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Bivariate cointegration among European monetarysystem exchange ratesStefan C. NorrbinPublished online: 01 Oct 2010.

To cite this article: Stefan C. Norrbin (1996) Bivariate cointegration among European monetary system exchange rates,Applied Economics, 28:12, 1505-1513, DOI: 10.1080/000368496327499

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1 Some authors believed that they had detected cointegration, but this ® nding was due to inappropriate critical values. For example Baillieand Bollerslev (1989) and Sephton and Larsen (1991) both detect cointegration using Johansen’s maximum likelihood estimators. Thecritical values used in these two studies are, however, from Johansen (1988). These critical values are only appropriate under theassumption that a potential drift parameter is known to be absent. The Baillie and Bollerslev (1989) study has recently been updated byDiebold et al. (1993) who show that using the updated critical values and allowing for a potential drift in the data generating process leadsto a rejection of the cointegration hypothesis.2 Therefore a perfectly ® xed exchange rate is cointegrated and would not imply an ine� cient market. If the exchange rate were perfectly® xed during the entire sample then the change in the spot rate would be zero, and speculation would be unnecessary. Furthermore, noexcess pro® ts could be earned from the knowledge that the cross-rate is ® xed.

Applied Economics, 1996, 28, 1505 Ð 1513

Bivariate cointegration among Europeanmonetary system exchange rates

STEFAN C. NORRBIN

Department of Economics, Florida State University, FL , USA

In past research on the long-run behaviour of exchange rates the possibility ofcointegration among spot rates has been rejected. This rejection is surprising as someexchange rates are bound by o� cial agreements to comove over time. The EuropeanMonetary System (EMS) is an example of such an o� cially coordinating system. Inthis paper we extend past research by focusing on only EMS rates and use potentiallymore powerful cointegration tests to show that EMS rates are cointegrated.

I . INTRODUCTION

Countries that belong to the European Monetary System(EMS) have agreed to coordinate their currencies so thatany one currency would not deviate too far from anothercurrency belonging to the EMS. This agreement imposesa challenge for the monetary and ® scal authorities in thatthey will have to alter their policies to ensure that theircurrency does not move too high or low relative to othercurrencies. This agreement places bounds on the move-ments between currencies resulting in an interdependence ofcurrencies. This interdependence forces currencies to looselyhang together over time, which is the de® nition used byGranger (1986) for a cointegration process.

In past research no bivariate cointegration has been de-tected between spot exchange rates. For example Hakkioand Rush (1989), MacDonald and Taylor (1989) and Cope-land (1991) found no cointegration in their tests of bivariatemodels.1 These papers also argued that ® nding cointegra-tion between exchange rates would imply ine� cient foreignexchange markets, because cointegration implies a forecas-tability of future exchange rates. Therefore, they argued,their ® ndings of a lack of cointegration supported exchange

rate market e� ciency. Dwyer and Wallace (1992) demon-strated, however, that cointegration does not necessarilyimply ine� cient markets. Instead, the cointegration testimplicitly becomes a test of the stationarity of the cross-ratebetween the currencies.2 Therefore ® nding no cointegrationimplies that the cross-rate has a unit root, thus being a freely¯ oating exchange rate. Such cross-rate behaviour would notbe expected in the EMS, and therefore the previous ® ndingsof no cointegration among currencies deserves some closeexamination.

This paper tests the adherence of the member currenciesto the EMS restrictions by examining bivariate EMS ex-change rates using two di� erent types of cointegration tests.The ® rst cointegration test procedure is the maximum likeli-hood procedure by Johansen (1988). This procedure uses thenull hypothesis of no cointegration. An alternative cointeg-ration procedure due to Park (1992) is the canonical coin-tegrating regressions (CCR). This procedure uses the nullhypothesis of cointegration and has been shown, forexample by Park and Ogaki (1991), to be more powerful insmall samples. The CCR procedure also allows for a directtest of deterministic cointegration. The EMS does not allowfor movements away from the central rates from either

