Journal of International Money and Finance
23 (2004) 799–816
www.elsevier.com/locate/econbase
Explaining currency crises: a duration
model approach
Merxe Tudela Macro Prudential Risks, HO-3, Bank of England, Threadneedle Street, London WC2R 8AH, UK
Abstract
In this paper we estimate a duration model for OECD countries during the 1970–97 period. We use semiparametric methods to estimate a model with unrestricted base-line hazards
and test if the time length already spent on a tranquil period is a determinant of the probability of exit into a currency crisis state. The results indicate, first, that increases in export
growth, bank deposits growth and openness decrease the probability of exit into a currency
crises state. Whereas, increases in import growth, claims on government and foreign portfolio investment, and appreciated REER, increase the probability of currency crises. And,
second, the existence of a highly significant negative duration dependence. The highest probability of exit into a currency crash state is given at the initial of the tranquil period.
# 2004 Elsevier Ltd. All rights reserved.
JEL classification: C41; F31
Keywords: Duration analysis; Semiparametric models; Hazard rate; Currency crises; Tranquil periods;
Exchange rate credibility
1. Introduction
In this paper we seek to explain the origins of currency crises for a group of
developed countries. Specifically, we attempt to illustrate the mechanism that generates currency crises by relating their occurrence first, to realizations of explanatory variables and, second, to the duration pattern of the non-crisis periods.
For 20 OECD countries we construct a data set for the period 1970–97, consisting of 81 tranquility spells. These spells are defined as those episodes for which a
particular currency does not suffer from a speculative attack; we call these episodes
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E-mail address: [email protected] (M. Tudela).
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doi:10.1016/j.jimonfin.2004.03.011
800
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
tranquil periods. We define a crisis state as a period characterised by the presence
of a speculative attack, either successful or not. The definition of a speculative
attack is based on an exchange market pressure (EMP) index (defined in Section 3)
of the type of Eichengreen et al. (1996b). If the value of the EMP index is above a
certain threshold, we define that period as a crisis state; otherwise the period is
defined as a tranquil state.
We use duration analysis to study the countries’ probability to leave a tranquil
state by exiting into a currency crisis state. The use of duration models is an innovative strategy for estimating the probability of exiting a currency peg. This
method allows us not only to study the determinants of the likelihood of a currency crash, but also the duration of spells of tranquility, how much this varies
over the business cycle, and how the duration of tranquil states varies across countries.1 The duration of the spells of tranquility is important in assessing currency
stability. Exchange rate credibility depends not only on the reaction to a speculative attack, but also on the time already spent in a tranquil episode.
Duration models allow us to test for the length of time already spent on the spell
as a determinant of the likelihood of exit into a turbulent episode. The specific pattern of the duration dependence lets us test if the likelihood of a devaluation is
higher for tranquil periods, say, in the first quarters, than for periods that have lasted longer, after controlling for other time-varying factors.
Klein and Marion (1997) suggest that, even if some of the determinants for the
duration of a fixed exchange-rate spell may remain constant over a spell, others
will change. A simple correlation of the length of each spell with some constant
measure of each explanatory variable fails to capture important information about
the time path of the variable during the spell. Therefore, they call for an empirical
approach that allows the consideration of time-varying determinants, rejecting
explicitly the use of ordinary least squares or duration analysis. They use logit
models instead. Nevertheless, in this paper we propose more sophisticated duration
models with the added feature of time-varying variables, so we do not miss the
explanatory power of time-varying determinants and, moreover, incorporate duration dependence.
The remainder of the paper is organized as follows. Section 2 concentrates on
methodological issues. Section 3 depicts the measure of speculative pressure. We
describe the data in Section 4. In Section 5 we present the main results, and Section
6 concludes.
2. Methodological issues
In analyzing the process of transition from a tranquil state to a crisis state, we
define a tranquil state as a period of time in which there is no pressure on the currency. A crisis state is defined as a period characterised by the presence of a speculative attack, whether this is successful or not.
1
These are the classical questions that Kiefer (1988) raised in his seminal paper on duration methods
applied to unemployment data.
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
801
Following Eichengreen et al. (1996b), we do not identify currency crises with
actual devaluations, revaluations and instances in which the currency is floated.
The reason for this is twofold. First, not all speculative attacks are successful. The
currency may be supported by the intervention of the national central bank via
expenditure of reserves, or by foreign central banks and governments or, even, by
the threat or actual imposition of capital controls. The use of interest rates and
austerity policies are other alternatives to repel an attack. Second, realignments are
undertaken in tranquil periods in order to preclude future attacks.
