Currency spillovers and tri-polarity: a simultaneous model of the US dollar, German mark and Japanese yen 5

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1 Journal of Inernaional Money and Finance 23 (2004) Currency spillovers and ri-polariy: a simulaneous model of he US dollar, German mark and Japanese yen 5 Ronald MacDonald a,, Ian W. Marsh b a Deparmen of Economics, Universiy of Srahclyde and CESifo, 100 Cahedral Sree, Glasgow G4 0LN, UK b Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, UK Absrac This paper presens a simulaneous model of exchange raes beween he US dollar, German mark and Japanese yen. In addiion o incorporaing long-run equilibria and shor-run dynamics, he model is designed o capure complex ineracion beween currencies no normally considered in exchange rae models. The model is demonsraed o be an economically and saisically superior forecasing ool over relaively shor horizons, hereby demonsraing ha he random walk paradigm no longer rules he roos. # 2003 Elsevier Ld. All righs reserved. JEL classificaion: F31; G15 Keywords: Tri-polariy; Exchange rae forecasing; Purchasing power pariy 1. Inroducion The adven of he European moneary inegraion means ha he inernaional moneary sysem is now characerized by a ri-polar currency srucure, consising of he US dollar, Japanese yen and euro. Recenly, here has been considerable ineres in policy circles regarding he operaion and design of his sysem. Should i coninue o be effecively a freely floaing sysem, a managed floa (based perhaps 5 The auhors are graeful o wo anonymous referees and he co-edior, Michael Melvin, for helpful commens on an earlier draf of his paper. Corresponding auhor. Tel.: ; fax: address: r.r.macdonald@srah.ac.uk (R. MacDonald) /$ - see fron maer # 2003 Elsevier Ld. All righs reserved. doi: /j.jimonfin

2 100 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) on a arge zone arrangemen) or one of complee fixiy? In his paper, we seek o shed some ligh on he operaion of he new sysem by considering a ri-polar exchange rae model consising of he US dollar, Japanese yen and German mark, which may be regarded as he aneceden o he new sysem. Because of he differen operaional objecives of he European Cenral Bank relaive o he Bundesbank, he euro may, of course, have differen properies o he mark. Neverheless, we believe ha he sudy of he dollar mark yen sysem is useful, boh in erms of indicaing how a ri-polar nework may be modelled, and also in suggesing how such a sysem may behave in erms of is long- and shor-run properies. Our ri-polar exchange rae sysem represens an exension of he join modelling of exchange raes, ineres raes and prices by Johansen and Juselius (1992), Juselius (1995), Juselius and MacDonald (2000), and MacDonald and Marsh (1997, 1999). We exend his lieraure in wo main ways. Firs, we seek o inerpre all he significan coinegraing vecors in an economic and saisical sense (MacDonald and Marsh, 1997, for example, only focus on he firs significan vecor). Second, and as we have noed, we use a ri-polar srucure, raher han a single currency analysis, which has been he norm in his lieraure, in order o capure currency spillovers. Alhough lile research has been underaken on modelling exchange rae spillovers (oher han by accouning for conemporaneous correlaion beween exchange markes), i seems a naural componen of an exchange rae model since i is widely acceped ha currency markes are no independen. One of he main conribuions of his paper is he emphasis laid on he complex dynamic ineracions among he variables in an exchange rae sysem. One of he deficiencies of many fundamenal-based models is ha hey ofen neglec he dynamics inheren in he exchange rae process. Even if exchange rae models do incorporae dynamics, hey are ofen very limied in scope. The economeric mehods proposed here ensure a very rich dynamic specificaion for he exchange rae relaionship and also for he equaions of he oher fundamenal variables driving he exchange rae. Our exchange rae model is assessed using sandard saisical crieria and also by wha has become he benchmark by which an exchange rae model is judged, namely is abiliy o ouperform a random walk model in an ouof-sample forecasing exercise. The ouline of he remainder of his paper is as follows. In he nex secion, we presen a moivaional discussion for he modelling approach adoped. In Secion 3, he economeric mehods are briefly oulined and our esimaed long-run coinegraion relaionships discussed. The ou-of-sample forecasing resuls are presened in Secion 4. The paper ends wih a concluding secion. 2. Moivaion and relaed research Long-run purchasing power pariy (PPP) forms he basis of our modelling exercise. Since, in one form or anoher, i is an assumed condiion for many exchange rae models, PPP has received vas aenion in he academic lieraure. While here is now general agreemen ha PPP does no hold in he shor-run, excep for case

