Curren Accoun Susainabiliy in he US: Wha do we really now abou i? Dimiris K. Chrisopoulos Deparmen of Economic and Regional Developmen, Paneion Universiy Miguel A. León-Ledesma Deparmen of Economics Universiy of Ken Ocober 24 Absrac We revisi he debae on he susainabiliy of he curren accoun dynamics in he US. Using he concep of susainabiliy as he abiliy o mee he long run ineremporal budge consrain, we es for uni roos in he US curren accoun for he 96-24 period. We argue ha here are several reasons o believe ha he curren accoun may follow a non-linear behavior under he null of saionariy. This is confirmed by a se of non-lineariy ess. We hen fi an ESTAR model o he curren accoun dynamics and reec he null of non-saionariy. Hence, we conclude in favor of susainabiliy. Furhermore, our resuls reveal ha only for he period 974-992 we can find significan deviaions of he curren accoun from equilibrium and a slower speed of mean reversion. JEL classificaions: C22, F32. Keywords: curren accoun susainabiliy; saionariy; non-linear models. Acnowledgemens: We would lie o han, wihou implicaing, Alan Carruh, Caharine Mann, Ole Rummel and Adolfo Sachida for heir useful commens. Address for correspondence: Dr. Dimiris K. Chrisopoulos, Deparmen of Economic and Regional Developmen, Paneion Universiy Leof. Syngrou 36, 767, Ahens, Greece Tel. +3-2-9224948, Fax: +3-2-922932, e-mail address: chrisod@paneion.gr. Miguel A. León-Ledesma, Deparmen of Economics, Keynes College, Universiy of Ken, Canerbury, Ken, CT2 7NP, UK. Phone: +44 ()227 82326. Email: m.a.leon-ledesma@en.ac.u
Curren Accoun Susainabiliy in he US: Wha do we really now abou i?. Inroducion The concep of curren accoun susainabiliy has long been he focus of research and policy debae in economics. The basic idea is appealing as i amouns o analyzing wheher a counry is able o mee is ineremporal budge consrain in he long-run wihou incurring episodes of fas and painful adusmen. Long periods of unsusainable curren accoun dynamics may end eiher abruply by generaing exchange rae crises and oupu collapse or by achieving a sof landing ha will ineviably imply invesmen and growh slowdowns. The concep of curren accoun susainabiliy is lined o he saionariy of he curren accoun balance, as non-saionary dynamics would imply a violaion of he iner-emporal budge consrain. Tesing for he presence of uni roos and coinegraion in he curren accoun dynamics of developed and emerging mares has been he focus of many papers such as Trehan and Walsh (99), Oo (992), Wicens and Ucum (993), Liu and Tanner (996), Wu (2) and Taylor (22). Their resuls yield mixed resuls depending on he counries, he sample and he esing procedures considered. As Taylor (22) poins ou, he speed of mean reversion of he dynamics of he curren accoun can also be considered as a summary saisic of he degree of capial mobiliy. This degree of capial mobiliy is subec o policy and insiuional changes. In he case of he US, he susainabiliy of he curren accoun has araced much aenion from boh academics and policy maers (see, recenly, Obsfeld and Rogoff 24, Mann 22, Cooper 2, McKinnon 2 and Venura 2). The increased curren accoun deficis have cerainly been a cause of concern. Figure plos he quarerly curren accoun balance o GDP raio in he US from 96: o 24:. I is easy o see ha he end of he 99s and beginning of he 2s has winessed levels of deficis previously unseen excep for he spell of dollar appreciaion in he mideighies. The accumulaed curren accoun defici in 23 averaged almos 5% of GDP. This concern is refleced in IMF (24) who claim ha one of he main riss for The daa used in his sudy is from he US Bureau of Economic Analysis.
