a markov regime switching model of crises and contagion: the case of the iberian countries in the...

Journal of Macroeconomics 34 (2012) 1141–1153

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Journal of Macroeconomics

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A Markov regime switching model of crises and contagion: The caseof the Iberian countries in the EMS

José Mário Lopes a, Luis C. Nunes b,⇑a Department of Economics, Cornell University, United Statesb Nova School of Business and Economics, Universidade Nova de Lisboa, Lisboa, Portugal

a r t i c l e i n f o

Article history:Received 2 September 2011Accepted 17 August 2012Available online 24 September 2012

JEL classification:C3F3F4

Keywords:Currency crisisContagionMarkov switchingVolatility

0164-0704/$ - see front matter � 2012 Elsevier Inchttp://dx.doi.org/10.1016/j.jmacro.2012.08.007

⇑ Corresponding author. Address: Nova School ofE-mail address: [email protected] (L.C. Nunes

a b s t r a c t

We develop a general econometric model of currency crises and contagion that integrates anumber of important features appearing in many different models recently proposed in theliterature. In particular, we consider a Markov regime switching vector autoregression con-ditional heteroskedastic model with time-varying transition probabilities allowing forshifting correlations. This model is used to study the case of the Portuguese escudo andthe Spanish peseta during the EMS crisis. The results show that, in a crisis situation, theinterest rate differential has different effects on the transition probability from the crisisstate to the non-crisis state: a perverse effect for Portugal, and a positive effect for Spain.We also find strong evidence of contagion, mostly from the Spanish peseta to the Portu-guese escudo, and to some extent from the Portuguese escudo to the Spanish peseta.

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1. Introduction

During the past few decades crises have drawn the attention of many economists. The current financial crisis furthermotivates increased interest in this topic. In this work we focus on the specific case of currency crises. When currencies comeunder attack the discussion can be particularly controversial, not so much in cases where bad policies are to blame, butmostly in situations where bad policies are not the greatest culprits. These latter cases have been the backbone of a newway of looking at currency crises, one that values contagion and expectations-driven switching from one equilibrium to an-other. An example where all these features come to mind is the European Monetary System (EMS) 1992 crisis. In general, forany country’s currency that came under attack in that event, the following questions arise naturally. How important werethe fundamentals, and did contagion play any role during the crisis?

We study the experiences of the Portuguese escudo and Spanish peseta exchange rates while in the EMS and the possiblecontagion effects between the two Iberian countries. There are a number of reasons that motivate a joint analysis of Portugaland Spain besides geographical and cultural proximity. First and foremost, having both come out of decades of authoritarianregimes in 1974 and 1977 respectively, both countries negotiated accession to the European Economic Community at thesame time and both eventually gained accession in the same year (1986). From that point on, both countries receivedsubstantial structural funds from the European Union and were able to sustain high growth rates. The two countriesmanaged to fulfill the Maastricht criteria and gained accession to the Euro at the same time. Finally, realignments of the

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1142 J.M. Lopes, L.C. Nunes / Journal of Macroeconomics 34 (2012) 1141–1153

currencies in the two countries within the EMS tended to chronologically occur close to each other. These striking similar-ities in the recent history of both nations make Iberia an interesting case in itself. Additionally, the Iberian economies haveconsistently displayed a significant degree of trade and financial integration.1 Such linkages, significantly heightened duringthe 1990s by political considerations involved in the decision of devaluing or not devaluing, provide channels through whichcontagion may occur.

In order to empirically address these questions, several econometric models have been considered in the literature. Mar-kov regime switching models are among the most popular models since they are able to characterize crises as jumps acrossdifferent equilibria (see Jeanne, 1997; Jeanne and Masson, 2000). These models have been extended by allowing the transi-tion probabilities to be time-varying, which constitutes a way to capture different underlying reasons for these movements,such as the coordination of expectations based on sunspots or changes in fundamentals (see Mouratidis, 2008). Anotherstrand of the literature considers the role of contagion in Markov switching models by allowing for a switching correlation(see Ramchand and Susmel, 1998) or for lead-lag relationships between the unobserved states in each country (see Solaet al., 2002).

We contribute to this literature by proposing an econometric model that integrates all these elements of currency crises.In particular, we develop a Markov regime switching vector autoregressive conditional heteroskedastic model with time-varying transition probabilities allowing for shifting correlations capturing possible contagion effects. The interest ratedifferential of each country’s currency vis-à-vis the German mark is used as an explanatory variable in the time-varyingtransition probabilities. In this way, we are able to assess the role of expectations in the shift from a crisis state to a non-crisis one and vice-versa. Finally, our model also allows us to study the direction of contagion between the two countries.

The rest of this article is organized as follows. Section 2 gives an overview of the literature on crises and contagion. Sec-tion 3 presents some historical facts regarding the EMS currency crises. Section 4 presents the econometric model. The dataare described in Section 5 and the estimation results are presented and discussed in Section 6. Section 7 concludes.

2. Crises and contagion literature

The theoretical and empirical literature on currency crises and contagion has evolved by incorporating the practical expe-riences of actual crisis episodes. Over time, Krugman’s (1979) early idea that crises arise due to bad policies, such as unsus-tainable budget deficits, has been reassessed and second-generation models, more concerned with the interaction betweenexpectations and the policy makers’ decisions have become increasingly popular (see Obstfeld, 1986, 1996, Obstfeld andRogoff, 1995, Cole and Kehoe, 1996). These second-generation models tend to value the way expectations influence macro-economic policy decisions with currency crises being determined by self-fulfilling expectations.2 Jeanne (1997) and Jeanneand Masson (2000) show how these interactions result in multiple equilibria and argue that sunspots, or waves of optimismor pessimism, coordinate expectations that lead the economy to move from one equilibrium to another. These authors, amongothers, further propose using a standard Markov regime switching model that is able to capture these jumps.3 In this model, themovements of the economy across different equilibria are captured by an unobservable state variable following a Markov pro-cess. Many studies also make the assumption that sunspots are independent of fundamentals, which translates into Markovstate transition probabilities that are constant over time.

