Srucural Breaks in he Real Exchange Rae and Real Ineres Rae Relaionship * Joseph P. Byrne and Jun Nagayasu 30 h Ocober 2008 Absrac: In his paper we empirically examine he relaionship beween he real exchange rae and real ineres rae differenials using recen economeric mehods robus o poenial srucural breaks. Generally, our sudy provides evidence of his relaionship in he long-run conex. More specifically, we firs focus on he UK-US relaionship, and ineresingly find limied evidence of his long-run relaionship using radiional mehods. Bu when an approach robus o endogenously deermined srucural breaks is employed, we find evidence ha he real ineres rae differenial is an imporan deerminan of he real exchange rae. Secondly, in order o invesigae he relevance of srucural shifs in a more global conex, we carry ou muliple counry analysis. While providing evidence of his long-run relaionship, European daa sugges ha he presence of srucural breaks is no very common across counries and is indeed counry-specific. Keywords: Real exchange rae; real ineres rae differenial; nonsaionariy; endogenously deermined srucural breaks; race ess JEL Classificaion: F31 Filename: JoeJun_Oc30_2008_GFJ * Byrne: Deparmen of Economics, Universiy of Glasgow, Glasgow, G12 8RT, UK, E-mail: <j.byrne@lbss.gla.ac.uk>. Nagayasu (Corresponding auhor): Graduae School of Sysems and Informaion Engineering, Universiy of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan, E-mail: <nagayasu@sk.sukuba.ac.jp>. We would like o hank Manuchehr Shahrokhi (edior) and anonymous referees for useful commens. However, all errors are ours. The second auhor received financial suppor from he Muraa Science Foundaion. 1
1. Inroducion A long-run relaionship beween he real exchange raes and real ineres rae differenial can be obained using he convenional equilibrium condiions ofen used in he inernaional finance lieraure. In paricular, Uncovered Ineres Pariy (UIP) and he Fisher Hypohesis can be considered as he saring poin of a heoreical link beween he real exchange raes and ineres raes. 1 A number of sudies have aemped o uncover evidence of an equilibrium relaion based on such an approach and provided mixed resuls (e.g., Campbell and Clarida 1987, Meese and Rogoff 1988 and Edison and Pauls 1993). A major concern among researchers is he low power of saisical ess o deec equilibrium relaionships in inernaional finance. Since a leas Perron (1989), i has been recognized ha incorrecly modelling economic variables as linear, when hey are subjec o subsanial, unusual and infrequen shocks, can affec he usefulness of saisical resuls. In paricular, convenional uni roo and coinegraion ess are biased owards he null when here is a srucural break in a ime series. Thus some recen evidence has highlighed he imporance of esing for breaks or non-lineariies when considering he real exchange rae-ineres rae relaionship. 2 For example, Nakagawa (2002) emphasizes non-lineariies in he relaionship beween real exchange raes and real ineres raes. Addiionally accouning for changing economic regimes and using a long hisory of daa (1921-2002), Kanas (2005) uncovers a relaionship beween he US/UK real exchange rae and he real ineres rae differenial. 1 Opimising models of exchange rae deerminaion are also suggesive of a link. See Obsfeld and Rogoff (1996). 2 Baxer (1994) also fails o find evidence of a saisical link beween real exchange raes and real ineres raes a he high frequency level, alhough in a more posiive vein of research finds more 2
In his paper we empirically examine wheher a long-run equilibrium relaionship exiss beween he real exchange rae and real ineres rae differenial. Therefore, in conras o Nakagawa (2002) and Kanas (2005), we emphasize he poenial nonsaionary characerisic of he daa, since here is widespread evidence of a nonsaionary real exchange rae, which is he failure of PPP, and a nonsaionary difference beween he real ineres raes across counries (Meese and Rogoff, 1988, and Edison and Pauls, 1993). For example, Kanas uses he Markov-Swiching Vecor Auo-Regressive model alhough he mehodology is primarily for saionary daa and addiionally presens evidence of a nonsaionary real exchange rae. In a similar view o our paper, Edison and Melick (1999) also consider he equilibrium relaionship beween he real exchange rae and real ineres rae differenial. They emphasize poenial nonsaionariy and also adjus for poenial srucural breaks by including shif dummies. Such an approach leads o evidence in favour of he exchange rae ineres differenial relaion. However, he dae of hese dummies is no endogenously deermined and he Johansen (1998) Trace es requires adjused criical values in he presence of srucural shifs (see Lükepohl, 2004). This paper is laid ou as follows. Secion 2 considers he heory relaed o he real exchange rae-ineres rae relaionship. Secion 3 considers our empirical mehodology. Secion 4 considers he daa used in his sudy, and presens and inerpres our empirical resuls. Secion 5 exends he analysis o oher indusrial counries using single counry and panel daa mehods in order o see if srucural breaks are common phenomena across counries. This paper ends wih Secion 6 ha summarizes our findings. evidence a he low frequency or business cycle level. 3