economic recovery was in achieving an orderly resoluion of global imbalances, noably he large US curren accoun defici and surpluses elsewhere (p.). Obsfeld and Rogoff (24), for insance, calculae ha he correcion of he US curren imbalance may lead o a real dollar depreciaion larger han 2% wih poenial serious consequences for real economic aciviy in he res of he world. Hence, i is undoubedly imporan o analyze he US curren accoun dynamics and adusmen as i has crucial consequences for boh he US and global economy. Our obecive in his paper is o analyze he saionariy of he US curren accoun using new economeric ess based on non-linear adusmen ha we consider more appropriae o describe he dynamics of he curren accoun. Wih a few excepions, 2 he wors previously menioned have assumed ha he adusmen of he curren accoun follows a linear behavior under he alernaive of mean reversion. Boh saisical evidence and heory argumens challenge his assumpion. Our approach has several advanages over previous ess. Firsly, raher han assuming linear adusmen, we es for lineariy in he daa. If non-lineariy is presen, hen he radiional uni roo ess suffer from an imporan loss of power ha may lead o erroneously acceping no-susainabiliy. Secondly, he ess presened show a richer se of dynamics in he curren accoun ha allows us o idenify periods of susainabiliy and no-susainabiliy and periods in which he curren accoun persisenly deviaes from is equilibrium (mean) value. Thirdly, by using ess ha allow for differen speeds of adusmen, we allow for he fac ha insiuional, preference and policy changes can affec he dynamic adusmen and equilibrium values of he curren accoun. 3 The paper is organized as follows. In he nex Secion, we discuss he concep of curren accoun susainabiliy. In Secion 3, we apply a series of non-lineariy ess o he US curren accoun. In Secion 4, we es for he saionariy of he curren accoun, and Secion 5 concludes. 2. Curren accoun susainabiliy The concep of curren accoun susainabiliy has been widely discussed in he lieraure. Mann (22) considers ha susainabiliy should be viewed boh from he 2 See Chorareas e al (24) for an analysis of deb susainabiliy in Lain America and Raybaudi e al (23) for he UK. 3 See Taylor (22). 2
domesic and inernaional finance poin of view. A susainable curren accoun is one ha does no rigger feedbac effecs on domesic variables (invesmen and savings) or does no lead o significan inernaional porfolio reallocaions leading o changes in ineres raes. Milessi-Ferrei and Razin (996) disinguish beween solvency and susainabiliy. An economy is solven if he expeced presen value of fuure rade surpluses equals is curren indebedness. Tha is, if he economy mees is exernal ineremporal budge consrain. Susainabiliy refers o he quesion of wheher he economy is able o mee is budge consrain wihou a drasic change in privae secor behavior or policy shifs. As Milessi-Ferrei and Razin (996) sae, he laer concep has more srucure as i conains behavioral implicaions. Neverheless, he concep of solvency is more general. In his paper, we will follow Taylor (22) and use he concep of susainabiliy as he abiliy of an economy o saisfy is long-run ineremporal budge consrain. This is a more general concep and does no depend on he paricular srucural model we have in mind. Also, his concep of susainabiliy is a sufficien condiion for oher conceps o hold. An aracive feaure of his idea is is esabiliy. As pu forward by Trehan and Walsh (99), curren accoun saionariy is a sufficien condiion for he ineremporal budge consrain o hold. Consider a sochasic model wih zero growh. The one period budge consrain is, C + I + G + B = Y + ( + r) B () where C, I, G, B and Y are consumpion, invesmen, governmen consumpion, ne soc of deb and income respecively. r is he world ineres rae. Rearranging () and from naional accouns ideniies we have ha, B = ( + r) B + NX (2) where NX is ne expors. Ieraing (2) forward and assuming ha he expeced value E( r ) ϕ = r, wih ϕ being he informaion se available in -, we ge B = E( NX+ ϕ ) + lim E( B+ T ϕ ) T r = + + r (3) T 3
Equaion (3) simply saes ha inernaional agens are able o lend o an economy if hey expec ha he presen value of he fuure sream of ne expors surpluses equals he curren soc of foreign deb. Hence, he susainabiliy hypohesis, or long run budge consrain implies ha: T lim EB ( + Tϕ ) = T + r (4) This ransversaliy condiion means ha he presen value of he expeced soc of deb when ends o infiniy mus equal zero. 4 Following Trehan and Walsh (99) 5, given ha he curren accoun CA = B B, a sufficien condiion for (4) o hold is ha he curren accoun is a saionary process. 6 In he more realisic case of an economy wih a posiive rae of growh of oupu, we have ha he susainabiliy condiion holds if he raio y CA = is saionary. This means ha susainabiliy is Y possible wih curren accoun deficis as far as hey do no grow faser han oupu in expeced value. 7 An obvious es of susainabiliy is hence a uni roo es on y. This is wha mos of he lieraure has previously used as a es of susainabiliy. However, noe ha we are dealing here wih expeced values of fuure evens. Changes in he agens percepions abou ris, porfolio allocaion decisions, fuure policy changes, ransacion coss in inernaional financial flows, ec. can lead o changes in he dynamics of curren accoun mean reversion and hence equilibrium values of he curren accoun. As previously menioned, Taylor (22) sees he speed of convergence owards equilibrium as a summary saisic of he degree of capial mobiliy. This is so because i reflecs how long agens are prepared o allow periods of curren accoun deficis (surpluses) above he perceived equilibrium value. If, given he inernaional financial environmen, agens percepions abou, for insance, he relaive ris of US dollar denominaed asses changes due o large observed curren 4 Tha is, a no-ponzi game condiion. 5 See also Taylor (22). 6 This susainabiliy condiion holds even for he case of a variable real ineres rae. 7 See Trehan and Walsh (99) for proofs. 4
