Current Account Sustainability in Seven Developed Countries

Transcription

1 Journal of Economic and Social Research 7(2), 4780 Curren Accoun Susainabiliy in Seven Developed Counries Fikre Dülger and Zeynel Abidin Ozdemir Absrac. This paper is an aemp o examine he G7 susainabiliy properies of curren accouns of seven developed counries, using a mehodology based on fracional processes. The purpose of his sudy is o es for he susainabiliy of curren accoun deficis in seven developed counries for he 1974:12001:3 period. The resuls indicae ha all counries curren accoun is covariance nonsaionary and hree counries (France, Ialy and Canada) curren accouns are mean revering so ha hey are susainable in he long run, while hose of Germany, UK, US and Japan are no mean revering and are unsusainable. These resuls should also signal a warning o crediors and policymakers, unless here are policy disorions or permanen produciviy shocks o he domesic economies. Furhermore, persisen deficis may lead o increased domesic ineres raes o arac foreign capial and, in addiion o his, he accumulaion of exernal deb owing o persisen deficis will imply increasing ineres paymens ha impose an excess burden on fuure generaions. JEL Classificaion Codes: F32, C22. Keywords: Curren Accoun, Long Memory Assisan Professor (Corresponding auhor), Faculy of Economics and Adminisraive Sciences, Deparmen of Economics, Cukurova Universiy, Balcali, Adana, Turkey. Tel.: +(90) (151); fax: +(90) address: fdulger@cu.edu.r. Assisan Professor, Deparmen of Economics, Gazi Universiy, Beşevler, Ankara, Turkey. *** We are indebed o anonymous referees for heir helpful suggesions and commens. Any remaining errors are our responsibiliy.

2 48 Fikre Dülger and Zeynel Abidin Ozdemir 1. Inroducion The curren accoun for individual counries is a baromeer for boh policymakers and invesors as i represens an indicaor of economic performance (Baharumshah e al. 2003, Goldberg, e al. 1995). Policymakers and invesors are ineresed in he aggravaion of curren accouns; and hey believe ha he curren build up of claims on he counry by foreigners violaes he solvency condiion wih respec o he res of he world. However, economiss are more ineresed in he counry s ineremporal solvency consrain han in indicaing he size of curren accoun deficis a any paricular poin in ime. This consrain emphasizes he longrun pah of he curren accoun (Hused, 1992; Wu e. al., 1996). Recenly, IMF (2002) warned ha he curren accoun defici in he US, a curren or higher raes, would ake he US ne foreign liabiliy posiion o overincreasing levels, and ha a same poin an adusmen will be needed. Leachman and Francis (2000) argue ha more recenly he US may be running a Ponzi gamble agains global capial markes. Such a gamble can be welfare improving, even in dynamically efficien economies, as long as he rae of growh remains above he real ineres rae on exernal deb. However, should he gamble fail, some generaions will be less well off and susainabiliy of curren accoun may be an issue. Temporary curren accoun deficis, reflecing reallocaion of capial o he counry in which capial is more producive, are no as bad as hey are hough o be. On he oher hand, persisen deficis may have some imporan effecs. Firsly, foreign capial inflows may increase he domesic ineres raes. Secondly, he accumulaion of exernal deb will probably reflec he increasing ineres paymens, which migh mean an excess burden in he fuure (Hakkio, 1995; Wu, 2000). Moreover, persisen curren accoun deficis migh serve as a leading indicaor of financial crises (Baharumshah e al. 2003). The series of economic crises in he 1990s showed ha large and persisen curren accoun deficis can generae a favourable environmen for exernal crises, especially when hose deficis are financed hrough shorerm capial inflows. In order o evaluae he sable longrun raecory of a counry s curren accoun, wo inerrelaed quesions are needed o be addressed. The firs one concerns he solvency properies of he debor counry; he second one concerns he susainabiliy properies of he curren accoun defici (Norh, 2002). Ineremporal solvency invesigaes he