In shor, using muliple-equaion esimaion mehods robus o poenial nonsaionariy, we uncover resuls consisen wih he previous lieraure in ha here is no evidence of coinegraion in he UK daa when radiional linear mehods are employed. However, adoping an approach se ou by Saikkonen and Lükepohl (2000, 2002) and Lanne, Lükepohl and Saikkonen (2002, 2003) and uilizing more powerful coinegraion ess which are addiionally robus o he possibiliy of endogenously deermined srucural breaks, we find evidence of a long-run relaion. However, we cauion he significance of srucural breaks in a global marke. Our muliple counry analysis suggess ha while providing evidence of his long-run relaionship, he presence of srucural breaks is no very common across indusrial counries and hus is indeed counry-specific. 2. Theoreical Model In deriving an operaional equaion for he relaionship beween he real exchange rae and real ineres raes, we essenially follow Edison and Pauls (1993). 3 The wo main componens of his model are UIP and he Fisher pariy condiion. We se ou each of hese in urn before defining an esimable equaion. Firsly, we define he real exchange rae ( q ) as follows: q + * = s p p (1) where s is he naural logarihm of he spo nominal exchange rae (domesic currency 3 An alernaive approach would be o adop Dornbusch's (1976) sicky price model, as used for example by Nakagawa (2002). However, his approach assumes a saionary real exchange rae, which is inconsisen wih he approach we adop in he empirical secion of his paper, since we find evidence ha he real exchange rae is nonsaionary, even once we accoun for possible srucural breaks. In seing ou our model we illusrae ha he Dornbusch sicky price model is no a necessary componen 4
unis per uni of foreign currency), p and * p are he logarihm of domesic and foreign price indexes, respecively. The UIP assers ha wih open capial markes and perfec foresigh, expeced changes in he nominal exchange rae are equal o he differenial in he nominal ineres rae. When invesors are no risk neural, UIP can be exended o include he risk premium. E + * ( s+ 1 s ) = i i u (2) where i and i * are domesic and foreign nominal ineres raes, E s + 1 is he curren period expecaions of he nex period exchange rae, and u is he exchange risk premium. Consequenly subsiuing ou he expeced nominal exchange rae we have E q E p + E p s = i i + u + 1 + 1 + 1 (3) Addiionally we assume ha he expeced change in inflaion is as follows E Δ p + 1 = E p + 1 p (4) EΔp + = E p+ 1 1 p (5) Furhermore, he ex-ane 1-period real ineres rae is equal o he nominal ineres rae minus expeced inflaion: r = i EΔp +1 (6) r = i EΔp+ 1 (7) From hese equaions, we can obain he following expression. E q E Δp + p + E Δp + p s = r + E Δp r + E Δp + u + 1 ( + 1 ) ( + 1 ) ( + 1) ( + 1) (8) Finally, we obain an expression for he expeced changes in he real exchange rae of he pariy condiion under consideraion. 5
E q p + p s = r r + u +1 (9) E q q = r r + u +1 (10) q + = r + r + Eq+ 1 u (11) One operaional problem in equaion (11) is ha he expeced values of he real exchange rae are no readily available o researchers. Several proxies have been previously considered, for example, Meese and Rogoff (1988) sugges he cumulaive rade balances and a consan. Alernaively ime dependence in he expeced real exchange rae may be modelled by a shif dummy if he equilibrium does no change ofen. In iniially laying ou he model here for simpliciy we assume he expeced real exchange rae is consan, as also considered by Meese and Rogoff (1988), Edison and Pauls (1993) and Baxer (1994). Our failure o suppor he long-run relaionship calls for furher invesigaion abou he assumpion relaed o he expeced real exchange rae. Then, we obain from equaion (11). 4 q = r + α r + cons an + u * * α (12) The ime-varying risk premium, u, is an unobservable componen in his equaion and is assumed o be saionary. Equaion (12) serves as he basis of our esimaion approach. The main suggesion is ha he real ineres rae differenial is negaively relaed o he real exchange rae of he domesic currency (i.e. α < 0 and α > 0 ). 4 One could consider imposing homogeneiy or symmeric resricions on parameers in equaion (12). 6
3. Empirical Mehodology A number of mehodological poins have been emphasized in he empirical lieraure on exchange rae modelling which also influences our paricular approach. These include: poenial nonsaionariy of daa and is implicaions for idenifying long-run relaions; a concern wih he low power of es saisics (i.e. inabiliy o rejec a false null hypohesis of uni roo or no coinegraion) and aemps o improve he power properies of our es saisics by increasing he ime span or he cross secional coverage of our daa se; and finally an issue wih srucure breaks in ime series models. We shall briefly review each of hese issues in urn. The firs quesion is relaed o poenial daa nonsaionariy, for example he real exchange rae, which necessiaes empirical ess and esimaors robus o he challenges ha are raised. Empirical sudies have ofen uilised single-equaion or sysem-of-equaion coinegraion echniques o uncover evidence of equilibrium relaionships and o provide reliable long-run esimaors. In erms of he real exchange rae-yield differenial symbiosis, single equaion approaches include Campbell and Clarida (1987), Meese and Rogoff (1988) and Edison and Pauls (1993). However, failure o uncover evidence may be due o he power of saisical ess, firs raised in a univariae conex by De Jong e al. (1992). Due o a concern wih he low power of our es saisics, wo veins of lieraure evolved when considering paricular hypoheses in he exchange rae lieraure: expanding he sample span by expanding he ime series or he cross secional dimension of daa ses. Panel daa ses which have boh ime series and cross secional dimensions have been However, equaion (12) wihou parameer resricions is more general and is more appropriae 7
