64)
-0.009*
(-1.89
-
-1.783**
(-2.14)
-0.008*
(-2.10)
-0.382
(-0.64)
-
-2.719**
(-2.00)
-0.007*
(-1.68)
0.197
(0.19)
0.915**
(3.19)
0.757
(0.99)
313.20
(κ=0) 0.97
(κ =1) 0.1
Theta
-
-3.064**
(-2.92)
-0.008*
(-1.69)
0.364
(0.39)
-
Sigma
-
-
-2.846**
(-3.26)
-0.007*
(-1.70)
0.229
(0.29)
1.205**
(15.16)
-
Kappa
-
-
-
1.145**
(14.21)
-
601.74
-
313.15
3.95
311.44
0.23
312.19
0.98
C A/GDP
Constant
AIC
LR[(df=1)]
Wald test
No of subjects
No of failures
Absolute z-statistics in parentheses.
Robust variance-covariance matrix used
* significant at 10% ; ** significant at 5%
154
72
5. Heterogeneity
In this section we repeat the parametric analysis of the previous section, but now we
include a new variable that can control for group heterogeneity. To that end, we have
identified two potential groups with different characteristics as shown in Figure 5 and Table
8:
-
A first group of currencies (that we shall denote as “core”, and that include: FF,
BFR, HFL and DKR), with a total of 92 observations, being the average
duration 7.17 quarters and 0.42 the average probability of change.
-
A second group (that we shall denote as “periphery”, formed by: IRL, LIT, PTA
and ESC), representing the 40.3% of the observations, being 5.79 quarters the
average duration and 0.53 the average probability of change.
Table 8. Descriptive statistics by group
CORE
Change
Duration
Mean
0.424
7.174
Dev. Std.
0.497
6.475
Variance
0.247
41.925
Skewness
0.308
0.919
Kurtosis
1.095
2.579
Observations
PERIPHERY
Change
Duration
0.532
5.790
0.503
5.087
0.253
25.873
-0.129
0.962
1.017
3.033
92
62
Figure 5: Duration of regimes in the EMS by group
CORE
PERIPHERY
.4
.3
.3
Fraction
Fraction
.2
.2
.1
.1
0
0
1
5
10
analysis time
15
20
1
5
10
analysis time
15
20
It is interesting to note that these two groups roughly correspond to those found in
Jacquemin and Sapir (1996), applying multivariate analysis techniques (i.e., principal
components and cluster analysis) to a wide set of structural and macroeconomic indicators,
to form an homogeneous group of countries. Moreover, these two groups are basically the
same that those found in Fernández-Rodríguez, Sosvilla-Rivero and Andrada-Félix (1999)
to have relevant information helping to improve the prediction of currencies in each group
based on the behavior of the rest of currencies, information that can be used to generate
simple trading rules that outperform the moving average trading rules widely used in the
markets [see Fernández-Rodríguez, Sosvilla-Rivero and Andrada-Félix (2002)].
Figure 6 plots the estimated survival functions for the currency groups. As shown,
the probability of maintaining a given regime quickly decreases in the short durations (less
than five quarters) for both groups. It is interesting to observe that the probability of
maintaining the regime in the periphery is smaller than in the core, with graded changes
that occur more often and are registered until the end of the period. However, in the core,
the probability of maintaining the regime is roughly constant as duration increases. This
result would suggest that the currencies in the core have been more stable. Nevertheless, it
should be note that the accuracy of the estimator is better for shorter durations, since
inferences about very long duration are based on fewer observations.
Figure 6. Kaplan-Meier survival estimates by group
Kaplan-Meier survival estimates, by group
1.00
0.75
CORE
0.50
0.25
PERIPHERY
0.00
0
5
10
analysis time
15
20
Finally, based on the results from Section 4, for each set of alternative explanatory
variables, we have re-estimated the model more appropriate to fit our data (log-normal for
the fundamental and nominal variables, and Weibull for the real variables), this time
including heterogeneity by groups of currencies. As can be observed in Table 9, the results
are consistent with those obtain in tables 5 to 7 in terms of statistically significance and
sign of the coefficients, except for the money supply differential (M1-M1*) in the case of
the nominal variables and the CA/GDP ratio in the case of the real variables. Notice that the
variable “group” (that takes value one for the group of currencies we have denoted as
“core”) always shows the correct sign and is significant in two of the three cases.