accoun deficis, he speed of mean reversion and he mean of he curren accoun iself would also change. Tha is, changes in he curren accoun affecing agen s percepions can rigger adusmen dynamics ha are no linear as commonly assummed. In his sense, i may well be he case ha ess for saionariy ha do no consider he possible non-linear dynamics arising from hese effecs are mispecified. In ha case, we may reach wrong conclusions abou he susainabiliy of he curren accoun or arrive a oo simplisic a descripion of curren accoun dynamics under he hypohesis of saionariy. In he nex secions we will es for he exisence of nonlineariy in he US curren accoun and, based on hese resuls, use a non-linear uni roo es ha capures hese effecs. 3. Lineariy ess In he ime series lieraure a commonly used es for he uni roo null hypohesis is he well now augmened Dicey-Fuller es (ADF). The es is based on he following regression model: y + δ y + γ + ε = = α + βy =,2,.T. (5) where y was previously defined as he raio of he curren accoun o GDP a ime, is he firs difference operaor and ε is a whie noise disurbance erm. is a linear deerminisic rend while he erms allow for serial correlaion and are designed y o ensure ha ε is whie noise. The null hypohesis is ha β =, which corresponds o a uni roo in y (ha is, no susainabiliy). The OLS based β saisic, which does no have a sandard normal disribuion, can be used o es his hypohesis. However his es has low power in he presence of non-linear adusmen, leading i o accep very frequenly he null hypohesis of a uni roo (see Shin and Lee, 2 and Killian and Taylor, 23). In oher words, as discussed before, he curren accoun daa could exhibi some non-linear srucure alhough sill saionary. For his reason, if he series presens non-lineariies, a proper uni roo es mus allow for 5
asymmeric adusmen under he alernaive. 8 Enders and Granger (998) reviewed many economic series ha confirmed his proposiion. The daa used in our analysis is he US quarerly curren accoun o GDP raio over he period 96:-24:. We firs carried ou hree linear uni-roo ess on he daa. These were an ADF es of he null of non-saionariy; he Modified Phillips- Perron es wih GLS de-rending (M GLS α ) of Ng and Perron (2) for he null of a uni roo; and Ellio e al s (996) mos powerful DF-GLS es for he null of a uni roo. The lag augmenaion was chosen using he Ng and Perron (2) Modified Informaion Crieria (MIC). 9 This mehod reduces very subsanially size disorions. The ess were carried ou using a consan erm and a consan and a deerminisic rend. The resuls are repored in Table. I is easy o see ha none of he ess is able o reec he null of a uni roo in he curren accoun o GDP raio of he US. These findings clearly indicae ha curren accoun susainabiliy canno be suppored, as he uni roo hypohesis could no be reeced by he daa. However, as noed before, linear ess have low power in he presence of mispecified dynamics leading o he non-reecion of he null hypohesis. Given his problem, we apply various non-lineariy ess o invesigae if he US curren accoun dynamics are governed by non-linear behaviour. There are a large number of ess developed in he lieraure for his purpose. Given heir differen naure, and in order o give a complee picure of he possible naure of non-lineariy, we have chosen o use he Ramsey (969) es, he Keenan (985) es, he Granger and Teräsvira (993) es and he Ludlow and Enders (2) es. The Ramsey es usually referred o as he RESET es proposed by Ramsey (969) explois he idea ha if here is non-lineariy, hen any non-linear ransformaion of he fied value of he curren accoun variable yˆ ) should no be useful in explaining he curren value ( y ). The es is based on he following auxiliary regression: ( p q + ˆ = + + ξ + = = for y g g y y e q, (6) 8 See for example Caner and Hansen (2), Shin and Lee (2) and Enders and Granger (998). 9 The resuls using oher informaion mehods such as AIC, he Panula e al. (994) principle or a general o specific mehod (GTS) did no change he conclusions abou uni-roos. 6
where g and ξ are parameers. An F -saisic can be used o es he null hypohesis H ξ... = ξ. : = q = The Keenan (985) es is based on Tuey s non-addiiviy es using y ˆ ) as in 2 he RESET es. Unlie he RESET es, he Keenan es invesigaes wheher ( yˆ ) has any addiional forecasing abiliy for y. To perform his es we have o follow a hree sep procedure. (a) We esimae a linear equaion of he ype = g + g y e (7) y + 2 and save he residuals eˆ ) and he fied values y ˆ ). (b) We regress ( y ˆ ) on y ) ( and generae he residuals ( ( ηˆ ) and (c) we regress ê on ηˆ and obain he residuals νˆ. The es saisic for he null hypohesis of lineariy is given by ( 2 ( ' ' ' eˆ ˆ( η ˆ η ˆ) η ˆ η eˆ K = ( T 4) χ 2 () (8) ' vˆ vˆ where ê, ηˆ, νˆ are T vecors of ê, ηˆ, νˆ respecively. Unlie he RESET and Keenan ess where he reecion of he null hypohesis does no provide a guidance as o he specificaion of an alernaive model Granger and Teräsvira (993) suggesed a es of he linear null hypohesis agains he alernaive hypohesis of an exponenial smooh ransiion (ESTAR) model. This approach includes he following arificial regression: 4 2 4 βo [ β β2 ] = y = y + y y + y y + e =,2,..T. (9) where e is an error erm. The lineariy es agains an ESTAR consiss of esing he null hypohesis H : β = β2 = for =,2,3,4 using he F -saisic version of he Lagrange-muliplier es in Teräsvira (994). is a delay parameer ha is chosen as he one ha maximizes he F-saisic for H. The common feaure of all previous parameric ess is ha hey need o specify he naure of he non-linear coefficien. Thus, he esimaed model may suffer from a specificaion error, which leads very frequenly o misguided conclusions. Ludlow In our daa we found = o be he opimal delay parameer. 7