uilised o examine he exchange rae ineres rae relaionship. For example, a panel approach o esimaing he relaionship beween real exchange raes and real ineres raes is adoped by Chorareas and Driver (2001). They find relaively successful evidence in favour of he exchange rae-ineres differenial relaion alhough his is focused on he bilaeral relaionships beween small open economies and no he G7. MacDonald and Nagayasu (2000) also use panel coinegraion mehods and find more evidence in favour of he real exchange rae-ineres rae link. However, here may be imporan differences in esimaed coefficiens across cross secions of he panel which may induce bias in dynamic esimaion (see Pesaran and Smih, 1995). Alernaively Campbell and Perron (1991) propose ha exending he span of he daa se would be one way o improve he power of saisical ess. This has resuled in daa ses which exend beyond he pos-breon Woods period of floaing exchange raes (see for example, Lohian and Taylor, 1996). However, Campbell and Perron (1991) also sugges ha exending he ime dimension used in empirical sudies can lead o problems wih srucural breaks and hence furher problems wih he power of hese ess. This is he view poin elicied by Perron (1989) such ha when here are srucural breaks in a univariae ime series his may sugges ha he series is nonsaionary. Likewise, for a coinegraing vecor, o he exen ha here are breaks in he equilibrium relaionship his may resul in ess for no coinegraion acceping he null hypohesis ha here is no an equilibrium relaionship when in fac one exiss. Edison and Melick (1999) sugges breaks in he real exchange rae-real ineres rae relaionship are imporan, when using sysem-of-equaion saisically due o measuremen errors which likely exis in any empirical research. 8
ess for coinegraion. 5 Recenly, Saikkonen, and Lükepohl (2000, 2002) have proposed a sysems approach o esing for equilibrium relaionships beween variables which is based on a vecor auoregressive approach wih srucural shifs and also uilises Generalized Leas Square (GLS) derending. 6 We discuss his approach shorly. 4. UK-US Empirical Evidence 4.1. Daa Daa are obained from he Inernaional Moneary Fund's Inernaional Financial Saisics (IFS). 7 Our sample period covers monhly daa from 1973M1 o 2005M5. The UK pound-us dollar real exchange raes ( q ), as se ou in equaion (1), is in logarihmic form based on end-of-period raes (IFS line AE). Real ineres raes ( r ) are calculaed by subracing expeced inflaion from he shor run ineres rae (Money Marke Raes, IFS line 60b) expeced nominal ineres raes (i.e. r i E Δp + 1). We have wo measures of expeced inflaion, ex ane ( Δp + 1 ) and ex pos ( Δ p = ) inflaion which are based on he realised consumer price index (CPI, IFS line 64). 8 The UK is he domesic economy ( r ) whils he US is he foreign counry ( r * ). 5 Imporanly Edison and Melick (1999) do no use nonsandard criical values when presening heir resuls which we discuss furher below. 6 See also Ellio e al. (1996) for an examinaion of he improved power properies of nonsaionary ess which uilize GLS derending. 7 This was obained from he Economic and Social Daa Service <www.esds.ac.uk>. 8 Meese and Rogoff (1988) also use acual inflaion raes. 9
4.2. Poenial Daa Nonsaionariy and Srucural Breaks To iniially esablish ha we are dealing wih nonsaionary ime series, we implemen wo ypes of uni roo ess: he Augmened Dickey-Fuller es (see Dickey and Fuller, 1979) and Saikkonen and Lükepohl (2002) es, henceforh known as S&L. Among several oher ess, S&L propose he uni roo es wih a simple shif dummy. The basic equaion for his es wihou linear rend can be summarized using he following equaion for a ime series y y = μ + f ( θ) γ + x 0 (13) The error erm, x, follows a finie-order AR( p ) represenaion α ( L )(1 ρl) x = u where α( p 1 2 L ) = 1 α1 L... α p 1L and iid(0, σ ) u. The parameer, ρ, is, 1 < ρ 1 and ρ = 1 indicaes he uni roo process. The shif funcion, f (θ), will be defined shorly. This equaion in firs difference form is: Δ y = Δf ) γ + ( θ v (14) where v 1 = α( L) u. Thus, he esimaion for he parameer, η = ( μ0, γ ), is conduced by minimizing he generalized sum of squared errors of his equaion, which alernaively can be expressed as: 2 1 Q (, ) ( ( ) η ) p α θ = Y Z θ Cov( V / σu) ( Y Z( θ) η) (15) where Y y, Δy,..., Δy ] and Z = Z : Z : ] where Z = [1,0,...,0], = [ 1 2 T [ 1 2 Z3 1 Z 2 = [1,1,...,1], and Z 3 = [ f1( θ), Δf2( θ),..., Δf ( θ) ] T, and V = [ v1, v2,..., v ] T. So far lile is said abou he shif funcion. This paper focuses on a case where a 10
