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1 Durham Research Online Deposied in DRO: 24 February 2015 Version of aached le: Acceped Version Peer-review saus of aached le: Peer-reviewed Ciaion for published iem: Chen, X. and MacDonald, R. (2015) 'Measuring he dollareuro permanen equilibrium exchange rae using he unobserved componens model.', Journal of inernaional money and nance., 53. pp Furher informaion on publisher's websie: hp://dx.doi.org/ /j.jimonn Publisher's copyrigh saemen: NOTICE: his is he auhor's version of a work ha was acceped for publicaion in Journal of Inernaional Money and Finance. Changes resuling from he publishing process, such as peer review, ediing, correcions, srucural formaing, and oher qualiy conrol mechanisms may no be reeced in his documen. Changes may have been made o his work since i was submied for publicaion. A deniive version was subsequenly published in Journal of Inernaional Money and Finance, 53, May 2015, /j.jimonn Addiional informaion: Use policy The full-ex may be used and/or reproduced, and given o hird paries in any forma or medium, wihou prior permission or charge, for personal research or sudy, educaional, or no-for-pro purposes provided ha: a full bibliographic reference is made o he original source a link is made o he meadaa record in DRO he full-ex is no changed in any way The full-ex mus no be sold in any forma or medium wihou he formal permission of he copyrigh holders. Please consul he full DRO policy for furher deails. Durham Universiy Library, Sockon Road, Durham DH1 3LY, Unied Kingdom Tel : +44 (0) Fax : +44 (0) hp://dro.dur.ac.uk

2 Measuring he Euro-Dollar Permanen Equilibrium Exchange Rae using he Unobserved Componens Model 1 Xiaoshan Chen 2 and Ronald MacDonald 3 Durham Universiy Business School Economics, Adam Smih Business School, Universiy of Glasgow 1 We would like o hank he Edior and wo anonymous referees for heir helpful and consrucive commens on previous drafs of his paper. 2 Correspondence o: Xiaoshan Chen. Xiaoshan.Chen@durham.ac.uk. Tel.: +44(0) Ronald.MacDonald@glasgow.ac.uk. Xiaoshan Chen acknowledges financial suppor from he ESRC (Award reference PTA ).

3 Absrac This paper employs an unobserved componen model ha incorporaes a se of economic fundamenals o obain he Euro-Dollar permanen equilibrium exchange raes (PEER) for he period 1975Q1 o 2008Q4. The resuls show ha for mos of he sample period, he Euro-Dollar exchange rae closely followed he values implied by he PEER. The only significan deviaions from he PEER occurred in he years immediaely before and afer he inroducion of he single European currency. The forecasing exercise shows ha incorporaing economic fundamenals provides a beer long-run exchange rae forecasing performance han a random walk process. JEL Classificaions: F31; F47 Key words: Permanen Equilibrium Exchange Rae; Unobserved Componens Model; Exchange rae forecasing.

4 1. Inroducion The Euro-dollar exchange rae has become he pivoal exchange rae in he inernaional moneary sysem, much as he German mark US dollar rae was prior o he formaion of he euro. Since is launch in 1999, he Euro-Dollar exchange rae has experienced large flucuaions. As Figure 1 shows, i depreciaed seadily from 1999 o 2002 before seadily rising unil This behaviour has puzzled many commenaors because i did no seem o be warraned by he radiional se of economic fundamenals (see, for example, Belloc and Federici (2010). Indeed, a he incepion of he Euro he perceived wisdom was ha i would say a pariy wih he US dollar. The sudy of such anomalous behaviour has given rise o a growing lieraure ha invesigaes he relaionship beween he Euro-Dollar exchange rae and economic fundamenals. They include he produciviy differenial beween Europe and he US (Corsei and Peseni, 1999, Alquis and Chinn, 2002, Schnaz e al, 2004, Miller 2008); he growh rae, inflaion differenials, curren accoun paerns (De Grauwe, 2000, De Grauwe and Grimaldi, 2005); ineres rae differenials and relaive raes of reurn in he US and euro area (Bailey e al., 2001, Heimonen, 2009). Ohers have focused on non-fundamenal facors, such as order flows (Dunne e al. 2010); differen quoing aciviy of invesors in response o announcemens (Omrane and Heinen, 2009) and he exisence of chaoic dynamics in he Euro-Dollar exchange rae when invesors have heerogeneous beliefs (Federici and Gandolfo 2012). Despie he large body of research in his area, he depreciaion of he Euro agains he dollar remains a puzzle. Undersanding movemens of he Euro-Dollar exchange raes also remains an imporan issue for boh academics and policy makers. In his paper, we sudy he equilibrium values of he Euro-Dollar exchange rae as, in 1