3 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) of (near) hyperinflaion, as a long-run proposiion, he evidence is much more favourable (see, for example, Froo and Rogoff, 1995; MacDonald, 1995). However, he fac ha he majoriy of empirical papers on PPP rejec he resricions of proporionaliy and symmery is raher worrying for a PPP-based sudy. While measuremen errors may parly accoun for he difference beween esimaed and heoreical values, he divergence is sufficienly large for us o conclude ha somehing more han measuremen errors is a hand. In line wih Cassel s synhesis of PPP and asse demand approaches o he exchange rae, we shall augmen he radiional PPP relaionship (see Holmes, 1967, for furher discussion). The paricular approach used here o augmen PPP is discussed in some deail by Johansen and Juselius (1992), Juselius (1995), MacDonald and Marsh (1997), and Juselius and MacDonald (2000) and essenially enails supplemening he PPP relaionship wih an ineres differenial. Johansen and Juselius (1992) and Juselius (1995) moivae such a model in erms of combining PPP wih a UIP condiion, while MacDonald and Marsh (1997) have labelled his approach o exchange rae modelling as Casselian PPP. The laer follows from Cassel s emphasis on he role of capial flows in prevening an exchange rae from always being a is PPP deermined level. In he work of Johansen and Juselius (1992), Juselius (1995), MacDonald and Marsh (1997) and Juselius and MacDonald (2000), he Casselian approach is shown o produce saionary combinaions of exchange raes, relaive prices and ineres differenials. However, in all hese papers, currency markes are analysed separaely. The main novely in he presen paper is o noe ha currency markes are closely linked and so any saisical analysis should explicily recognize his in our economeric modelling. For he US dollar bilaeral exchange raes of he Japanese yen and German mark, our ri-polar approach amouns o analysing he following daa vecor: x ¼ s GER ; s JAP ; p GER ; p JAP ; p US ; i GER ; i JAP ; i US 0 ; ð1þ where s denoes he (log) bilaeral spo exchange rae agains he US dollar, p denoes he (log) price level and i he shor-erm ineres rae and he superscrips have an obvious inerpreaion. We hen propose esing hypoheses on his vecor which allow us o pariion he long-run coinegraing space ino wo long-run saionary relaionships of he form: b GER x ¼ x GER 1 i GER b GER x ¼ x JAP 1 i JAP i US i US x GER x JAP 2 p GER 2 p JAP p US p US þ s GER ; þ s JAP : Alhough here are no spillovers from one currency marke o he oher in hese long-run relaionships, here may neverheless be informaion conained in he join process from he wo markes which is imporan in defining he long-run and would be ignored by simply condiioning on he informaion se from one marke. However, direc spillovers do appear in he shor-run dynamic equaions. For example, he dynamic equaion for he Japanese yen exchange rae would have he