Today’s general consensus has achieved a synthesis between these views: it considers that fundamentals matter but arenot enough to explain either the severity, the scope, or the timing of a crisis. In particular, bad fundamentals, such as veryhigh current account deficits lasting for a very long time, may put an economy in a risk zone. However, a run from its cur-rency may not occur until private investors coordinate their expectations (see Cooper and Willis, 2010). In fact, asEichengreen (2000) points out, the EMS displayed several of the features of a currency crisis that were to be seen later inthe Mexican crisis (1995),4 the Asian crisis (1997),5 the Russian crisis (1998),6 and the Argentina crisis (2001).7 Although dif-ferent fundamentals have been emphasized in the literature for each of these crises (current account deficit for Mexico, debtlevel and bad supervision for Asia, the Russian debt default, and Argentina’s ‘‘crony capitalism’’ and real exchange appreciation),both first-generation and self-fulfilling elements have been associated with these crises and their spreading pattern. Peria

1 Considering intra-EU27 trade, Eurostat reports that by 1997, Portugal was the destination of 12.4% of Spanish exports and was the source of 4% of Spanishintra-EU imports. On the other hand, Spain was the destination of 17.9% of Portuguese exports and the source of 30.7% of Portuguese imports. Other majortrading partners for both economies were in general major European economies such as France or Germany. Financial integration has also been a relevantfeature. To give but one example, in 1996, 21.5% of the stock of EU Foreign Direct Investment into Portugal originated in Spain and 35% of the stock ofPortuguese outward FDI went into Spain. From Spain’s perspective, FDI originating in Portugal was also increasing, although in percentage terms it remainedmuch smaller.

2 An example from Pesenti and Tille (2000) goes as follows: suppose an economy subject to a peg (but willing to leave if necessary to boost growth) hasborrowed from outside, with the debt denominated in domestic currency. Investors know that in the face of a devaluation, their assets will be worth less. If theyexpect the devaluation as of today, they will lend at a higher cost. Faced with higher borrowing costs and reduced growth, the domestic policy makers will needto devalue, thus realizing the investors’ initial expectation.

3 Sarno and Valente (2009), along the lines of Engel and Hamilton (1990), also argue that regime switching models improve the performance of exchange rateforecasts when compared to a basic random walk model.

4 For a detailed account of the Tequila crisis, see Sachs et al. (1996) and Calvo and Mendoza (1996).5 See Corsetti et al. (1998) and Radelet and Sachs (1998).6 See Duffie et al. (2003).7 See Paolera and Taylor (2003).

J.M. Lopes, L.C. Nunes / Journal of Macroeconomics 34 (2012) 1141–1153 1143

(2002), Cipollini et al. (2008), and Mouratidis (2008) incorporate these views in the context of the Markov regime switchingmodel by allowing the switching probabilities to be time-varying and dependent on the fundamentals. These empirical studiesconfirm the superiority of these models in identifying speculative attacks and the importance of both fundamentals and expec-tations in driving state transition probabilities.

The related literature on contagion evolved alongside the more general literature on crises. Its focus has been on trying tounderstand the transmission mechanisms across countries. As it stands, the literature distinguishes mainly two types of con-tagion. First, fundamental related contagion, including the simple transmission of shocks from one country to another be-cause of the mere interdependence of countries through existing economic channels (see Eichengreen, 1996). Thisincludes real linkages: a depreciation of another country’s currency makes the task of competing with it harder and inducesa depreciation of the own currency.8 It also includes financial linkages due to the mere integration of economies, which canhinder credit between them when a financial crisis hits one of them.

Second, non-fundamental related contagion, arising when bad fundamentals are not enough to explain the spillover of acrisis, that is, when comovements are greater than what fundamentals would induce. This concept relates to second-generation models emphasizing strategic complementarities among authorities and investors (Jeanne and Masson, 2000)or among investors themselves (as in Morris and Shin, 1998). The most prominent justification for such a contagion is infor-mational asymmetries. If information is difficult to gather, one group of agents may depend on another group’s informationto gain an opinion of the quality of securities in some economies. However, if they cannot observe the actual information ofthe informed agents, but only the size of their buying/selling orders, they are faced with a ‘‘signal extraction’’ problem. Thismeans that if the informed agents merely face margin calls, their selling actions may be understood as a sign of badfundamentals. These informational cascades induce herding, and a ‘‘currency run’’ will follow (on this matter seeBikhchandani et al., 1998, Calvo, 1999, and Shiller, 1995).

A phenomenon that can sometimes be erroneously perceived as contagion is the occurrence of ‘‘monsoonal’’ effects (seeMasson, 1998) which are common shocks that have a direct effect over a whole group of countries at the same time; it can bean increase in the Federal Funds Interest Rate drawing funds away from other countries or the collapse of a large hedge fund(such as the Long Term Capital Management) linked to several economies. By the same token, a weakening of the dollar orincreasing oil prices have global effects that will jam the tracking down of pure contagion. This type of phenomenon shouldnot be conceptually mixed with contagion though it may be observationally equivalent to it at times.

The issue of contagion has a specific place inside the crisis literature. By studying contagion, we are analyzing not onlywhy a crisis occurs, but how different countries or world regions interact with each other while going through turmoil.As stated by Dornbusch et al. (2000), contagion in multiple equilibria models can be understood as the influence that oneeconomy has over the shift of a second economy from a good to a bad equilibrium.

Rigobon (1999) chooses to categorize the propagation of shocks as crisis-contingent9 and non-crisis contingent.10 Forbesand Rigobon (1999) add that a quick and significant impact of a crisis in one economy on another economy may be nothingmore than the effect of an already high correlation that binds the two economies, that is, of simply interdependence. Hence,it is more appropriate to use the term contagion when there is a significant change in the transmission mechanism. As the sec-ond-generation crises models suggest, this is especially relevant in exchange rate markets where expectations can play a majorrole during crisis periods.