5 heory, a currency's value should graviae in he direcion of is long-run equilibrium over ime. There are a large variey of mehods available for calculaing a counry s equilibrium exchange rae, from he inernal-exernal balance approach, o he behavioural and permanen equilibrium approaches (BEER and PEER), hrough o he new open economy macroeconomic (NOEM) approach (see MacDonald (2000) and Driver and Wesaway (2004) for a survey of he lieraure). All of hese approaches have heir own advanages and disadvanages. 4 This is perhaps why end users (such as cenral banks and praciioners) use a range of esimaing echniques in coming o a view as o wheher an exchange rae is misaligned. In his paper we focus on an exension o he so-called PEER approach. In summary, his approach relies on decomposing an acual real exchange rae ino is permanen and ransiory componens, and hen using he permanen componen as a measure of he equilibrium exchange rae. A variey of ime series mehods have been used o exrac he permanen componen including he Beveridge-Nelson (1981) decomposiions (Huizinga, 1986; Cumby and Huizinga, 1990), srucural vecor auoregression (Clarida and Gali, 1994), coinegraion-based mehods (Clark and MacDonald, 2004), and he unobserved componens (UC) approach (Berger and Kempa, 2011). This paper esimaes he Euro-Dollar PEER using he UC framework. However, in conras o he UC model specificaion in Berger and Kempa (2011), 4. The equilibrium exchange rae deermined under he inernal-exernal balance framework requires ha any curren accoun imbalance mus be susainable. However, his approach conains a normaive elemen in defining wha is mean by susainabiliy and inernal balance. In conras, he BEER approach is no normaive. The exchange rae relaionship deermined under he BEER approach is subjec o saisical esing. However, he BEER is consisen wih he observed economic fundamenals. Therefore, business cycle facors may conribue heavily o he measure of equilibrium exchange raes. Finally, he NOEM models assume he opimizing behaviour of consumers ha has implicaions for he curren accoun and exchange raes. However, he NOEM models canno produce a rend appreciaion of real exchange raes such as hese observed for he Cenral and Easern Europe economies (Éger e al. 2006). 2

6 which is based on a small open economy model, our UC model incorporaes a se of economic fundamenals ha are mos frequenly applied when using he BEER approach (See Clark and MacDonald, 1999). We analyse he PEER, insead of a BEER, because here are wo major advanages of using he UC model specified in his paper o obain he PEER. Firs, compared o he BEER approach, our UC model seup clearly disinguishes beween he impac of he long-erm and shor-erm componens of an economic fundamenal on he real exchange rae. This helps us o separae business cycle facors from he equilibrium exchange rae movemens. This addresses he weakness of he BEER approach discussed in Éger e al. (2006). Second, he UC model enables us o obain rue, ex-ane exchange rae forecass incorporaing long-run relaionships beween he real exchange rae and economic fundamenals. In conras o he VECM or error correcion models used in MacDonald and Taylor (1993), Chinn and Meese (1995) and Cheung e al. (2005), we do no have o impose a pre-esimaed coinegraion vecor or long-run relaionship prior o producing exchange rae forecass. The forecass of real exchange raes from T 1 o T o l are obained using observaions of pas exchange raes and fundamenals up T. In addiion, alhough we found a coinegaion relaionship beween he Euro- Dollar exchange rae and is economic fundamenals, in he case of exchange raes where coinegraion is no idenified, our UC model seup is sill applicable. Failure o find coinegraion beween he real exchange rae and he economic fundamenals can occur because he BEER approach is no based on any specific exchange rae model and in ha sense may be regarded as a very general approach o modelling equilibrium exchange raes. The rejecion of coinegraion may be due, for example, o omied variables from he coinegraion relaionship. In his case, sandard regression and coinegraion analysis canno obain robus esimaes of a long-run 3

7 relaionship. However, as demonsraed by Everaer (2010), he UC model can overcome his issue. The remainder of his paper is srucured as follows. In he nex secion we ouline our unobserved componen models of he PEER. In secion 3 we discuss he daa used. Secion 4 conains our esimaes of he unobserved componen models, while Secion 5 conains he ou-of-sample forecasing resuls. Secion 6 concludes. 2. The model 2.1 Permanen and ransiory decomposiion of he real exchange raes This paper implemens he UC model o obain he Euro-Dollar PEER and esimae he subsequen misalignmen from 1975Q1 o 2008Q4. 5 The UC model decomposes observed ime series ino heir unobserved elemens, such as is permanen (rend) and ransiory (cycles) componens. The permanen componen represens he long-erm developmen of a ime series, while he ransiory componen represens he business cycle movemens. Each unobserved componen is formulaed as a sochasic process. The decomposiion of an observed ime series ino is unobserved componens provides a beer undersanding of he dynamics of he series. I also enables us o forecas fuure observaions in he series (Harvey, 2006). Using he UC framework o obain he PEER and misalignmen is no compleely new. For example, Berger and Kempa (2011) implemen a UC model based on a small open economy model o esimae he Canadian-US PEER. Our UC model specificaion differs from his approach as i incorporaes a se of economic fundamenals suggesed by Clark and 5 We have chosen o end he sample period in 2008 o avoid he effecs of financial crisis and he grea recession which we believe would dominae he daa se and preven our UC based esimaes being comparable o oher esimaes. 4