3 Curren Accoun Susainabiliy in Seven Developed Counries 49 counry s abiliy o repay is exernal deb. For a counry o become ineremporally solven, he presen discouned value of fuure rade surpluses mus be equal o he presen value of is foreign deb (Milesi Ferrei and Razin, 1996). This is he concep of ineremporal solvency implying ha all debs will be repaid in he longrun. This issue has been quie exensively covered in recen empirical research by implemenaion of applied saionariy and coinegraion ess o examine ineremporal solvency condiion. These sudies include Raybaudi e. al.(2004), Masubayashi (2004), Chorareas e al (2004), Baharumshah e al (2003), Arize, (2002), Wu and e al (2001), Irandous and Söö (2000, 2004), Apergis e al. (2000), Leachman and Francis (2000), Founas and Wu (1999), Yan (1999), Bodman (1997), Wu and e al (1996), Liu and Tanner (1996, 1995), Sawada (1994), Hused (1992), Hakkio and Rush (1991), among ohers. As a resul of above researches susainabiliy of exernal deb, a saionary curren accoun is consisen wih a finie exernal debognp raio. Thus, here is no condiion o encourage he counry o defaul on is inernaional debs (Wu, 2000). Furhermore, he saionariy of he curren accoun is also essenial for he validiy of he modern ineremporal model of he curren accoun. Theoreically, o inerpre he curren accoun acing as prevenion o smooh consumpion in he face of shocks, he modern ineremporal model of curren accoun deerminaion combines he assumpions of perfec capial mobiliy and consumpionsmoohing behaviour. This emphasizes ha he curren accoun series should be a saionary series. Empirically, lieraure saes he Campbell and Shiller (1987) echnique o es he validiy of he ineremporal model of he curren accoun (e.g. Oo (1992), Ghosh (1995), Shibaa and Shinani (1998)). Saionariy ess on curren accouns were uilized for he US by Trehan and Walsh (1991), Wickens and Ucum (1993) and for he US and Canada by Oo (1992), and for wenyhree counries by Gundlach and Sinn (1992). These aricles sae he evidence ha curren accouns are nonsaionary for many indusrialized counries, including he US, he UK, Canada, Germany, and Japan. Bu a common feaure of hese aricles is he resuls found: a nonsaionary curren accoun using he ADF uniroo ess and he oher uniroo ess. Wu (2000) using he panel daa uniroo es of Im e al. (1997) has reexamined he imeseries propery of curren accoun among indusrial counries. His empirical findings suppor saionariy of curren accoun series of hese counries. This also leads o suppor he modern ineremporal model of he curren accoun approach.

4 50 Fikre Dülger and Zeynel Abidin Ozdemir Addiionally, hese findings also sae ha he curren accoun deficis among indusrialized counries are susainable. Susainabiliy ess, however, do no provide a consensus because resuls vary wih he approach adoped, he sample period, he specificaion of he ransversaliy condiion, and he economeric mehodology used (Chorareas e al. 2004). For example, Gundlach and Sinn (1992) analyse ime series daa and reec a nonsaionary curren accoun for mos of OECD counries exceping Germany, Japan and he US. Taylor (1996, 2002) analyses hisorical daa series for a sample of 12 counries, which include Germany, Japan and US, and esablishes curren accoun saionary for he enire sample. Chorareas e al. (2004) used a new mehodology (NonLinear Saionariy Tess) ha suppors susainabiliy in he deb of a se of Lain America counries. Convenional uniroo ess have low power when he roo is close o one. In parallel, Shiller and Perron (1985) find ha he power of he ADF uniroo ess is low wih shor ime spans. Hence, a main reason for he failure of reecing he nonsaionariy of he curren accoun migh be he low power of he es in he exising lieraure. Moreover, Diebold and Rudebusch (1991) and Sowell (1990) found ou ha convenional uniroo ess such as he DickeyFuller es could have low power agains fracional alernaives. The radiional views of modelling curren accoun series eiher as rend deerminisic I(0) or as sochasic rends (or uni roos), I(1) processes seem oo resricive compared o he wide scope of possibiliies covered by he fracionally inegraed I(d) processes. These processes belong o a broader class called long memory, owing o heir abiliy o display significan dependence beween disan observaions in ime (GilAlana, 2002a). Thus, he ime series properies of curren accoun of G7 counries are analyzed in his aricle using he fracional mehods, such as Lo s R/S mehod, Robinson s score es and While s approximae maximum likelihood esimaor. The purpose of his sudy is o examine he behaviour of curren accoun of seven developed counries for 1974:12001:3 ime period using fracional mehods. The sudy concenraes on he following maor poins: Firs, we deermine wheher curren accoun series reflec a long memory process. If a curren accoun series is covariance nonsaionary bu long memory process, hen i is classified as meanrevering process. Thus, he shock has no permanen effec on he values of series. Deermining wheher he curren accoun series are meanrevering process is a prerequisie for he analysis of hese series. Second, if we view he curren accoun as he series