and Enders (2) (LE hereafer) recommend a deerminisic ime dependen coefficien model wihou firs specifying he naure of non-lineariy. To es for nonlineariy following he mehod proposed by LE we ransformed he linear AR() model y = α y + e =,2,..T. () l where y is a saionary random variable and e is an error erm, as follows: y = α() y + e () l where α() is a deerminisic bu unnown funcion of ime. LE have shown ha he funcion α() can be exacly represened by a sufficienly long Fourier series so ha, s 2π 2π α( ) = Ζ + [ Ζ sin + Η cos ] (2) T T = where s refers o he number of frequencies conained in he process generaing α () and is an ineger in he inerval o T / 4. Z and H are parameers o esimae. In order o idenify he paricular Fourier coefficien we perform he following seps. Firs, we esimae an AR(p) model in firs differences form: p + α i i= y = φ y + e (3) i The model wih he smalles SBC is seleced as he bes fi model. Nex we replace he original series y by he residual ê derived from model (3). Second, for each value of in he inerval o T / 4 we esimae: eˆ 2π 2π = [ Ζ sin + Η cos ] y T T L (4) The inerval o T / 4 refers o quarerly daa. 8
If he incorporaion in (4) of he mos significan does no reduce SBC we erminae he search. Addiionally, we use Suden s disribuion o es he null hypohesis Ζ = and H =. Third, having idenified he frequency and he associaed non-zero values Ζ and H we esimae: y 2π 2π = φ e (5) p n q i i + α i y i + [ Ζ sin + Η cos ] y L + β ie i + i= i= T T i= If he value of Ζ or sequence displays asymmeries. H is saisically significan we can conclude ha he y Table 2 presens RESET, Keenan and Granger and Teräsvira ess for nonlineariy in he daa while Table 3 repors he LE ess. The findings in Table 2 show ha he US curren accoun presens imporan non-lineariies according o he Keenan and Granger and Teräsvira non-lineariy ess. However, his is no he case for he RESET es which fails o reec he null hypohesis. To examine furher he issue of non-lineariy we presen in Table 3 he resuls of he LE non-linear es. The radiional -saisics on he Ζ and H parameers show ha sin and cos erms are saisically significan a convenional levels of saisical significance. This means ha he curren accoun in he USA presens imporan non-lineariies. However, since he -disribuions for sin and cos erms are idenical and he regressors are orhogonal LE calculae a single saisic based on Mone Carlo simulaions. According o hese values, which are higher han hose of he radiional - disribuion, we observe ha only a few coefficiens remain saisically significan. Neverheless, LE noe ha he power of his es depends on he size of φ relaive o Z. Thus, hey sugges he analysis of he dynamic behaviour of he ime varying coefficien α (). A close loo a he ime pah of coefficien α() shown in Figure 2 reveals ha i behaves in a highly non-linear fashion. In paricular, in some cases he coefficien α() exceeds.5 while in ohers he coefficien is less han.5. This finding is no in line wih he resuls of a linear AR(p) model where he auoregressive coefficien is assumed consan over ime. 9
Given he resuls of he various ess for non-lineariy in he US curren accoun dynamics, we can conclude wih a cerain degree of safey ha i follows a non-linear adusmen mechanism. In his case, ess ha assume a linear adusmen under he alernaive of saionariy would be mispecified. This also confirms ha, far from being a consan, he speed of adusmen o he long-run budge consrain is subec o changes and asymmeries. 4. Uni roo ess Given he possible exisence of non-lineariy in ime series daa, several aemps have been made o develop ess ha have beer power han he classical ones. Here we will use a es based on he smooh ransiion family of models. 2 These models assume ha, in our case, he curren accoun balance aduss o is equilibrium wih a differen speed depending on wheher previous changes in he curren accoun are above or below a hreshold. This change of regime is smooh and no radical, and hence aes an adusmen period ha is daa deermined. The exisence of his ind of dynamics would be indicaive ha he curren accoun adusmen reacs o changes in he macroeconomic environmen ha affec he curren accoun. For insance, for large changes in he curren accoun away from equilibrium we migh expec he speed of mean reversion o be faser as mares would no be willing o susain deviaions from equilibrium for a long period. Obviously, his asymmery of adusmen would also have an impac on he equilibrium value owards which he curren accoun converges. The uni roo es is based on Kapeianos e al (23) and furher developed by Kilic (23). Kilic (23) proposed an alernaive framewor which has a linear nonsaionary process under he null agains a non-linear saionary aleraive, while a he same ime is more powerful han he non-linear uni roo es proposed by Kapeanios e al. (23). Given he power of he es, we will use in wha follows he Kilic (23) esing procedure. 2 We also considered he oin asymmery and uni roo es framewor in a hreshold auoregressive framewor (TAR) proposed by Caner and Hansen (2). Our resuls showed lile evidence of self exracing TAR srucure in he US curren accoun. We hence concluded ha he non-lineariy was no of he ind posulaed by his model, i.e. where ransiion beween he differen saes is immediae. Resuls are available on reques.