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3 See Hakkio and Rush (1991) for a discussion on the importance of frequency in cointegration tests.4 Note, however, the error correction models will have di� erent short run response depending on the frequency of data used. Therefore, anextension of this research to focus on the potential excess pro® ts of speculating on error correction mechanisms may be a� ected by thechoice of the frequency of the data.

stochastic or deterministic sources. Therefore an appropri-ate test should include a long-run comovement of both thestochastic and deterministic components. Such a joint test isproposed in Park (1992) and is called a deterministic coin-tegration test, and will be tested in this paper.

The paper begins with a discussion of the past researchand the implications of detecting cointegration among spotexchange rates. Section III examines the data and theeconometric methodology. The fourth section discusses thedi� erences between stochastic and deterministic cointegra-tion and the empirical results for cointegration among EMSrates. Finally some conclusions are provided.

II . BACKGROUND AND PREVIOUSFINDINGS

If currencies are cointegrated this means that they do notdeviate too far apart. For any two currencies this may beunrealistic, but for the EMS currencies we anticipate this tobe the behaviour. In March of 1979 eight countries, namely:Germany, France, Italy, the Netherlands, Belgium, Den-mark, Ireland and Luxembourg, decided to organize them-selves in a monetary union where, by o� cial agreement nosingle currency could deviate by more than a 2.25% marginfrom the c̀entral’ rate of any other currency in the system(even though Italy began with a wider margin of 12%).Therefore we would anticipate intervention by any countrythat approaches such a limit.

Cointegration between EMS currencies does not meanthat spot markets are ine� cient. If we examine the dollarvalue of the Belgian Franc and the French Franc, we knowthat triangular arbitrage should set the cross-rate equal toa linear combination of the two rates (abstracting fromtransactions costs). For example for the Belgian Franc andthe French Franc the triangular arbitrage would be:

S$/BFranc - S$/FFranc = SFFranc /BFranc (1)

where S represents the logarithm of the spot value of thecurrency in the denominator in terms of the currency in thenumerator. Thus a linear combination of the two dollarrates would be stationary if the cross-rate is stationary asshown by Dwyer and Wallace (1992). A test of a linearcointegrating vector (1, - 1) therefore implicitly tests thestationarity of the cross-rate. Granger’s (1986) original sug-gestion that two prices of assets in an e� cient marketcannot be cointegrated is then quali® ed as in this case thetwo assets are pricing the same good due to the perfectsubstitutability ensured by o� cial authorities. The vectorerror correction process for the cointegrating relationship in

Equation 1 can then be derived for the Belgian Franc andthe French Franc as:

D S$/BFranc , t = a 0 1 + a 1 1 (S$/BFranc - S$/FFranc )t ± 1 + e 1 t(2)

D S$/FFranc , t = a 0 2 + a 1 2 (S$/BFranc - S$/FFranc )t ± 1 + e 2 t

if we assume a VAR(1) model, with a 1 1 and a 1 2 being theerror correction coe� cients to the cointegrating vectors.Finding signi® cant error correction coe� cients then impliesthat Equation 1 holds in the long run or in other words theFrench Franc/Belgian Franc cross-rate is stable.

II I . DATA AND ECONOMETRICMETHODOLOGY

In this section we ® rst examine the data and then proceed bydiscussing the econometric methodology necessary to dealwith nonstationary processes.

Data and unit roots tests

This section examines six EMS currencies, namely theDeutsche Mark, French Franc, Dutch Guilder, BelgianFranc, Danish Krone and Irish Punt. Luxembourg wasexcluded as it is comoving with Belgium, and Italy wasexcluded as it started with a much wider margin from thec̀entral’ rate. The data are the logarithms of end-of-monthspot rates from the OECD database for 1979:3 Ð 1992:9. Thechoice of data frequency deserves some comment. Mac-Donald and Taylor (1989) use monthly data whereas Cope-land (1991) uses daily data. However, for the test of cointeg-ration the frequency of the data is less important than thelength of the time period.3 The earlier study uses the1973 Ð 1985 period, while the latter study uses the 1976 Ð 1990period. The number of years for this study is comparable tothese earlier studies except the coverage starts at a later dateto coincide with the creation of the EMS.4 Table 1 examinesthe possibility of a unit root in these variables. All variablesshow a clear possibility of having a unit root process, as thelevel process is nonstationary while the ® rst-di� erence isstationary.