This said, it must be stressed that there is no single definition of contagion in the literature, at either a theoretical orempirical level. However, two main types of propagation of shocks can always be traced: first, we have the mere interdepen-dence of countries, through fundamental driven linkages; then, we have contagion as comovements greater than what fun-damentals would induce. Several authors refuse to call the former contagion; others are at ease with the word but prefer tospecify the latter as ‘‘pure contagion’’. Billio and Caporin (2010) mention these various shades of the definition of contagionand label the latter as a restrictive form of contagion.11

Again, the Markov regime switching model is especially well suited to deal with contagion effects by allowing the corre-lation between the shocks to the different currencies to change in different regimes. Compared to earlier empirical tests ofcontagion (e.g., Forbes and Rigobon, 1999) where different crisis periods had to be defined exogenously, the Markov switch-ing model presents a further advantage in that both model parameters and regimes are jointly estimated. Moreover, thedirection of contagion across different countries can also be studied by estimating a bivariate or multivariate regimeswitching model. For recent applications of the Markov switching model to currency markets see Gravelle et al. (2006)and Mandilaras and Bird (2010). For applications to other financial markets see Sola et al. (2002, 2007), Edwards and Susmel(2003), Rodrı́guez (2007), Gallo and Otranto (2008), Qiao et al. (2008), and Mouratidis et al. (2010). Note that most of theresearch on this issue does not allow for time-varying transition probabilities.

8 Notice that the two countries do not have to actually trade heavily between themselves – it is sufficient to have competing exports (as in Corsetti et al.,2000).

9 In this case we would find: the multiple equilibria channel; liquidity shocks that force agents to rebalance their portfolio; asymmetric informationtranslated into herding behavior that aggravates capital outflows after informed agents start to leave; and political contagion, i.e., the fact that when onecountry leaves the peg, it becomes less costly for others to do so.

10 Here, we find channels that are the result of a stable link between economies.11 Contrary to Forbes and Rigobon (1999), who emphasize interdependence, Corsetti et al. (2005) present strikingly different views on this matter, uncovering

more evidence in favor of contagion.


3. EMS historical overview

The EMS came into effect in March 1979. Its main features were a currency basket (ECU), the creation of the ExchangeRate Mechanism (ERM) through which each country agreed to maintain the value of its currency vis-à-vis currencies withinthe system, and the establishment of a mechanism for financing monetary intervention. Capital controls were admissible(France used them in 1981). Nevertheless, after some tension in the early 1980s, followed by less frequent realignments to-ward the end of that decade and a remarkably stable period after the Single Act, severe currency crises occurred in 1992–1993. The collapse of the Soviet Union and the German unification (and tighter German monetary policy) triggered exchangerate crises across Europe. The Finnish markka and Swedish krona came under attack in mid-1992, and the pound sterling andItalian lira later that year. The Spanish peseta and the Portuguese escudo, which had joined the ERM with a 6% band in June1989 and April 1992, respectively, also came under attack. Eventually, as a result of these crises, the UK chose to leave theEMS and several currencies devalued vis-à-vis the Deutschmark.

Although both Portugal and Spain realigned their currencies by 6% in November 1992, the two countries continued understrong pressure to devalue in early 1993. Eichengreen (2000) describes what happened with Portugal as a spillover of whatwas happening in Spain: with reduced economic growth and increasing unemployment in Spain, the peseta was in a crisiszone. This ignited speculative pressure over the peseta, and the escudo suffered simultaneously. A new devaluation of theescudo and the peseta occurred in May 1993.12

Eventually disagreements between French and German authorities emerged as all currencies came under attack. Finally,on the 2nd of August of 1993, the bands were widened to 15% and exchange rate stability was achieved. A final realignmentof the escudo and the peseta occurred in March 1995.

The explanations advanced for this crisis follow the reasoning presented above. First, we can ascribe the main reason tocompetitiveness problems, which means that overvalued currencies in a fixed-but-adjustable rates regime had no otherchoice but to devalue. A second explanation could involve a prediction by market investors of an inevitable future policyshift. Facing a difficult choice between respecting the peg and enduring unemployment or abandoning the peg altogether,most governments could find it more reasonable to choose the latter in the face of a tight German monetary policy. Also,in the context of the post-Single European Act EMS, capital control elimination would eventually make fixed parities hardto defend in an economy with free capital mobility. In a nutshell, both of the possible interpretations of this crisis hingeon the same criterion that enables us to distinguish between those models focusing mainly on the current account and sec-ond-generation models (where capital account has a somewhat more autonomous role, highly susceptible to changes in sen-timent or perception of fundamentals).

4. The econometric model

In this section we describe an econometric model that integrates several different approaches that have been proposed inthe literature of currency crises and contagion. It consists of a Markov regime switching vector autoregressive conditionalheteroskedastic model allowing for time-varying transition probabilities and shifting correlation.

In the Markov regime switching model, first introduced by Goldfeld and Quandt (1973) and later revived by Hamilton(1989), variables are treated as originating from a multiple state model with movements from one state to another deter-mined according to a Markovian process with state transition probabilities given by:

12 Forvolatilitaccountmembeachieve

Probðst jst�1; st�2; st�3; . . .Þ ¼ Probðstjst�1Þ; ð1Þ

where st denotes the unobserved state variable. In the initial models, these transition probabilities were considered as fixedparameters to be estimated.

Krolzig (1997) develops a Markov-switching vector autoregression (MSVAR) model merging the VAR literature going backto Sims (1980) and the Markov regime switching model. However, this model is more useful for very low frequency datathan for high frequency data with more complex processes for the variance. The first work seeking to estimate bivariate re-gime switching ARCH models is Hamilton and Susmel (1994). After that, Ramchand and Susmel (1998) applied it to stockmarkets, and Edwards and Susmel (2003) to interest rates. A bivariate model, allowing for a switching variance is the bivar-iate SWARCH model proposed by Hamilton and Lin (1996).