4 102 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) following form: Ds GER=JAP ¼ c 0 þ Xl þ Xl þ Xl c 1i Ds GER i c 4i Dp JAP i þ Xl þ Xl c 2i Ds JAP i c 5i Dp US i þ Xl þ Xl c 3i Dp GER i c 6i Di GER i c 8i Di US i þ a 1b GER x 1 þ a 2 b JAP x 1 þ Xl c 7i Di JAP i where l represens he lag lengh of he differenced VAR. Hence, spillovers arise boh hrough dynamic ineracions and also hrough he significance of he coinegraing relaionships (he alphas). As we shall see in our empirical secion, boh hese effecs urn ou o be imporan in our analysis. ð2þ 3. Economeric mehods and resuls 3.1. Economeric modelling In his secion, we briefly ouline he economeric mehods used o esimae our exchange rae models. In shor, we use a vecor auoregressive (VAR) model o deermine he number of coinegraing relaionships and o define he coinegraing vecors. This par of our analysis is based on he mehods of Johansen (1995). The familiar VAR represenaion is: x ¼ Xlþ1 A i x i þ wd þ v ; which may be reparameerized ino he VECM represenaion as: ð3þ Dx ¼ Xl C i Dx i þ Px 1 þ wd þ v ; where x is a vecor of variables enering he sysem, D conains deerminisic componens (consan, rend, cenred seasonal dummies and even dummies) and v is assumed o have mean 0, be homoscedasic and serially uncorrelaed. The order of he VAR is assumed finie o exclude moving average componens, and he parameers A i, U i, w, and R (he covariance marix of v) are assumed consan. P is inerpreed as he marix of long-run responses. If he daa coinegrae, P mus be of reduced rank, r < n, where n is he number of variables in x and i may be facored as (see Johansen, 1995): P ¼ ab 0 ; where b and a are n r marices, which give he coinegraing vecors (empirical long-run relaionships) and associaed adjusmen marix, respecively. Due o he ð4þ

5 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) reduced form naure of he coinegraing vecors, here is an increasing rend owards performing ransformaions and imposing resricions on he esimaed coinegraing space o reveal meaningful economic relaionships. The imposiion of resricions on he coinegraing vecor or adjusmen marix will change he esimaed shor-run dynamics of Eq. (4) and he coefficiens of he deerminisic variables. These new coefficiens are denoed by a ilde. If we also denoe he resriced coinegraion space by P ¼ a b 0, he consrained VAR (CVAR) can be wrien as: Dx ¼ Xl ~C i Dx i þ Px 1 þ wd þ w ; ð5þ This is he full vecor form of he dynamic equaion (4) above Long-run equilibria in he ri-polar sysem Our eigh variable sysem comprises wo bilaeral exchange raes (dollar mark and dollar yen), hree price indices and hree shor-erm ineres raes. The expeced exchange rae changes are no included in he vecor of variables as hese will be I(0) under he weakes assumpions of raionaliy. The daa run from January 1983 hrough Sepember 1998 and are exraced from he IMF s Inernaional Financial Saisics CD-ROM. The sar dae for esimaion is se o exclude urbulence in he ineres rae markes in he early 1980s caused by changes in he Federal Reserves operaing procedures, and which necessiaed he use of many inervenion dummies in our previous work (MacDonald and Marsh, 1997). The final daa poin in our sample was chosen o be Sepember 1998, raher han December 1998, in order o exclude some marke urbulence in he run up o European Moneary Union in January Jus wo dummies are needed in his sysem (1985:11 and 1986:01), primarily o remove wo ouliers in he Japanese ineres rae series. Four lagged levels in he VAR, chosen afer performing a baery of ess, cenred seasonal dummies and an unconsrained consan are included in he sysem. Some of he ess indicaed a shorer lag lengh, bu we chose o include he maximum amoun of relevan informaion albei a he possible cos of esimaion accuracy. The ineres raes used in his sudy are shor-erm (3 monhs) eurocurrency ineres raes raher han he long-erm bond yields used in our previous work (MacDonald and Marsh, 1997). There are wo jusificaions for his. Firs, shorerm raes have been used successfully by oher auhors who exploi similar sysems (Fisher e al., 1990; Johansen and Juselius, 1992; Lee e al., 1994). Second, facors such as axaion, duraion and liquidiy effecs can cause bond yields o differ from he pure ineres rae which we would like o observe. These facors are no only less prevalen in he shor-erm euromarkes, bu are also more similar beween currencies leading o, we hope, a beer proxy for capial flows. Consumer prices are our preferred price measure for Germany and he US, while for Japan, we use he wholesale price index. This change is moivaed primarily by he marked differences in behaviour of he Japanese consumer and wholesale price