If the EMS rates are independent unit roots then thenonstationarity is caused by independent permanentstochastic shocks to each of the exchange rates. Examiningthe time series of these rates in Fig. 1a and 1b shows that theseries appear closely related over this time period, which isnot surprising considering the o� cial agreement to coordi-nate these spot rates among the EMS countries. The FrenchFranc appears to be di� erent from the other currencies in

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Table 1. Augmented DickeyÐ Fuller tests on spot exchange rates

Level First-di� erence

Variables without trend with trend without trend with trend

Irish Punt (Punt) - 1.809 - 1.659 - 3.990* - 4.540*Belgium Franc (BFranc) - 1.368 - 1.718 - 3.697* - 4.233*Danish Krone (Krone) - 1.560 - 2.035 - 3.767* - 4.373*Netherland Guilder (Guilder) - 0.834 - 1.939 - 3.891* - 4.244*French Franc (FFranc) - 1.778 - 1.619 - 3.729* - 4.292*Deutsche Mark (DM) - 0.726 - 1.988 - 3.904* - 4.262*

All tests are sixth-order augmented Dickey Ð Fuller tests. The critical value without a deterministic trend inthe regression in - 2.876 and with a trend the critical value is - 3.483.* Indicates a rejection of the null of nonstationarity at 5% signi® cance.

5 See, for example, Stock and Watson (1993) for a comparison of several testing procedures including the OLS method.

Note: The exchange rates are indices with 1.00= 1979:3

Fig. 1. Comparison of exchange rates

Fig. 1b. This is an artefact of the grouping. The FrenchFranc is in fact very close to the currencies in Fig. 1a. Someof the spot rates may, however, drift apart over time which

is inconsistent with the EMS agreement. Therefore the ex-change rates may be cointegrated, although the stochasticprocess generating the cointegrated series may also containa deterministic drift. This would mean that the rates tend tomove apart deterministically, but any stochastic shocks a� ectall rates, resulting in an equilibrium relationship with drift.

To test the potential cointegration of the nonstationaryprocesses we need an appropriate econometric methodo-logy as OLS has been found to be biased in handling unitroot variables.5

Empirical methodology

Two approaches to testing for cointegration are used, the® rst is Johansen’s maximum likelihood approach and Parkand Ogaki’s nonparametric canonical cointegrating regres-sion (CCR) method. The Johansen approach has been ex-tensively documented so we will only briefly describe thesetup and testing procedure. The interested reader is re-ferred to the detailed discussion in Johansen (1988) andJohansen and Juselius (1990).

Johansen (1988) uses the vector error correction model(VECM) as a starting point for estimation. From a vectorautoregression (VAR) of order k the p 3 1 vector of I(1)variables Xt can be de® ned as:

Xt = m +k

+j = 1

Aj Xt ± j + et (3)

where et is an i.i.d. error term. The VECM can be found bysolving the change in Xt:

D Xt = m +k ± 1

+j = 1

G j D Xt ± j + P Xt ± 1 + et (4)

where

G j = - (I - A1 - ¼ - Aj ) j = 1, ¼ , k - 1

P = - (I - A1 - ¼ - Ak ).

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6 An additional advantage of the CCR approach in comparison to the MLE approach is the possibility of ARCH processes in the exchangerate data. Whereas the MLE approach requires a Gaussian error structure, the CCR approach is applicable to a wider set of errorprocesses. See Park and Ogaki (1991) and Park (1992) for a detailed discussion.