An important weakness regarding the initial Markov switching models concerns the nature of the transition probabilities.For instance, in the particular case of the EMS, the probability of jumping from a low volatility to a high volatility state shouldbe made dependent on variables such as the distance from the parity or the upper limit of the band (see Engel and Hakkio,1996). However, the determination of these variables is far from random, as Filardo (1998) explains. In fact, Hamilton’s(1994) filter, which determines smoothed and filtered probabilities of being in state st, can only be used if we assume away

a deeper analysis of the Portuguese path from the 1970s to the euro, see Macedo et al. (2003, 2004). They show that, under convertibility, conditionaly of the exchange rate was actually less than under inconvertibility, which in a way reaffirms the idea behind the Delors Report of opening capital

right at the beginning of the convergence process. Bacchetta (1997) studies the experience of the Spanish peseta and concludes that the ERMrship made the peseta the target of speculative attacks, and that the exchange rate-based disinflation program and the overall policy mix failed totheir objectives.


endogeneity problems by using variables that are contemporaneously uncorrelated with the latent state variable. TheMSVARCH13 model used in this paper extends the models proposed in Hamilton and Susmel (1994), Ramchand and Susmel(1998), and Edwards and Susmel (2003). There are two states for each country’s exchange rate: a low volatility state sc

t ¼ 1and a high volatility one sc

t ¼ 2, with c denoting each currency. In our empirical application that is described in the followingsections, c = x stands for the escudo’s exchange rate vis-à-vis the Deutschmark and c = y stands for the peseta’s exchange ratevis-à-vis the Deutschmark. Overall, the four possible combinations can be captured by a single state variable s�t taking fourpossible values:

s�t ¼ 1 : escudo low variance sxt ¼ 1, peseta low variance sy

t ¼ 1;s�t ¼ 2 : escudo low variance sx

t ¼ 1, peseta high variance syt ¼ 2;

s�t ¼ 3 : escudo high variance sxt ¼ 2, peseta low variance sy

t ¼ 1;s�t ¼ 4 : escudo high variance sx

t ¼ 2, peseta high variance syt ¼ 2.

Without assuming any restriction on the transition probabilities, P s�t ¼ jjs�t�1 ¼ i� �

¼ p�ij; i; j ¼ 1; . . . ;4, there is a total of 12parameters to estimate in the transition matrix. These models require the estimation of a large number of parameters andtheir estimation is computationally very intensive. Therefore, to simplify the parameterization, the transition probabilitiesmay be modeled assuming independence of each country’s state variable towards the other as in Ramchand and Susmel(1998) and Sola et al. (2007). As an example, some of these probabilities are defined below:

13 MS14 The15 We

appearprocessequatio

P s�t ¼ 1js�t�1 ¼ 1� �

¼ P sxt ¼ 1jsx

t�1 ¼ 1� �

P syt ¼ 1jsy

t�1 ¼ 1� �

;

and

P s�t ¼ 1js�t�1 ¼ 2� �

¼ P sxt ¼ 1jsx

t�1 ¼ 1� �

P syt ¼ 1jsy

t�1 ¼ 2� �

:

In a constant transition probabilities model, these probabilities are modeled for each currency as

Pðsct ¼ 1jsc

t�1 ¼ 1Þ ¼ pc11; ð2Þ

and

P sct ¼ 1jsc

t�1 ¼ 2� �

¼ pc21: ð3Þ

In such a model, which will hereinafter be called Model 1, there are only four parameters associated with the transitionprobabilities, px

11; px21; p

y11; p

y21.

As contagion may also refer to the influence that one economy may have on the switch in equilibria in another economy,we also explore an alternative specification of the transition probabilities. In particular, we consider the possibility that theunobserved state in one country leads the unobserved state in the other by one period. This implies a restricted transitionmatrix as described in Sola et al. (2002).

In a time-varying transition probabilities model, which will be called Model 2, these probabilities depend on a certainexogenous variable denoted by zc

t . Consequently, the transition probabilities are redefined as:

P sct ¼ 1jsc

t�1 ¼ 1� �

¼ U dc11 þ kc

11zct�1

� �; ð4Þ

and

P sct ¼ 1jsc

t�1 ¼ 2� �

¼ U dc21 þ kc

21zct�1

� �; ð5Þ

where U is a monotonic function that transforms the argument into a positive number in the unit interval (for instance, thecumulative normal distribution function).14

In this paper we explore the role that the interest rate differential may have in affecting these probabilities and set zct�1

equal to the lagged interest rate differential of the country with currency c versus the Deutschmark. A priori, it is not possibleto say what the signs of the kc

11 and kc21 coefficients are, as the interest rate differential can have conflicting effects over the

probability of changing to a crisis state. Beyond the effect on payoffs and subsequent positive impact on the demand for thehome currency, there are expectational effects to consider: on the one hand, an increase in the differential may be inter-preted by investors as a solid defense of the current peg and coordinating them toward the ‘‘good’’ equilibrium; on the otherhand, it may be viewed as a public signal of distress and of an upcoming devaluation, hence coordinating investors towardthe ‘‘bad’’ equilibrium. Assessing these sensitivities empirically is one of the goals of this paper. As a robustness check, inSection 6 we extend this feature of the model by allowing the transition probabilities to depend on the interest rate differ-entials of both countries.15

VARCH stands for Markov switching vector autoregression conditional heteroskedasticity.transition probabilities can be made dependent on several explanatory variables by letting zc

t�1 consist of a vector.note that we are using a reduced form model for the exchange rates where the fundamentals are captured by the interest rate differentials which

lagged in the time-varying transition probabilities to avoid endogeneity issues. It would also be possible to allow the fundamentals to follow a Markovas in Mouratidis et al. (2010). To incorporate such dynamics in our framework would require a four-equations model (for each country we would have

ns for the exchange rate and the fundamental).