For the specification of the duration model,2 we use the Cox (1972) approach of
proportional hazards. With this specification, it is possible to estimate the
unknown parameters without specifying the form of the base-line hazard, thus providing a partially non-parametric estimator for those constants. The proportional
hazard model seem a reasonable compromise between the Kaplan-Meier estimate
(a non-parametric approach) and the possibly excessively structured parametric
models, given the absence of a theory we can follow in determining the specification of the hazard function.3
The proportional hazard specification in continuous time leads to a hazard function of the form:
kðt; xðtÞ; b; k0 Þ ¼ /ðxðtÞ; bÞ k0 ðtÞ:
ð1Þ
Here x(t) denotes time dependent variables, b is a vector of unknown coefficients
and k0(t) is the base-line hazard corresponding to /ðÞ ¼ 1. It is common practice
to measure the regressors so that /ðÞ ¼ 1 at the mean value of the regressors.
Then k0(t) has an interpretation as the hazard function for the mean individual
(country) in the sample. The first component of Eq. (1), /(), describes the way in
which k shifts between individuals endowed with different x’s at given length of
time t spent on a tranquil period. The second component, the base-line hazard, is a
functional form for the dependence of k on t. A commonly used specification of / is:
/ðxðtÞ; bÞ ¼ expðxðtÞ0 bÞ:
ð2Þ
This specification is convenient because the non-negativity of / does not impose
restrictions on b.
In the discrete specification used for the estimation, the hazard function denotes
the probability of moving to a crisis state in period t þ 1 conditional on being in a
tranquil state until period t. After some calculations we can write the hazard function as:
hðtÞ ¼ 1 expfexpðxðtÞ0 b þ cðtÞÞg;
2
ð3Þ
See Kiefer (1988) and Lancaster (1990) for a discussion of these models. See also Narendranathan
and Stewart (1993) as an application of these type of models.
3
The hazard function is a conditional probability, the probability of moving into a crisis state in period t þ Dt conditional on being in a tranquil state until period t.
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M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
where
cðtÞ ¼ ln
ð tþ1
k0 ðuÞdu :
ð4Þ
t
We have to express these probabilities in terms of a likelihood function to be
estimated. The contribution to log likelihood made by the ith observation, which
fails or is censored4 in the interval tj is:
Li ðhÞ ¼ di lnðhi ðtÞÞ þ
tj 1
X
lnð1 hi ðtÞÞ
ð5Þ
t¼1
tj 1
X
Li ðhÞ ¼ di ln 1 exp exp xi ðtj Þ0 b þ cðtj Þ
exp xðtÞ0 b þ cðtÞ ;
ð6Þ
t¼1
where h is the set of parameters to be estimated (b,c(t)), di ¼ 1 if the ith spell is
uncensored—the transition from a traquil state to a currency crisis state is
observed—and di ¼ 0 if censored—the transition is not observed.
There still remains one more consideration about the correct likelihood function.
Our data consist of N countries, each of which can experience multiple transitions.
This is what is called multiple-cycle data. In that case, the hazard functions may
depend upon the number of previous entries to the tranquil state, which is known as
occurrence dependence. Or it may depend upon the lengths of previous visits to the
tranquil state, which is known as lagged duration dependence. In order to write the
log likelihood function for a given country let us define dc ¼ 1 if crisis state is entered
at the end of the cth cycle and 0 otherwise. We summarize the transition intensities,
hc(t,s), as the hazard function for the cth cycle at calendar time t and elapsed duration s (duration of cycle cth). Then, for a country which we observe over Ci cycles,
the last of which may be right censored, the log likelihood contribution will be:
(
)
tj 1
Ci1
X
c i i X
Li ðhÞ ¼
ln hi tc ; sc ; tj þ
ln 1 hci tic ; sic ; t
c¼1
t¼1
tj 1
C
X
i
þ di ln h ðtCi ; sCi Þ þ
ln 1 hCi ðtCi ; sCi ; tÞ ;
ð7Þ
t¼1
where h() is given by Eq. (3).5
3. Measuring Exchange Market Pressure
The first issue in any empirical analysis of currency crises is to define speculative
attacks. As stated previously, in our definition of currency crises we also want to
4
A spell is censored when we do not observe the duration of the spell until its conclusion. We do not
have information on the transition to a currency crisis state.
5
For an empirical application of duration models, interpretation of their coefficients, and significance
and hazard functions see Narendranathan and Steward (1993).
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
803
capture those unsuccessful attacks that have been warded off by central banks and
governments: running down their international reserves or by raising interest rates.