The long-run information is found in the P matrix andthe rank of this matrix determines the number of cointegrat-ing relationships. If the rank of P equals p (the size of theXt matrix) then Xt themselves are stationary. If the rank isless than p but greater than zero then some independent unitroots exist. If p equals zero, then all unit roots are indepen-dent. If the rank r is 0 < r < p then P can be decomposedusing a reduced rank regression into P = a b 9 . Because therank of P is usually unknown, Johansen proceeds to devel-op test procedures to test the rank of P . The tests are basedon the eigenvalue solution to the reduced rank regression.The test statistics are:

Trace statistic = - TN

+i = q+ 1

ln (1 - l à i ) (5)

where l à i is the estimated eigenvalue and q is the null hypo-thesis that at most q cointegrating vectors exist. The alterna-tive hypothesis is that at least one more cointegrating vectorthan the null exists (i.e. r > q).

Park’s (1992) nonparametric method for estimating re-gressions where cointegration is present may have severaladvantages as compared to Johansen’s maximum likelihoodapproach. The CCR method does not require any assump-tion about the lag speci® cation as the estimation is donedirectly on the cointegrating regression. In addition, the testprocedure for the CCR regression takes as a null hypothesisthat a cointegrating vector exists, which improves the powerof detecting a cointegrating relationship. Finally, Park andOgaki (1991) show that in Monte Carlo simulations theCCR procedure consistently outperforms the Johansen ap-proach in small samples. Asymptotically the CCR andJohansen’s approach will give the same result, if the numberof lags in the VAR is the t̀rue’ number for the Johansenapproach. 6

The original CCR approach is presented in Park (1992)and the extended estimation including VAR prewhitening isdescribed in Park and Ogaki (1991). Because of the detaileddescription in these sources we will only briefly discuss themain ideas. Consider our p vector time series used in theJohansen approach. Pick one of these as a time series Y t andleave the other p - 1 components as Xt. All variables areassumed to be integrated processes of order one. Assumethat no cointegration exists among the Xt variables, but letY t and Xt be cointegrated as

Y t = b 9 Xt + ut (6)

where b 9 is the uniquely determined cointegrating vector.The above equation indicates that a long-run equilibrium

relationship exists between Y t and some linear combinationof the Xt variables.

The above equation can be used directly for estimatingthe cointegrating vector using a stationary transformationbased on the process:

W t = (ut , D Xt) (7)

which is assumed to be a general stationary process,without any precise speci® cation of the dynamic structureof W t. The only assumption needed is that it satis® esthe invariance principle (see Phillips, 1991, for the neces-sary conditions for the invariance principle to hold). Usingthe stationary process in Equation (7) we can now trans-form the variables Y t and Xt and Equation (6) can berewritten as

Y *t = b 9 X*t + u*t (8)

This regression is called the CCR and can be estimatedusing OLS on the transformed variables. Park and Ogaki(1991) show that the CCR regression itself is comparable insmall sample Monte Carlo simulation to Johansen’s ap-proach. Including a prewhitening procedure will, however,improve the estimates substantially.

The goal of the estimation procedure is to estimate theasymptotic variance of W t . This can be achieved by ® ttinga VAR model of order k such as:

W t =k

+i = 1

Q i W t ± i + et (9)

where Q i are coe� cients in the VAR system. As ex-plained by Andrews and Monahan (1992), a consistent esti-mate of W t can be obtained by r̀ecolouring’ the spectrumof et.

Once the CCR equation is estimated the regression can betested by adding spurious deterministic polynomials of dif-ferent degrees. If these polynomials can be detected then thenull hypothesis of cointegration is rejected as the residual ofthe CCR equation must have some remaining nonstationar-ity. The test procedure is shown by Park et al. (1988) to usea simple x 2 statistic to test the combined e� ect of di� erentorder polynomials.