8 MacDonald (1999), which relae he real exchange rae movemens o he economic fundamenals, such ha q Z (1) ' Where q is he real exchange rae, Z conains a se of economic fundamenals. is a random disurbance and is a vecor of coefficiens. In his paper, we assume ha Z o, pd, gov, rid, and o, pd, gov and rid denoe he erms of rade differenial, he produciviy differenial, he relaive governmen expendiure o GDP raio and he real ineres rae differenial beween he euro area and he US, respecively. 6 The real exchange rae can be affeced by hese economic fundamenals. For example, he erms of rade is he raio of expor prices o impor prices and is relaed o a counry s curren accoun and balance of paymens. If he price of a counry's expors rises by more han is impors, is erms of rade will improve. This, in urn, resuls in rising demand for ha counry's currency and an appreciaion of is real exchange rae. In addiion, a counry s fiscal balance can be a key deerminan of is exchange rae. A permanen increase in governmen expendiure o GDP raio may lead o moneisaion of governmen deb. A large deb burden may prove worrisome o foreign invesors if hey believe he counry risks defauling on is obligaions. Therefore, hey may become less willing o own securiies denominaed in ha currency and his will lead o a depreciaion of he real exchange rae. Conversely, a 6 The relaion beween he real exchange raes and real macroeconomic fundamenals is discussed in Faruqee (1994), MacDonald (1997) and Fell (1996). Alhough here is a srong heoreical case for including ne foreign asses in an equilibrium exchange rae relaionship, ne foreign asses ypically do no prove o be significan in he kind of specificaion used here, largely because our deerminans will ulimaely be he drivers of he evoluion of ne foreign asses and here will be collineariy issues. The NFA erm seems o work beer in simpler models, such as ha of Lane and Milesi-Ferrei (2002) where i is a (he) key driver of he equilibrium exchange rae. 5

9 fiscal ighening ha permanenly improves he ne foreign asses posiion of a counry will lead o a real exchange rae appreciaion (Frenkel and Mussa 1988). Furhermore, real ineres rae differenials are frequenly inroduced as a deerminan of he real exchange rae via he uncovered ineres rae pariy condiion. Higher ineres raes in a counry relaive o oher counries will arac foreign capial and cause is exchange rae o rise. Alhough economic heory suggess ha he ineres rae differenial should end o equalise across counries in he long run, in he shor o medium erm i will impac on he real exchange rae. Finally, he impac of produciviy differenials on he real exchange rae is illusraed by Balassa-Samuelson heory, which saes ha he relaively larger increases in produciviy in he raded goods secor are associaed wih a real appreciaion of a counry s currency. In he UC framework, he real exchange rae can be direcly relaed o he permanen and ransiory componens of he above four fundamenals, such ha q o pd gov o pd gov rid, (2) where o, pd and gov are he permanen componens of he fundamenals, ofen modelled as random walk processes, whils o, pd, gov and rid are he ransiory componens. As wih mos of he exising lieraure, we find ha rid is a saionary variable, and hus does no have a permanen componen. 7 We allow he permanen and ransiory componens of each fundamenal o have differen coefficiens in equaion (2). This is moivaed by he idea ha he permanen and 7 Uni roo es saisics presened in Appendix B sugges ha rid is a saionary variable, and is herefore a sum of an AR process and irregular erm. 6

10 ransiory componens of he fundamenals may no have a uniform impac on real exchange rae movemens. 8 However, if he real exchange rae does no consiue a coinegraing relaionship wih he permanen componens of a se of seleced fundamenals, will be an I 1 error erm in equaion (2). Failure o find coinegraion should be aken as evidence agains he exisence of a sable long-run equilibrium relaionship beween he real exchange rae and he permanen componens of seleced fundamenals. However, Everaer (2010) demonsraes using a Mone Carlo experimen ha here may sill be long-run relaionships beween inegraed bu non-coinegraed variables. Following Everaer (2010), we specify as he sum of an irregular erm, 1, and a random walk componen, v : ~ 0,, v 1 v v, 1 1 (3) 1 NID 1 1 ~ NID 0, 1 (4) where v represens any I 1 omied variables from he coinegraion relaion. Sudies which use he UC models o accoun for omied variables from he coinegraion relaionship, include Harvey e al. (1986), Saranis and Sewar (2001) and Berger and Everae (2010). 9 The long-run relaionship beween non-coinegraed 8 For example, according o Frenkel and Mussa (1988), he permanen componen of he relaive governmen expendiure o GDP raio may be negaively relaed o he real exchange movemens, as permanen increases in governmen expendiure may lead o moneisaion of governmen deb and pressure on currency depreciaion in he long-run. However, in he shor o medium-run, he real exchange rae can be posiively affeced by a rise in governmen spending as i may likely o increase ne domesic demand. 9 Harvey e al. (1986) implemen a UC model o accoun for an underlying produciviy rend in he employmen-oupu relaion. Saranis and Sewar (2001) use an UC model o capure he omied variables such as wealh from he consumpion-income relaion. Berger and Everae (2010) implemen a panel UC model o coun for labour marke insiuion in he unemploymen and labour ax raes. 7

11 variables can be esimaed consisenly wih maximum likelihood (ML) using he Kalman filer and he significance of he long-run relaionship beween noncoinegraed variables can be esed using sandard Wald or a likelihood raio (LR) ess (Chang e al., 2009 and Everaer, 2010). Moreover, he UC model can easily accommodae a coinegraion analysis using he mehods proposed by Nyblom and Harvey (2000); if 1 0 in equaion (4), v reduces o a consan, and coinegraion is found beween real exchange rae and he permanen componens of economic fundamenals in equaion (2). Clark and MacDonald (1999) define he PEER as he elemens of he real exchange rae driven by he permanen componens of he economic fundamenals. Therefore, heir PEER is measured by 1o 2 pd 3 gov v, where v is inerpreed as he permanen componens of any omied fundamenals from he coinegraion relaionship. The oal misalignmen is hen defined as he difference beween he real exchange rae and he PEER, 1 o 2 pd 3 gov 4 rid Permanen and ransiory decomposiion of economic fundamenals The erms of rade differenial, he produciviy differenial (Balassa-Samuelson effec) and he relaive governmen expendiure o GDP raio are he non-saionary variables, and are considered o have a long-erm effec on he real exchange rae movemens. Therefore, he hree fundamenals are decomposed ino he permanen, ransiory and irregular componens as follows: Y =Y Y Y (5) 8

