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1 Cenre for Inernaional Capial Markes Discussion Papers ISSN Are he Balic Counries Ready o Adop he Euro? A Generalised Purchasing Power Pariy Approach Guglielmo Maria Caporale, Davide Ciferri, Alessandro Girardi No

2 ARE THE BALTIC COUNTRIES READY TO ADOPT THE EURO? A GENERALISED PURCHASING POWER PARITY APPROACH Guglielmo Maria Caporale a, Davide Ciferri b and Alessandro Girardi b,c a Brunel Universiy, London b Universiy of Tor Vergaa, Rome c Insiue for Economic Sudies and Analyses, Rome June 2008 Absrac This paper focuses on macroeconomic inerdependencies beween he Euro area and hree ransiion economies (Esonia, Lihuania and Lavia), wih he aim of esablishing wheher he laer are ready o adop he Euro. The heoreical framework is based on he Generalised Purchasing Power Pariy (GPPP) hypohesis, which is empirically esed wihin a Vecor Error Correcion (VEC) model. Using boh monhly and quarerly daa over he period , i is found ha GPPP holds for he real exchange rae vis-à-vis he Euro of each Balic counry, reflecing a degree of real convergence consisen wih Opimum Currency Area crieria. Furher, he adoped join modelling approach for he real exchange raes of he Balic region ouperforms a number of alernaive models in erms of ou-of-sample forecass. Keywords: Transiion economies, Euro area, (Generalised) Purchasing Power Pariy, Vecor Error Correcion models JEL Classificaion: C32, E00, F36. Corresponding auhor: Professor Guglielmo Maria Caporale, Cenre for Empirical Finance, Brunel Universiy, Uxbridge, Middlesex UB8 3PH, UK. Tel.: +44 (0) Fax: +44 (0) Guglielmo- Maria.Caporale@brunel.ac.uk [1]

3 1. Inroducion Following he European Union (EU) enlargemen of 2004, he nex sep in he European inegraion process is expeced o be he (possible) expansion of he European Moneary Union (EMU) o allow he new member saes o join he Euro. How fas (slow) his process should be depends on several facors affecing boh old and poenial candidae members. Wha moivaes he ransiion economies of Easern Europe (Balkan, Balic, Cenral Europe, and Commonwealh of Independen Saes (CIS) 1 counries) o seek EMU membership is heir expecaion of being able o enjoy he benefis of a moneary union, in paricular policy discipline, deeper economic and financial inegraion wih he incumben counries, a reducion in ransacion coss, and lower ineres raes (Läemäe and Randveer 2004). Of hese economies, Esonia, Lavia and Lihuania appear o be bes prepared o adop he Euro, especially in erms of nominal convergence, wih Lihuania seeming o be he sronges candidae a presen. As poined ou by Havrylyshyn and Wolf (1999), he Balic counries had a higher rae of growh compared o oher ransiion economies, owing o beer iniial condiions such as less disorions and heir being closer o marke sysems. Alhough some reforms began in he las years of he Sovie Union, he main ransiion process in hese economies sared a he end of 1991, when hey achieved poliical independence. According o Wachel and Korhoen (2004), wihin he whole package of poliical and economic reforms, a key role was played by he adopion of fixed exchange rae regimes, which resuled in credibiliy for boh he new currencies and he economic sysem as a whole and lower and sable inflaion. Furher, boh heir degree of openness and foreign direc invesmen flows conribued o heir success relaive o he oher ransiion counries. The issue of how ready for EMU membership he accession counries are can be addressed using wo main ses of crieria: insiuional ones, i.e. he convergence crieria of he Maasrich Treay, and economic ones (Breuss e al., 2004). As fiscal policy in he Balic counries in recen years has generally been consisen wih he Maasrich crieria, joining EMU will no require significan furher changes in his respec, and hus he benefis from EMU membership should ouweigh he coss. In paricular, heir fiscal parameers broadly mee he EU requiremens, which reflecs policy choices being made during he ransiion process o achieve exchange rae sabilisaion as well as he conrol of he inflaion. 1 The CIS includes he former Sovie republics of Armenia, Azerbaijan, Belarus, Georgia, Kyrgyz and Uzbekisan. [2]

4 From a more heoreical perspecive, price convergence represens a necessary condiion o sabilise boh he nominal (explici policy arge) and he real exchange rae (implici policy arge), safeguarding he inra-regional compeiiveness of member counries and avoiding incenives o implemen beggar-hy-neighbour policies. However, Ahn e al. (2002) sress ha a Purchasing Power Pariy (PPP)-based approach may capure only parially he significan changes in economic policies and he resrucuring process in Europe. A more useful framework is given by he Generalised PPP (GPPP) heory, which suggess ha he (possible) non-saionariy of real exchange raes may be relaed o ha of heir long-run macroeconomic deerminans. Empirically, GPPP beween he EMU and he Balic counries holds if i is possible o idenify (a leas) one saionary linear combinaion of bilaeral real exchange raes vis-à-vis he Euro. The exisence of an equilibrium pah for a linear combinaion of he real exchange raes rules ou real asymmeries (Bayoumi and Taylor, 1995), and herefore he GPPP hypohesis can be inerpreed in erms of long-run susainabiliy of a common currency area (see Mundell, 1961). This paper aims o esablish wheher economic condiions in hese hree Balic economies are in fac such ha hey are ready o join he Euro area, puing an end o he ransiion phase of he las fifeen years. Coinegraion echniques are applied o es he GPPP hypohesis, afer invesigaing he saionariy of each real exchange rae. The adoped economeric framework is a Vecor Error Correcion (VEC) model. More specifically, his paper aims o analyse in sequence: a) wheher he GPPP hypohesis holds beween he Euro area and he Balic region; b) he shor-run dynamics of real exchange raes for he hree Balic counries; c) he relaive conribuion of global and regional shocks o he inernaional compeiiveness of hose economies; d) he ou-of-sample forecasing performance of our mulivariae ime-series model relaive o a number of alernaive models. The overall picure emerging from he esimaes using boh monhly and quarerly daa over he period suggess ha he GPPP hypohesis is no be rejeced by he daa. Global (symmeric) shocks seem o explain mos of he real exchange rae dynamics of he Balic area, even hough he difference in he size of regional shocks beween counries is no negligible. Furher, he adoped specificaion generally ouperforms rival models describing he behaviour of he real exchange raes of he Balic counries. The paper is organised as follows. In Secion 2 he heoreical framework is oulined. Secion 3 presens he esimaions resuls. In Secion 4, he resuls from dynamic simulaions based on impulse response analysis are discussed, while robusness and forecasing analysis are repored in Secion 5. Some final remarks follow in he concluding Secion 6. [3]