Eichengreen et al. (1996c) construct a measure of speculative pressure by means
of an index. This index is a weighted average of exchange rate changes, changes in
reserves, and interest rate changes.6 The index of exchange market pressures is
defined as:
EMPi;t ¼ aDei;t þ bDðii;t it Þ cðDsi;t Drt Þ;
ð8Þ
where a, b and c are the chosen weights, Dei,t is the change in the exchange rate, ii,t
denotes the domestic interest rate, it corresponds to the same variable but for the
country of reference, si,t is the ratio of foreign reserves to domestic money for the
domestic country and, rt denotes the same concept for the country of reference.
Defining the EMP index of Eq. (8) as an unweighted measure has the obvious
advantage of simplicity. The disadvantage is that the volatility of exchange rates,
interests rates, and reserves are very different. Eichengreen et al. work with the
EMP index weighting the three components so as to equalize their volatilities. In
this way they prevent any of the components from dominating the index.
The next step is the identification of a currency crisis using the EMP indicator.
Eichengreen et al. identify quarters in which their index is at least one and a half
standard deviations above the sample mean as instances of speculative attacks. To
avoid counting the same crisis more than once, they exclude the later observation(s) when two (or more) crises occur in successive quarters.
The EMP measure by Eichengreen et al. has the advantage of being consistent
but it cannot capture those episodes in which the monetary authorities were very
successful in controlling a speculative attack, yet, ended with an important loss of
reserves. Examples are Denmark in 1992 and 1993 at the time of the tensions in the
European Exchange Rate Mechanism (ERM). In late 1992, Denmark warded off
attacks by a huge loss in foreign reserves. A similar example is France, 1992. For
this reason we construct a third measure of speculative pressure. We use the same
three indicators (exchange rate changes, changes in reserves, and interest rate changes7) but in a rather different way. Episodes where changes in the exchange rate are
greater than +1.5 standard deviations over the means are selected first as episodes
of speculative attacks. For the remaining episodes we look at the reserves indicator. If changes in relative foreign reserves are below the –1.5 standard deviation
band, we classify them as crisis episodes. As new episodes of currency crisis we add
those ones for which the interest rate differential is above the +1.5 standard deviation band.
The remaining observations are classified as periods of tranquility. Some
remarks are in order here. First, whenever we find that only one of the three
6
This is a common measure used in several studies by the same authors (Eichengreen et al., 1996a,b)
and by Sachs et al. (1996) as well as Kaminsky et al. (1998), with variations in the weights given to the
three components.
7
These variables are measured in relative terms with those prevailing either in Germany or in the US,
depending on the country of interest. Australia, Canada, New Zealand and Japan are related to US.
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M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
variables lies outside the band, we look at the deviation from the band and the
behavior of the two other variables. If the case is such that the deviation from the
band is marginal and the two other variables show a normal behavior, we disqualify that episode as a turbulent one and it is classified as tranquil period. If, on the
contrary, we observe that the three variables are in the margin of the band, we
qualify the episode as turbulent. In order to prevent the continuation of a speculative episode from being identified as a new episode, we exclude the later observation(s) when two (or more crises) occur in successive quarters.
To check the sensitivity of the results to the definition of currency crises we use
both measures in the estimations, but the emphasis is made when using the third
measure, since it is our preferred measure.
Before explaining the results of our estimates, we report some of the characteristics of the duration of the spells of tranquility. Information about the duration of
the spells is provided in Table 1. The first set of columns in Table 1 includes all
spells identified, whereas the second set of columns refers to completed spells only,
that is, spells that are not right censored. It is assumed that one spell ends when
the country leaves that state (tranquil state) to enter another one (here a currency
crises state), otherwise the spell is right censored. In econometric duration models,
right censoring is usually modelled by a dummy variable that takes on the value of
1 if an exit is observed and 0 otherwise. In our estimations we use all the spells,
that is, completed and right censored spells.
From Table 1 we see that the exit rate into a turbulent episode is higher in the
early quarters of a tranquil period. One third of the spells in the sample end in the
first year of a tranquil period, and half of them end or are right censored within
two years and a half. In addition, 64 percent of the durations are below four years
in length. According to these proportions and given the limited number of crises,
we concentrate the estimates for the behavior of the base-line hazard (that is, of
the duration parameters) in the four years since the beginning of the tranquil
period.8
4. The Data
We have assembled quarterly data from 1970 through 1997 for twenty OECD
countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France,
Greece, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal,
Spain, Sweden, Switzerland, the United Kingdom and the United States. The data
base is constructed from the International Financial Statistics (IFS) published by
the International Monetary Fund and the Main Economic Indicators dataset published by the OECD.