shif dae, T B, can be characerized as he shif dummy, d, and has he following form: 0 < TB f (θ ) d = (16) 1 TB Obviously, when he shif dae is known, we can readily esimae equaion (13). Lanne, Lükepohl, and Saikkonen (2002) suggess ha he deerminisic erm be esimaed by he GLS mehod, and hen apply he ADF ype es o he adjused daa ha can be obained by subracing he deerminisic componen from he original daa. However, his requires a priori knowledge of break daes. Thus, Lanne, Lükepohl, and Saikkonen (2003) propose a procedure given he lag order p. Their recommendaion is consisen wih minimizaion of smalles value of Q p and he shif dae is deermined by he one corresponding o he Q p. Like he ADF, a saisic for his es does no possess a sandard disribuion, hence criical values provided by Lanne, Lükepohl, and Saikkonen (2002) are used in order o evaluae he null hypohesis of he uni roo. The resuls from he uni roo ess are summarized in Table 1 where he appropriae lag lengh is deermined by he Akaike Informaion Crierion (AIC). 9 The ADF uni roo ess sugges ha we canno rejec he null of nonsaionariy for he real exchange rae and ex ane and ex pos real ineres raes for he UK and US. This is consisen wih evidence in Edison and Pauls (1993) and Chorareas and Driver (2001). 10 For he S&L uni roo ess, we find evidence of nonsaionariy for he real exchange rae and US real ineres raes. 9 Since he objecive of research a his sage is o consruc he general model, he AIC is used raher han ohers such as he Schwarz-Bayesian Informaion Crierion as suggesed by Lanne, Lűkepohl and Saikkonen (2002). 10 The overall conclusion from he S&L es is consisen wih ha from Perron's es (1997), which also akes ino accoun unknown regime shifs. 11
However, here is evidence of saionariy for UK real ineres raes. The nonsaionariy of a leas wo variables, he real exchange rae and he US ineres rae, ensures ha he long-run relaionship in equaion (12) is no necessarily unbalanced. Table 1 here Regime shif daes obained from he S&L es are also repored in Table 1. For he real exchange rae, he shif daes are 1985M3 which coincides wih he end of he srong dollar in he early 1980s. Tha was he period when he Plaza Accord was made in New York and whereby G5 member counries agreed o srenghen he dollar in order o comba US curren accoun deficis. For he UK ineres raes he endogenously deermined break daes are 1979M7 for ex ane inflaion and 1979M8 for ex pos inflaion, which coincides wih a new moneary policy regime in he UK and he Thacher Governmen. The break dae for he US ineres rae is 1980M12 and 1980M7, for ex ane and ex pos inflaion respecively, which again coincides wih a change in US moneary policy. Given our primary ineres in modelling he real exchange rae, he subsequen par of his paper considers a possible regime shif in he equilibrium rae in 1985M3 for boh sysems (i.e. wih eiher ex ane or ex pos measures of he real ineres rae). Thus our shif dummy can be defined as for and oherwise. I should be noed ha he inroducion of his dummy in he mulivariae seing is also suppored by Bai, Lumsdaine and Sock (1998) Sup-W and Exp-W ess, which are a saisical mehod for deecing and idenifying common srucural breaks in he mulivariae ime-series (VAR). The resuls from his es show he presence of srucural shif in 1985M5 wih a 90 percen confidence inerval of 12
1983-86. 11 Therefore, we reain 1985M3 as our break dae in he subsequen analysis, since his is well wihin his confidence inerval, and also coincides wih he end of he prolonged appreciaion of he dollar, and a period of susained foreign exchange inervenion by he Federal Reserve Bank of New York on he eve of he Plaza Agreemen (see Bordo and Schwarz 1990). Finally, in order o ensure ha our exchange rae conains a leas one saisically significan srucural shif, we implemen muliple regime shif ess developed by Bai and Perron (1998). Amongs he ess hey proposed, his paper employs so-called double maximum ess (UD max and WD max ess) which examine he null hypohesis of no regime shif agains he alernaive of he unknown number of shifs. In addiion, he SupF( i + 1 i ) es, which analyzes he null of i regimes agains i+1 regimes where i=1 o 4, is employed in order o sudy he number of regime shifs in he exchange rae. Then, we find evidence of a leas one shif according o he double maximum ess and he exisence of only one shif in he daa from he SupF es (Table 2). 4.3. Evidence of Coinegraion Table 2 here Given he evidence in he previous secion suggesing ha our daa are nonsaionary, we analyse he possibiliy of a long-run relaionship beween he real exchange rae and real ineres raes using nonsaionary mehods. In paricular, we employ hree coinegraion ess: he Johansen (1988, 1995) and he Saikkonen and Lükepohl 11 However, his resul should be inerpreed wih cauion since here is a possibiliy ha our daa in he VAR may no be saionary. We have also invesigaed possible shifs in he VAR using he firs difference of he daa. However, we failed o obain he resuls because of he singulariy problem. 13