Our intention with this kind of modeling is to devise an empirical model where both fundamentals and expectationalshifts have some bearing. Recently, discussing exchange market pressure indices and interest rate differentials, Mouratidis(2008) argued that both elements may be important, and justified the presence of Markov switching and time-varying tran-sition probabilities on those grounds. In an empirical study of the EMS crises using a VAR framework, Peria (2002) similarlyargued in favor of time-varying transition probabilities and in favor of the relevance of both expectational shifts and funda-mentals in explaining exchange rates, reserves, and interest rates. Alvarez-Plata and Schrooten (2006) made the same argu-ment for the Argentinian crisis.

In our model, exchange rates are specified as a VAR(1) process as follows:

16 As17 The

Det ¼ a0 þ a1Det�1 þ et; ð6Þ

where Det is a 2 � 1 vector containing the difference of the natural logarithms of the exchange rates of both countries versusthe Deutschmark, a0 = (a0, a1)0 is a 2 � 1 vector of constants terms, a1 is a 2 � 2 matrix

a1 ¼a11 a12

a21 a22

� �;

of own- and cross-autoregressive terms, and et ¼ ext ; ex

t

� �0 is a 2 � 1 vector of error terms with a distribution et � N(0,Ht). Thediagonal elements of Ht, denoted by hx

t and hyt , are modeled as state dependent ARCH(q) processes as in Ramchand and

Susmel (1998):

hct

ccst

¼ bc0 þ

Xq

i¼1

bciec2

t�i

ccst�i

: ð7Þ

As a normalizing assumption, we set cx1 ¼ cy

1 ¼ 1. As in Bollerslev (1990), we first assume that the correlation qx,y betweenex

t and eyt is constant, so that the covariances are given by

hx;yt ¼ qx;y hx

t hyt

� �1=2: ð8Þ

Later, we relax this assumption.Finally, we allow for the possibility of contagion in our model by letting the correlation be state dependent. We define

contagion as follows. There is contagion from A to B if, when A jumps from a low volatility state to a high volatility state,there is an increase in the correlation between the two currencies. If the converse does not occur, there is no contagion fromB to A. If this is the case, contagion is said to flow only from A to B.

As mentioned above, many different definitions of contagion exist in the literature. Ours, in the terminology of Billio andCaporin (2010), may be considered to be narrow (as theirs). For alternative definitions see Dornbusch et al. (2000), Pericoliand Sbracia (2001), and Dungey et al. (2005). In a different framework, where the timing of crises was exogenously imposedand no Markov-Switching or GARCH effects were imbedded in the model, Forbes and Rigobon (1999) argue that under het-eroskedastic conditions, the estimates of the correlation coefficient in the high volatility state are biased. As in Edwards andSusmel (2001), our approach explicitly models heteroskedasticity and corrects for that effect. Moreover, an important aspectof this methodology is that the dependence tests are based on the Markov regime switching process.

First, we check whether, when Portugal moved to a high volatility state, the correlation between the two currencies in-creased or stayed the same. The former possibility will favor the contagion hypothesis (from Portugal to Spain). To this end,we follow Ramchand and Susmel (1998), and allow the correlation to depend on the state sx

t . In this case, the covariancebecomes:

hx;yt ¼ qsx

t ;x;y hxt hy

t

� �1=2; ð9Þ

where qsxt ;x;y denotes the correlation coefficient, now taken as dependent on Portugal’s state sx

t .16

The opposite direction of contagion is also possible, that is, when an increase in volatility in Spain increases correlationbetween the two currencies. In this case, the correlation changes with sy

t (i.e., Spain’s state):

hx;yt ¼ qsy

t ;x;y hxt hy

t

� �1=2: ð10Þ

Finally, we also consider the case where the correlation may differ across all four possible combinations of sxt and sy

t suchthat:

hx;yt ¼ qsx

t ;syt ;x;y hx

t hyt

� �1=2: ð11Þ

All our models are estimated by maximum likelihood. The estimation and filtering process involves some modifications ofthe method described in Hamilton (1994). All computations were implemented in Gauss by adapting a program written byRamchand and Susmel (1998).17

in Ramchand and Susmel (1998), more than two values for the correlation are not allowed for, in order to avoid heavy losses in degrees of freedom.Gauss code used to implement all estimations in this paper is available from the authors upon request.

Table 1Descriptive statistics for the PTE/DEM and ESP/DEM returns.

PTE/DEM ESP/DEM

Mean 0.012 0.015Median 0.006 0.001Maximum 4.696 3.912Minimum �1.755 �2.046Std. dev. 0.308 0.388Skewness 2.96 1.33Kurtosis 53.44 20.68Jarque–Bera 123919 15356

(0.00) (0.00)ARCH-LM 6.10 11.67

(0.01) (0.00)

Notes: Returns defined as 100 times the log-difference. P-values in parentheses.

Table 2Variances and correlation in different sample periods.

Var(escudo) Var(peseta) Correlation

December 17, 1992–December 30, 1997 0.10 0.15 0.68December 17, 1992–August 2, 1993 0.34 0.34 0.76August 3, 1993–December 30, 1997 0.06 0.12 0.64


5. Data and descriptive statistics

The sample used in our empirical application is based on daily observations of 3-month interest rates (LISBOR, FIBOR, andMIBOR) obtained from Bloomberg, and of daily exchange rates of the Portuguese escudo versus the German mark and of theSpanish peseta versus the German mark from the webpage of the Federal Reserve Bank of St. Louis.18 Holidays were deletedfrom the final sample. The full sample runs from December 17, 1992, to December 30, 1997, comprising a total of 1153 obser-vations.19 Descriptive statistics of the percent changes (defined as 100 times the difference of the logarithm) of the escudo andthe peseta exchange rates vis-à-vis the Deutschmark are presented in Table 1. Both series clearly display ARCH effects, as shownby the results of the LM tests.