6 104 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) Table 1 Johansen coinegraion analysis ri-polar sysem Null hypohesis Trace Trace criical (95%) r ¼ r r r r r r r Noe: Trace criical values from Oserwald-Lenum (1992). indices. In many counries, hese proxies for he price level follow similar rends. For Japan over he period sudied hey do no, and our use of he wholesale index produces resuls which are more in conformiy wih he basic model. In paricular, we are able o impose he correc coefficien resricions on he Japanese sysems when he Japanese WPI is used, bu no wih he CPI. We have no good explanaion for his finding, bu noe ha here is a conroversy in he PPP lieraure as o he appropriae price series o use in a PPP calculaion (see, for example, Frenkel, 1981), and our ess seem o indicae ha for Japan, he appropriae series is he wholesale price index. I could be ha disribuion coss are much imporan for Japan han for he oher counries in our sample and ha his drives an imporan wedge beween he CPI and WPI, rendering he CPI an inappropriae price measure for Japan (see MacDonald and Ricci, 2001 for a furher discussion of he imporance of disribuion coss in PPP calculaions). Diagnosic ess (no repored here o save space bu available from he auhors on reques) indicae ha he residuals are random, bu ha here are normaliy problems in our sysem. Reassuringly, his is due o kurosis, raher han o skewness, and herefore should no affec our resuls (see Paruolo, 1995). Incorporaing furher dummy variables ino he VAR models proved unsuccessful in removing his kurosis. The Johansen coinegraion Trace es resuls are deailed in Table 1. These indicae wo significan relaionships, a finding suppored by he presence of wo noiceably larger eigenvalues and an analysis of he roos of he companion marix (no repored). 1 Alhough a number of he coefficiens are correcly signed in he unresriced coinegraing relaionships repored in Table 2, he relaionship does no conform closely o he hypohesized relaionships. However, i may be ha coefficiens which appear quie large in absolue erms in he wo equaions (say, he Japanese price coefficien in he firs vecor and he coefficien on he German price series in 1 In paricular, he number of roos close o uniy in he companion marix was he same as he number of common sochasic rends in he coinegraed VAR, namely 6.

7 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) Table 2 The normalized coinegraion relaionships and he adjusmen marices Sandardized bea vecor Sandardized alpha vecor Vecor 1 Vecor 2 Vecor 1 Vecor 2 s ger (1.57) (1.28) s jap (0.05) (2.77) p ger (0.34) (4.53) p jap (0.34) (3.02) p US (4.36) (2.04) i ger (4.86) (2.70) i jap (0.69) 0.80 (0.28) i US (1.21) (0.98) Noe: Numbers in parenhesis are numerical -values. he second) are in fac insignificanly differen from 0. Exclusion and homogeneiy resricions are formally esed below. The normalized alpha erms indicae clear adjusmen o he wo disequilibrium errors. For example, boh US prices and he German ineres rae adjus significanly o he firs disequilibrium error. The German exchange rae also adjuss (negaively) o his error, alhough he significance is quie weak. The paern of adjusmen is much richer wih respec o he second disequilibrium error, wih all he prices adjusing in addiion o he German ineres rae and Japanese yen. The eviden spillovers we are picking up here would seem o reinforce he use of he ri-polar framework. Tess of he resricions implied by he heory are summarized in Table 3. Simple PPP (wih symmery and proporionaliy imposed) is rejeced for boh exchange raes (see hypohesis A1 A3). Casselian PPP canno be rejeced for eiher exchange rae (hypohesis B1 and B2), and he ess would seem o indicae ha PPP augmened by he relevan ineres differenial is an accepable descripion of boh coinegraing relaionships (hypohesis B3). Table 3 Resricions on coinegraion space ri-polar sysem Hypohesis Economic inerpreaion Implied resricions Disribuions Tes saisic A1 PPP for Germany b 1 ¼ð1; 0; 1; 0; 1; 0; 0; 0Þ 0 v 2 (6) (0.00) A2 PPP for Japan b 2 ¼ð0; 1; 0; 1; 1; 0; 0; 0Þ 0 v 2 (6) (0.00) A3 PPP holds for boh b 1 ¼ð1; 0; 1; 0; 1; 0; 0; 0Þ 0, v 2 (12) (0.00) b 2 ¼ð0; 1; 0; 1; 1; 0; 0; 0Þ 0 B1 PPP plus ineres differenial b 1 ¼ð1; 0; 1; 0; 1; m; 0; mþ 0 v 2 (5) 2.65 (0.75) for Germany B2 PPP plus ineres differenial for Japan b 2 ¼ð0; 1; 0; 1; 1; 0; n; nþ 0 v 2 (5) 8.29 (0.14) B3 PPP plus ineres differenial for boh Noe: Numbers in parenhesis in he final column are p-values. b 1 ¼ð1; 0; 1; 0; 1; m; 0; mþ 0, v 2 (10) (0.05) b 2 ¼ð0; 1; 0; 1; 1; 0; n; nþ 0