(2000) Trace ess wih and wihou srucural breaks. The Johansen es is he sandard approach o es for coinegraion wihin a sysem of equaions. The Johansen s Likelihood Raio (LR) saisics are non-sandard under he null, and are dependen on he size of K - r (where K is he number of variables and r is he number of coinegraing vecors under he null hypohesis) and he composiion of deerminisic erms. We focus on he more convenional Trace es saisic. LR Trace K ( r) = T j = r + 1 log(1 λ j ) (17) and λ j are he smalles eigenvalues of he corresponding deerminan equaion and T is he ime span. While Johansen (1995) provides criical values for his es, including he shif dummy in he sandard es requires a compuaion of he disribuion for he saisics ha should differ from he one provided by Johansen. In paricular, Edison and Melick (1999) use a shif dummy wihin he Johansen-ype approach and find greaer evidence of he real exchange rae-real ineres rae yield differenial nexus. However, hey do no make allowance for he non-sandard disribuion of heir saisics when here is a shif dummy. 12 We ake accoun of hese difficulies using he mehods developed by Saikkonen and Lükepohl (2000). Consider he DGP of he daa wih shif dummy y d + x = μ 0 + δ (18) The shif dummy, d, has he same definiion as before, and hus he shif dae idenified in he uni roo es is used for he coinegraion sudy. Then, a VECM can be 12 See Lűkepohl (2004) for a deailed discuss of hese issues. 14
expressed as: Δ y p 1 p 1 1 y = v + Π ΓjΔy + γ jδd j + d + 1 1 j= 1 j= 0 u (19) where v = Πμ0 and Π = α[ β : θ], where θ = β δ. Table 3 here Firsly we presen resuls based on radiional mehods which are consisen wih much of he previous evidence from he lieraure. The resuls from he Johansen Trace es (1988, 1995) are shown in Table 3. We incorporae a consan in he coinegraing vecor. 13 This model for boh ex ane and ex pos ineres raes is consisen wih lile visual evidence of a deerminisic rend in he exchange rae or ineres rae daa. Table 3 provides no evidence of coinegraion in our sysem based on he Johansen Trace es, wih p-values from Trenkler (2004) a he five percen, or indeed en percen, significance level. 14 Table 4 here The resuls from he S&L Trace es wihou a shif dummy are repored in Table 4. We find somewha more evidence of an equilibrium relaionship beween our hree variables (i.e. a he seven percen significance level and welve percen significance level for ex ane and ex pos real ineres raes o rejec he null of no coinegraion) han he Johansen es. However, here is no paricularly srong evidence supporing he exisence of 13 There is lile evidence ha he real exchange rae has a endency o proxy he behaviour of a deerminisic rend, hence we exclude a ime rend from he esimaion. 14 Addiionally we experimened wih bivariae relaionships and found we could no rejec he null hypohesis of no coinegraion a he five percen level, following he approach of Johansen and Juselius (1992). This was also he case wih he S&L Trace ess wih and wihou a dummy. Wu and Founas (2000) es real ineres rae pariy using coinegraion mehods ha allow for srucural breaks and uncover mixed evidence of real ineres rae convergence agains he US. In conras o our sysem of equaions approach, Wu and Founas use single equaion mehods. 15
he long-run relaionship under consideraion. Therefore, a shif dummy may be imporan as suggesed by he break in he real exchange rae from Table 1 and Table 2, he possibiliy of a shif in he equilibrium exchange rae (see he discussion in Secion 1), he economeric heory of Perron (1989) and evidence in Edison and Melick (1999). 15 The shif dummy was derived from he esimae of a break dae for he real exchange rae from he esimaed confidence inerval, using he mehods of Bai e al. (1998), and from Table 1 (i.e. 1985M3). Table 5 presens resuls for he S&L es incorporaing a shif. Unlike he sandard Johansen es and also he uncorreced S&L es, we find some evidence of coinegraion beween he real exchange rae and real ineres raes for he ex ane real ineres rae a he five percen level and for he ex pos real ineres rae a he six percen level. Thus, one of reasons for he poor performance of he real ineres rae differenial in explaining real exchange rae movemens repored in previous sudies is due o lack of consideraion of regime shifs in he daa. 16 Table 5 here 4.4. Esimaing he Long-Run Relaionship and Furher Sabiliy Tess Given evidence of coinegraion, we can esimae our sysem in Vecor Error Correcion Model (VECM) and obain long-run esimaes for he real exchange rae-ineres rae relaionship. 17 The VECM is conduced for real exchange raes based on one 15 We incorporae one shif dummy in our empirical model, Hansen (2001) is of he view ha once we consider more han one break he difference beween saionary processes wih breaks and non-saionary process becomes less worhwhile. This argumen can be exended o coinegraing relaionships. 16 We experimened wih he inclusion of seasonal dummies and he resuls remained quaniaively he same. 17 Here, in addiion o he model wih he ex ane real ineres rae, we also consider he model wih he ex pos real ineres rae since he p-value obained from he S&L es wih a shif dummy (Table 5) is very close o five percen. 16