Table 9: Parametric estimation with group heterogeneity
Fundamental
Monetary
Real
-
-
-
-
-
-
-
-
Varitation of Reserves
0.086**
(4.50)
-2.801**
(-2.27)
-1.369**
(-4.44)
-1.120**
(-5.54)
-
-
M1 – M1G
-
Share Index
-
IPI
-
-0.888**
(-3.22)
0.040
(0.73)
-0.782**
(-3.44)
-
C. Account/GDP
-
-
Group
-0.482**
(-2.13)
0.261
(0.75)
-
-0.464**
(-2.16)
-0.814**
(-4.27)
-
-0.007
(-1.41)
-0.068
(-0.26)
0.237
(0.30)
1.203**
(14.94)
Sigma
0.936**
(15.57)
1.021**
(14.05)
Log Likelihood
No of subjects
No of failures
-132.17
-142.48
Ln M3 – Ln M3G
Pr. Index – Pr. IndexG
Credibility
Reserves/GDP
Constant
Theta
Absolute z-statistics in parentheses.
Robust variance-covariance matrix used
significant at 10% ; ** significant at 5%
G
refers to Germany
-2.813**
(-3.12)
-151.67
154
72
6. Concluding remarks
In this paper we have examined the regime changes in the Exchange Rate
Mechanism (ERM). To that end, we have applied the duration model approach to quarterly
data of eight currencies participating in the ERM, covering the complete EMS history. We
have studied the time spells between two consecutive changes in the ERM, estimating the
survival and hazard functions of such variable.
First, we have made used of the nonparametric (univariate) analysis, concluding that
the probability of maintaining the current regime decreases very rapidly for the short
durations (less than 4 quarters), to register then smoother variations as time increases.
Therefore, for those regimes with high durations, the ERM would have been relatively
stable, while for the (more common) regimes associated with short durations would have
been more unstable. The probability of maintaining a certain regime is estimated to be
0.56.
Second, we have applied a parametric (multivariate) analysis to investigate the role
of other variables in the probability of a regime change. In particular we consider three
alternative theoretical frameworks to select potential explanatory variables: exchange-rate
determination models, first generation models of currency crisis and second generation
models of currency crisis. Our results suggest that the money supply differential with
Germany would have negatively affected the duration of a given regime, while credibility,
price differential with Germany, the reserves/GDP ratio, changes in reserves and the
evolution of the Share index would have positively influenced such duration. On the other
hand, we have undertaken an exhaustive analysis to compare and validate alternative
models, concluding that the log-normal model would be the more appropriate to fit the data
in the cases of the variables suggested by the exchange-rate determination models and the
first generation models of currency crisis, while the Weibull model could be better in the
cases of the explanatory variables proposed by second generation models of currency
crisis.
Third, when distinguishing between groups of currencies, we observe that those in
the core are more stable than those in the periphery. After repeating the estimations
including a dummy variable to control for the heterogeneity by groups of currencies,
previous findings remained unaltered.
We consider that our results are of interest, not only for the European experience in
the 1979-1998 period, but also for the analysis of other possible target zones as the new
ERM (ERM II), linking the currencies of non-euro area Member States to euro (both
current European Union Member States and future candidates) (see ECOFIN, 2000).
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APPENDIX: Definition of the variables and data sources for the parametric
estimation
A) Variable names and definitions:
Dependent variable:
Probability of change
Explanatory variables:
CA =
current account balance (IFS, line 78ald).
credibility = marginal credibility indicator αt, defined as:
st - Et-1(st) = γ + αt [ct - Et-1(st)] + ut
(16)
where ct is the logarithm of the central parity, the expectation operator is
conditional to the information available in t-1, and ut is a random
disturbance. Note that different value of αt is obtain for each time period in
the sampler.
Share Index = share price index (MEI).
i=
short-term interest rate (IFS, line 60c).
M=
money supply: M1= local currency (IFS, line 34 a.u) + deposits (IFS, line 34.b.u)
M3= M1 + quasi-money (IFS)
ΔM = changes in money supply
M/R = the ratio money supply to reserves
Y=
real income: GDP = gross domestic product (IFS line 99b.c)
IPI = index of industrial production (MEI)
P=
consumer price index (IFS, line 64)
R=
international reserves (IFS, line 1l.d)
UR = unemployment rate (IFS, line 67r)
B) Data sources
The data base is the International Financial Statistics (IFS) published by the International
Monetary Fund and Main Economic Indicators (MEI) published by the Organisation for
Economic Co-operation and Development.