5 2. Some Theory The desirabiliy for a given counry of joining a common currency area is generally assessed hrough cos-benefi analysis. Poenial gains are mainly hough of in erms of higher economic efficiency, whereas poenial losses are mosly aribued o he loss of macroeconomic policy insrumens (such as he exchange rae) o respond o asymmeric shocks (see, among ohers, Mongelli, 2002). However, despie some recen developmens (see, for example, Demopoulos and Yannacopoulos, 1999), he opimum currency area (OCA) paradigm, originally proposed by Mundell (1961), sill does no provide any formal crierion o esablish he opimal iming and ways of creaing a currency area (Eichengreen, 1990). Recen conribuions focus on he role of public finances insead of he role of real exchange raes as an oupu sabiliser. From his perspecive, wheher domesic money can be used by he governmen as a ool for budgeary finance hrough seigniorage rens or wheher counries differ in he coss associaed wih he collecion of axes are crucial issues in esablishing he condiions o join a currency union (Buier and Eaon, 1984; Canzoneri and Rogers, 1990; Aizenman, 1992). Mos researchers poin ou ha hese facors can hardly be idenified empirically (Baldwin, 1991; Buier, 2000). Moreover, here is disagreemen on he economic effecs of moneary inegraion wih respec o income correlaion among member counries and inra-area rade flows. 2 Following Rose (2000), a number of sudies have used graviy models (de Nardis and Vicarelli, 2003, among ohers) o analyse he effec of joining a common currency area by esing he hypohesis of growing inra-area rade flows induced by he inroducion of a common currency. Here, insead, we focus mainly on he role of cross-counry income correlaions o esablish wheher he Balic counries are ready o join he Euro area, his being he crierion advocaed by Aris (2003) and oher auhors o decide upon he adopion of a common currency. More in deail, our heoreical framework is based on Enders and Hurn (1994); i enables us o obain a measure of convergence (hrough empirical validaion of he GPPP 2 The specializaion hypohesis (Krugman, 1993, and Krugman and Venables, 1996) posulaes ha as counries become more and more inegraed, heir indusrial srucure will develop according o heir comparaive advanages (Eichengreen and Bayoumi, 1996). Consequenly, he economic sysems of each member counry of an OCA should become more secorally concenraed and vulnerable o supply shocks. Opposie implicaions arise from he endogeneiy hypohesis (Frankel and Rose, 1997), which posis ha a posiive link beween income correlaion and rade inegraion exiss, suggesing ha counries joining a currency union may saisfy he properies of an OCA ex-pos even if hey do no ex-ane. [4]

6 hypohesis) beween he Balic counries and he Euro area. According o he GPPP heory, bilaeral real exchange raes which are individually non-saionary migh be coinegraed if heir long-run macroeconomic deerminans are highly correlaed. In ha case, he parameers of he coinegraing vecor(s) depend on he funcional form of he naional aggregae demand funcions. If i is possible o idenify (a leas) one saionary linear combinaion of oherwise non-saionary real exchange raes, hen he long-run equilibrium condiion(s) can be inerpreed in erms of he economic inerdependencies beween he Euro area and Balic counries, such as commercial and financial ransacions, echnology ransfers and migraion flows A reduced-form model for he Balic economies As already menioned, he Balic counries have some disinguishing feaures wih respec o he oher Easern European ransiion economies. Afer heir separaion from he former Sovie Union mos of heir rade was re-oriened owards he neighbouring Wesern European counries. Moreover, he main explici policy objecives were defined aking ino accoun he possibiliy of joining EMU in he shor erm. However, links wih he US also played an imporan role in he ransiion period: for insance, Lihuania pegged is currency o he US Dollar and exernal deb was mainly denominaed in US Dollars. 3 Thus, our chosen framework analyses inerdependencies beween he Balic economies allowing for he possible influence of boh he US and he Euro area economies. Accordingly, we consider five economies (indexed by i= 0,,4): he US ( 0 ), he Euro area (1), Esonia ( 2 ), Lavia (3 ), and Lihuania ( 4 ). The US is he reference counry in he model. For each counry i, we specify he following equaion for aggregae oupu: * * ( 0 ) y = f y, q, i for i= 0,..., 4 (1) i i i where y i sands for domesic oupu; y 4 * i = ξij yi j= 0, j i indicaes foreign oupu, calculaed as a weighed average of oher counries oupu; q 4 * i = υij qij j= 0, j i is he real effecive exchange rae, consruced as a weighed average of he bilaeral real exchange raes q ij, beween 3 Esonia was he firs o inroduce in 1992 a new currency, he kroon, which was pegged o he German Mark hrough a currency board. In Lihuania he new currency was inroduced in The higher inflaion wih respec o he oher Balic counries forced he auhoriies o adop a currency board and he lias was linked o he US Dollar. In Lavia, afer an iniial period in which he emporary currency had a fixed pariy wih respec o he Russian rouble, in 1992 he auhoriies decided o adop a managed floa regime in order o preven he hyperinflaion experienced by Russia and hen he la was pegged o he IMF s Special Drawing Righs (SDRs). [5]