8 106 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) Table 4 Loadings associaed wih resriced coinegraing vecors Variable CV 1 CV 2 s ger (1.08) (0.67) s jap (0.88) (3.18) p ger (2.38) 0 (0.34) p jap 0 (0.11) (1.89) p US (1.74) (2.01) i ger (4.31) (2.57) i jap (1.23) (1.88) i US (0.14) (0.38) Noe: Numbers in parenhesis are -values. The final resriced coinegraing vecors are as follows: CV 1 ¼ s GER p GER þ p US þ 0:135 i GER i US ; CV 2 ¼ s JAP p JAP þ p US þ 0:375 i JAP i US : These vecors closely accord wih he view discussed in Secion 2 ha ineres differenials reflec capial mobiliy. I may seem surprising ha he unconsrained esimaes repored in Table 2, which seem o be quie far from he hypohesized priors, can be consrained o such ighly defined relaionships. However, he consrained esimaes ake accoun of he variance of he coefficiens, somehing ha canno be gleaned from an inspecion of he poin esimaes hemselves. 2 The loadings marix associaed wih he wo coinegraing vecors, repored in Table 4, shows he imporance of he ri-polar naure of he sysem. In paricular, he fac ha German ineres raes, and o a lesser exen US prices, significanly adjus o remove disequilibrium in boh coinegraing vecors implies ha disurbances will be ransmied around he whole sysem, even if a shock occurs o jus one leg. For example, if here is a shock o Japanese prices which pushes CV 2 ou of equilibrium, no only will Japanese variables ac o resore equilibrium, bu so will US prices and even German ineres raes. Since boh hese laer erms help o form CV 1, disequilibrium spills from one exchange rae o anoher. This seems o confirm he convenional wisdom on how foreign exchange markes work, alhough i has no o our knowledge been demonsraed formally before in he conex of his kind of model. The fac ha US ineres raes appear o be weakly exogenous in he above sysems is perhaps no surprising given ha US ineres raes are usually seen as leading (i.e. pushing) world financial markes. Indeed, a formal es ha he wo alpha erms in he US ineres rae equaion are insignifican (plus hypohesis B3) produces a chi-squared saisic (wih 12 degrees of freedom) of and an associa- 2 Indeed, one good reason for explicily esing he consrains is ha he unconsrained esimaes may simply reflec collineariy amongs he variables enering our VAR.

9 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) ed p-value of Tha US prices appear o be adjusing in he above sysems is probably inuiive enough given he large US curren accoun imbalances necessiaing relaive price adjusmens beween he US and is rading parners. The formal es ha he alpha erms on he wo error correcion erms in he US price equaion produces a chi-squared saisic of and a p-value of One issue which we have no addressed in he above modelling is he poenial I(2) ness of our price series. For example, Juselius and MacDonald (2000) have demonsraed ha in he kind of modelling framework used here ha prices are likely o be I(2). However, hey also noe ha, despie his, he real exchange rae is an I(1) process. Since in our consrained model we work wih he real exchange rae, we do no pursue he I(1) vs. I(2) issue in his paper alhough we believe i is an ineresing opic for fuure research, paricularly in insances when he degree one homogeneiy of he nominal exchange rae in relaive prices is no saisfied Forecas accuracy While he equilibrium esimaes for he ri-polar model look plausible, ever since Meese and Rogoff (1983), he real es of he validiy of an exchange rae model lies in is forecasing power. The above analysis has been performed on he sysem esimaed up o Sepember To allow he compuaion of ou-of-sample forecass, he enire model was reesimaed over he period January 1983 December The long-run coinegraing relaionships were reimposed, namely PPP augmened by ineres differenials, bu he coefficiens on he ineres differenials were reesimaed. Ou-ofsample forecass for 1 12 monhs ahead were hen made. One observaion was hen added o he end of he sample and he enire process repeaed, including esimaion of he model. The final esimaion is for he period January 1983 Sepember The free coefficiens in he coinegraing relaionships and he shor-run dynamics were herefore allowed o change over ime. The coefficien on he ineres differenial in he German relaionship varies beween and 0.134, while he coefficien on he Japanese differenial in he second vecor lies in he range The relaive sabiliy of he German vecor srenghens our belief ha we have capured a meaningful relaionship. However, he movemens in he Japanese coefficien may indicae ha we have excluded an imporan variable from our simple model, and we quesion he appropriaeness of (shor-erm) ineres raes as a proxy for capial flows in he Japanese case. Furher refinemens of he model migh usefully employ somemeasure of sock marke performance which may be qualiaively more imporan for Japanese capial flows. 3 An anonymous referee has poined ou ha he exisence of I(2) rends will affec he criical values of he Trace saisics. However, and as we have noed, he esimaed eigenvalues and he roos of he characerisic polynomial from our sysem seem o suppor he exisence of wo saionary coinegraing vecors.