To define the indices of speculative pressure, we use data from the IFS. The
exchange rate is expressed in terms of the national currency of country i at time t
over DM or USD. We use market rates, that is the exchange rate determined lar8
This restriction does not strongly affect the results (see Fig. 2).
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
805
Table 1
Distribution of Tranquil Spells
Duration
of Spell in
Quarters
Total Spells
Completed Spells
Frequency
Percent
Cum.
Frequency
Percent
Cum.
1
2
3
4
5
6
7
8
9
10
11
13
15
16
18
19
20
21
22
23
33
35
36
37
38
40
47
54
Total
Mean
Standard
Deviation
7
8
6
6
4
1
2
2
2
3
1
3
1
6
1
4
4
4
2
2
1
2
1
1
2
2
2
1
81
14
13
8.64
9.88
7.41
7.41
4.94
1.23
2.47
2.47
2.47
3.70
1.23
3.70
1.23
7.41
1.23
4.94
4.94
4.94
2.47
2.47
1.23
2.47
1.23
1.23
2.47
2.47
2.47
1.23
08.64
18.52
25.93
33.33
38.27
39.51
41.98
44.44
46.91
50.62
51.85
55.56
56.79
64.20
65.43
70.37
75.31
80.25
82.72
85.19
86.42
88.89
90.12
91.36
93.83
96.30
98.77
100
7
8
6
6
4
1
2
2
1
3
1
3
1
2
0
3
0
4
2
2
0
2
1
1
2
2
1
1
68
13
13
10.29
11.76
8.82
8.82
5.88
1.47
2.94
2.94
1.47
4.41
1.47
4.41
1.47
2.94
0.00
4.41
0.00
5.88
2.94
2.94
0.00
2.94
1.47
1.47
2.94
2.94
1.47
1.47
10.29
22.06
30.88
30.88
45.59
47.06
50.00
52.94
54.41
58.82
60.29
64.71
66.18
69.12
69.12
73.53
73.53
79.41
82.35
85.29
85.29
88.24
89.71
91.18
94.12
97.06
98.53
100
gely by market forces and defined as period averages. The discount rate, preferably, or the money market rate, depending on the availability of data, is the measure of the interest rate entering the definition of the EMP index. International
reserves enter the EMP index as a ratio of reserves (excluding gold) to narrow
money (M1).
The independent variables can be grouped as follows. As indicators of the economic domestic conditions we introduce real GDP growth at 1990 prices, the Consumer Price Index (CPI) to construct the inflation indicator, and the rate of
unemployment.
To measure the external conditions we consider merchandise exports and merchandise imports, as a ratio to GDP and in terms of growth rates. We also consider
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M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
an indicator of the degree of openness of the country (exports plus imports as a
ratio to GDP).
A Real Effective Exchange Rate index (REER) is defined as the nominal effective
exchange rate index adjusted for relative movements with a national cost indicator
of relative normalized unit labor costs in manufacturing.
As an indicator of the domestic monetary condition we include domestic deposits. This variable is defined as demand deposits plus time and saving deposits,
deflated by GDP and in terms of rate of growth. Domestic credit, claims on government, and claims on private sector are our indicators of a possible credit expansion
or lending booms.
To take into consideration the debate on capital account liberalization and the
extent to which measures to increase transaction costs may alter the composition
of capital flows and influence the vulnerability to sudden outflows, we include portfolio flows and foreign direct investment (FDI) in the analysis.
5. Results
In Table 2 and Fig. 1 we report the results for the benchmark model. The dependent variable is the probability of leaving a tranquil state. The estimates for the
parameters of the model are shown in the second column with the z-statistics in the
third column.9 The expected sign for the coefficients of the explanatory variables
are reported in the last column.
The baseline rate has been defined through a set of dummy variables, one for
each quarter till the fifth. From the sixth to the eleventh it has been defined with a
dummy for every two quarters. One more dummy is introduced for the next five
quarters. From then on, we do not include any more duration dummies, since we
only estimate the base-line hazard for the four first years due to the reasons stated
previously. The main feature of this kind of function is that it is constant in each
interval, but may vary from one interval to the other. The first interval is used as
the reference level.
5.1. Time-Varying Variables
Variables from quarter t are used to determine the probability of exit in quarter
t þ 1 in order to avoid feedback effects of the occurrence of a currency crash into
the macroeconomic variables.