In Table 2 we present variances and correlations for the full sample and for different subperiods. The choice of August 2,1993, was not random, of course. It stands as a distinctive barrier between two different eras. It was on this date that thebands were widened. As can be seen in this table, the variances decrease substantially after this period. The correlationwas also greater during the crisis, here defined somewhat intuitively as ending on the 2nd of August. It would actuallynot be absurd if correlation increased after this. If we compare only the period until March 31, 1993 with the period betweenthe 1st of April of 1995 and December 31 of 1997, there is actually an increase in correlation from 0.45 to 0.56, probably dueto the upcoming (credibly announced) entry of both currencies in the Eurozone.

This tells us that it is not obvious that greater correlation is associated with the contagion of a crisis, since correlation canincrease outside of crisis episodes. However, the increased correlation at the height of the EMS crisis (closer to August 1993),hints that correlation indeed increases in a particularly abrupt manner in crises episodes. In fact, excluding the first sub-sample of the period between April and August actually reduces the correlation immensely. Correlation is 0.45 if we computeit between December, 1992 and March 31, 1993; but if it is computed for the period between April 1, 1993 and August 2,1993, it is 0.74.

6. Estimation results

We first consider the estimation results obtained for three variants of the model assuming constant transition probabil-ities as defined in Eqs. (2), (3), (6), and (7), which we called generally Model 1: a model with a constant correlation coefficientas in Eq. (8) that will be denoted as Model 1.1; a model with a correlation coefficient shifting with sx

t , the Portuguese escudo’sstate, as in Eq. (9) and denoted as Model 1.2; and a model with a correlation coefficient shifting with sy

t , the Spanish peseta’sstate, as in Eq. (10), and denoted as Model 1.3. Estimation results for these three models appear in Table 3.

18 These were constructed from bilateral rates between each of those three currencies and the US dollar.19 The absence of data prior to December 17, 1992 (coinciding with the first escudo realignment) is due to the difficulty in finding data for 3-month interest

rates for Portugal. Lisbon Interbank Offered Rates (LISBOR) started to be released only in December 1992.

Table 3Estimation results for models with constant transition probabilities.

Parameter Model 1.1 Model 1.2 Model 1.3

Estimate t-Stat Estimate t-Stat Estimate t-Stat

a10 0.0009 0.18 0.0011 0.21 �0.0003 �0.07a20 �0.0005 �0.08 �0.0003 �0.05 �0.0011 �0.18a11 �0.1865 �5.39⁄⁄ �0.1869 �5.43⁄⁄ �0.1778 �5.08⁄⁄

a12 0.0621 2.96⁄⁄ 0.0618 2.84⁄⁄ 0.0586 2.81⁄⁄

a21 �0.0609 �1.96⁄⁄ �0.0608 �1.92⁄⁄ �0.0599 �1.88⁄⁄

a22 �0.0324 �0.92 �0.0327 �0.87 �0.0332 �0.89bx

0 0.0151 8.97⁄⁄ 0.0153 8.58⁄⁄ 0.0150 10.18⁄⁄

by0

0.0282 10.50⁄⁄ 0.0288 10.23⁄⁄ 0.0266 10.14⁄⁄

bx1 0.2743 5.26⁄⁄ 0.2747 5.16⁄⁄ 0.2855 5.75⁄⁄

by1

0.1319 2.87⁄⁄ 0.1290 2.72⁄⁄ 0.1380 2.97⁄⁄

px11 0.9429 56.18⁄⁄ 0.9414 53.08⁄⁄ 0.9529 67.47⁄⁄

px21 0.0980 3.04⁄⁄ 0.1007 2.97⁄⁄ 0.0769 3.06⁄⁄

py11

0.9561 91.10⁄⁄ 0.9569 91.03⁄⁄ 0.9560 92.14⁄⁄

py21

0.0997 4.13⁄⁄ 0.0999 4.10⁄⁄ 0.1032 4.26⁄⁄

cx2 9.3641 10.72⁄⁄ 9.1547 9.92⁄⁄ 9.8209 10.74⁄⁄

cy2

11.689 10.89⁄⁄ 11.540 10.59⁄⁄ 13.324 9.98⁄⁄

qx,y 0.6883 38.64⁄⁄ – – – –q1;x,y – – 0.6993 28.01⁄⁄ 0.6326 24.02⁄⁄

q2;x,y – – 0.6740 22.30⁄⁄ 0.7581 31.93⁄⁄

lnL 196.77 196.95 202.14

⁄Denote significance at the 10% level.⁄⁄ Denote significance at the 5% level.


There are several conclusions to be taken from these results. First, comparing Model 1.1 with Model 1.2 through a like-lihood ratio test, which, under the null of no shift in correlation, follows a v2

ð1Þ distribution,20 we obtain a value of 0.37. Hence,we conclude that the correlation does not shift with Portugal’s state. Second, comparing Models 1.1–1.3, we obtain a likelihoodratio statistic of 10.38. Once again, it follows a v2

ð1Þ distribution under the null. Thus, we reject the null and favor Model 1.3 overModel 1.1, thereby concluding that the correlation shifts with Spain’s state. These results imply that there is no contagion fromthe escudo to the peseta but that the opposite (contagion from the peseta to the escudo) occurs: when the peseta jumps from anon-crisis state to a crisis state, correlation increases significantly from 0.63 to 0.76.

One major criticism regarding these models relates to the independence assumption while writing the joint transitionprobabilities. Another criticism that this analysis may draw is that the correlation may actually be shifting among the fourpossible states instead of shifting with the state of only one country. To cope with these criticisms, we generalize the pre-vious model by allowing for a 4 � 4 unrestricted transition matrix and a correlation coefficient that shifts with the four pos-sible values of s�t corresponding to the four possible combinations of sx

t and syt , as in Eq. (11). This model is denoted as Model

1.4 and the corresponding estimation results appear in Table 4. We find, perhaps unsurprisingly, that the state where cor-relation is highest is the one where both Portugal and Spain are in a crisis state. Moreover, we find that given that Spain is ina crisis state, the fact that Portugal goes into a crisis state increases the correlation from 0.61 to 0.80, whereas in a situationwhere Portugal is in a crisis state, if Spain goes into a crisis state the correlation increases more sharply from 0.37 to 0.80.Still, in this more general model, contagion seems to flow both ways.