IV . COINTEGRATION AND EMPIRICALRESULTS

The ® rst part of this section develops a common trendsmodel for the EMS spot exchange rate case and shows how

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stochastic and deterministic cointegration di� er. The meth-odology discussion is then followed by a discussion of theresults for both stochastic and deterministic cointegrationtests.

Stochastic and deterministic cointegration in the EMS

If we model the spot exchange rates as being functions ofpotential deterministic trend and an underlying commontrend unit root process then:

Si , t = m i , t + Ai t 1 , t + e i , t (10)

and

t 1 , t = t 1 , t ± 1 + ut

where Si , t is one of the EMS spot rates, m i , t is the potentialdeterministic trend, t 1 , t is the underlying unit root processthat may be shared as a common unit root with other spotrates, and e i , t and ut are martingale errors. Note that the unitroot process is unobserved. It may be thought of as anyprocess a� ecting all EMS rates causing them to be I(1)series. Stochastic cointegration then argues that a linearcombination between Si , t and a di� erent Sj , t spot rate existssuch that:

Si , t - b i j Sj , t = m i j , t + e i j , t (11)

where (Ai - b i j Aj ) t 1, t = 0, m i j , t = (m i , t - b i j m j , t) , e is a mar-tingale di� erence sequence, and b is the cointegratingvector. This cointegrating condition is important as it showsthat I(1) properties of the exchange rates in the EMS areshared, but it is not su� cient to ensure stability within theEMS system.

The m i j , t deterministic drifts will propel the exchange ratesapart until a realignment must take place. For the EMSsystem to be stable a stronger condition of deterministiccointegration must exist. In this case the b cointegratingvector must eliminate both the stochastic nonstationarityand the deterministic nonstationarity and:

Si , t - b ij Sj , t = e i j , t (12)

with (Ai - b ij Aj ) t 1 , t = 0, and ( m i , t - b ij m j , t) = 0. This con-dition will be tested using the canonical cointegratingregression (CCR) procedure that allows for general deter-ministic trend processes without modi® cation, and thestochastic cointegration condition will be tested usingboth the conventionally used MLE procedure and the CCRprocedure.

Stochastic cointegration results

Using Johansen’s maximum likelihood approach we test thebivariate relationship between the currencies, as in Equa-tion 11, in Table 2. With six currencies we have 15 uniquecombinations. The Table reports the coe� cient of the bi-variate relationship together with the Trace statistic, testing Tab

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Table 3. Stochastic cointegration tests using CCR

Coe� cientsa Spurious regressor testsb

Test of unitc

Variable Trend Elasticity H (1,4) H (1,5) elasticity

DMPunt 0.0026* 0.833* 1.498 1.790 1.494

(0.0005) (0.137) (0.682) (0.774) (0.222)BFranc 0.0012* 0.724* 16.116* 16.737* 20.637*

(0.0003) (0.061) (0.001) (0.002) (0.001)Krone 0.0017* 0.840* 3.377 3.382 11.865

(0.0002) (0.046) (0.337) (0.496) (0.001)Guilder 0.0002* 0.974* 6.222 6.344 18.186

(0.0001) (0.006) (0.101) (0.175) (0.001)FFranc 0.0022* 0.743* 3.919 4.638 8.793

(0.0004) (0.087) (0.270) (0.326) (0.003)

FFRANCPunt 0.0001 1.151* 1.493 2.809 37.191

(0.0001) (0.025) (0.684) (0.590) (0.001)BFranc - 0.0010* 0.982* 5.133 5.134 0.870

(0.0001) (0.019) (0.162) (0.273) (0.351)Krone - 0.0009* 1.059* 3.939 7.339 3.287

(0.0001) (0.033) (0.268) (0.119) (0.069)Guilder - 0.0030* 1.279* 1.444 1.483 4.860*

(0.0005) (0.126) (0.695) (0.830) (0.027)