7 counry i and counry j ; ξ ij and υ ij are counry-specific weighs; i 0 represens he ineres rae of he reference counry and is an indicaor of he moneary policy sance prevailing in he world a ime. Assuming a linear specificaion for each equaion in (1), we have: or equivalenly: y = a y + b q + c i * * i i i i i i (2) y = a ξ y + b υ q + c i = η y + ψ q + c i i i ij i i ij ij i 0 ij i ij ij i 0 j= 0, j i j= 0, j i j= 0, j i j= 0, j i where ηij ai ξ ij and ψij bi υ ij Empirical implemenaion We follow Enders and Hurn (1994) and use he mulivariae specificaion of he five equaions in (2) where aggregae demand in each counry only depends on facors driving demand in he reference counry. As Appendix A shows, i is possible o obain he reducedform soluion for he four independen bilaeral real exchange raes vis-à-vis he reference counry: q = C y (3) 0 where C is a full rank marix. 4 5 Nex, we assume ha y evolves over ime according o a Vecor AuoRegressive (VAR) process of order p p y = l l + l= 1 y A y ε or, in is isomorphic Vecor Error Correcion (VEC) form where p 1 y y = 1 + l l + l= 1 y Π y P y ε, ε N (, ) 0 Σ (4) Σ ε is he ime-invarian variance-covariance marix associaed o he vecor of residuals ε. Combining condiion (4) and (5), we obain he k -variae baseline model used in he empirical analysis, which describes he join dynamics of he bilaeral real exchange raes vis-à-vis he reference counry: p 1 q q 0 = 0, 1+ l 0, l + l= 1 q Π q P q u (5) ε where u = C ε, q y A C= C A, and Π C= C Π. q l y l [6]

8 VEC modelling builds on he associaion beween he economic concep of long-run and he saisical concep of saionariy and focuses on he idenificaion of saionary linear combinaions of he daa, known as coinegraion vecors. In he presence of coinegraion q Π has reduced rank r k 4 < = and can be decomposed as Π = α β, where he marix α q conains he feedback coefficiens (loadings) and he marix β he r < 4 heory-based longrun relaionships o which he series converge, once all he effecs of ransiory shocks have been absorbed (Johansen, 1995). These coinegraing relaionships are hi by 4 r permanen shocks (he common rends). y q On he basis of he rank of marix Π, and, hus, of marix Π, i is possible o disinguish beween five differen cases, which can be associaed o a relevan economic hypohesis, as deailed in Table 1. All possible oucomes share he common feaure ha he join dynamics of he real exchange rae (he observed variable) closely mirror hose of domesic oupu (he relevan variables for policy consideraions on he feasibiliy of a common currency area). [TABLE 1] y Assume, for insance, ha p = 1 and A 1 is an ideniy marix. Sysem (4) simplifies o = + y I5 y 1 ε. In his case, all he elemens of he vecor y are uni roo processes, and he y q rank of marix Π, as well as of marix Π, will be equal o zero. In oher words, he only way o deal wih a saionary sysem [in erms of model (4) or (5)] is by firs-differencing. y Now, assume insead ha A 1 is a null marix: y Π will be equal o (minus) I 5, i.e. i will be a full-rank marix, consisenly wih he case of all real exchange raes being mean-revering processes. Finally, any inermediae resul beween he full and he null rank assumpion for y marix Π (or equivalenly, marix (1994) call he GPPP hypohesis. q Π ) represens a validaion of wha Enders and Hurn 3. Esimaion resuls 3.1. Daa descripion and model specificaion Monhly daa for he real exchange raes of he Euro, and he currencies of Esonia, Lavia and Lihuania vis-à-vis he US are used o esimae sysem (5) over he period 1993:1-2005:12. Boh nominal exchange raes and price daa for he US and he Balic counries are [7]