12 To save space, Y represens he permanen componens (i.e. o, pd and gov ) and Y denoes he ransiory componens (i.e. o, pd and gov ). The permanen componen, Y, is referred o as he permanen (equilibrium) value of he fundamenals. The ransiory componen, Y, measures he exen o which he acual fundamenal deviae from is equilibrium level. Y and Y are modelled as follows, Y Y 1, Y Y 2 ~ NID 0, Y Y, (6) 2 L 1 Y Y, Y Y ~ NID 0, Y Y. (7) In conras o he above hree fundamenals, he real ineres rae differenial is a saionary variable, and is considered o have a shor o medium erm effec on real exchange rae movemens. Therefore, he real ineres rae differenial is modelled as he sum of a ransiory componen and an irregular erm. Finally, he above UC model, consising of equaions (2)-(7), can be recas ino sae-space form for esimaion. The sae-space model is presened in Appendix A. The hyperparameers in he UC model can be esimaed by maximum likelihood using he predicion error decomposiion produced by he Kalman filer. Since nonsaionary variables, such as o, pd, gov and v, appear in he sae vecor, he Kalman filer requires a diffuse iniialisaion, and we use he iniialisaion mehod developed by Koopman and Durbin (2003). Esimaing he mulivariae UC model, 9

13 we can obain he unobserved permanen and ransiory componens and he coefficiens on he real exchange rae equaion simulaneously Daa Our empirical analysis is based on he Euro-Dollar real exchange rae, and he four fundamenals: he erms of rade differenial, he produciviy differenial, he relaive governmen expendiure o GDP raio and he real ineres rae differenial of euro area relaive o he US. The synheic euro area daa is consruced by aggregaing counry-specific variables of he member counries. The series are aken from he IMF Inernaional Financial Saisics (IFS), and from he OECD Labour produciviy growh daase. Appendix B ses ou in more deail how he daa was consruced. All variables, wih he excepion of he real ineres rae differenial, are ransformed ino logarihms for he esimaion. 4. Esimaion resuls 4.1 The baseline model The parameer esimaes of he UC model (hereafer, Model 1) oulined in Secion 2 are repored in Table Table 1 presens he coefficiens of he real exchange rae equaion (2). In general, hese coefficiens are consisen wih sandard predicions in he lieraure. The coefficien of he permanen componen of he erms of rade differenial, 1, appears posiive and saisically significan indicaed by he LR 10 All he compuaions were performed using he library of sae-space funcions in SsfPack 3.0 developed by Koopman e al. (2008) and Ox 5 by Doornik (2006). 11 Inspecion of he auxiliary residuals allows us o deec wo ouliers occurring during 1980Q1 and 2008Q3 for he real ineres rae differenial and he erms of rade, respecively. Two dummy variables are used for hese ouliers. The coefficiens on boh dummy variables are saisically significan. 10

14 saisic. This reflecs a subsiuion effec generaed by higher prices of expored goods relaive o impored goods. Higher expor prices will iniially lead o higher wages in he radable secor relaive o he non-radable secor, and evenually raise he overall price level in he domesic counry and an appreciaion of he domesic currency. The coefficien of he permanen componen of he relaive governmen expendiure o GDP raio, 3, is negaive and significan. This is consisen wih he argumen of Frenkel and Mussa (1985) ha a permanen increase in he governmen expendiure o GDP raio will lead o moneisaion of governmen deb and real exchange rae depreciaion in he long-run. Alhough he oher coefficiens in equaion (2) are saisically insignifican, hey all have he expeced signs. 12 Diagnosic es saisics are also presened in Table 1. Boh he Ljung-Box saisics for auocorrelaion in he one-sep-ahead predicion errors and he Jarque-Bera saisics for normaliy are insignifican. This indicaes ha Model 1 is appropriaely specified. {Table 1 abou here} 4.2 AR(2) specificaion for he ransiory componen of he real exchange rae Esimaion resuls from Model 1 sugges ha he real Euro-Dollar exchange rae movemens are primarily driven by he permanen componens of he erms of rade differenial and he relaive governmen expendiure o GDP raio. None of he ransiory componens of he economic fundamenals seem o have significan 12 is posiive as suggesed by he Balassa-Samuelson effec (Balassa, 1964 and Samuelson, 1964): 2 higher produciviy in he domesic relaive o he foreign economy is expeced o resul in an appreciaion of he domesic currency. In addiion, Frenkel and Mussa (1985) suggess ha in he shor o medium-run, he real exchange rae appreciaes if a rise in governmen spending increases ne domesic demand, and hus is expeced o be posiive. Finally, a counry ha has higher ineres 20 rae yields, will have pressure on is currency o appreciae, and hus is posiive