Kapeianos e al (23) and Kilic (23) consider he following univariae smooh ransiion AR() model y = y + y Φ z + (6) ρ ρ [ γ, θ; ] ε where 2 yis saionary ergodic and ε ~ iid(, σ ). The ransiion funcion Φ [ γ, θ; z ], allows for non-linear mean reversion in y. Kilic (23) adops he exponenial ransiion funcion, Φ = (7) 2 [ γ, θ; z] exp[ γ( z θ) ] where γ ( γ > ) deermines he speed of ransiion beween he wo exreme regimes, θ is a hreshold value and z is he ransiion variable which could be predeermined or exogenous and sricly saionary. In our case, as in many economic applicaions, we chose z = y and is an ineger denoing he delay parameer. In his case equaion (7) is ermed an exponenial STAR (ESTAR) model. The ESTAR model accouns for smooh ransiion beween wo exreme regimes while i is symmerically U-shaped around zero. The middle regime corresponds o when Φ [ ] = and equaion (7) reduces o he linear AR() model y = θ, y = ρ + ε (8) y The ouer regime corresponds o lim[ y θ ± ( Φ[ γ, θ; y ] = ) so equaion (7) becomes a differen AR() model ] y = + ρ ) y ( ρ + ε (9) The AR() models in equaions (8) and (9) will differ in heir speed of mean reversion as long as ρ. Re-wriing equaion (6) as
y y [, ; y ] p = ~ ρy + ρ Φ γ θ + ζ y + ε (2) i i i When ρ < and ~ ρ + ρ < hen equaion (2) describes a process ha is locally non-saionary (given he uni roo in he linear erm) bu globally saionary. This indicaes ha y locally follows a uni roo in he region of y = θ ( ~ [ ρ + ρ Φ( θ; y )] = ) while large values of y would resul in an approximaely AR() process wih he sable roo ~ ρ + ρ provided ha 2 < ρ <. Nex, he auhor imposes ~ ρ = in (2) and considers a esing procedure for H : ρ (2) = H : ρ, (22) < ha could be based on ˆ ( γ, ). However, since γ and θ are no idenified under θ ρ = he null (Davies, 987) he null hypohesis (2) canno be esed. To es direcly he null hypohesis (2) Kilic (23) developed he following - saisic Sup- = sup ˆ ρ ( γ, θ ) s. e.( ˆ ρ ( γ, θ )) ( γ, θ ) Γ Θ ρ = (23) where Γ = [ γ, γ ] and Θ = [ θ, θ ] are such ha < γ < γ < γ and < θ < θ < θ. This corresponds o he values of γ and θ yielding he smalles sum of squared residuals. The value of γ is esimaed using a grid search mehod while for he value of θ he Caner and Hansen (2) mehodology could be adoped 3. In paricular, he possible value of θ could be seleced from he ordered values of y afer having discarded % of he highes and smalles observaions. This procedure will guaranee ha he boundaries θ and θ do no depend on any unnown parameer. Based on Mone Carlo simulaions, Kilic (23) concluded ha he sup has superior power o he ADF and PP ess under he alernaive of an ESTAR model. I was also found ha he sup saisics performs beer and is more powerful han he 3 Kilic (23) noes ha we should no mae he inerval oo wide as a very large values of γ may mae he ransiion funcion Φ become fla. 2
non-linear ADF es of Kapeanios e al. (23). Asympoic criical values for he sup are abulaed in Kilic (23). Before applying his es we regressed he y series on a consan and saved he residuals, generaing hus a new variable which is de-meaned. Table 4 repors he esimaed ESTAR model (6) as well as he uni roo es and oher diagnosic saisics of he model. Examinaion of Table 4 reveals ha he sup saisic reecs he uni roo null hypohesis a he 5% significance level. This finding is no in line wih he resuls based on linear uni roo ess. Hence, as posulaed earlier in he paper, assuming a linear behaviour of he mean reversion and equilibrium value of he US curren accoun may drive us o misleading conclusions abou is susainabiliy. In our ess we show ha he sufficien condiion for he long-run budge consrain o hold is me for he US economy. From he resuls we can also see ha he speed of mean reversion is subsanially faser when he curren accoun changes above he hreshold, which is consisen wih he idea ha he AR parameer reflecs he degree of capial mobiliy which, in urn, depends on agens percepions abou he relaive ris of he US economy. The speed of ransiion beween he differen regimes appears o be relaively fas. Furhermore, our resuls show ha our ESTAR model is saisfacorily esimaed according o he differen misspecificaion ess proposed by Eihheim and Terasvira (996). The diagnosic es F LM indicaes he absence of serial correlaion in he residuals. The F nl es indicaes no remaining non-lineariy in he model. Finally, he Medeiros and Veiga (23) es for parameer consancy in non-linear models also indicaes ha we canno reec he null of consancy. 4 Therefore we can conclude ha our specificaion is an adequae model describing he dynamics of he US curren accoun. Given he flexibiliy of his model, anoher advanage ha i offers is ha i allows us o ge furher insighs ino he dynamics of he curren accoun. In paricular, we can consruc indicaors of boh he degree of deviaion from he mean or equilibrium value and he degree of mean reversion. We follow Taylor and Peel (2) and measure he imporance of misalignmens aing ino accoun he sign and size of he 4 See he appendix for deails of his es. 3