9 from he IMF s Inernaional Financial Saisics (IFS), while hose for he Euro area are from he Eurosa Newcronos daabase. The real exchange rae is defined as he produc of he nominal exchange rae (naional currency per US dollars) and he raio beween US and domesic prices. Thus, an increase (decrease) in he real exchange rae means a real depreciaion (appreciaion). All he variables are expressed in consan prices (base year 2000=1). As a preliminary sep, we es for uni roo behaviour of each of he four series. ADF (Dickey and Fuller, 1979) ess as well as uni roo ess allowing for unknown breaks are performed on he four series, boh in levels and firs differences (upper par of Table 2). 4 The deerminisic componen includes an inercep and, when saisically significan, a linear rend, while he number of lags is chosen such ha no residual auocorrelaion is eviden in he auxiliary regressions. Consisenly wih many sudies of he PPP hypohesis in ransiion counries (see, among ohers, Sarno and Taylor 2001 and Éger 2004), in each case, we are unable o rejec he uni roo-null hypohesis a convenional nominal significance levels, even when conrolling for breaks in he series. On he oher hand, firs-differencing he series appears o induce saionariy. The KPSS (Kwiakowski e al., 1992) saionariy ess, presened in he lower par of Table 2, corroborae hese conclusions. Given he evidence of I(1) -ness for all individual real exchange rae series, esing for coinegraion among hem is he logical nex sep. [TABLE 2] Esimaing (5) requires wo seps. Firs, he lag lengh p is chosen such ha he esimaed residuals resemble he muli-normal disribuion as closely as possible, his being an essenial requiremen for correc saisical inference. Second, he long-erm componen of he model is idenified on he basis of he race and he maximum eigenvalue es (Johansen, 1995). The general-o-specific procedure, wih maximum order of auoregression se o 12, suggess choosing p = 9. The resuls of he main univariae (Table 3, upper par) and mulivariae (Table 3, lower par) diagnosic ess indicae ha he esimaed residuals mach he muli-normal disribuion in a saisfacory way boh a he single equaion and he sysem level. 5 4 Criical values for hese ess are provided by MacKinnon (1996) and Lanne, Lükepohl and Saikkonen (2002), respecively. We have also carried ou alernaive uni roo ess (Philips and Perron, 1998) o check for robusness. The resuls are qualiaively similar (available from he auhors upon reques). 5 Alhough some deparures from normaliy and some ARCH effecs are found in he case of Lihuania, Gonzalo (1994) and Rahbek e al. (2002) have shown ha he esimaes of a VAR model are usually robus o hese forms [8]

10 [TABLE 3] Trace and maximum eigenvalue es saisics sugges he presence of hree coinegraion relaionships in he sysem a he 5 percen significance level [Table 4 - Panel (a)]. 6 In he remainder of he Table exclusion, saionary and weakly exogeneiy ess are repored. Tesing separaely he null hypohesis of each coefficien being equal o zero suggess ha all variables are saisically differen from zero [Panel (b)]. Furher, no variable is saionary by iself in he coinegraion space, consisenly wih he univariae uni roo and saionariy ess [Panel (c)]. Finally, excep for he Euro/US dollar equaion, here is no clear evidence of weak exogeneiy [Panel (d)]. [TABLE 4] 3.2. Modelling he long-run: he srucure of he β marix A key issue in he empirical invesigaion is esablishing wheher he coinegraion vecors can be idenified in erms of he srucure described in Table 1 above. If he resricions canno be rejeced by he daa, hen each vecor in he β marix validaes he PPP condiion for each Balic counries vis-à-vis he Euro area. This implies he following longrun for model (5): q01, q 02, 1 β q 0, 1 = q 03, q04, 1 Using a sandard LR raio es wih 3 degrees of freedom following a 2 χ disribuion, he es saisics (4.63), calculaed using he Barle small-sample correcion (wih an esimaed facor of 4.72), indicae ha he resricions are no rejeced by he daa a he usual significance levels (p-value of 0.20). 7 of misspecificaion. 6 The choice of he coinegraion rank is also robus o a graphical analysis of he recursive race ess. Since he race saisic is given by T j ln(1 λ i ), wih j = T,..., 1 T, i grows over ime as long as λi 0, while i mus be consan if λi 0. In pracice, he firs r race saisics should grow linearly, while he ohers mus be consan over ime. Graphs (no included, bu available from he auhors upon reques) show ha he firs hree saisics in fac grow linearly as expeced, while he fourh one is less clearly increasing. 7 Noe ha hese conclusions are robus o possible parameer insabiliy, as when we compue he LR es saisic recursively he resuls remain sable. Specifically, we performed he esimaion for he sub-sample 1993:1 o 1997:9, imposing he resricions on he hree vecors and compuing he value of he LR es saisic. Then we added recursively one observaion a a ime ill unil he end of he sample (2005:12) and in each sep we re-calculaed he value of he es saisic. Ploing hese values, we noe ha he resricions are suppored by 2 he daa, since he saisics are always below he value of he χ wih 3 degree of freedom. (The graph of he [9]

11 This is one of he key findings of he presen paper, as he exising lieraure usually concludes ha real exchange raes in he case of ransiion counries are no saionary (for a comprehensive review, see Éger 2004). 8 To model deviaions from PPP, many auhors invoke he dominance of Harrod-Balassa-Samuelson (HBS) effecs for hese economies, which, during he ransiion process, display high produciviy growh in he raded goods secor (see, among ohers, Coricelli and Jazbec 2004). 9 In he case of he Balic economies, De Broeck e Sløk (2001) argue ha even if produciviy gains in he radeable secor may lead o a real exchange rae appreciaion, his does no erode heir compeiiveness level because of he iniial undervaluaion of he naional currencies and of he process of conrolling inflaion. Moreover, Kocenda (2001) suggess ha he Balic counries show a higher degree of convergence boh amongs hemselves and wih he Euro area in he main macroeconomic fundamenals compared o oher groups of ransiion economies. Consequenly, he empirical resuls favouring he join PPP hypohesis vis-à-vis he Euro area could reflec boh he weak role played by he radiional facors (i.e. HBS effecs) and robus convergence of he macroeconomics fundamenals, which is he key condiion for GPPP and, hus, joining a currency union. Figure 1 presens he coinegraion relaionships from he R-model. 10 There appears o be a clearly idenifiable coinegraing relaionship in he case of Esonia, especially afer By conras he years are characerised by slighly higher variabiliy, corresponding o he firs phase of economic reform a he beginning of Similar consideraions apply o he Lihuanian case, alhough he period of high variabiliy appears o be longer (unil he end of 1999) because of a slower ransiion process. The graph of he coinegraing relaionship for Lavia is qualiaively similar o ha of Lihuania, he higher variabiliy in he firs years mos likely being relaed o he iniial currency peg o he Russian recursive LR es saisics is no included bu is available on reques). 8 In order o check he robusness of our findings, we have also carried ou he analysis in he conex of hree bivariae VEC models, each including one Balic counry and he real exchange rae of he Euro vis-à-vis he US Dollar. The general-o-specific procedure suggess an auoregression order of nine, one and six for he Esonia- Euro, Lavia-Euro and Lihuania-Euro model (in heir isomorphic VAR represenaions), respecively, and an unresriced consan for all sysems. For each model he race es saisic indicaes he presence of a unique coinegraing vecor a he 5 percen significance level. Imposing resricions of he form [1,-1] on each of hese vecors leads o a value of he χ 2 saisic (correced using he Barle facor) of 0.44 [0.80], 5.56 [0.06], 0.82 [0.36], respecively, where p-values are repored in squared brackes. These resuls are fully consisen wih he evidence repored in he main ex, giving furher evidence of he validiy of he PPP condiion for each Balic counries vis-à-vis he Euro area. 9 For an overview of he impac of he Balassa-Samuelson effec on long-run PPP deviaions, see Sarno and Taylor (2001). 10 The R-model is compued esimaing he VEC represenaion of he sysem deleing all dummies and he shor -run dynamics. The resul is a model where only he long-run properies of he daa are isolaed (see, Johansen, 1995). [10]