15 influence on he real exchange rae. Our resul reflecs he limiaion of using radiional economic fundamenals in explaining exchange rae flucuaions in he shor-run. As discussed in Frankel and Rose (1995) and Rogoff (2001) he exchange rae is known o have a low correlaion wih oher economic variables expec a low frequencies. The shor-run movemens of exchange raes are herefore likely o be driven by non-fundamenal facors, such as noise rading and irraional behaviour. Therefore, we model he ransiory componen of he real exchange rae, q ˆ, as an exogenous AR process, qˆ Lqˆ 1, q q and equaion (2) herefore becomes: 13 ˆ q o pd gov q, (8) The parameer esimaes of his modified model (Model 2) are repored in Table 2. We observe a moderae increase in he size of 1, 2 and 3 compared o Model 1. However, he significance of hese coefficiens does no aler. {Table 2 abou here} Alhough Models 1 and 2 can provide a non-spurious long-run relaion beween he real exchange rae and he permanen componens of he fundamenals, 13 As he real ineres rae differenial does no appear in equaion (8), when ransiory componen of he real exchange rae is modelled as an AR process we exclude his variable for Model 2. 12

16 regardless wheher hese variables are coinegraed, we found ha he esimaes of 1 in equaion (4) are close o zero for Models 1 and 2. This may indicae he exisence of a coinegraion relaion. We used Nyblom and Harvey (2000) o es he null hypohesis ha 1 0. The es saisics are presened in he upper panel of Table 3. They confirm ha he real exchange rae consiues a coinegraion relaion wih he permanen componens of he inegraed fundamenals. The null hypohesis ha 1 0 canno be rejeced when he lag lengh m As a robusness check, he race and maximum eigenvalue saisics obained from Johansen s coinegraion approach are presened in lower panel of Table 3. They also indicae he exisence of a coinegraion relaion beween he real exchange rae and he inegraed economic fundamenals. {Table 3 abou here} 4.3 The PEER and oal misalignmen Figure 1 plos he permanen and ransiory componens of he real exchange rae and economic fundamenals obained from Model 1. I shows ha he euro was relaively close o is equilibrium values and he oal misalignmen was modes during he 1970s and 1980s. The period 1975 o 1980, following he adven of floaing exchange raes, is characerized by an overvaluaion of he euro. The real Euro-dollar exchange rae is above is PEER. However, he dollar srenghened significanly during he second half of he 1980s. In response, o he appreciaion of he dollar during his period and he subsanial US curren accoun defici, he 14 The deails of he es are discussed in Nyblom and Harvey (2000). 13

17 Sepember 1985 Plaza Accord was signed beween he US and he G5 o induce a gradual depreciaion of he dollar. Our resuls sugges ha he appreciaion of he dollar agains he euro was primarily due o a shif in he PEER during his period. From mid-1985 he rend of dollar appreciaion rapidly reversed. Srong signs ha he dollar was undervalued became apparen in This corresponds o a period of weakness of he dollar agains he major European currencies. Finally, following he launch of he euro in 1999 he Euro-Dollar real exchange rae was considerably undervalued relaive o he PEER unil As shown in Figure 2, Models 1 and 2 produce consisen esimaes for he PEER and he oal misalignmen. Considering he period , our findings are broadly consisen wih earlier conribuions (Maeso-Fernandez e al. 2002; Deken e al., 2002; Duval 2002). Maeso-Fernandez e al (2002) esimae a BEER and PEER of he euro effecive exchange raes using various model specificaions. The auhors found periods of dollar undervaluaion agains he euro in he lae 1970s and in 1987 in he afermah of he Louvre Accord. There are also periods of dollar overvaluaion idenified during he mid 1980s and 2000, alhough he magniude of overvaluaion varies depending on he model specificaions used. Duval (2002) builds a dynamic model for he Euro- Dollar real equilibrium exchange rae using he NATREX and he BEER approaches. Their findings sugges ha he euro was undervalued agains he dollar in he mid- 1980s and from 1999 onwards. Deken e al. (2002) esimae equilibrium values of he euro effecive exchange raes. Their resuls confirm ha he euro was overvalued in he second half of he 1970s unil he beginning of he 1980s. They also found wo periods of srong undervaluaion of he effecive Euro exchange rae during he mid- 1980s and, from 1998 unil he end of heir sample in

18 In addiion o using our UC models, we also use Clark and MacDonald's (2004) coinegraion-based PEER approach o esimae he PEER as a robusness check. 15 The PEER and he oal misalignmen coinegraion-based PEER, obained using he Granger and Gonzalo (GG) (1995) decomposiion, are also presened in Figure 2. They appear o be broadly consisen wih hose esimaed from Models 1 and 2, alhough he resuls from Models 1 and 2 seem o sugges ha he euro is closer o is equilibrium value han implied by he coinegraion-based approach. The degree of uncerainy surrounding he esimaes of equilibrium exchange raes is also highlighed in Deken e al. (2002) and Maeso-Fernandez e al (2002) when differen model specificaions and approaches are used. Alhough our resuls are generally robus in erm of idenify periods of over-/undervaluaion, we are cauious when inerpreing he magniude of hese over-/undervaluaion. {Figures 1 and 2 abou here} 5. Ou-of-sample forecasing Using Models 1 and 2 o forecas exchange raes, we do no need o impose he coinegraion vecor or any long-run relaions obained from a separae esimaion procedure prior o exchange rae forecasing, as is he case when VECM or error correcion models being used, as in MacDonald and Taylor (1993), Chinn and Meese (1995) and Cheung e al. (2005). This is because he UC model has a naural saespace represenaion, and he saisic reamen can be based on he Kalman filer. A convenien propery of he Kalman filer is ha i handles missing observaions in a 15 Esimaion resul of he VECM model is available upon reques. 15