5 Curren Accoun Susainabiliy in Seven Developed Counries 51 realizaion of a sochasic process, he auocorrelaion funcion exhibis persisence which is neiher consisen wih uni roo process nor saionary process. Fracionally inegraed process is relaed o he rae of decay associaed wih he impulse response coefficiens of a process. Thus, we esimae he fracionally inegraed auoregressive moving average model for each curren series for G7 counries and analyze he calculaed impulse response coefficiens based on hese esimaed models. The maor findings of his sudy are: Firs, all counries curren accouns are covariance nonsaionary. Second, hreecounries (France, Ialy and Canada) curren accouns are mean revering so ha hey are susainable, fourcounries (Germany, UK, US, and Japan) curren accouns are no mean revering, and herefore unsusainable. The paper is organized as follows: Secion II conains some economic foundaions of curren accoun susainabiliy. Secion III provides economeric mehodology uilized in analysis. Empirical resuls are repored and inerpreed in Secion IV. Finally, Secion V conains some concluding remarks. 2. A Framework for Tesing The recen lieraure on he subec under invesigaion has esablished he imeseries implicaions of he ineremporal solvency condiion. The key resul of his lieraure is ha if a counry s ineremporal budge consrain is saisfied, hen he counry is solven and is pah of curren accoun imbalances becomes susainable. The sandard heoreical crierion for assessing curren accoun imbalance is he noion of solvency: a counry is solven o he exen ha he discouned value of he expeced sock of is foreign deb in he infiniely disan fuure is nonposiive. One of he mos common univariae approaches is aken by Liu and Tanner (1996). This approach sars from he perperiod budge consrain faced by he counry expressed in real erms: f f M X + r B 1 = ΔB 1 (1) f where M is impors in period, X is expors in period, B is he sock of one period foreign deb issued in period and r is he oneperiod world ineres rae. Assuming ha he ineres rae is saionary wih mean r (r1 = r + v,, wih v a zeromean random error), forward ieraion of (1) gives

6 52 Fikre Dülger and Zeynel Abidin Ozdemir B M X B v f f ++ 1 i ++ 1 i ++ 1 i ++ 1 i = + lim + i+ 1 i (1 ) i i r + + = + (1 + r) i= 1 (1 + r) (2) Now, assuming ha expors and impors series are I(1) and aking expeced values, equaion (2) may be wrien as; f B + k+ i CA = θ + lim E ω, k 1 i + + (3) (1 + r) where ω is a saionary error erm and θ is a consan. This is he no Ponzi condiion, in which exernal deb repaymens are susainable, or he curren deb mus be equal o he expeced presen value of fuure curren accoun surpluses. If he erm in he limi was negaive, he economy would be consuming and invesing more han presen value of is fuure curren accoun surpluses ha never converges o zero. If he erm in he limi was greaer han zero, he counry would be paying he old mauriy deb by issuing new deb, which reveals ha curren accoun is no susainable in he longrun. If he solvency condiion holds, hen he second erm on he righ hand side of equaion (3) is equal o zero. Therefore, he solvency condiion requires ha curren accoun mus be a saionary process around a consan mean (see Trehan and Walsh (1991)). An alernaive way of esing he solvency condiion requires invesigaing he coinegraion of expors and impors. Indeed, Liu and Tanner (1996, p.741) emphasize hree imporan advanages of he saionary es. Firs, he saionariy es is somewha sronger han he coinegraion es, as i imposes a vecor of coinegraing coefficien of [1, 1] on he variables expors and impors. Second, as Trehan and Walsh (1991) show, while he ineres rae mus be saionary for he coinegraion es, i need no be so for he saionariy es. Third, in he saionary es, expors and impors need no follow random walks for he es o be valid. For hese reasons, he saionariy es is more appropriae han he coinegraion es. The saionariy of he curren accoun is imporan o he validiy of he ineremporal model of he curren accoun. Theoreically, his approach combines he assumpions of perfec capial mobiliy and consumpion smoohing behavior o predic ha curren accoun acs as a buffer o smooh consumpion in he face of shocks and implies ha curren accoun will ypically be a saionary variable. Therefore, he solvency consrain requires ha he curren accoun be a saionary variable. This means ha curren

7 Curren Accoun Susainabiliy in Seven Developed Counries 53 accoun is meanrever. In his paper, we also sudy he order of inegraion of curren accoun using a mehodology based on fracional inegraion. In he uniroo ess, he knifeedge disincion beween I(0) and I(1) processes of he curren accoun can be oo resricive. If he process is I(1), i is no meanrever and he effec of shock is persisen. In he longmemory models, if he degree of inegraion of curren accoun is wihin (0, 0.5) inerval, curren accoun is covariance saionary and is mean rever. If he degree of inegraion of curren accoun is wihin (0.5,1) inerval, he curren accoun is no covariance saionary, bu i is mean revering, wih he effec of shocks dying away in he long run. Finally, if he d 1, curren accoun is nonsaionary and nonmean revering. In his conex, he curren accoun defici susainabiliy condiion holds if and only if he fracional inegraion parameer of he curren accoun series is less han uniy. There exis many approaches of esimaing and esing he fracional differencing parameer d (e.g. Geweke and PorerHudak, 1983). 3. Economeric Mehodology Over he las wo decades, here has been a growing lieraure modelling he macroeconomic and financial ime series in erms of fracionally inegraed processes. These processes consiue a generally class of flexible ime series models. They are useful for modelling lowfrequency dynamics, because of heir flexibiliy and simpliciy in heir specificaion (Granger and Joyeux, 1980; Hosking, 1981). Le y, = 1, 2, K, T, be he ime series of ineres. In he frequency domain, assume ha y is weakly saionary process and is specral densiy funcion, f(λ), a frequency λ (π,π] saisfying π γ = E[( y E( y ))( y + E( y ))] = f ( λ)cos( λ) dλ, = 0, ± 1, ± 2,K (4) π where λ are he auocovariance of y. Specral densiy funcion of y saisfy f(λ) ~ c 1 λ 2d as λ 0 + for 0 < c 1 < (5) and auocovariances follow γ c 2 2d1 as for c 2 < (6)