12 ruble and, subsequenly, o he IMF s SDRs wih he aim of prevening he hyperinflaion experienced by Russia. Only mos recenly has he la been pegged o he Euro. [FIGURE 1] 3.3. Adjusmen owards equilibrium Once he coinegraion space is idenified, he long-run properies of sysem (5) are analysed by looking a heir persisence profiles (Pesaran and Shin, 1996), which make i possible o assess how long he sysem akes o rever o is seady-sae pah, afer being hi by a sysem-wide shock. By consrucion hese profiles should end o zero as he number of simulaion periods increases only if he coinegraion vecor is genuinely saionary, while in he case of I (1) (or near inegraed ) series hese can be differen from zero for a long period. Figure 2 presens he absorpion pah of deviaions from he PPP relaionship beween each Balic counry and he Euro area, over a simulaion horizon of 60 monhs (5 years). 11 [FIGURE 2] In all cases, we observe convergence owards he seady-sae, wih he adjusmen process being compleed wihin he fifh year of he simulaion. The half-life of he deviaion from he seady-sae for Esonia and Lihuania is close o four monhs, while i is larger for Lavia (15 monhs). 12 Persisence profiles are also a useful ool o calculae convergence loss measures (CL ) for pair-wise comparisons of he speed of convergence, as poined ou in Girardi and Paesani (2008). Once he CL is compued, he null of equivalen loss beween he wo eniies of reference can be esed by means a sandard wo-sided -es. 13 Naural symmeric loss funcions are he absolue loss and he squared loss. The CL obained from an absolue loss over he chosen simulaion horizon for Esonia, Lavia and Lihuania are equal o 0.14, 0.24 and 0.09, respecively. The es of equaliy yields a p-value of 0.24 for he Esonia-Lihuania simulaion, while i is equal o 0.01 and 0.00 in he Esonia-Lavia and Lihuania-Lavia cases, respecively. 14 This confirms ha Esonia and Lihuania follow a similar dynamic pah, while 11 The size of all he shocks analysed in his secion is se equal o one sandard deviaion. 12 Half-life is defined as he number of monhs which have o pass before he deviaion from he seady-sae falls o half he size of he iniial shock. 13 To do his, we calculae he deviaion from he seady sae f a he simulaion horizon k. Given a nonnegaive loss funcion L, we define he CL as 1 * k * k k = 0 * L( f ), where k is a runcaion lag such ha f * A F-es on he variance raios indicaes ha all he disribuions are heeroscedasic. k k [11]

13 he absorpion process for Lavia is somewha slower relaive o he one of he wo oher Balic counries. 4. Modelling inerdependencies beween he Balic counries This Secion analyses possible spillovers in he adjusmen owards he long-run equilibrium condiion(s) by focusing on he srucure of he feedback marix α. 15 I also considers a srucural represenaion of he mulivariae ime-series model in order o ascerain he role of global and idiosyncraic shocks hiing he Balic counries Modelling he shor-run: he srucure of he α marix The shor-run dynamics of (5) are modelled using a parsimonious (subse) VEC model, obained dropping he parameers of he marices α and P q l wih p-values lower han a hreshold, 16 according o he Sequenial Eliminaion of he Regressors Tesing Procedure (SER/TP) proposed by Brüggemann and Lükepohl (2001). Specifically, he saisically significan parameers of α give useful informaion abou how our regional model moves around he long-run equilibrium pah. Moreover, he rows of α conaining only zeroes allow o idenify possible (weakly) exogenous variables. Table 5 repors he coefficiens esimaed by 3SLS. The LR es does no rejec he 80 zero-resricions. Of hese, only six concern he α marix; however, each regressor is presen in (a leas) one equaion of he sysem, which suppors he chosen model specificaion. The analysis of he elemens of he loading coefficiens marix allows o highligh some ineresing ε1 ε2 ε3 resuls: i) since α =α =α = 0, he bilaeral Euro/US dollar real exchange rae is a eu eu eu weakly exogenous variable (forcing variable) for he long-run parameers; ii) ee, lv and l are obviously affeced by he coinegraion residuals ( ε 1, ε 2 and ε 3 respecively) which idenify he PPP relaionships vis-à-vis he Euro area; iii) he (absolue) values of he feedback coefficiens indicae ha he speed of adjusmen owards equilibrium is higher for Esonia 15 This analysis of spillovers is consisen wih a siuaion where, alhough each real exchange rae may behave differenly in he long run, here may be imporan relaions among hem in he shor run reflecing similar macroeconomic condiions and/or ransiion processes. This propery is direcly relaed o he well-known noion of separaion and coinegraion developed by Konishi and Granger (1993), Granger and Swanson (1996) and Granger and Haldrup (1997). Furhermore, if some rows of he associaed feedback conain only zeros, hen i migh be possible o idenify weakly exogenous variables driving he sysem in he long run (see Pesaran e al., 2000). 16 The AIC crierion wih = 1.60 is used as a significance hreshold level for he shor-run parameers. This is moivaed by he idea ha, in he reducion process of he model, i is preferable o keep he coefficiens whose saisical significance is unclear. [12]