Consider the first variable, GDP growth. The negative sign of the estimated
parameter indicates that a decline in GDP growth leads to an increase in the probability of ending the spell of tranquility. An increasing rate of growth may generate
buoyancy in the domestic asset markets, attracting capital inflows and, therefore,
9
We used the Maximum Likelihood method to estimate the parameters. The standard errors are calculated by the inverse of the Hessian (the Hessian is estimated by the secant method BFGS: Broyden,
Fletcher, Goldfarb, and Shanno).
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
807
Table 2
Maximum Likelihood Estimates
Parameters
Estimates
Est./s.e.
Expected sign
Growth
Inflation
Unemployment growth
Export Growth
Import Growth
Openness
REER (deviation from trend)
Deposits/GDP (rate of growth)
Claims on Government/GDP
Portfolio Investment/GDP
FDI/GDP
0.06
0.08
0.01
0.04
0.03
0.01
0.08
0.05
0.01
0.06
0.01
0.76
0.09
0.47
1.97
1.92
1.81
2.38
1.47
1.49
2.41
0.08
+
+
+
+
+
, and indicate significance at 10%, 5% and 1% respectively.
Note: the inclusion of a dummy variable to account for lagged duration dependence turns out to be not
significant, so we excluded it from our analysis.
supporting the currency. Conversely, if growth is declining there would be pressures to ease financial policies, among them currency depreciation, to stimulate
activity. Notwithstanding, the coefficient is not significant.
Fig. 1. Estimated Base-line Hazard.
808
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
The inflation variable has the expected sign but it is not significant. High
inflation increases the likelihood of exit into a turbulent period. Kumar et al.
(1998) argue that high inflation can increase vulnerability to crises through an
impact on resources allocation, competitiveness, and macroeconomic stability.
As expected, high unemployment increases the vulnerability to crises. The slump
in economic activity, reflected in a rise of unemployment, makes the central bank
more attentive to domestic objectives, compromising the exchange rate target. But
the coefficient is not significant.
As variables that reflect the health of the foreign sector we have included:
exports, imports, and an indicator of openness. The different studies on currency crises emphasise the role of a sharp slowdown in export growth as a key
contributor to currency vulnerability. A slowdown in exports is likely to
increase the probability of a crisis. This result is confirmed here: the sign for
the coefficient of the export variable is negative and significant, a result consistent with Kumar et al. (1998). According to our estimates, import growth
increases in advance of a speculative attack, reflected by the positive sign and
significant coefficient.
Milesi-Ferreti and Razin (1998) argue that more open economies are less likely
to suffer an exchange rate crash. The benefits of trade openness outweigh the
higher vulnerability to external shocks. As expected, we obtain a negative and significant sign, in line with Milesi-Ferreti and Razin’s argument, and with the results
of Kumar et al. (1998).
Past studies on currency crises found that REER is one of the most important indicators in assessing likely pressures against a currency—see Kaminsky
et al. (1998). We can consider the REER as a possible proxy for the loss of
international price competitiveness, as well as for exchange rate misalignment.
Following Kumar et al. (1998), REER can act as a channel for the contagion
effect via a competitiveness effect: when one currency is devalued, the trading
partners’ position deteriorates vis à vis that economy. A higher value of the
exchange rate index implies a more appreciated domestic real exchange rate.
Therefore, we expect the coefficient on the real effective exchange rate index to
be positive.
On the other hand, an appreciation of the real exchange rate relative to its historical value increases the degree of misalignment. Trend measures of the REER
(based on the Hodrick Prescott filter) can provide an approximate measure of significant disequilibrium in the real exchange rate. We introduce the variable REER
as deviations from this trend therefore, expecting a negative sign. According to
Table 2, the deviation of the REER from its trend variable is significant and has
the correct sign.
Extending the previously mentioned studies, we introduce deposits over GDP (in
terms of their growth rate) that serve as a proxy for the existence of deposit runs
and loss of confidence in the banking system, or of the shrinkage of banks’ balance
sheets for other reasons. The results show that the coefficient for this variable has
the expected sign and that it is statistically significant.
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
809
In order to capture Krugman’s effect10 (domestic credit expansion) on the likelihood of a speculative attack, past empirical studies include the domestic credit
variable. This variable is the sum of claims on central government, local governments, nonfinancial public enterprises, private sector, other banking institutions
and non-bank financial institutions. But what Krugman emphasises is not the
behavior of all those components of the total domestic credit, but the credit to the
government: the credit expansion due to the monetization of the government budget deficit. In order to capture the effect of this variable on the likelihood of a
speculative attack, we should take into consideration only the claims on government (in net terms) by the central bank and other banks. The coefficient for the
claims on government to GDP ratio is positive and statistically significant.