8 54 Fikre Dülger and Zeynel Abidin Ozdemir where he symbol means ha he raio of he lef hand side and righ hand side ends o 1, as in equaion (6), and as λ 0 + in equaion (5). For d (0.5,0.5), y follows a long memory process. Condiion equaion (5) and equaion (6) are no always equivalen, bu Yong (1974) and Zygmund (1995) give condiions under which boh expressions are equivalen (Brockwell and Davis, 1991; Robinson, 1995a,b; Baillie, 1996). A general class of fracional inegraed processes ARFIMA (p,d,q) is described by d φ ( L) (1 L) y = θ ( L) ε (7) where L is lag operaor, φ ( L ) = 1 φ L K φ and 1 L p p θ L θ L θ L q ( ) = 1 K 1 q are polynomials wih sable roos, ε is whie noise, d is long memory parameer and he fracional differencing operaor, (1 L) d, yields an infinieorder lag polynomial wih slowly declining coefficiens as bellows: (1 L) d = k = 0 Γ( k d) L k /{ Γ( k + 1) Γ( d)} where Γ( ) is he sandard gamma funcion. These processes belong o long memory due o heir abiliy o reveal significan dependence beween disan observaions in ime. The order of inegraion d is no resriced o ineger values and can ake any value on he real line. Uni roo processes are included as a special case wih d = 1. Saionary case is wih d = 0. For d (0,0.5), y is said o have long memory. When d (0.5,0), y is called anipersisen or inermediae memory. For d 0.5, y is covariance saionary bu no inverible. For d 0.5, y is nonsaionary and has infinie variance. For d (0.5,1), where y displays srong persisence, bu mean revers in he sense ha he impulse response funcion is decaying (Granger and Joyeux, 1980; Hosking, 1981). The meanrevering propery depends on wheher d < 1. The impac of a shock is known o be persisen forever when d = 1. The effec of any shock on he fracionally inegraed process wih d < 1 slowly dies ou. This

9 Curren Accoun Susainabiliy in Seven Developed Counries 55 can be seen by sudying he moving average represenaion for follows: ( 1 L)y as ( 1 L) y = A( L) ε (8) 2 1 where A( L) = (1 + θ L + θ L + ) obained from (1 L) d Φ( L) 1 2 K 1 wih Φ ( L) = φ ( L) θ ( L). The impulse responses are given by he coefficiens θ k of A(L). The impac of a uni innovaion a ime on he value of y a + is equals o equaion 9. C = 1+ θ + θ + K + θ ) (9) ( 1 2 In equaion 9, as, C = A(1). Tha is he measure of he long run impac of he innovaion (Campbell and Mankiw, 1987). Cheung and Lai (1993) show ha for he fracionally inegraed process wih d < 1, C = 0 implying no longrun impac of he innovaion on he value of y. For d 1, C 0. So, he effec of a shock has permanen effec on he value of y. When he d < 1, he y process is meanrevering (Cheung and Lai, 1993; Cheung and Lai, 2001). Tesing Procedures for Fracional Inegraion Hurs (1951) developed rescaled range saisic (R/S) deecing evidence of srong dependence in ime series. I is popularised by Manderbold (1972). Lo (1991) shows ha shorrange dependence may compromise inferences abou he presence of longrange dependence. He derives an adusmen o he classical R/S saisics accouning for general forms of shorrange dependence. The modified R/S saisics replaces he usual variance esimae wih a consisen esimaor of he long run variance. Cavaliere (2001) proposes a new generalized R/S saisics. Robinson (1994a) proposes a very general esing procedure for esing uni roo and oher hypohesis in raw ime series. Unlike mos of uni roo ess embedded in auoregressive alernaives, Robinson s score es is nesed in a fracionally inegraed model. Le and Schmid (1996) propose he es of Kwiaowski, Phillips, Schmid and Shin (1992), KPSS, as a es for he null of saionariy agains he alernaive hypohesis of fracional inegraion. Dolado, Gonzalo and