Finally, we check for evidence of contagion in terms of lead-lag relationships between the unobserved states of the twocountries. We do this by considering a restricted transition matrix as in Phillips (1991), Sola et al. (2002), and Mouratidiset al. (2010), to account for leading patterns. However, the results obtained using the unrestricted matrix, Model 1.4, suggestthat the transition matrix is very different from the restricted forms accounting for leading patterns. For instance, as can bechecked in Table 4, the diagonal elements are significantly different from zero, which suggests that such restrictions are notvalid. To confirm this, we formally tested the validity of the restrictions by computing likelihood ratio tests comparing Model1.4 with restricted versions. We strongly reject all the restrictions as the likelihood ratio equals 189.56 taking as the re-stricted model one where the escudo leads the peseta, and equals 157.86 taking as the restricted model one where the pesetaleads the escudo.21

As for Model 2, the one with time-varying transition probabilities, as specified in Eqs. (4) and (5), we report results forthree variants of this model: the model with a constant correlation coefficient (Model 2.1), the model with a correlation coef-ficient shifting with the Portuguese escudo’s state (Model 2.2), and the model with a correlation coefficient shifting with theSpanish peseta’s state (Model 2.3). Results are shown in Table 5.

20 The critical values for a v2ð1Þ distribution are 2.076 at 10% and 3.841 at 5%.

21 These values compare with the 5% critical value of 18.31 from a v2ð10Þ distribution.

Table 4Estimation results for the model with constant and unrestricted transition probabilities (Model 1.4).

Parameter Estimate t-Stat Parameter Estimate t-Stat

a10 0.0011 0.24 cx2 11.483 11.97⁄⁄

a20 �0.0017 �0.30 cy2

16.382 12.02⁄⁄

a11 �0.1877 �5.48⁄⁄ p�11 0.8851 45.92⁄⁄

a12 �0.0716 �2.57⁄⁄ p�21 0.0631 1.19a21 0.0508 2.74⁄⁄ p�31 0.2070 3.46⁄⁄

a22 �0.0621 �1.96⁄ p�41 0.0919 3.25⁄⁄

bx0 0.0110 14.00⁄⁄ p�12 0.0049 0.76

by0

0.0187 13.94⁄⁄ p�22 0.8894 14.84⁄⁄

bx1 0.3291 7.98⁄⁄ p�32 0.0000 0.00

by1

0.2299 4.54⁄⁄ p�42 0.0198 1.53

q1,1;x,y 0.6546 22.90⁄⁄ p�13 0.0660 3.47⁄⁄

q1,2;x,y 0.6137 8.32⁄⁄ p�23 0.0000 0.00q2,1;x,y 0.3653 3.27⁄⁄ p�33 0.6091 7.11⁄⁄

q2,2;x,y 0.7959 35.01⁄⁄ p�43 0.0806 2.03⁄⁄

lnL 242.69

⁄ Denote significance at the 10% level.⁄⁄ Denote significance at the 5% level.

Table 5Estimation results for models with time-varying transition probabilities.

Parameter Model 2.1 Model 2.2 Model 2.3

Estimate t-Stat Estimate t-Stat Estimate t-Stat

a10 0.0028 0.56 0.0029 0.62 0.0012 0.27a20 0.0008 0.14 0.0009 0.16 �0.0011 �0.21a11 �0.1910 �5.73⁄⁄ �0.1917 �5.74⁄⁄ �0.1728 �4.85⁄⁄

a12 0.0588 2.67⁄⁄ 0.0580 2.67⁄⁄ 0.0357 2.13⁄⁄

a21 �0.0582 �1.88⁄⁄ �0.0577 �1.88⁄⁄ �0.0483 �1.89⁄⁄

a22 �0.0420 �1.09 �0.0430 �1.15 �0.0875 �3.47⁄⁄

bx0 0.0136 8.64⁄⁄ 0.0137 8.77⁄⁄ 0.0115 12.46⁄⁄

by0

0.0257 8.82⁄⁄ 0.0263 8.98⁄⁄ 0.0174 14.01⁄⁄

bx1 0.3161 5.80⁄⁄ 0.3187 5.70⁄⁄ 0.3316 7.90⁄⁄

by1

0.1503 3.05⁄⁄ 0.1473 3.03⁄⁄ 0.2483 4.93⁄⁄

dx11 1.5723 4.93⁄⁄ 1.5422 4.36⁄⁄ 1.7652 5.79⁄⁄

dx21 0.2168 0.51 0.2557 0.43 �0.1938 �0.46

dy11

2.6219 8.12⁄⁄ 2.6168 7.91⁄⁄ 2.7683 7.29⁄⁄

dy21

�2.3447 �4.42⁄⁄ �2.3538 �4.21⁄⁄ �2.6589 �6.98⁄⁄

kx11 �0.0550 �0.91 �0.0529 �0.81 �0.0867 �1.39⁄

kx21 �0.2319 �3.09⁄⁄ �0.2357 �2.33⁄⁄ �0.1938 �2.44⁄⁄

ky11

�0.2650 �3.26⁄⁄ �0.2595 �3.12⁄⁄ �0.3393 �3.77⁄⁄

ky21

0.2780 2.25⁄⁄ 0.2790 2.15⁄⁄ 0.3563 3.62⁄⁄

cx2 9.7569 10.85⁄⁄ 9.4978 10.01⁄⁄ 10.221 12.28⁄⁄

cy2

12.077 10.59⁄⁄ 11.852 10.24⁄⁄ 14.819 12.67⁄⁄

qx,y 0.6953 39.25⁄⁄ – – – –q1;x,y – – 0.7099 26.29⁄⁄ 0.6057 22.36⁄⁄

q2;x,y – – 0.6791 22.55⁄⁄ 0.7565 41.48⁄⁄

lnL 208.76 209.00 214.19

⁄ Denote significance at the 10% level.⁄⁄ Denote significance at the 5% level.