deviaions 5 from equilibrium as well as he degree of mean reversion of he curren accoun a a paricular poin in ime using he following ransformed ransiion funcions: { ˆ γθ } Gy ( ) = Φ (,, y sgn[ y ] (24) H ( y ) = Φˆ [ γ, θ; y ], (25) where y sgn[ y ] =. ( y ) y G and H ) measure deviaions from equilibrium ( y and he degree of mean reversion respecively. Figure 3 conains he plos of he Φˆ [ γ, θ; ], G ) and H ) funcions y ( y ( y (FUSA, GUSA and HUSA respecively in he graph). Firs, we observe ha he graphs indicae ha he duraion beween wo exreme peas or depressions is shor excep for he 98-83 and 989-9 periods where i lass several quarers. Therefore we can conclude ha he USA curren accoun is characerized by frequen flucuaions showing no persisen dynamics (see upper and lower panel in Figure 3). Second, we idenify hree periods 96-974, 975-99 and 992 23 of he US recen curren accoun hisory. The firs and he las sub-periods are characerised by very small percenage (posiive or negaive) deviaions of he US curren accoun relaive o is equilibrium value. On he oher hand, he period 975-99 reflecs difficulies in conrolling he curren accoun deviaions (see middle panel in Figure 3). Hence, in general, we find ha he 96-974 and 992-23 periods show boh small deviaions from equilibrium and rapid mean reversion. The 974-992 period is characerised by larger deviaions from equilibrium and slower mean reversion. This can be easily relaed o changes in world macroeconomic environmen. The lae sevenies and eighies were characerised by oil price shocs, deb crises in emerging counries and a srong dollar appreciaion in he mid-eighies. Given his environmen, agens were prepared o allow larger curren accoun deficis for a longer period of ime as he relaive ris percepion of he US economy improved given he siuaion elsewhere. This can also be relaed o agen s expecaions of fuure higher growh 5 Since he ransiion funcion measures he imporance of he deviaion from equilibrium irrespecive of he sign and he size, i canno ell us wheher hese deviaions are posiive or negaive. 4
raes in he US and dollar depreciaion. This would mean ha inernaional financial mares allowed larger curren accoun deficis for longer periods of ime as he expeced fuure pah of ne expors and growh relaive o he res of he world improves. As regards he recen period, we did no find evidence of imporan curren accoun disequilibria. Neverheless, in he final period of esimaion he repored deviaion becomes larger and always negaive. We also find evidence of rapid mean reversion dynamics. This may reflec an increasing sensiiviy of capial mares o excessive US curren accoun deficis. 5. Conclusions The quesion of wheher or no he US curren accoun follows a susainable pah has gained imporance in recen years in boh academic and policy debaes. In his paper we es wheher he dynamics of he US curren accoun are compaible wih a long-run ineremporal budge consrain. We ae he saionariy of he curren accoun as a sufficien condiion for his definiion of susainabiliy. However, we argue ha given possible changes in ris percepions, macroeconomic environmen, porfolio allocaion decisions, insiuional environmen, ec., he usual assumpion of a linear process for he curren accoun under he alernaive hypohesis of saionariy may no be a correc represenaion. We esed for non-linear dynamics in he US curren accoun and found subsanive evidence of non-lineariy according o differen ess. We hen esed for uni roos by specifying an ESTAR model, which capures adusmen asymmeries and allows us o ge furher insighs abou he dynamic adusmen of he US curren accoun for he period 96: o 24:. Various diagnosic ess show ha he model is a correc specificaion describing he dynamics of he curren accoun. Our resuls reec he null hypohesis of no-susainabiliy of he US curren accoun. Tha is, he US curren accoun behaves in a non-linear bu saionary fashion. Furhermore, our resuls reveal ha only for he period 974-992 we can find significan deviaions of he curren accoun from equilibrium and a slower speed of mean reversion. The 96-974 and 992-23 periods show rapid mean reversion and small deviaions from equilibrium. 5