10 56 Fikre Dülger and Zeynel Abidin Ozdemir Mayoral (2002) proposed a Fracional DickeyFuller es (FDF) for esing he null hypohesis of I(d 0 ) agains he alernaive hypohesis I(d 1 ), d 1 < d 0. In his paper, we use he Lo s modified R/S saisics and Robinson s score es saisics deecing or esing he long memory in curren accoun series of G 7 counries. Also, reduced form of While esimaor is used for he long memory models. Thus, hese are briefly oulined in his secion. Lo s Modified R/S Saisics The modified R/S es for long memory considers he null hypohesis of a shor memory agains he alernaive hypohesis of long memory. Le y be he sample mean of ime series { y, y, 1 2 K y T }. The modified R/S saisics, Q n, q, is given by he range of cumulaive sums of derivaions of ime series from is mean, rescaled by a consisen esimae of is sandard deviaion: k k n, q q 1 = 1 n k T 1 k T = 1 1 Q = S {max ( y y ) min ( y y )} (10) 2 where S q is a heeroskedasiciy and auocorrelaion consisen variance esimaor (Andrews, 1991), S 2 q = T 2 q T { ( yi y) / T + 2 τ ( q) ( ( yi y)( yi y) )/ T} = = = + i 1 1 i 1 wih he weighing funcion τ ( q) = 1 / zt and a runcaion lag q deermined by n q = In[ z T ], z T = (3T / 2) 1/ 3 2 {2ρ /(1 ρ )} 2 / 3, where In[ z T ] denoes he ineger par of he z T and ρ is he firsorder auocorrelaion of he series. The modified R/S saisics is differen from he classical one on he normalizaion of he range measure. The denominaor in equaion (10) normalizes he range measure boh by he sample variance (q = 0) (as considered in classical R/S analysis) and by a weighed sum of sample auocovariances for q > 0. Such modificaion conribues o he robusness of

11 Curren Accoun Susainabiliy in Seven Developed Counries 57 he modified R/S analysis o ake care of shorerm dependence and heeroskedasiciy. The limiing disribuion of he Q n, q saisic sandardized by he square roo of he sample size may be esablished under he null hypohesis of no long memory. Lo (1991) provides he criical values for he modified R/S ess. Robinson LM Tes Robinson (1994a) proposes a very general procedure for esing uni roos as well as oher nonsaionary alernaives. Unlike he oher uni roo ess (e.g. Dickey and Fuller, 1979; ec.), esing for auoregressive (AR) uni roo, Robinson s (1994a) procedure allows esing for fracional order of inegraion in addiion o oher appealing hypohesis. Robinson s (1994a) ess are nesed in a fracionally inegraed model. Denoing he y ime series, we employ hroughou he model, y = β z + x, = 1, 2, K, (11) d ( 1 L) x = u, = 1, 2, K, (12) where y is ime series we observe for = 1, 2, K, T, β is a (k 1) vecor of unknown parameers; z is a (k 1) vecor of deerminisic regressors, such as polynomials in (usually an inercep and a linear ime rend), x is he regression error, d is a given real value and u is a covariance saionary process wih specral densiy funcion which is posiive and finie a he zero frequency. Robinson (1994a) proposes a score es of he null hypohesis, defined by: H : d = 0. (13) 0 d The score saisic for above esing he hypohesis proposed by Robinson (1994a) is given by r ˆ = ( T / Aˆ) ( aˆ / ˆ σ ), (14)

12 58 Fikre Dülger and Zeynel Abidin Ozdemir where T is he sample size and aˆ = ( 2π / T) T 1 = 1 ψ ( λ ) g( λ ; ˆ) τ 1 I( λ ); 2 ˆ σ = (2π / T ) T 1 = 1 g( λ ; ˆ) τ 1 I( λ ); 1 T 1 ( ˆ( ε λ ) ˆ( ) ) ˆ( ) ( ) ε λ ε λ ψ λ = T 1 2 T 1 Aˆ (2/ T) ψ( λ ) ( ) ˆ( ) = 1 ψ λ = 1 ε λ 1 T i I λ ) uˆ = e 1 2πT = ; ψ( λ) = log2sin( λ / 2); ˆ( ε λ ) = logg( λ; ˆ); τ λ = (2π / T). τ 2 λ ( where I( λ ) is he periodogram of û obained as: = 1 xˆ = y ˆ, ˆ βz β = T 1 T d ( z ), ˆ = (1 ) ˆ z z y u L x, = 1,2, K, = 1 = 1 and g above is a given funcion coming from he specral densiy funcion of 2 û : f ( λ; τ ) = ( σ / 2π ) g( λ; τ ), wih τˆ obained by minimising σ 2 ( τ ). If u is whie noise, g 1. If u is an AR process from: φ ( L) u = ε, 2 iλ g = φ ( e ). Therefore, AR coefficiens are funcion of τ. p Under he null hypohesis given in (13) Robinson (1994a) esablished ha rˆ d N(0,1) as T, (15) under he cerain regulariy condiions. This limiing disribuion holds independenly of he regressors included in z and he various ypes of I(0) disurbances assumed for u including he general weakly saionary in (12). An approximae onesided es of H 0 : d = d 0 is reeced agains he alernaive: H a : d > d 0 ( d < d 0 ) a he α % level will be given by he rule Reec H 0 if rˆ > z ( ˆ α r < zα ), where he probabiliy of a sandard normal variae exceeding z α is α. The above version of he Robinson es is used in