14 (abou 8 percen per monh); iv) furhermore, here is evidence of some influence of ε 1 and ε 3 on lv and ee, respecively. [TABLE 5] Overall, hese resuls sugges ha he Balic counries exhibi heerogeneous pahs of convergence owards heir own equilibrium, wih Lihuania appearing o be less affeced by deviaions from he long-run equilibrium condiion han he wo oher Balic counries, while Esonian reform policies seem o have insured a quicker ransiion process From a reduced-form o a srucural represenaion The model reducion process has wo furher implicaions. Firsly, dynamic simulaions may differ, even markedly, from hose derived from an unresriced model (Brüggemann and Lükepohl 2001). Secondly, dropping saisically coefficiens can improve he qualiy of he forecass generaed by he model (Clemens and Hendry, 2001, p. 119). Here we focus on he former issue, while he laer is discussed in he following Secion. As emphasised in he radiional OCA lieraure (see Aris, 2003), deecing he sources of shocks affecing an economic sysem has imporan implicaions: if economies are hi by dissimilar disurbances o he ones hiing heir parner counries, he cos of joining a currency union can be correspondingly large. Thus, we analyse o wha exen global, regional and domesic economic condiions affec domesic real exchange rae variabiliy, considered as proxies of oupu flucuaions. To do his, we carry ou forecas error variance decomposiion (FEVD), which aims a providing informaion on he relaive imporance of he forecas error variance of each shock as a funcion of he simulaion horizon. The reduced form residuals in model u and he srucural residuals v are linked hrough he relaionship u = B v, where B is a nonsingular marix (Warne, 1993). Rerieving he v s from u s requires he unique deerminaion of he k 2 = 16 elemens in B. In our idenificaion scheme, a firs se of 10 consrains arises from assuming ha srucural shocks are orhonormal. The coinegraion space gives rk ( r) = 3 addiional resricions and allows o disinguish ransiory shocks (hree in our case) from permanen (one) innovaions. The remaining 3 resricions are obained by imposing a recursive scheme on he marix of he ransiory shocks where he causal order of he variables is chosen according o he size of he adjusmen coefficiens esimaed previously. Thus, he causal order is he following: Lihuania, Esonia and Lavia. The permanen shock is derived from he permanen componen of he sysem (ha is, he [13]

15 common rend) and represens he global-exernal shocks ha hi in a symmeric way all Balic counries. By conras, ransien impulses hi in an asymmeric way each counry according o heir differen degree of inerdependency. Furhermore, emporary shocks are aggregaed so as o quanify he overall relevance of regional facors in explaining real exchange rae flucuaions. Table 6 shows he percenage of he variance of each variable of he sysem explained by global, regional and idiosyncraic shocks, where he laer are expressed as a percenage of regional impulses. The las column (mean) presens he average conribuion of he shocks over he enire simulaion period (60 monhs). [TABLE 6] As can be seen, he disurbance from he Euro area (he global shock), which represens he symmeric shock hiing he Balic region, is he main driving force of real exchange rae movemens for all Balic counries, especially in he case of Esonia, where i explains abou 97.6% of he forecas variance, compared o 88.4% in Lavia and 74.6% in Lihuania. In general, his shock accouns for a considerable percenage of he variance of he whole sysem (86.9%). The relaive imporance of regional shocks in explaining he dynamics of each real exchange rae differs across counries. Is size is negligible in Esonia (2.42%), while i is bigger in Lavia (11.5%) and even more so in Lihuania (25.25%). Moreover, for he laer counry he percenage of he regional shock due o he idiosyncraic componen is equal o 91%. This means ha he asymmeric shock plays a big role, while i is smaller for he oher wo counries. In summary, alhough he symmeric shock is he bigges source of he variabiliy of he real exchange rae for all he counries, he relaive imporance of regional shocks and of heir idiosyncraic componens varies considerably beween hem. 5. Robusness and exensions 5.1 Evidence from quarerly daa As a robusness check of our findings, we re-esimae model (5) using quarerly daa. Uni roo ess, even in he specificaion wih unknown srucural breaks in he deerminisic componen, and saionariy ess confirm ha he series are realisaions of inegraed [14]