References Caner, M., and B.E. Hansen, 2, Threshold auoregression wih a uni roo, Economerica 69, 565-596. Chorareas, G.E., Kapeanios, G. and Ucum, M., 24, An invesigaion of curren accoun solvency in Lain America using non-linear nonsaionariy ess, Sudies in Nonlinear Dynamics and Economerics 8, aricle 4. Cooper, R.N. 2, Is he US curren accoun defici susainable? Will i be susained? Brooings Papers in Economic Aciviy, 27-226. Davies, R.B., 987, Hypohesis esing when a nuisance parameer is presen under he alernaive, Biomeria 64, 247-254. Eihheim, O. and Teräsvira, T., 996, Tesing he adequacy of smooh ransiion auoregressive models, Journal of Economerics 74, 59-75. Ellio, G., Rohenberg, T. J. and Soc, J.H., 996, Efficien Tess for an Auoregressive Uni Roo, Economerica 64, 83-836. Enders, W. and Granger C.W.J., 998, Uni roo ess and asymmeric adusmen wih an example using he erm srucure of ineres raes, Journal of Business of Economic and Saisics 6, 34-32 Granger, C.W.J. and Teräsvira, T., 993, Modeling Non-Linear Economic Relaionships, Oxford Universiy Press, Oxford. Inernaional Moneary Fund, 24, World Economic Ouloo. IMF, Washingon DC. Kapeanios, G, Shin, Y. and Snell, A., 23, Tesing for a uni roo in he nonlinear STAR framewor, Journal of Economerics 2, 359-379. Keenan, K.L, 985, A Tuey non-addiiviy ype es for ime series non-lineariy, Biomerica 72, 39-44. Kilic, R., 23, A esing procedure for a uni roo in he STAR model, Woring Paper, School of Economics, Georgia Insiue of Technology Killian, L. and M. Taylor 23, Why is i difficul o bea he random wal forecas of exchange raes? Journal of Inernaional Economics 6, 85-7. Liu, P. and Tanner, E., 996, Inernaional ineremporal solvency in indusrialized counries: evidence and implicaions, Souhern Economic Journal 62, 739-749. Ludlow, J. and Enders, W., 2, Esimaing non-linear ARMA models using Fourier coefficiens, Inernaional Journal of Forecasing 6, 333-347. Mann, C.L., 22, Perspecives on he US curren accoun defici and susainabiliy, Journal of Economic Perspecives 6, 3-52. McKinnon, R.I., 2, The inernaional dollar sandard and he susainabiliy of he US curren accoun deficis, Brooings Papers in Economic Aciviy, 227-238. Medeiros, M.C. and Veiga, A., 23, Diagnosing checing in a flexible nonlinear ime series model, Journal of Time series Analysis 24, 46-482. Milesi-Ferrei, G.M. and Razin, A., 996, Susainabiliy of persisen curren accoun deficis, NBER Woring Papers 5467. Ng, S. and Perron, P., 2, Lag Lengh Selecion and he Consrucion of Uni Roo Tess wih Good Size and Power, Economerica 69, 59-554. Obsfeld, M. and Rogoff, K., 24, The unsusainable US curren accoun posiion revisied. Mimeo, Universiy of California Bereley. Oo, G., 992, Tesing a presen-value model of he curren accoun: evidence US and Canadian ime series, Journal of Inernaional Money and Finance, 44-43. Panula, S.G., Gonzalez-Farias, G. and Fuller, W.A., 994, A comparison of uni roo es crieria, Journal of Business of Economics and Saisics, 2, 449-459 6
Ramsey, J.B.969, Tess for specificaion errors in classical linear leas squares regression analysis, Journal of he Royal Saisical Sociey B 3, 35-37. Raybaudi, M. Sola, M. and Spagnolo, F., 23, Red signals: rade deficis and he curren accoun, CARISMA Brunel Universiy, CTR 9/3. Shin, D.W. and Lee, O., 2, Tes for asymmery in possibly nonsaionary ime series daa, Journal of Business and Economic Saisics 9, 233-244. Taylor, A.M., 22, A cenury of curren accoun dynamics, Journal of Inernaional Money and Finance 2, 725-748. Taylor, M. and Peel, D., 2, Nonlinear adusmen, long-run equilibrium and exchange rae fundamenals, Journal of Inernaional Money and Finance 9, 33-53. Teräsvira, T., 994, Specificaion, esimaion and evaluaion of smooh ransiion auoregressive models, Journal of he American Saisical Associaion 89, 28-28. Trehan, B. and Walsh, C., 99, Tesing ineremporal budge consrains: heory and applicaions o US federal budge deficis and curren accoun deficis, Journal of Money, Credi and Baning 26, 26-223. Venura, J. 2, A porfolio view of he US curren accoun defici, Brooings Papers in Economic Aciviy, 239-252. Wicens, M.R. and Ucum, M., 993, The susainabiliy of curren accoun deficis: a es of he US ineremporal budge consrain, Journal of Economic Dynamics and Conrol 7, 423-44. Wu, J-L., 2, Mean reversion of he curren accoun: evidence from he panel daa uni roo es, Economics Leers 66, 29-224. 7
Figure : US Curren Accoun o GDP Raio 96-24 (%) 2-96 4 962 2 963 4 965 2 966 4 968 2 969 4 97 2 972 4 974 2 975 4 977 2 978 4 98 2 98 4 983 2 984 4 986 2 987 4 989 2 99 4 992 2 993 4 995 2 996 4 998 2 999 4 2 2 22 4-2 -3-4 -5-6 8
Figure 2: The AR() coefficien over ime.5..5. -.5 -. -.5 6 65 7 75 8 85 9 95 AT 9