19 daa se. When he Kalman filer is used for forecasing purposes, i reas he observaions in he forecasing period as a se of missing observaions, and produces observaion forecass and heir forecas error variances (See Commandeur and Koopman, 2007). A rolling sample approach is used, wih he full-sample period firs divided ino a pre-forecasing period from 1975Q1 o 1995Q4 and a forecasing period from 1996Q1 o 2008Q4. 16 The pre-forecasing sample moves forward quarer-by-quarer and he model s hyperparameers are re-esimaed a each sep unil he end of he sample is reached. In oal, 53 one-quarer-ahead forecass and 42 welve-quarerahead forecass are calculaed. We compare he ou-of-sample forecasing abiliy of Models 1 and 2 wih he random walk process of he real exchange rae. To conduc a ransparen comparison beween he UC models wih he random walk process, we firs compare he ou-of-sample forecasing abiliy of a univariae UC model of he real exchange rae, where he real exchange rae is decomposed ino is permanen and ransiory componens. 17 If Models 1 and 2 are beer han he random walk process in erms of forecasing, bu he univariae UC model is no, his suggess ha he inclusion of he economic fundamenals do help o predic fuure real exchange raes. Table 4 repors he raios of roo-mean-squared errors (RMSE) of boh he univariae and mulivariae UC models relaive o he random walk process. One sriking resul revealed from Table 4 is ha he relaive RMSEs of he univariae UC model wih respec o he random walk process are very close o one and remain relaively consan across differen forecasing horizons. However, for Models 1 and 2, he longer he forecasing horizons, he smaller he RMSE produced by hese 16 The choice of 1996Q1 is ad hoc. However, i provides a sufficienly large sample for iniial esimaion and for evaluaing ou-of-sample forecasing performances of he UC models. 17 As wih Berger (2011), we assume ha he permanen componen of real exchange rae follows a random walk process, and he ransiory componen is a saionary AR(2). 16

20 models relaive o he random walk process. We also implemen boh Diebold and Mariano (DM) (1995) and Harvey, Leybourne and Newbold (HLN) (1997) ess of equal forecas accuracy o deermine wheher differences in forecasing errors beween a UC model and he random walk process are significan. Boh he DM and HLN saisics are calculaed under he null hypohesis ha he UC model is equivalen in forecasing accuracy o he random walk process. The es saisics in Table 4 ha are highlighed in bold indicae ha he null hypohesis of equivalen forecasing accuracy is rejeced. I can be seen ha none of he null hypoheses ha he univariae UC model is equivalen in forecasing accuracy o he random walk process can be rejeced. However, Model 1 is significanly beer in erms of forecasing fuure exchange raes han he random walk process from eigh-quarerahead forecasing horizons onwards. This indicaes ha he economic fundamenals help o predic he long-run movemen of real exchange raes. Furhermore, Model 2, which allows he ransiory componen of he real exchange rae o be modelled independenly o follow an AR process, improves he shor-run forecasing accuracy wih respec o Model 1. {Table 4 abou here} 5. Conclusions This paper employs a UC model incorporaing a se of economic fundamenals o esimae he Euro-Dollar PEER from 1975Q1 o 2008Q4. The advanages of using he UC model are wo-fold. Firs, compared o he BEER approach, our UC model seup clearly disinguishes beween he impac of he long-erm and shor-erm componens of an economic fundamenal on he real exchange rae. This helps us o separae business cycle facors from he equilibrium exchange rae movemens. Second, he 17

21 UC model allows us o obain rue, ex-ane exchange rae forecass incorporaing long-run relaionships beween he real exchange rae and economic fundamenals. I does no require he long-run relaionship o be esimaed separaely prior o forecasing, as is he case when VECM or error correcion models are used. Moreover, alhough we found a coinegraion relaionship beween he Euro-Dollar exchange rae and is economic fundamenals, our UC model can obain robus esimaes of he long-run relaionship regardless of wheher or no coinegraion is found. Our esimaed PEER suggess ha he euro was overvalued during he second half of he 1970s and he firs half of he 1990s. These ime periods correspond o a period of weakness of he dollar agains he major European currencies. Two periods of undervaluaion of he euro are also idenified during he mid-1980s and in he firs hree years following he launch of he euro in The undervaluaion of he euro in he mid-1980s is associaed wih he period of significan dollar srengh prior o he Plaza Accord. However, he appreciaion of he dollar agains he euro was primarily due o a shif in he PEER and hus he oal misalignmen was modes during his period. On he conrary, he oal misalignmen following he euro s launch in 1999 was more severe. The depreciaion of he euro during his period was more associaed wih ransiory facors han a downward shif in he PEER. Many argumens have been pu forward o explain his phenomenon. However, heories remain incomplee. Our resuls also sugges ha he Euro-Dollar real exchange rae is predominaely driven by he permanen componens of he erms of rade differenial and he relaive governmen o GDP raio beween he euro area and he US. The impac of he ransiory componens of he economic fundamenals on he real exchange rae appears minimal. This is consisen wih he argumens of 18