coinegraing vecor, and is esimaed by he wo-sage mehod proposed by S&L. The firs sage involves he esimaion of he long-run relaionship. Since only one coinegraing relaionship is found from he S&L es, his relaionship is obained in he conex of he single equaion of he VECM which is esimaed by he OLS, and is re-parameerized by normalizing he coefficien of he real exchange rae. The second sage involves he esimaion of he whole sysem by he OLS which includes he coinegraing vecor specified in he firs sage as well as exogenous variables. Our esimaes for he long-run coinegraing vecor are presened in Table 6. The appropriae lag orders are deermined by he AIC, and -saisics are repored in parenhesis. Table 6 here These esimaes are consisen wih he exchange rae ineres differenial relaionship. The fac ha he parameer for he exchange rae is normalized in he long run relaionship makes inuiive sense; he real exchange rae is negaively (posiively) correlaed wih UK (US) ineres raes. 18 This suggess ha an increase in UK real ineres raes is associaed wih a UK pound appreciaion. In addiion, he esimaes for he coinegraing parameers now exhibi sabiliy. The sabiliy of heir relaionship has been checked using he recursive mehods developed by Johansen (1995) and Hansen and Johansen (1999) (see Figures 1 and 2). Simple recursive esimaes of eigenvalues are shown wih a 95 percen confidence inerval (Johansen, 1995) which can be used o examine he exisence of coinegraion over ime. A more formal es of consancy of eigenvalues is he τ saisic (Hansen and Johansen, 1999) which analyzes he null of 18 For he UK-US real exchange rae Chorareas and Driver (2001) find a coefficien of -0.021 on he 17
model sabiliy. Since hese recursive eigenvalues and τ saisics are fairly sable and below he criical value respecively, we can conclude ha our coinegraing parameers are reliable since hey are based on a sable model. 5. Muliple Counry Evidence 5.1. Daa To wha exen are srucural breaks significan in oher pairs of counries? In his secion we examine muli-counry and panel evidence on he relaionship beween he real exchange rae and real ineres rae differenials, aking accoun of poenial srucural breaks. Our sample of counries includes Ausria, Belgium, Canada, Finland, France, Germany, Ialy, Neherlands, Norway, Spain, Sweden and Swizerland. We use daa beween 1978M1 o 1998M12. This sample was chose o have a balanced daa se, wih a number of inernaional currencies and he span was limied by he commencemen of European Moneary Union. Our daa source is he IFS. To consruc he real exchange rae we use end of period bilaeral exchange rae via-a-vis US dollar and also use he CPI. For he real ineres rae we use money marke ineres raes and inflaion based on he CPI. Here, we focus on he relaionship beween he real exchange rae and ex pos real ineres rae spread. 5.2. Resuls In Table 7, we firsly examine wheher we can rejec he null hypohesis of nonsaionariy for our muli-counry ime series, using he ADF and Saikkonen-Lükepohl ess. Given ha we consisenly find evidence of nonsaionariy in he real exchange rae ineres rae differenial based on linear models and CPIs. 18
and ex pos real ineres rae in Table 7 and a nonsaionary US real ineres rae (Table 1), i is appropriae o use nonsaionary mehods o approach his quesion. The weak evidence of saionariy provided for some series (i.e. hree ou of 48 ess) is consisen wih a reasonable nominal size for such a large number of uni roo ess. Wih regards o he locaion of srucural breaks, many counries (i.e. Ausria, Belgium, Germany, Neherlands and Spain) experienced a srucural break in early 1991 probably reflecing he effecs of Germany reunificaion. Ialy, Sweden and Finland all experienced a srucural break in he real exchange rae a he ime of he 1992 ERM crisis. Table 7 here In Table 8, we consider wheher here is evidence of a long-run relaionship beween he real exchange rae and relaive real ineres raes in our large sample of counries. Using he convenional Johansen es, we find evidence of a coinegraing relaion for he majoriy of counries (9 ou of 12 cases) a he 10 percen significance level. This resul is more favorable o he real exchange rae-ineres rae relaionship han previous sudies and is aribuable o he recen economic and financial inegraion paricularly in Europe. However, of he hree cases where no coinegraion is obained, we could find a coinegraion relaionship on one occasion (Swizerland) when we ake accoun of breaks using he S&L es. This suggess ha here is a degree of heerogeneiy for our sample of counries over his paricular sample period. The real exchange rae-ineres rae spread relaionship does no seem o hold in Ausria and Neherland. This may be because hese counries moneary condiions were closely aligned wih Germany. Including he UK invesigaed in Secion 4, we sudied 13 European counries and could 19
obain a coinegraing relaion in 11 counries. Thus our evidence seems o sugges he long-run relaionship beween he real ineres rae and ineres raes alhough he srucural shif may no be a very prevailing phenomenon across counries. Table 8 here Indeed, when we uilised Weserlund (2006) panel LM es saisic which akes accoun of srucural breaks in a panel framework, we rejeced he null hypohesis of a coinegraing vecor for all counries agains a null hypohesis of no coinegraing vecor for some counries. Tha is o say he es saisic (38.219 and 32.096 for Fully-Modified OLS and Dynamic OLS respecively) was greaer han he 5 percen criical value of 1.64. 19 In he ligh of Table 8, his rejecion of homogeneous panel coinegraion may well be due o heerogeneiy in our sample of counries. In conras UK Serling may have a sizable concordance wih he dollar for our sample period, while having pursued European inegraion for only a shor period during he enire sample which subsequenly failed in he ERM collapse (see Blake and Byrne, 2002). In shor, our muli-counry analysis suggess ha he real exchange rae-ineres rae spread relaionship can be viewed as a long-run equilibrium condiion. This is confirmed by counry-specific and panel daa mehods. While his condiion holds in mos indusrial counries wihou consideraion of srucural breaks, hey are imporan in some counries like Swizerland and he UK. Thus imporance of srucural breaks seems o be counry-specific. 19 We were unable o rejec he null hypohesis of panel coinegraion using Weserlund (2006) panel 20