The last two variables included in the regression analysis reflect the composition
of capital inflows: portfolio investment and FDI, both variables deflated by domestic GDP. As Frankel and Rose (1996) and Kumar et al. (1998) argue, the
hypothesis is that FDI is a safer way to finance investment than is portfolio investment. First, FDI is said to be directly tied to real investment in plants, equipment
and infrastructure; whereas the other type of investment goes to consumption and,
therefore, does not help to add productive capacity to the system, which is necessary to generate exports that go into the service of debt in the future. Second, the
difference between these two types of capital inflows may be an important factor in
determining the vulnerability of a country to its capital inflows. Portfolio flows are
very sensitive to any changes in the international financial environment as well as
to changes in investor sentiment. In the event of a crash, investors can suddenly
dump portfolio investments, but multinational corporations cannot quickly sell
their factories.
Portfolio investment is highly significant and has the expected sign: increases in
portfolio investment raise the probability of occurrence of a currency crisis. Nonetheless, FDI is not significant, even if it has the expected sign. We can only compare
these results with those of Kumar et al. (1998), since Eichengreen et al. (1996b) do
not consider the effects of this kind of variables. Kumar et al. (1998) obtain the
same effect regarding portfolio investment: a positive and significant effect. Regarding FDI, Kumar et al. (1998) find a significant, but negative effect, meaning that
increases in FDI result in higher likelihood of a crisis. The reason is probably due
to the different group of countries under study: emerging markets in their work,
OECD countries in ours. Moreover, during the period and countries considered in
this study the vast majority of FDI was in mergers and acquisitions more than in
real investment. This may justify why the FDI variable is not significant.
Summarizing and comparing with Eichengreen et al. (1996b) (that is the closest
paper to this one, both in terms of country sample and the construction of the
dependent variable based on an EMP index), we find a wide range of significant
variables, in contrast to Eichengreen, Rose and Wyplosz’s two macroeconomic significant variables (unemployment rate and inflation) plus the contagion variable.
10
See Krugman (1979).
810
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
5.2. Estimated Base-Line Hazard
The scaled estimated base-line hazard for our semiparametric function model is
plotted in Fig. 1. With the base-line hazard we want to test whether time already
spent on a tranquil period has an independent effect on the likelihood of a currency
crisis event, that is, whether there is a duration dependence beyond the control of
time-varying variables.
The base-line hazard function shows a general downward slope from the second
quarter after the start of a tranquil period. That is, the likelihood of exit into a currency crisis state declines with the length of the spell of tranquility. Therefore, we can
clearly state a negative duration dependence: the probability of leaving a tranquil
state decreases with duration. Our hypothesis on the existence of duration dependence, even after controlling for time-varying factors, is confirmed, and hence, the use
of duration analysis to model the likelihood of currency crises is the correct approach.
More specifically, in the first quarter, the probability of a speculative attack is
lower than in the second quarter. That probability increases from the second quarter and remains around that level for the first year of a tranquil period. These two
facts seem to show that at the beginning of a tranquil period the agents are not
very confident in the stability of the currency. After the first quarter, agents test the
stability of the currency resulting in a higher likelihood of existing the tranquil
spell in that quarter. After the first year, the probability of exit into a currency crisis state declines sharply, stabilizing by the end of the second year, to recover a little bit in the initial months of the third year, and turning into a flat line afterwards.
5.3. Robustness tests
In order to check for the robustness of the results presented in the previous sections, we have estimated our benchmark model including new variables, excluding
some of the initial variables, changing the definition of the duration dummies, and
using a different indicator of exchange market pressure. We also estimate a probit
model that includes the same explanatory variables as the benchmark model and
dummies variables as indicators of the duration of the spell.
Table 3, column (1), estimates the benchmark model but including REER instead
of its deviation from trend. The sign of this variable is as expected and the coefficient is significant. Including REER of its deviation from trend has no effect either
on the rest of the variables or on the shape of the base-line hazard function. Therefore, we support the hypothesis of REER as, first, a competitiveness indicator, with
deteriorations of that indicator leading to higher probabilities of speculative attacks,
and, second, as a measure of exchange rate misalignment, appreciations beyond its
natural trend result in stronger likelihood of exit into a turbulent episode.