13 Curren Accoun Susainabiliy in Seven Developed Counries 59 empirical applicaions by in GilAlana and Robinson (1997) and GilAlana (1999, 2000, 2001, 2002b). Esimaion mehod for long memory models In his paper, we will evaluae he persisence for esing of ineremporal solvency using he impulse response funcions of he esimaed ARFIMA models. In order o obain impulse responses, we firs need o esimae parameers of he models. There exis differen approaches for esimaing parameric models like equaion (7) and analysis may be carried ou in he frequency and in he ime domain. Fox and Taqqu (1986) proposed a frequency domain mehod o esimae ARFIMA models by minimizing he While funcion (ha is an approximaion o he exac likelihood funcion). Dalhaus (1989) proposed anoher mehod o esimae ARFIMA models by minimizing he exac likelihood funcion in frequency domain. Sowell (1992) analyzed in he ime domain he exac maximum likelihood (EML) esimaes of he parameers of an ARFIMA model using recursive procedures allowing quick evaluaion of he likelihood funcion. As Hauser (1999) moioned hese esimaors are asympoically equivalen, bu While maximum likelihood (WML) wih respec o he EML esimaor is more reliable in small samples. Thus, WML esimaor is used in his paper. The WML esimaes are obained by maximizing an approximaion of he likelihood funcion of he ARFIMA model in equaion (7) in he frequency domain. In his mehod, he parameer vecor θ = (α1,,αp,d,β1,,βq) is esimaed by minimizing he following approximae log likelihood funcion log L W I 2 1 ( λ ) ( θ, σ u ) = (16) 2 f ( λ θ, σ ) m m 2 logf ( λ θ, σ u ) = 1 2π = 1 where I(λ) is he periodogram defined a he h λ = 2π/T, = 1,...,m, T 1 ( ) = T = 1 iλ 2 u Frourier frequency, I λ ( y y) e (17) m = [( T 1) / 2], [ ] is he ineger par. The reduced form of L W wih 2 respec o he error variance σ u is

14 60 Fikre Dülger and Zeynel Abidin Ozdemir logl * W m 1 I( λ ) ( θ ) = mlog(2π ) mlog log g( λ ) m (18) m = 1 g( λ ) m 2 2* 1 2 wih σ u = σ u = m = ( I( λ ) / g( λ 1 )) where f ( λ ) = σ u g( λ) /(2π ) wih g ( λ) = g( λ θ ). In his paper, he parameers of each ARFIMA(p,d,q) model for real exchange rae series are esimaed by reduced form of L W (Hauser, 1999). IV. Daa and Empirical Resuls The quarerly daa are aken from Inernaional Moneary Fund s Balance of Paymens Saisics (CDROM, Version Apr. 2002) for he 1974:1 2001:3 period. The series are seasonally adused using X11 procedure. The modified R/S es is performed on curren accoun series, and he resuls are repored in Table 1. The modified R/S es saisics are provided ogeher wih he opimal lag seleced and used in consrucing he corresponding saisics. The resuls for he curren accoun series for G7 counries show ha in all cases he null hypohesis of shormemory can be reeced a he 5 percen significance level. This finding shows he presence of long memory in curren accoun for G7 counries. Table 1: Resuls of modified R/S analysis for curren accoun series Counry R/S Saisic qlag seleced Canada 3.081* 0 Germany 1.955* 3 Ialy 2.109* 1 USA 2.555* 1 UK 2.205* 2 France 1.909* 3 Japan 1.878* 2 Noes: The lag parameer q used for he modified R/S es is deermined by Andrews s (1991) daadependen rule. A he 5% significan level, he null hypohesis of a shormemory process is reeced if he modified R/S saisics does no fall wihin he confidence inerval [0.809, 1.862]. * shows ha he null hypohesis is reeced a he 5 percen significan level.

15 Curren Accoun Susainabiliy in Seven Developed Counries 61 In Appendix A, able 1, 2, 3, 4, 5, 6, and 7, repor he values of he onesided es saisics rˆ of equaion (14). The significan negaive values of his saisics are consisen wih H a : d < d 0, whereas he significan posiive values are consisen wih H a : d > d 0. Thus, a monoonic decrease in he value of he rˆ saisic is expeced wih increasing d values, because if he null hypohesis is reeced for a cerain value of d, hen a more significan resul should be expeced for esing values han his value of d. In his sudy, we consider wo cases for he Daa Generaing Process (DGP) for u. In he firs case, we assume ha u is whie noise. In he second case, u is assumed o be follow an AR(1) process. In hese ables, we presen he resuls based on various z including z = 0 (i.e., including no regressors in he undifferenced regression), z = 1 (i.e., including an inercep) and z = (1,) (i.e., including an inercep and a linear ime rend). In all cases, he values of he rˆ saisics are monoonically decreasing wih increasing d values. Thus, he model is no likely o be misspecified. The firs rows of ables give he values of d considered under he null hypohesis in equaion (13). The nex rows presen he resuls for z = 0, z = 1 and z = ( 1, ). The firs panel of Table 1 repors he values for whie noise disurbances, while in second panel of Table 1 we allow AR(1) disurbances for Canada. In he firs panel of Table 1, if he curren accoun series of Canada is modelled wih z = 0, z = 1 and z = ( 1, ), he range of d values is acceped by he Robinson es a he five percen significan level beween , and , respecively. If an AR(1) process is assumed for he disurbances u wih z = 0, z = 1 and z = ( 1, ), he range of d values acceped by he Robinson es is beween , and , respecively. I is observed ha, in he Table 2, saring wih he case of whie noise disurbance, null hypohesis canno be reeced when he range of d values is beween 0.95 and However, if we allow weakly paramerically auocorrelaed disurbances (AR(1) disurbance case) along wih he z = 0, z = 1 and z = ( 1, ) componens, hen he order of inegraion values acceped by Robinson es is beween 1.00 and 1.05 for z = 0 and z = 1, respecively, and is 1.00 for z = ( 1, ). If we look a Table 3, resuls of Ialy show us ha he nonreecion values of d range from 0.90 o 1.10 for z = 0 and = ( 1, ), respecively, and range from 0.90 o z