6. Conclusion There has been subsanial ineres in inernaional pariy condiions in inernaional finance, in paricular, ineres in wheher here is a relaionship beween he bilaeral real exchange rae and real ineres rae differenial. The findings of previous sudies are mixed, bu more consisen and supporive evidence is repored when srucural breaks are aken ino accoun. Breaks are imporan when using poenial nonsaionary daa since sandard ess may sugges ha here is no equilibrium relaionship. Due o problems wih low power wih exising es saisics, we uilize recen innovaions in ess for coinegraion which ake accoun of breaks, in paricular he mehods of Saikkonen and Lükepohl (2000, 2002). We iniially examine he UK/US daa and confirm he resuls from he previous lieraure using linear mehods of no evidence of a real exchange rae-real ineres rae differenial relaion. However, once srucural breaks are aken ino accoun, we find much sronger evidence of an equilibrium relaionship beween he pound-dollar real exchange rae and he differenial beween UK and US real ineres raes. For example, here is evidence of one coinegraing relaionship, and he model has reasonably sized, reasonably signed and significan long-run parameers. These are imporan resuls, we believe, given he widespread pracice of uilizing longer daa ses which may poenially encompass differen policy regimes and changes in economic srucure. However, he imporance of srucural breaks seems raher differen among counries. In order o check he relevance of srucural shifs in a more global conex, we exended our sudy o include oher indusrial counries. Our counry-specific and panel LM es even when we allowed for up o hree srucural breaks. 21
daa sudies show ha while he exchange rae-ineres rae relaionship exiss in mos counries, he imporance of srucural breaks are less pronounced in addiional (i.e., non-uk) counries since his relaionship is suppored even if srucural breaks are no considered. Since mos addiional counries are European, our findings would appear o highligh one disinguishing feaure of he Briish economy in Europe. Finally, i should be noe ha our finding is based on he heoreical specificaion which is probably he mos resricive because he expeced real exchange rae is assumed o be consan. The inroducion of he ime-varying expeced rae, which we expec o move more in line wih he acual rae, will probably provide sronger evidence of he relaionship beween he real exchange rae and ineres rae spread. 22
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Table 1: ADF and Saikkonen and Lükepohl Uni Roo Tess Tes saisic ADF S&L Shif dae q -2.311 (1) -2.460 (1) 1985M3 Wih ex ane inflaion r -2.549 (12) -3.161 (12) 1979M7 r -1.742 (11) -1.410 (11) 1980M12 Wih ex pos inflaion r -2.279 (12) -3.656 (12) 1979M8 r -1.826 (12) -1.540 (12) 1980M7 5% Criical value -2.860-2.880 Noes: Sample period 1973M1 o 2005M5. Lag lenghes in parenheses (.) are deermined by he Akaike Informaion Crierion wih a maximum of 12 lags. Asympoic criical values a he 5% level for he ADF es are from Davidson and MacKinnon (1993). Criical values a he 5% level for he Saikkonen and Lükepohl (2002) S&L es are from Lanne e al. (2002). A consan is included in he boh uni roo ess. 26
Table 2: Muliple Regime Shif (Bai-Perron) Tes for he Real Exchange Rae Tess Saisics Criical values 5% 10% UD max es 7.970 8.880 7.460 WD max es (5%) 15.004 9.910 -- WD max es (10%) 13.872 -- 8.200 Sup( i + 1 i ) es i =1 1.255 8.580 7.040 i = 2 3.338 10.130 8.510 i = 3 0.305 11.140 9.410 i = 4 0.016 11.830 10.040 Noes: Sample period 1973M1 o 2005M5. The rimming weigh of 0.15 is used for calculaing he saisics. The heerogeneiy and auocorrelaion consisen residuals are obained using Andrews mehod. The criical values are provided in Bai and Perron (1998). 27
Table 3: Johansen Trace Tess Null Hypohesis H : r 0 H : r 1 H : r 2 Lag 0 = 0 = 0 = Wih ex ane inflaion q, r, r 31.86 [0.109] 11.59 [0.495] 5.37 [0.255] 12 r, r 10.94 [0.556] 3.50 [0.503] -- 12 q, r 13.72 [0.317] 5.47 [0.244] -- 12 q, r 16.38 [0.160] 4.42 [0.365] -- 12 Wih ex pos inflaion q, r, r 27.67 [0.260] 10.79 [0.570] 4.80 [0.317] 12 r, r 9.15 [0.724] 2.67 [0.650] -- 12 q, r 12.76 [0.392] 4.67 [0.333] -- 12 q, r 14.31 [0.275] 4.32 [0.379] -- 12 Noes: Sample period 1973M1 o 2005M5. P-values are in square brackes [.] for he Johansen Trace es and are based on criical values from Johansen (1995). Lag lenghs of he VARs are deermined by he Akaike Informaion Crierion wih a maximum of 12 lags. A consan is included in he coinegraing vecor. 28