GUIL DERPunt 0.0027* 0.867* 3.319 3.905 1.253

(0.0005) (0.119) (0.419) (0.418) (0.263)BFranc 0.0012* 0.763* 8.726* 9.486 13.548*

(0.0003) (0.064) (0.033) (0.050) (0.001)Krone 0.0017* 0.848* 2.299 3.808 8.579*

(0.0002) (0.052) (0.513) (0.433) (0.003)

KRONEPunt 0.0009* 1.078* 3.063 3.437 2.515

(0.0002) (0.049) (0.382) (0.487) (0.113)BFranc 0.0001 0.917* 2.544 7.833 25.030*

(0.0001) (0.017) (0.467) (0.098) (0.001)

BFRANCPunt 0.0011* 1.186* 2.164 2.194 10.320*

(0.0002) (0.057) (0.539) (0.700) (0.001)

a Coe� cients from bivariate cointegration with standard errors in parentheses.b Joint test of the signi® cance of spurious polynomial trends. The values are X2 -statistics with p-values inparentheses.c X2 -statistics with one restriction with p-values in parentheses.

7 In all cases the inference from the maximum eigenvalue statistic was the same.

the null of no cointegration.7 Five signi® cant cointegratingrelationships exist, namely: DM Ð Krone, DM Ð Guilder,FFranc Ð Punt, Guilder Ð Krone and Krone Ð BFranc. Fur-thermore, the tests of unit elasticity of the cointegratingvector cannot be rejected in three of the ® ve signi® cantrelationships. This indicates that these three currencies haveonly stationary deviations from a long-run equilibrium.This ® nding supports a ® xed exchange rate system between

these three currencies. The French Franc and the Irish Puntappear to form a separate stable system, but in this systemthe unit elasticity can be rejected, indicating that the FrenchFranc overadjusts relative to the Irish Punt. The ® nal coin-tegrating relationship is puzzling. If the Krone and DM arecointegrated and the Krone and Belgian Franc are cointeg-rated then the Belgian Franc and the DM should also becointegrated. To investigate this puzzle and to see if the

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Table 4. Deterministic cointegration tests using CCR

Spurious regressor testsb

Test of unitVariables Coe� cientsa H (1,4) H (1,5) elasticityc

DMPunt 0.835* 12.336* 12.569* 23.364*

(0.034) (0.015) (0.028) (0.001)BFranc 0.786* 12.914* 13.273* 44.982*

(0.032) (0.012) (0.021) (0.001)Krone 0.787* 19.269* 19.548* 24.397*

(0.043) (0.001) (0.002) (0.001)Guilder 0.996* 19.374* 19.601* 0.082

(0.014) (0.001) (0.001) (0.774)FFranc 0.725* 14.805* 15.249* 88.060*

(0.029) (0.005) (0.009) (0.001)FFRANC

Punt 1.152* 1.534 2.870 37.569*(0.025) (0.821) (0.720) (0.001)

BFranc 0.981* 5.088 5.397 0.113(0.056) (0.278) (0.369) (0.736)

Krone 1.030* 2.739 3.674 0.566(0.040) (0.602) (0.597) (0.452)

Guilder 1.116* 17.712* 22.036* 1.710(0.089) (0.001) (0.001) (0.191)

GUIL DERPunt 0.872* 12.446* 12.610* 18.047*

(0.030) (0.014) (0.027) (0.001)BFranc 0.811* 10.182* 10.200 31.811*

(0.034) (0.037) (0.069) (0.001)Krone 0.827* 12.687* 12.696* 14.234*

(0.046) (0.013) (0.026) (0.001)KRONE

Punt 1.087* 2.738 3.338 2.552(0.055) (0.603) (0.648) (0.110)

BFranc 0.916* 3.613 9.466 26.711*(0.016) (0.461) (0.092) (0.001)

BFRANCPunt 1.204* 4.092 4.372 5.481*

(0.087) (0.394) (0.497) (0.019)

a Coe� cients from bivariate cointegration with standard errors in parentheses.b Joint test of the signi® cance of spurious polynomial trends. The values are x 2 -statistics withp-values in parentheses.c x 2 -statistics with one restriction with p-values in parentheses.