10 108 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) Table 5 Ou-of-sample forecasing performance of ri-polar model Horizon Deusche mark Japanese yen RMSE raio (model) Direcion (model) RMSE raio (VAR) Direcion (VAR) RMSE raio (model) Direcion (model) RMSE raio (VAR) Direcion (VAR) Noes: The superscriped numbers 1, 2 and 3 in he columns labelled RMSE raio are 10%, 5% and 1% significance levels calculaed using he Diebold Mariano es saisic wih a correcion for serial correlaion impared by he overlapping forecass.

11 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) As in he original Meese and Rogoff sudy, and in many aricles since, we ake he drifless random walk as he benchmark agains which we judge our model. The forecas performance is deailed in Table 5. For each horizon, i gives he raio of he RMSE of he exchange rae forecass from our preferred model wih he weak exogeneiy of US ineres raes imposed, 4 o hose from a random walk model, he proporion of correc direcional forecass, and he RMSE raio of a VAR se up in differences bu wih no coinegraing vecors. Good performance would be indicaed by an RMSE raio less han uniy and direcional abiliy in excess of 50%. The significance of he relaive forecas accuracy of he model compared o ha of he random walk alernaive is esed using he Diebold Mariano (1995) procedure. The resuls are clearly impressive. For he deusche mark, he forecass from he ri-polar model are boh more accurae han he random walk and more likely o correcly sugges he direcion of change han chance would sugges a all forecas horizons. The relaive accuracy becomes saisically significan a he 4-monh forecas horizon. The yen forecass become significanly more accurae han he random walk a he 5-monh horizon. In erms of direcional forecas abiliy, he yen forecass again prove beer han pure chance would sugges a all horizons over 1-monh. Wihou seeking o denigrae he resuls, we would poin ou ha over he longer forecas inervals, he yen consisenly depreciaed over he forecas period which explains he excepional direcional abiliy shown by he model from he 8-monh forecas horizon. However, he model can only be asked o forecas realiy, and we feel ha he impressive predicions of he more volaile German uni validae is performance. The RMSE raios for he differenced VAR (i.e. no coinegraing relaionships) are clearly inferior o boh he VECM formulaion and a random walk. The imporance of including he coinegraing vecors is made apparen by his forecasing exercise. Furhermore, he imporance of imposing resricions o reveal meaningful economic relaionships, as noed in Secion 3.1 above, is made clear by considering he forecas performance of he model wih unresriced coinegraing vecors. Alhough no repored in Table 5 o save space, he RMSE raio of he unconsrained sysem was greaer han uniy for boh exchange raes a all horizons, and he direcional abiliy noiceably inferior o ha of he consrained model for he boh raes a all horizons in excess of 1 monh. These resuls confirm he finding in he lieraure ha he use of resricions on he coinegraing relaionships improves he long-run forecas performance of error correcion models and also exends i o encompass shor horizons. 4 The resuls are in fac very similar when he alpha erms on he US ineres raes are lef unresriced.