Table 4: The Saikkonen and Lükepohl Trace Tes Wihou Regime Shifs Null Hypohesis H : r 0 H : r 1 H : r 2 Lag 0 = 0 = 0 = Wih ex ane inflaion q, r, r 23.20 [0.066] 5.37 [0.522] 0.31 [0.638] 12 r, r 6.41 [0.393] 0.71 [0.454] -- 12 q, r 7.27 [0.304] 0.04 [0.880] -- 12 q, r 5.27 [0.535] 1.69 [0.226] -- 12 Wih ex pos inflaion q, r, r 21.24 [0.115] 4.90 [0.585] 0.31 [0.639] 12 r, r 3.72 [0.749] 1.55 [0.249] -- 12 q, r 6.74 [0.357] 0.03 [0.910] -- 12 q, r 5.25 [0.538] 1.40 [0.276] -- 12 Noes: Sample period 1973M1 o 2005M5. P-values are in square brackes [.] and are based on Trenkler (2004) which are in urn based on criical values for he Trace es from Saikkonen and Lükepohl (2000). This es rejecs he null hypohesis of r=i where he p-value is less han 0.05. Lag lenghs are deermined by he Akaike Informaion Crierion wih a maximum of 12 lags. A consan is included in he coinegraing vecor. 29
Table 5: The Saikkonen and Lükepohl Trace Tes Wih Regime Shifs Null Hypohesis H : r 0 H : r 1 H : r 2 Lag 0 = 0 = 0 = Wih ex ane inflaion q, r, r, d85m 3 25.66 [0.031] 7.67 [0.268] 0.54 [0.523] 12 r, r, d85m 3 8.18 [0.226] 0.37 [0.607] -- 12 q, r, d85m 3 11.92 [0.057] 0.95 [0.379] -- 12 q, r, d85m 3 11.45 [0.069] 3.40 [0.077] -- 12 Wih ex pos inflaion q, r, r, d85m 3 23.58 [0.059] 7.07 [0.323] 0.91 [0.390] 12 r, r, d85m 3 5.24 [0.539] 1.01 [0.362] -- 12 q, r, d85m 3 10.26 [0.108] 1.24 [0.308] -- 12 q, r, d85m 3 10.94 [0.084] 5.63 [0.021] -- 12 Noes: Sample period 1973M1 o 2005M5. P-values are in square brackes [.] and are based on Trenkler (2004) which are in urn based on criical values for he Trace es from Saikkonen and Lükepohl (2000). This es rejecs he null hypohesis of r=i where he p-value is less han 0.05. Lag lenghs are deermined by he Akaike Informaion Crierion wih a maximum of 12 lags. D85M3is a shif dummy which is zero before 1985M3 and one hereafer. A consan is also included in he coinegraing vecor. 30
Table 6: Esimaes of Coinegraing Vecor Ex ane Ex pos q 1.000 1.000 r 0.019 (2.256) 0.015 (1.670) r -0.043 (-2.791) -0.040 (-2.464) d 85M 3 0.031 (0.364) 0.070 (0.805) consan -4.549 (-63.478) -4.570 (-61.101) Noes: Sample period 1973M1 o 2005M5. Lag lenghs are deermined by he Akaike Informaion Crierion. The -saisics are in square brackes [.], and d85m3is a shif dummy which is zero before 1985M3 and one hereafer. Table 7. ADF and Saikkonen and Lükepohl Uni Roo Tess ADF S&L q r q r Ausria -1.524(0) -2.067(11) -1.183(0) [1991M3] -1.868(11) [1983M6] Belgium -1.756(0) -2.606(12) -1.495(0) [1991M3] -1.573(12) [1984M3] Canada -0.863(11) -3.169(11)* -1.216(11) [1982M6] -2.716(11) [1980M12] Finland -1.604(0) -1.299(11) -1.542(0) [1992M9] -1.668(11) [1983M12] France -1.653(0) -2.057(11) -1.677(0) [1982M6] -2.455(11) [1982M11] Germany -1.667(0) -2.764(11) -1.319(0) [1991M3] -2.353(11) [1993M1] Ialy -1.675(1) -2.028(12) -1.340(0) [1992M9] -2.498(12) [1980M2] Neherlands -1.864(0) -1.401(11) -1.555(0) [1991M3] -1.449(11) [1987M3] Norway -1.978(0) -1.546(12) -1.661(0) [1986M5] -1.065(11) [1993M1] Spain -1.292(0) -3.095(12)* -1.129(0) [1991M3] -2.1846(12) [1986M10] Sweden -1.641(1) -2.468(11) -1.428(1) [1992M11] -1.4919(11) [1991M3] Swizerland -1.706(0) -1.812(11) -1.647(0) [1978M11] -3.599(11)* [1982M11] 5% Criical Value = -2.860 5% Criical Value = -2.880 Noes: Sample period 1978M1 o 1998M12. Lag lenghs in parenheses (.) are deermined by he Akaike Informaion Crieria wih a maximum of 12 lags. Significance a he five percen level is indicaed by an aserisk (*). Asympoic criical values a he five percen level for he ADF es are from Davidson and MacKinnon (1993). Criical values a he five percen level for he Saikkonen and Lükepohl (2002) S&L es are from Lanne e al. (2002). A consan is included in boh he uni roo ess. We use ex pos ineres raes. Shif Dae is in square brackes [.]. 31
Table 8. Johansen and S&L Trace Tes for Coinegraion Null Hypohesis H 0 :rank=0 H 0 :rank=1 H 0 :rank=2 Dummy Lag Johansen Trace Tes Ausria 12.71 [0.68] 10.72 [0.58] 3.89 [0.45] -- 12 Belgium 197.38 [0.00] 77.32 [0.00] 3.31 [0.53] -- 1 Canada 32.28 [0.09] 7.65 [0.85] 0.95 [0.94] -- 12 Finland 43.13 [0.00] 18.83 [0.08] 6.28 [0.18] -- 12 France 40.48 [0.01] 18.89 [0.08] 4.79 [0.32] -- 7 Germany 195.27 [0.00] 79.22 [0.00] 2.82 [0.62] -- 1 Ialy 36.29 [0.04] 14.57 [0.26] 5.61 [0.20] -- 12 Neherlands 20.52 [0.69] 10.46 [0.60] 3.15 [0.56] -- 12 Norway 40.84 [0.01] 17.76 [0.11] 5.30 [0.26] -- 12 Spain 32.47 [0.09] 16.03 [0.17] 4.56 [0.35] -- 12 Sweden 33.09 [0.08] 15.94 [0.18] 7.44 [0.11] -- 10 Swizerland 22.02 [0.60] 11.27 [0.52] 4.02 [0.42] -- 10 S&L Trace Tes Ausria 12.14 [0.70] 2.42 [0.91] 2.07 [0.18] 1991M3 12 Neherlands 17.56 [0.28] 8.89 [0.18] 3.98 [0.05] 1991M3 12 Swizerland 41.82 [0.00] 29.75 [0.00] 2.57 [0.13] 1978M11 3 Noes: Sample period 1973M1 o 2005M5. P-values are in square brackes [.] and are based on Trenkler (2004) which are in urn based on criical values for he Trace es from Saikkonen and Lükepohl (2000). This es rejecs he null hypohesis of rank = i where he p-value is less han 0.05. Lag lenghs are deermined by he Akaike Informaion Crierion wih a maximum of 12 lags. A consan is also included in he coinegraing vecor. 32
Figure 1: Sabiliy Tes wih he Ex Ane Ineres Raes A. Recursive eigenvalues B. τ-saisics Figure 2: Sabiliy Tes wih he Ex Pos Ineres Raes A. Recursive eigenvalues B. τ-saisics 33