In order to check the accuracy of Krugman’s effect and our claim that it is the variable claims on government the adequate instrument to capture this effect, we have estimated the benchmark model using domestic credit instead. The result of this estimation
is shown in Table 3, column (2). The variable domestic credit is not significant. To
double check, we have also estimated the model including both claims on government
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
811
Table 3
Robustness Testsa (1)
Growth
Inflation
Unemployment growth
Export growth
Import growth
Openness
(1)
(2)
(3)
0.07
(0.90)
0.10
(1.22)
0.01
(0.57)
0.04
(2.01)
0.03
(1.94)
0.01
(1.76)
0.07
(0.87)
0.80
(1.04)
0.01
(0.39)
0.04
(2.16)
0.03
(2.20)
0.01
(1.76)
0.08
(2.34)
0.07
(0.80)
0.07
(0.77)
0.01
(0.43)
0.04
(2.01)
0.03
(1.84)
0.01
(1.87)
0.08
(2.43)
0.05
(1.56)
0.05
(1.49)
0.01
(1.73)
0.00
(0.51)
REER (deviation from trend)
REER
Deposits/GDP (rate of growth)
Claims on government/GDP
0.02
(1.54)
0.05
(1.38)
0.01
(1.57)
Claims on the private sector/GDP
Domestic credit/GDP
Portfolio Investment/GDP
FDI/GDP
0.07
(2.55)
0.01
(0.10)
0.00
0.32
0.06
(2.31)
0.00
(0.02)
0.06
(2.47)
0.01
(0.12)
, and indicate significance at 10%, 5% and 1% respectively.
Note: The inclusion of a dummy variable to account for lagged duration turns out to be not significant,
so we excluded it from our analysis.
a
z-statistics in parenthesis.
and claims on the private sector—see Table 3, column (3). The first remains significant
and with the correct sign, but the latter is not significant. Moreover, Eichengreen
et al. (1996b) introduce credit growth and fail to find a significant influence of this
variable on the likelihood of occurrence of a currency crises. Therefore, we conclude
that claims on government is the variable that better reflects Krugman’s effect.
Given that neither growth, nor unemployment growth, nor inflation, are significant in our model, in Table 4, column (1), we have excluded unemployment and
observe the effect on the rest of variables. Growth and inflation are still not significant. Only excluding growth, unemployment and REER variables inflation
becomes significant—see column (2) of this same Table.
Finally, in Table 4, column (3), we substitute export growth and import growth
variables, and the openness indicator for the current account to GDP ratio.
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M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
Table 4
Robustness Tests (2)
(1)
Growth
Inflation
(2)
(3)
0.07
(0.85)
0.08
(0.98)
0.11
(1.39)
0.05
(0.71)
0.03
(0.32)
0.01
(0.48)
0.04
(2.02)
0.03
(1.80)
0.01
(1.95)
0.04
(2.31)
0.03
(1.84)
0.01
(1.86)
Unemployment growth
Export growth
Import growth
Openness
Current Account/GDP
REER (deviation from trend)
Deposits/GDP (rate of growth)
Claims on government/GDP
Portfolio Investment/GDP
FDI/GDP
0.08
(2.41)
0.05
(1.44)
0.01
(1.56)
0.06
(2.31)
0.01
(0.08)
0.04
(1.24)
0.01
(1.56)
007
(2.62)
0.02
(0.16)
0.13
(2.89)
0.07
(2.26)
0.03
(0.96)
0.01
(1.59)
0.06
(2.39)
0.05
(0.40)
, and indicate significance at 10%, 5% and 1% respectively.
Note: The inclusion of a dummy variable to account for lagged duration turns out to be not significant,
so we excluded it from our analysis.
The sign is as expected, the higher the current account GDP ratio, the lower the
likelihood of exit into a currency crisis state.
To check if the results regarding the particular form of the baseline hazard (the
duration pattern) are driven for our particular definition of currency crises, we
have estimated the benchmark model using the EMP index11 as in Eichengreen
et al. (1996b). The results of this estimation are presented in Table 5 and Fig. 2.
Regarding the explanatory variables, growth and inflation are the significant variables, whereas the variables export and import growth and deviation of REER
from its trend are not significant. The base-line hazard maintains a negative duration dependence feature from the second quarter onwards—see Fig. 2. That is, in
the first quarter of the duration of a tranquil period the probability of a speculative
attack is lower than in the second quarter (as it was the case using our own definition of currency crises). That probability increases in the second quarter and then
decreases with the duration of the spell. It is worth noting that the likelihood of
11
The threshold adopted in the definition of this index is the 1.5 standard deviations over the mean.