To test for the presence of time-varying transition probabilities, we also use the likelihood ratio test (which follows a v2ð4Þ

under the null).22 Performing the test where Model 1.1 is the restricted model and Model 2.1 the unrestricted one, we obtain avalue of 23.98, thereby rejecting the null of constant transition probabilities. Comparing Models 1.2–2.2 and Models 1.3–2.3yields similar results. Thus, we conclude that a time-varying specification for the transition probabilities is preferred.

Second, we test for the shifts in correlation as we did for Model 1 and we draw similar conclusions. Here, once again, wedo not reject the null when we test for a correlation coefficient shifting with Portugal’s state (the likelihood ratio equals0.49), but we reject the null when testing for a correlation coefficient shifting with Spain’s state (the likelihood ratio equals10.39). Correlation increases when Spain shifts from a non-crisis state to a crisis state from 0.61 to 0.76. However, the

22 The critical values for a v2ð4Þ are 7.779 at 10% and 9.488 at 5%.

Fig. 1. Smoothed Pr sxt ¼ 1; sy

t ¼ 1� �

, escudo and peseta in low volatility states, for Model 2.3.

Fig. 2. Smoothed Prðsxt ¼ 1; sy

t ¼ 2Þ, escudo in low volatility state and peseta in high volatility state, for Model 2.3.


transition matrix generalization of Model 1.4 cannot be pursued for the time-varying models since the dimensionality wouldbe unmanageable (the transition matrix alone would have 24 parameters). Nevertheless, we generalized the model, whilekeeping the independence assumption, by including both interest rate differentials in all transition probabilities in orderto account for any direct effect of one country’s fundamentals on the other country transition probabilities. For these models,the conclusion regarding the test on the correlation coefficients does not change: using these more general versions ofModels 2.1–2.3, we find that the likelihood ratio for Model 2.2 compared to Model 2.1 is 0.08 and the likelihood ratio forModel 2.3 compared to Model 2.1 is 7.04.23 Additionaly, as before, we also estimated a model where the correlation is allowedto change across all four possible combinations of the unobserved states in the two countries. The same conclusions discussedabove apply.

Looking at the results for our models in general, there are several other points to be made. All ARCH parameters are sig-nificant in all the models. Also, the shifting term in the ARCH specification (cc

2 in Eq. (7)) is always greater in Spain for allmodels considered. Crossed effects terms a12 and a21 are also significant in all models.

23 Both tests follow a v2ð1Þ distribution under the null.


t ¼ 1� �

, escudo in high volatility state and peseta in low volatility state, for Model 2.3.


t ¼ 2� �

, escudo and peseta in high volatility states, for Model 2.3.


In Figs. 1–4 we present the smoothed probabilities of each of the four possible states s�t ¼ 1;2;3;4, obtained for Model 2.3.The graphs obtained with the other models are similar. Two very clear conclusions can be drawn from these graphs. First, theprobability that both countries are in the crisis state stays at very high levels for most of the periods until mid-sample anddecays to negligible values thereafter (see Fig. 4). Second, the probability that both countries are in the low volatility regimebecomes prevalent as we approach 1998 (see Fig. 1). The observation of these two graphs indicates that credibility of thecurrency union became well established a few years after the crisis and well before the actual beginning of the use of thesingle currency.

Finally, we interpret the estimated slopes kx11; k

x21; k

y11, and ky

21, capturing the impact of the interest rate differentials on thestate transition probabilities in Eqs. (4) and (5). From the estimated kx

11 (see Table 4) it is clear that in Portugal there is anambiguous effect of the lagged interest rate differential over the probability of staying in state 1, given that it is in state 1.This parameter is significant only in Model 2.3 (at the 10% level) and it is estimated as negative, which can be seen as evi-dence of a relatively important expectational effect of the increase in interest rates. Looking at kx

21, we see that if the interest


rate differential increases and Portugal is in a crisis state, the probability of jumping to a non-crisis state decreases. Thus, theexpectations perverse effect seems to be even stronger here.

As for ky11, it is estimated as negative and significant. This means that if Spain is in a non-crisis state, an increase in the

interest rate differential may induce a crisis further ahead. However, checking ky21, we notice that if Spain is in a crisis state,

an increase in the interest rate differential will actually work in the favorable way, significantly increasing the probability ofjumping to a non-crisis state.

7. Conclusions

In this paper we describe a Markov regime switching model with time-varying transition probabilities that is able to cap-ture important features of currency crises and contagion. This model is used to study the case of the Portuguese escudo andthe Spanish peseta in the EMS during the 1990s. We have addressed several questions. First, was there clear evidence of con-tagion from Spain to Portugal, and/or vice-versa, during the crisis episodes throughout this period? Second, how did the prob-ability of regime switching during the period analyzed react to a raw measure of past credibility, embodied in the pastinterest rate differential versus Germany?

From the estimation results it is possible to conclude the following. There is very strong evidence in favor of shifts in vol-atility during the sample time period. Moreover, correlation between the two currencies is very high, indicating a strongomnipresent link between the two currencies. Furthermore, there is strong evidence of contagion, from Spain to Portugal,in all versions of the model. There is an increase in correlation during the peseta’s crisis periods, whereas the occurrenceof crisis periods in Portugal for most models does not significantly translate into an increase (or decrease) in correlation.Thus, there seems to be some support for the contagion-driven complaint of the Portuguese authorities at the time of theEMS crisis when they claimed that the attack on the escudo was motivated by the weakness of the peseta. But it is importantto stress that there is also some evidence of contagion going both ways. In particular, given that one of the two countries isalready in a crisis state, correlation increases when the other country goes into a crisis state. Still, the rise in correlation issharper if this other country entering a crisis state is Spain. Finally, perverse effects of an increase in the interest rate differ-ential were found for both currencies, but only for Spain did an increase in the interest rate differential in a high volatilitystate translate into an increase in the probability of jumping to the non-crisis state.

Acknowledgements

The authors would like to thank two anonymous referees for their useful comments.

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