16 62 Fikre Dülger and Zeynel Abidin Ozdemir 1.15 for z = 1 in case of whie noise disurbances; beween 0.95 and 1.00 wih AR(1) disurbances. Table 4 shows ha if u is whie noise wih z = 0 and z = 1, nonreecion values range beween 1.15 and 1.30 for USA. On he oher hand, for he z = ( 1, ), he order of inegraion is beween 1.20 and When he disurbances are assumed o follow an AR(1), he order of inegraion is beween 1.20 and 1.30 for hree differen deerminisic regressors. Resuls of U.S. show ha curren accoun series of U.S. is no susainable. Table 5 presens he resuls for U.K. For he resul given in he firs panel in he Table 6 he range of values for ha he null hypohesis for z = 0, z = 1 and z = ( 1, ) canno be reeced is beween 0.80 and The second panel shows ha he range of values d ha is no reeced a he five percen significance level under he null hypohesis is beween 0.85 and Excep d = 1.00 case for U.K., he curren accoun series of U.K. can be represened by a covariance nonsaionary and long memory process. Thus, he curren accoun series is meanrevering series showing ha i is susainable. Bu, i is no susainable in he laer case. The resuls given in firs panel of he Table 6 for France are obained by assuming a whie noise process for he disurbances wih z = 0, z = 1 and z = ( 1, ) deerminisic regressors. For he firs wo deerminisic cases (no deerminisic regressors and an inercep case) and las deerminisic case, he range of values for which he null hypohesis canno be reeced is from 0.80 o 1.00 and from 0.75 o 1.00, respecively. In he case where we assume an AR(1) process for disurbances and he same se of deerminisic regressors, we see ha he range of d values acceped by he Robinson es is beween 0.85 and For Japan, if we consider he whie noise u and hese deerminisic regressors, we can see ha degrees of inegraion of curren accoun series is bigger han If we allow an AR(1) process for u along wih hese deerminisic regressors, we see ha he nonreecion value of d is 1.30 in case of no deerminisic regressors; ranges beween 1.20 and 1.30 wih an inercep; ranges beween 1.25 and 1.30 wih an inercep and a linear ime

17 Curren Accoun Susainabiliy in Seven Developed Counries 63 rend. These resuls show ha curren accoun series of Japan is no susainable. For each series we presen he esimaing resuls differen ARFIMA(p,d,q) models where boh p and q are less han or equal o hree. The selecion of he bes ARFIMA model is based on he Schwarz informaion crierion (SIC). For he p,q > 3, differen ARFIMA models are also esimaed. Bu, esimaion of hese models eiher failed or, when esimaion was successful, hey always had lower SIC values. Therefore, we do no consider hese higher order ARFIMA models. For breviy only he resuls of ARFIMA model esimaes having he minimum SIC will be presened. The parameers of he ARFIMA models are esimaed using he WML mehod. Sandard errors for he ARFIMA esimaes are calculaed using he asympoic formula in Robinson (1994b) and Beran (1995). The esimaion resuls for he parameric ARFIMA models for each counry are given in Table (2). Based on he minimum SIC crieria, he bes ARFIMA model for each counry is an ARFIMA(3,0.67,3) for he Canada, an ARFIMA(1,1.09,0) for Germany, an ARFIMA(2,0.57,0) for Ialy, an ARFIMA(0,1.05,0) for USA, an ARFIMA(2,1.06,0) for UK, an ARFIMA(2,0.54,3) for France and an ARFIMA(0,1.14,0) for Japan, respecively. The esimaed fracional differencing parameer of each curren accoun series of each counry exhibis fracional dynamics wih longmemory feaures. They range from 0.54 o 1.14 for he series under consideraion. The esimaed values of d are significanly differen from zero a he 5% level for each counry. Therefore, each series is no covariance saionary and exhibis longmemory behaviour. When compared o he esimaed value of d of hese series, he esimaed value of d for Germany, USA, UK and Japan is larger han 1. Hence, lower band of confidence inervals for long memory parameers of hese series should be checked. Calculaed confidence inervals show ha lower bands of hese are 0.91, 0.91, 0.84 and 0.98, respecively. Also, his indicaes ha hese curren accouns are no explosive series.