22 Frankel and Rose (1995) and Rogoff (2001) ha economic fundamenals are weakly relaed o exchange rae flucuaions in he shor-run. Finally, our forecasing resuls sugges ha Models 1 and 2, which include he economic fundamenals, provide more accurae exchange rae forecass over a longrun forecasing horizon han a random walk process. Furhermore, Model 2, which allows for he ransiory componen of he real exchange rae o be modelled as an AR process, improves he shor-run forecasing accuracy in comparison o Model 1. In shor, we demonsrae ha he mehod proposed in his paper can be a useful echnique for cenral banks o esimae he equilibrium exchange rae and o predic long-run exchange rae movemens. In fuure research our approach could usefully be exended o oher currencies and also perhaps o effecive exchange raes using a muli-counry panel framework, for example. 19

23 Appendix A. Sae-space model represenaion of Model 1 The sae-space represenaion of Model 1 is given by Y Za Gε a d Ta Hη 1 where Z, T, d, G and H are ime-invarian marices conaining he hyper-parameers of he model: Z I T1 T T, 04 3 I I1 1, o , o , pd , 0 0 pd T 1, T 0 0 1, gov 0 2, 0 0 2, gov , rid , rid d o, pd, gov,0,0,0,0,0,0,0,0,0, G diag,,,, and, o, pd, gov, rid 1 H. diag, o,, pd,, gov,, o,, pd,, gov,, rid,04 4, 1 The observaion vecor Y o,,,, pd gov rid q is known and he sae vecor a o, pd, gov, o, pd, gov, rid, o, pd, gov, rid, v conains he unobserved componens. Since non-saionary variables o, pd, gov and v are in he sae vecor, he Kalman filer requires a diffuse iniialisaion and we used he iniialisaion mehod developed by Koopman and Durbin (2003). 20

24 Appendix B. Daa consrucion and uni roo es The real Euro-Dollar exchange rae for welve euro area members prior o 1999 (based on consumer prices) is compued as a weighed geomeric average of he bilaeral exchange raes of he eleven currencies agains he dollar. 18 Therefore, a rise in he Euro-Dollar exchange rae means an appreciaion of he Euro agains he Dollar. The weighs are given by he share of exernal rade of each euro area counry in oal euro area rade (aking ino accoun hird marke effecs) for he period The consumer price indices and bilaeral nominal exchange raes were aken from IMF Inernaional Financial Saisics (IFS), lines 64 and rf, respecively. A counry s erms of rade is compued as he raio of is expor prices o impor prices. The same weighs used o consruc he synheic euro-dollar exchange rae prior o 1999 are used o compue he raio for he euro area. Finally, he erms of rade differenial is compued as he raio of he euro erms of rade relaive o he US. Expor and impor prices for Ausria, Finland, Germany and he US were obained from IFS, lines 76 and 76.x, respecively. Since he daa are no available for he remaining counries, expor and impor uni values aken from IFS, lines 74 and 75, are used. 20 In he absence of daa on oal facor produciviy, some previous sudies have focussed on price measures of produciviy, such as he relaive price of non-raded o rade goods prices. In his sudy we measure he produciviy differenial as he raio of real GDP o he number of employed persons in he euro area compared wih 18 Belgium and Luxembourg have a common currency. 19 Weighs used for each currency are 34.49% for Deusche mark, 17.75% for French franc, 13.99% for Ialian lira, 9.16% for Duch guilder, 7.98% for Belgian and Luxembourg franc, 4.90% for Spanish pesea, 3.76% for Irish pound, 3.27% for Finnish markka, 2.89% for Ausrian schilling, 1.07% for Poruguese escudo, 0.74% for Greek drachma. 20 For France, he daa series of expor and impor uni values are available from 1990Q1 onwards, herefore he erms of rade daa aken from he OECD daabase is used before 1990Q1. 21

25 he same raio for he US. Real GDP series were obained from IFS, line 99bv; Employmen daa was aken from he OECD Labour produciviy growh daase. Relaive governmen expendiure o GDP raio is compued as he raio of governmen expendiure o GDP in he euro area relaive o he same raio for he US. For he euro area, he governmen expendiure o GDP raio is obained from he Area Wide Model consruced by Fagan e al. (2001). The corresponding variable for he US is consruced using GDP and governmen expendiure a curren prices aken from IFS, lines 99b and 91f. Finally, he real ineres rae differenial is he difference beween real ineres raes for he euro area and he US. Daa on bond yields for he US and a geomeric weighed average of long-run ineres raes of counries consiuing he euro area are used. The expeced rae of inflaion is proxied by he annual rae of consumer price inflaion in he previous year. The nominal long-erm ineres raes for he euro area counries and he US were aken from IFS lines 61. These refer o yields o mauriy of governmen bonds or oher bonds ha would indicae longer erm raes. The mauriy of he ineres raes varies beween counries ranging from 10 o 15 years. The saionariy of he consruced daa are examined using he ADF es. Tes saisics presened in Table B sugges ha apar from he real ineres rae differenial, all he oher variables are I (1). The Euro-Dollar real exchange rae being an I (1) process violaes he PPP assumpion. The persisen naure of he real exchange rae may reflec ha i was driven by a se of real fundamenals. In addiion, he real ineres differenial being a saionary variable is consisen wih he lieraure (see Clark and MacDonald, 2004; Hoffmann and MacDonald, 2009). 22