12 110 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) Conclusions In his paper, we have sough o model he mark, dollar and yen using a simulaneous ri-polar srucure, which allows for spillovers beween he currencies. The modelling sraegy may be judged successful since we produced an inerpreable exchange raio model wih desirable economic properies. Mos significanly, perhaps, when confroned wih wha is aken o be he mos severe es of an exchange rae model is ou-of-sample forecasing abiliy he model is capable of producing predicions which compare exremely well o wo indusry sandard benchmarks. This performance is saisically significan and, we believe, of pracical relevance forecass from models closely relaed o hose presened here are currenly used by corporae eniies as par of heir financial decision-making processes. Given he curren ineres in academic and policy circles in he behaviour of he ri-polar relaionship beween he euro, dollar and yen, we believe our resuls are suggesive of he funcioning of such a sysem. Our approach suggess, for example, ha such a sysem will exhibi boh long- and shor-run predicabiliy (and he ineracion amongs variables accords wih economic inuiion) and his may be useful from he perspecive of seing arge zone bands and monioring heir evoluion over ime. Furhermore, our analysis suggess ha shocks o he sysem, originaing in he sysem iself, do no creae excess exchange rae volailiy. This in urn may give comfor o hose who favour a freely floaing srucure for he ri-polar grouping since i seems o imply ha he sysem will be more sable han a sysem based on muliple bilaeral relaionships. References Diebold, F.X., Mariano, R.S., Comparing predicive abiliy. Journal of Business and Economic Saisics 13, Fisher, P.G., Tanna, S.K., Turner, D.S., Wallis, K.F., Whiley, J.D., Economeric evaluaion of he exchange rae in models of he UK economy. Economic Journal 100, Frenkel, J.A., Flexible exchange raes, prices and he role of news. Journal of Poliical Economy 89, Froo, K.A., Rogoff, K., Perspecives on PPP and long-run real exchange raes. In: Jones, R.W., Kenen, P.B. (Eds.), In: Handbook of Inernaional Economics, vol. 3. Norh Holland, Amserdam. Holmes, J.M., The purchasing power pariy heory: in defence of Gusav Cassel. Journal of Poliical Economy 75, Johansen, S., Likelihood-based Inference in Coinegraed Vecor Auoregressive Models. Oxford Universiy Press, Oxford. Johansen, S., Juselius, K., Tesing srucural hypohesis in a mulivariae coinegraion analysis of he PPP and he UIP for he UK. Journal of Economerics 53, Juselius, K., Do purchasing power pariy and uncovered ineres rae pariy hold in he long-run? An example of likelihood inference in a mulivariae ime series model. Journal of Economerics 69, Juselius, K., MacDonald, R., Inernaional Pariy Relaionships Beween Germany and he Unied Saes: A Join Modelling Approach. Global Economic Insiuions Working Paper No. 50. Lee, K., Pesaran, M.H., Shin, Y., Exchange Rae, Price and Ineres Rae Dynamics in he UK: An Applicaion of he Generalised Impulse Response Analysis. Mimeo, Universiy of Cambridge.

13 R. MacDonald, I.W. Marsh / Journal of Inernaional Money and Finance 23 (2004) MacDonald, R., Long-run exchange rae modeling. Inernaional Moneary Fund Saff Papers 42, MacDonald, R., Marsh, I.W., On fundamenals and exchange raes: a Casselian perspecive. Review of Economics and Saisics 79, MacDonald, R., Marsh, I.W., Exchange Rae Modelling. Kluwer, Dordrech. MacDonald, R., Ricci, L., PPP and he Balassa Samuelson Effec: The Role of he Disribuion Secor. IMF Working Paper No. 01/38. Meese, R., Rogoff, K., Empirical exchange rae models of he sevenies: do hey fi ou of sample? Journal of Inernaional Economics 14, Oserwald-Lenum, M., A noe wih fraciles of he asympoic disribuion of he maximum likelihood coinegraion es saisics: four cases. Oxford Bullein of Economics and Saisics 54, Paruolo, P., On he deerminaion of inegraion indices in I(2) sysems. Journal of Economerics 72,