18 64 Fikre Dülger and Zeynel Abidin Ozdemir Table 2: Parameer Esimaes of Bes ARFIMA(p,d,q) models for CA Counry loglik d α1 α2 α3 β1 β2 β3 SIC Canada (0.11) (0.73) (0.99) (0.69) (0.64) (0.84) (0.64) Germany (0.09) (0.12) Ialy (0.31) (0.31) (0.10) USA (0.07) UK (0.11) (0.13) (0.11) France (0.15) (0.25) (0.22) (0.27) (0.24) (0.16) Japan (0.08) The esimaes given in he Table are for he models ha have he minimum SIC. The values in parenheses are sandard errors of parameers. Sandard errors are calculaed under he asympoic formula in Robinson (1994b) and Beran (1995). As an alernaive confirmaion of he solvency of curren accoun, we analyse he impulse responses implied by he ARFIMA models seleced by he SIC for each counry. Persisence of curren accoun dynamics can be analysed hrough he sequence of C, as given by equaion (9). The funcion, ha gives he sequence of C values a differen ime horizon afer a uni shock, can be compued based on equaion (8) for curren accoun series. In Appendix A, Figure (1) displays he plos of he impulse responses for he seleced model in each counry when hey are shocked by one sandard deviaion. Graphs of he firs 20 dynamic responses show differen dynamics. For France, Ialy and Canada, adusmen process has zero longrun persisence confirming ha curren accoun series of hese counries are susainable. However, for he Canadian case, he graph exhibis nonlineariy. In his case, he process of adusmen shows nonlineariy in he direcion of adusmen because of cyclical responses o he iniial shock. In Germany, UK, USA and Japan, adusmen process has no zero longrun persisence. In oher words, curren accoun series of hese counries are no meanrevering indicaing ha hese are unsusainable.

19 Curren Accoun Susainabiliy in Seven Developed Counries 65 V. Concluding Remarks In his aricle we have examined he susainabiliy of G7 curren accoun by means of fracional inegraion echniques. Using a version of he Robinson (1994) for esing uni and fracional roos, he resuls show ha all counries curren accoun is covariance nonsaionary and fourcounry (France, UK, Ialy and Canada) curren accouns are mean revering so ha hey are susainable. Germany, US, and Japan s curren accoun are no mean revering and hence are unsusainable. The resuls here reinforce he exisence of mean reversion in he curren accoun, hough, in view of he values of d, ranging in mos cases beween 0.5 and 1, he adusmen process owards equilibrium will ake a very long ime. The persisence graphs show differen dynamics. For France, Ialy and Canada, adusmen process has zero longrun persisence confirming ha curren accoun series of hese counries are susainable. However, for he Canadian case, he graph exhibis nonlineariy. In Germany, UK, USA, and Japan adusmen process has no zero longrun persisence. In oher words, curren accoun series of hese counries are no meanrevering indicaing ha hese are unsusainable.

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27 Curren Accoun Susainabiliy in Seven Developed Counries 73 Appendix A Table 1: CANADA Tesing he order of inegraion wih he ess of Robinson and whie noise disurbances Z /d Z = Z = Z = (1,) Tesing he order of inegraion wih he ess of Robinson and AR(1) disurbances Z = Z = Z = (1,) Noes: * and in bold indicae nonreecion values a he five percen significance level.

28 74 Fikre Dülger and Zeynel Abidin Ozdemir Table 2: GERMANY Tesing he order of inegraion wih he ess of Robinson and whie noise disurbances Z /d Z = * 0.76 * 0.04 * 0.6 * 1.16 * 1.65 Z = * 0.58 * 0.14 * 0.78 * 1.35 * 1.84 Z = (1,) * 0.4 * 0.33 * 0.97 * 1.54 * 2.03 Tesing he order of inegraion wih he ess of Robinson and AR(1) disurbances Z = * 0.98 * Z = * 1.42 * Z = (1,) * 1.83 Noes: * and in bold indicae nonreecion values a he five percen significance level

29 Curren Accoun Susainabiliy in Seven Developed Counries 75 Table 3: ITALY Tesing he order of inegraion wih he ess of Robinson and whie noise disurbances Z /d Z = * 0.34 * 0.25 * 0.79 * 1.27 * Z = * 0.55 * 0.08 * 0.65 * 1.17 * 1.63 * Z = (1,) * 0.32 * 0.27 * 0.8 * 1.28 * Tesing he order of inegraion wih he ess of Robinson and AR(1) disurbances Z = 0 Z = * 0.94 * * 0.91 * Z = (1,) * 0.51 * Noes: * and in bold indicae nonreecion values a he five percen significance level.