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
813
Table 5
Robustness Tests (3)
EMP index
Growth
Inflation
Unemployment growth
Export growth
Import growth
Openness
REER (deviation from trend)
Deposits/GDP (rate of growth)
Claims on government/GDP
Portfolio Investment/GDP
FDI/GDP
duration 2Q
2Q < duration 1 year
1 year < duration 2 years
2 years < duration 3 years
constant
0.30
(1.73)
0.33
(1.35)
0.02
(0.75)
0.04
(1.04)
0.03
(0.82)
0.02
(1.69)
0.02
(0.48)
0.12
(2.04)
0.16
(1.93)
0.14
(2.21)
0.01
(0.10)
Probit (1)
Probit (2)
0.04
(0.65)
0.12
(2.04)
0.01
(1.23)
0.02
(1.56)
0.02
(1.52)
0.01
(1.98)
0.10
(4.30)
0.00
(0.10)
0.00
(0.36)
0.05
(2.10)
0.03
(0.35)
0.61
(1.94)
0.53
(1.56)
0.08
(0.28)
0.09
(0.26)
3.01
(9.94)
0.04
(0.65)
0.12
(2.04)
0.01
(1.24)
0.02
(1.55)
0.02
(1.51)
0.01
(1.98)
0.10
(4.33)
0.00
(0.10)
0.00
(0.37)
0.05
(2.10)
0.03
(0.35)
0.63
(2.09)
0.55
(1.68)
0.11
(0.36)
3.03
(10.45)
, and indicate significance at 10%, 5% and 1% respectively.
Note: The inclusion of a dummy variable to account for lagged duration turns out to be not significant,
so we excluded it from our analysis.
exit in the second quarter of the spell is much higher than with our own definition
of currency crises, but the pattern and level of the base-line hazard after the second
quarter are very similar to the base-line hazard of our benchmark model. This
result reinforces out conclusion of a negative duration dependence.
In Fig. 2 we have also plotted the base-line hazard for a model that includes the
same explanatory variables as the benchmark model, but we have estimated one
duration dummy every two quarters. The base-line hazard for this models shows
once again a clearly negative duration dependence.
In the last robustness check we have estimated a probit model that includes the
same explanatory variables that our benchmark model with some additional
dummy variables that measure the time already spent on the spell. The signs of the
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M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
Fig. 2. Base-line Hazards for Alternative Specifications.
explanatory variables remain the same, but the significance of some of them are
different. The inflation variable is significant but the export and import growth
variables are not significant. What is clear is the duration dependence. We have
include a set of time dummy variables in a similar way as Klein and Marion
(1997). We consider time dummies for quarters 1–2, quarters 3–4, quarters 5–8 and
quarters 9–12. So the base group are those spells that have lasted more than 3
years. Table 5, column (2) shows these results. The first dummy is significant and
positive, indicating that the likelihood of a speculative attack is higher for pegs in
the first half year than for pegs that had lasted more than 3 years. In column (3)
we use as a base group spells that lasted more than 2 years. The results indicated
that the probability of a speculative attack is higher for spells of tranquility in the
first year than for longer spells (more than 2 years). Both results reinforce the
result of negative duration dependence of the duration model and are consistent
with the findings of Klein and Marion (1997).
These tests indicates that the negative duration dependence found in our benchmark model is robust across different specifications. Notwithstanding, some of the
explanatory variables change their level of significance.12
12
As a further test we construct a dummy variable that takes the value of one if a general election took
place on that quarter. The inclusion of this variable (lagged one period) in the estimations does not alter
the previous results. Moreover, this dummy variable is not significant.
M. Tudela / Journal of International Money and Finance 23 (2004) 799–816
815
6. Concluding Remarks
In this paper, we have adopted a duration model approach towards the determination of the origins of a currency crisis event. We concentrate on the likelihood of
a crisis for a country in a given period related to some explanatory variables. The
use of duration models allows us to account for duration dependence among the
determinants of the likelihood of speculative attacks, without neglecting the use of
time-varying explanatory variables as used by other researchers. One of the main
objectives of this study is to test for time dependence, that is, the length of the time
already spent on a tranquil period as a determinant of the probability of exit into a
crisis state.
. From our estimates, we first state the influence of some important macroeconomic variables on the likelihood of exit into a turbulent state.
. Regarding the duration dependence which characterizes our data, the maximum
probabilities of exit are given at the start of the tranquil period, but with a clear
tendency to decrease after the first year. That is, we can clearly state a negative
and highly significant duration dependence.
Acknowledgements
I thank Danny Quah, Vassilis Hajivassiliou, Maia Güell and Hélène Rey for
helpful comments and suggestions. All remaining errors are my own. The views
expressed in this paper are those of the author and do not necessarily reflect those
of the Bank of England.
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