16 processes of order On he basis of he general-o-specific procedure, he specificaion of our quarerly model includes hree lags (in he levels), consisenly wih he pre-esimaion period used in he monhly specificaion (nine lags in he levels). Table 7 summarises he main diagnosic ess. As before, deparures from normaliy are found in he case of Lavia, bu now no evidence of ARCH effecs in he residual is deeced in any equaion. [TABLE 7] Boh he race and he maximum eigenvalue saisics indicae ha here are hree coinegraion relaionships [see Table 8, Panel (a)], ha all variable are joinly significan in he coinegraing space, and ha no variable can be considered weakly exogenous and saionary by iself [Panel (b), Panel (c), and Panel (d), respecively]. [TABLE 8] The over-idenifying resricions discussed in Secion 3 above are sill valid a he quarerly frequency: he Barle-correced (wih esimaed correcion facor of 4.53) χ 2 - disribued LR es saisics is equal o 2.97 wih a p-value of This finding provides furher evidence of he saionariy of he bilaeral real exchange rae, and hus of he join validiy of he PPP condiion beween each Balic counry and he Euro area. 19 The persisence profiles ploed in Figure 4 are roughly similar in he case of he monhly esimaes. For all he equaions, he period required o absorb he shock compleely is five years, as in he monhly simulaions. In he case of Esonia, he half-life is close o 4 quarers, and greaer han ha shown by he monhly esimaes. However, in he oher wo coinegraion vecors, which represen he Lavian and Lihuania long-run equilibrium relaionships, he half-lives are close o 3 and 1 quarers respecively, very similar resuls o he earlier ones. The absolue convergence losses are equal o 0.20, 0.23 and 0.08 for Esonia, Lavia and Lihuania, respecively. The former wo are similar o hose obained in he monhly esimaes, while he laer (i.e. Esonia) is higher. This migh depend on he firs 17 The resuls (available on reques) are no repored for he sake of breviy. 18 The hree coinegraion vecors are ploed in Figure 3. As in he previous model wih monhly observaions, he Esonian vecor seems o be saionary, especially afer he firs period of ransiion, while he oher wo show higher variabiliy of he long-run equilibrium condiions, as a consequence of a slower ransiion process. 19 As before (see foonoe 8), we carried ou he analysis using hree bivariae VEC models in which we can sudy separaely each real exchange rae of he Balic counries and he real exchange rae of he Euro vis-à-vis he US Dollar. The lag lengh in he hree models for Esonia, Lavia and Lihuania suggesed by usual generalo-specific procedure is hree, wo and wo, respecively. We also include an unresriced consan in all models. The race es saisic indicaes he presence of a unique coinegraing vecor a he 5 percen significance level, confirming he resuls obained in he general model wih four variables. The resricions of he form [1,-1] are sill valid for he hree differen vecors, wih a value of he χ 2 saisic (correced using he Barle facor) of 0.13 [0.72], 2.66 [0.11], 1.63 [0.20], respecively (p-values in squared brackes). This furher confirms he robusness of he resuls discussed in he main ex, boh a he monhly and quarerly frequency. [15]

17 period of simulaion which in he case of Esonia seems o be characerised by higher variabiliy wih respec o boh he oher wo counries and he simulaion carried using monhly observaions. [FIGURE 4] Table 9 repors he coefficiens of he subse VEC model esimaed by 3SLS using he SER/TP mehod where saisically irrelevan parameers are deleed according o he AIC crierion wih a significance hreshold level of = The 26 zero-resricions are no rejeced by he daa, he p-value of he LR es saisic wih a 2 χ disribuion being equal o The resricions on he feedback marix α confirm ha he Euro real exchange rae is weakly exogenous; furhermore, spillover effecs seem o be richer, wih evidence of feedbacks in he case of Esonia and Lavia, bu no in he Lihuanian one. As before, he speed of adjusmen owards equilibrium is markedly higher for Esonia. [TABLE 9] In summary, robusness analysis confirms he main resuls obained from esimaing he base model wih monhly observaions. 5.2 Ou-of-Sample Forecasing In his Secion he ou-of-sample forecasing performance of he model is evaluaed in order o esablish wheher he esimaed subse VEC models can describe saisfacorily real exchange rae movemens for he Balic counries over he period 2006:1-2007:12. In paricular, we compare heir forecasing performance agains hree alernaive models: a similar VEC model wihou resricions on he shor-run parameers; a VAR including he hree real exchange raes of he Balic counries vis-à-vis he Euro; finally, a random walk 20. The firs comparison is wih a model also including he variables dropped from our chosen specificaion on he grounds of saisical insignificance. The VAR models 21 are esimaed o 20 For each of he hree real exchange raes, a random walk model wih drif is esimaed. The sample period goes from 1993:10 o 2005:12, and has been chosen for consisency wih he VEC models, where firs-differencing and he lag lengh chosen shoren he original sample by 9 observaions. 21 The choice of a VAR as an alernaive model follows direcly from he saisical properies of he hree Balic real exchange raes wih respec o he Euro. We consider a simple hree-variable sysem of he real exchange raes of he Balic currencies vis-à-vis he Euro, and we expec ha each variable included in he sysem is saionary. In order o es his ype of hypohesis, we esimae a VAR model wih nine lags (in he levels) and an unresriced consan erm. Then, we se up he Taylor and Sarno s (1998) mulivariae uni-roo es, labelled as [16]