26 Table B: Uni roo ess (1975Q1-2008Q4) Variables in level Consan +Trend Variables in firs difference Consan +Trend q *** o *** pd *** gov *** rid ** *** Noes: Variables in Table B are consruced as illusraed above. All variables wih he excepion of rid are ransformed ino logarihms. In addiion, he ADF ess use a log lengh of 4; Significan es saisics are marked using sars wih *, ** and *** denoing he 10%, 5% and 1% significance level respecively. 23

27 Table 1: Parameer esimaes of Model 1 Coefficiens on he exchange rae equaion *** *** (0.515) (0.467) (0.288) (1.149) (3.303) (5.369) (1.048) AR erms, consan drifs and damping facor 1,o 2,o 1, pd 2, pd 1,gov 2,gov 1,rid 2,rid 0.944*** ** 1.399*** ** 1.925*** *** 1.633*** *** (0.132) (0.105) (0.285) (0.272) (0.049) (0.046) (0.122) (0.118) Sandard deviaions of he shocks o permanen and ransiory componens,o, pd,gov,o, pd,gov,rid (0.200) (0.092) (0.120) (0.253) (0.176) (0.039) (0.071) (0.370) D80q1 D08q *** 0.040*** (0.003) (0.011) H 0 : 1 =0, H 0 : 2 =0, H 0 : 3 =0, H 0 : 4 0 =0, R LogL = , R LogL = , R LogL = , Dummy variables Likelihood raio ess R H : 1 =0, LogL = , 2 (1) = *** 2 (1) = R LogL = , 2 (1) = (1) =2.258 H 0 : 2 =0, 2 (1) =0.018 H 0 : 3 =0, R H : , LogL = , 2 (4) =6.496 R H : , 0 LogL LogL = , 2 (3) =63.438*** Residual diagnosics R LogL = , R LogL = , 2 (1) = (1) = 7.942** Q (12) o Q (12) pd Q (12) rid Q (12) gov Q (12) q JB o JB pd JB rid gov JB JB q Noes: Numbers in parenheses are sandard errors compued using he dela mehod; The sandard deviaions of variaions of variances parameers are muliplied by 100; *, ** and *** indicae significance a he 10%, 5% and 1% level, respecively. 24

28 Table 2: Parameer esimaes of Model *** ** (1.210) (0.804) (0.636) Coefficiens on he exchange rae equaion AR erms, consan drifs and damping facor 1,o 2,o 1, pd 2, pd 1,gov 2,gov 1,q 2,q 0.994*** ** 1.122*** ** 1.453*** ** 1.348*** (0.132) (0.142) (0.095) (0.087) (0.267) (0.254) (0.298) (0.283) Sandard deviaions of he shocks,o, pd,gov,o, pd,gov q, (0.226) (0.627) (0.285) (0.248) (0.050) (0.272) (1.440) (0.116) D08q *** (0.010) H 0 : 1 =0, H 0 : 2 =0, H 0 : 3 =0, 0 R LogL = , Dummy variables Likelihood raio ess 2 (1) = *** R LogL = , 2 (1) = R LogL = , R H : , LogL 2 (1) = 8.074*** LogL = , 2 (3) =43.840*** Residual diagnosics Q (12) o Q (12) pd Q (12) gov Q (12) q JB o JB pd JB gov Noes: Numbers in parenheses are sandard errors compued using he dela mehod; The sandard deviaions of variaions of variances parameers are muliplied by 100; *, ** and *** indicae significance a he 10%, 5% and 1% level, respecively. JB q 25

29 Table 3: Tess for coinegraion Nyblom and Harvey (2000) m=0 m=1 m=2 m=3 m=4 Model * Model ** 0.361* Johansen and Juselius (1990) Trace 5% criical value Max. Eigenvalue 5% criical value None ** ** A mos Noes: m is lag lengh seleced o modified Nyblom and Harvey s (2000) es saisic o allow for serial correlaion. The criical values wih 1 degree of freedom a he 10%, 5% and 1% level are 0.347, and 0.743, respecively (See Harvey, 2001, Table 1); Significan es saisics are marked using sars wih *, ** and *** denoing he 10%, 5% and 1% significance level respecively. Table 4: Ou-of-Sample Forecass ( ) Relaive Roo-Mean-Squared Errors H=1 H=2 H=4 H=6 H=8 H=9 H=10 H=11 H=12 Univariae UC model Vs. RW DM HLN Model 1 Vs. RW DM ** 2.43*** 2.55*** 2.62*** 2.75*** HLN ** 1.97** 2.00** 1.98** 2.00** Model 2 Vs. RW DM ** 1.88** 2.27** 2.66*** 2.76*** 2.85*** 2.88*** 2.90*** HLN ** 1.75** 2.01** 2.22** 2.24** 2.23** 2.18** 2.11** Roo-Mean-Squared Errors of he random walk process RW Noe: he firs row of each model (Vs. RW) denoes he relaive RMSE of he mulivariae model wih respec o he RW model; he rows (DM and HLN) presen he DM and HLN saisics; ** and *** indicae significance a he 5% and 1% level, respecively. 26

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