Fig. 2. Comparison of three cointegrating vectors for France

remaining exchange rates are cointegrated we examine thebivariate relationships using the potentially more powerfulCCR procedure.

Our null hypothesis is that all currencies in the EMSsystem respond to the same common trend. Some country-speci® c policies may, however, create di� erent deterministictrends. We allow for this possibility by testing for cointegra-tion with di� erent deterministic trends. Examining thestochastic cointegration case in Table 3, where di� erentdeterministic trends are allowed, we ® nd evidence for a largenumber of cointegrating relationships. In fact we can onlyreject cointegration in two cases: the DM Ð BFranc with ap-value of 0.001, and marginally the Guilder Ð BFranc witha p-value of 0.033. Thus we ® nd evidence for cointegrationbetween all currencies, except potentially the Belgian Franc.Cointegration between the Belgian Franc and the Krone

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8 The underlying common trend is here inobservable. Examples of such permanent shocks would be US de® cits or oil priceshocks.

and FFranc is marginally accepted, implying that theBelgian Franc may also be part of the stable system.The results show that in the six-currency system one or atmost two common trends exist. Hence all currencies, or allexcept the Belgian Franc, respond to the same permanentshock.

The unit elasticity of the response is, however, rejected ina large number of cases. The DM, Punt and Guilder appearto have the same responses to the common trend, whereasthe French Franc, Krone and Belgian Franc have similarresponses. Furthermore a possible determinstically di� erentpattern is detected in all but two cases. The evidence fromTable 3 thus indicates that the EMS currencies respond tothe same underlying common trend, but may drift awayfrom each other over time.8

Deterministic cointegration results

The EMS currencies should not deviate from each other dueto stochastic or deterministic sources. The EMS agreementtherefore calls for a stronger form of cointegration, namelythe deterministic cointegration discussed in Equation 12.The results of the test for this possibility are presented inTable 4. The results indicate that a subset of currencies showevidence of deterministic cointegration. The French Franc,Punt, Krone and Belgian Franc all have x 2 -statistics thatfail to reject the null hypothesis of cointegration. Thisimplies that these currencies form a stable subsystemin the EMS. In contrast for the DM we can reject deter-ministic cointegration with all other currencies. Similarlyfor the Guilder we can reject cointegration with all othercurrencies.

Focusing on the four currencies that exhibit evidenceof deterministic cointegration we also want to see ifthe unit elasticity assumption can be supported. TheFrench Franc appears to have a unit elasticity withthe Belgian Franc and Danish Krone, but not with theIrish Punt. The Danish Krone has a unit elasticity withthe Punt, but not with the Belgian Franc, whereas theunit elasticity between the Belgian Franc and the Puntcan be rejected. These results lead to the conclusion thatthe Punt and the Krone appear to adjust similarly to theunderlying common trend, with the French Franc and Be-lgian Franc adjusting similarly, but di� erently from theKrone and Punt. Therefore the four-currency subsystem isstable, but will in the long run itself be divided into twoparts. These two parts will be stable without any necessaryrealignments. The DM and Guilder, however, will deter-ministically drift away from the others causing a need forrealignments.

V. CONCLUSIONS

In this paper we examine the potential cointegration be-tween EMS currencies. In contrast to past studies we ® ndthat most of the currencies within the EMS system are atleast stochastically cointegrated. The reason for the di� er-ence in results from past research is the use of a time periodduring which the currencies in the EMS system were closelylinked and the use of a potentially more powerful cointegra-tion technique. We also test for deterministic cointegrationamong EMS spot rates, and ® nd that a subset of the rates,namely: the French Franc, the Irish Punt, the Danish Krone,and the Belgian Franc, are deterministically cointegrated.This implies that these exchange rates share a common unitroot as well as a common drift.

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