18 evaluae he adequacy and he robusness of boh he GPPP-represenaion and he resricions on he coinegraing space. Finally, assessing he subse VEC model agains a random walk model gives us informaion on how well he daa are described by saionary processes raher han by uni roo behaviour. The daase available a ime 2005:12 (he las monh of he esimaion period) is used o projec he coinegraing relaions over he enire forecas horizon. Acual daa from 2006:1 o 2007:12 are used o evaluae he sysem forecass. Table 10 shows he resuls of he forecasing exercises for he real exchange raes of Esonia (par a), Lavia (par b) and Lihuania (par c). The mean square error (MSE) and mean average error (MAE) values for he subse VEC model are given in levels (column 1), while for he ohers, as in Clarida and Taylor (1997), we consider heir raio for he VEC model and for each alernaive model (column 3,4 and 5 in he able). Thus, a raio of less han one indicaes ha he forecasing performance of he subse VEC specificaion is superior o he alernaive ones. Moreover, p-values of he Diebold-Mariano es are also repored. [TABLE 10] For all hree subse VEC models, he values of he MSE and he MAE are increasing wih he size of he emporal window used for he forecas. Thus, for example, he value of he MSE (MAE) for Esonia rises from 1.29e-04 (9.57e-03) for he one-monh horizon o 4.03e- 03 (3.97e-02) for he weny-four-monh one. This is sill rue in he case of Lavia and Lihuania, where he values for he one-monh horizon are 4.64e-04 (1.74e-02) and 1.68e-04 (1.00e-02), while for he weny-four-monh horizon hey are 4.04e-03 (5.27e-02) and 1.24e- 03 (3.15e-02), respecively. The forecasing analysis for he Esonian real exchange rae shows ha he subse VEC model generally ouperforms he rival models. In paricular, only in he case of he one- and six-monh horizon do measure of forecasing accuracy indicae ha he unresriced VEC model is preferable. he JLR es, in which he null hypohesis is ha a leas one of he series in he sysem is non-saionary. As hey sugges, we compare he es saisics wih he criical values of a χ2(1) disribuion adjused by he facor (T/T(- p-k)) o ake ino accoun he finie sample bias (where p is he number of lags included in he VAR and k is he number of counries). The resuls (no repored) confirm ha here are hree saionary series, which can be viewed as he PPP condiions for each of he Balic counries vis-à-vis he Euro area. [17]

19 In he Lavian case, he resuls also sugges ha he forecasing performance of he subse VEC specificaion is superior. The raios of he MSE and MAE for he subse VEC and he unresriced VEC model is always less han one, while only in hree cases 22 i is bigger han one when comparing he resuls of he subse VEC model o hose of he VAR specificaion. The resuls for he Lihuania real exchange rae are less supporive of he subse VEC specificaion. The resriced VEC model always ouperforms he unresriced specificaion, bu he VAR model is found o be superior in mos cases. Neverheless, five ou of eigh imes he Diebold-Mariano es indicaes ha he values are no saisically differen. In all oher cases his es confirms he previous resuls, always suggesing ha he forecas accuracy of he subse VEC model is subsanially beer he raio being less han one. Finally, he subse VEC model generally beas he random walk model in he case of he Esonian and Lavian real exchange raes, while he forecasing accuracy of he naïve specificaion is always beer in he case of he Lihuanian equaion. In all cases, as expeced, he uni roo behaviour dominaes he saionary subse VEC specificaion as he forecasing emporal window increases (ha is, he value of he raio increases). Overall, he resuls of Table 11 provide srong suppor for he choice of he subse VEC model as he appropriae one for he real exchange raes of he Balic counries. 6. Conclusions This paper focuses on macroeconomic inerdependencies beween he Euro area and a group of hree ransiion counries, namely Esonia, Lihuania and Lavia. Is aim is o es, using a heoreical framework based on he GPPP hypohesis, if he ransiion process undergone by hese economies in recen years has made hem srong candidaes o join he Euro area in he near fuure. Coinegraion echniques are used o es he GPPP hypohesis beween each Balic counry and he Euro area. Persisence profiles and impulse responses are also compued in order o ake ino accoun he possible influence of global and regional shocks which hi he equilibrium condiions of each real exchange rae. The resuls sugges ha he GPPP hypohesis holds for each of he real exchange raes of he Balic counries over he period 1993:1-2005:12, confirming ha, as sressed De 22 Noe ha in he case of he 12-monh horizon he resuls are mixed. In fac, using he MAE crierion suggess ha he forecas performance of he resriced VEC model is superior o ha of he VAR one, while using he MAE crierion yields he opposie resul. [18]

20 Broeck e Sløk (2001), Harrod- Balassa-Samuelson effecs have played a modes rule during he ransiion process of hese economies, and ha insead here has been significan real convergence owards he Euro area. In paricular, we find evidence of more pronounced mean-reversion properies in he equaion describing he behaviour of he Esonian kroon - Euro real exchange rae, wih he presence of spillover effecs beween he equilibrium condiions, especially in he case of Esonia and Lavia. Quarerly daa produce qualiaively similar resuls, confirming he robusness of all our main findings. Moreover, forecas error variance decomposiion analysis shows ha symmeric shocks are he main driving force of he real exchange raes in he Balic counries, wih asymmeric shocks playing a more imporan role in explaining heir variabiliy in he case of Lihuania and Lavia (less so in Esonia), and ou-of-sample forecasing analysis generally shows ha he seleced subse VEC specificaions ouperform rival models of he real exchange raes of he Balic counries. I is imporan o noe ha he empirical validaion of he GPPP hypohesis is only one of possible crieria for an OCA - oher sudies have relied insead on measures such as rolling correlaions or on srucural VAR approaches o analyse he degree of synchronisaion of shocks (for an exensive lieraure review, see Fidrmuc and Korhonen 2006). The fac ha GPPP (or PPP as in our case) holds does no enail ha he economies are synchronised, bu i does imply ha he exchange raes are driven by economic fundamenals and share common rends in he presence of a high degree of convergence. Therefore, alhough his is only an implici convergence measure, i does sugges ha he ransiion process in he Balic economies has resuled in a sable and credible economic framework which makes hese counries srong candidaes for EMU membership. [19]

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