Figure 3: Mean- reversion dynamics and degree of misalignmen..8.6.4.2. 6 65 7 75 8 85 9 95 FUSA 2 8 4-4 -8 6 65 7 75 8 85 9 95 GUSA..8.6.4.2. 6 65 7 75 8 85 9 95 HUSA 2
Tables Table : Linear uni roo ess. ADF M α GLS ERS DFGLS Consan -.24.4.38 Consan and rend -2.5 -.69 -.73 Noes: he 5% criical values for he ADF, M α GLS and DF-GLS ess are -2.86, -.98 and -.98 for he consan only case respecively. For he consan and rend case hese are -3.4, -2.9 and -2.9. Table 2: Tess for non-lineariy in he daa. RESET- p values Keenan x 2 es Granger and Teräsvira p -values =.43 34.52.5 = 2.6 = 4.45 Noe: The criical value for he Keenan 2 x es is 6.63. Bold values indicae reecion of he null hypohesis a 5% significance level. 2
Table 3: Esimaes of Fourier model (5). Parameers Coefficiens raios φ..68 y -.47 -.65 y -.349 -.579 2 y.27.595 3 Z y = 33 = 62 = 33 = 62.26 -.343 2.474-3.246 Z y = 8 = 33 2.26 -.26 = 8 = 33 2.278-2.5 Z y = 33 = 62 = 33 = 62 3 -.293 -.462 2.27-4.298 H y = 3 = 3.232 2.232 H y 2 = 49 = 49 -.293-2.958 H y 3 Noe: We esimaed firsly an ARMA(p) model and used he SBC o find which model fis bes he daa.. We chose an ARMA(3) model. Figures in braces indicae absolue -raios. Diagnosic saisics (normaliy and auocorrelaion) for he ARMA(3) model were also performed. According o hese resuls he ARMA(3) model seems o be free from specificaion errors. () indicaes saisical significance a he 5% saisical level. Bold values denoe saisical significance using he wo sided es. The criical value for Z or H is aen from LE (Table ) and i is 2.83 a he 5% level. sands for he mos imporan frequencies in he inerval o T / 4. 22
Table 4: Non-linear sup uni roo es and esimaed ESTAR model Variables Coefficiens p values ζ.4.8 ζ -.3.72 2 ζ.2. 3 ρ -.8 γˆ. θˆ. sup -.68 F LM.35 F.82 nl LM PS 4.79 Noes: The number of coefficiens ( ζ -ζ 3 ) was seleced by regressing y on is lagged values. The opimal highes lags were obained by using Schwarz crierion. The delay parameer y is equal o one and was seleced by minimizing he squared residuals of corresponding regression. Since γˆ and θˆ were obained hrough a grid search mehod, he have no p values. The criical value for sup es for observaions is.53 a 5% saisical level. The γˆ was normalised by he sample variance of he ransiion variable, so as o mae γˆ approximaely scale free. If we remove he sandardizaion we obain a value for he γˆ equal o 6.3. F LM denoes he Eihheim and Terasvira (996) F -saisic of serial dependence. The Fnl es represens he Eihheim and Terasvira (996) es for he null hypohesis ha here is no remaining non lineariies. The LM PS es is he Medeiros and Veiga (23) LM es for parameer consancy and is disribued as a χ 2 (4) [see Appendix for deails]. An () indicaes reecion of he uni roo hypohesis a 5% saisical level. 23
Appendix To chec for parameer consancy we adop a recenly suggesed es by Medeiros and Veiga (23). This es is fully parameric and allows he parameers o change smoohly as a funcion of ime under he alernaive hypohesis. We wrie our nonlinear model as follows: y = G X + ε = + Φ ] + ε (A) ' ' (, Z ; Ψ) β X ξ X [ γ, θ; Ζ where X is a p vecor of lagged values of y, he funcion Φ γ, θ; Ζ ] is he [ exponenial funcion, Z is a q vecor of ransiion variables and γ and θ are parameers. ' Nex, we consider ha β and ξ are ime varian parameers ha is β = β ( ) and ' ξ = ξ ( ) and hey are given by B ~ β ( ) = β + β Φ( ς ( h )) (A2) = = B ~ ξ ( ) = ξ + ξ Φ( ς ( h )) (A3) In order o ensure he idenifiably of he model we have o impose he resricions: h h... h B and ξ >, =,2,3,... B. h B and 2 ξ are parameers. When ξ equaions A2 and A3 consiue a model wih B srucural breas. Using expressions A2 and A3 and considering ha B = he model A can be wrien as follows: y { β + ~ ' Φ( ς ( h ))} X + { ξ ' + ξφ( ς ( h ))} X Φ[ γ, θ; Z + ε = β ] (A4) The null hypohesis of parameer consancy is H : ς. Since ς is no idenified = under he null hypohesis we have o adop he following procedure. In paricular, we expand Φ( ς ( h)) ino a firs-order Taylor expansion around ς =. I is given by 24
=.25ς ( h) + Η( ; ς, ) (A5) h where Η ( ; ς, h) is he remainder. Replacing Φ( ς ( h)) in A4 by A5 we have y = ( ι + µ ) X + ( ι + µ ) X Φ[ γ, θ; Z ] + ε ' ' (A6) ~ ~ ~ where ι = β β / 4, µ = / 4, ι = ξ ξh / 4 and µ = ξ / 4. h β Now he null hypohesis is H = µ = µ (A7) = I is now easy o obain he log lielihood funcion in he naionhood of H for observaion and ignoring he remainder Η( ; ς, h) as l = 2σ ' ' ' ' { y ( ι + µ ) X ( ι µ ) X Φ[ γ, θ; Z ]} 2 2.5ln(2π ).5lnσ 2 (A8) The LM es can be wrien as follows LM T T T T T T ' ' ' ' ' = ˆ ε v vˆ vˆ vˆ gˆ ( gˆ gˆ ) gˆ vˆ vˆ ˆ ε 2 ˆ σ = = = = (A9) = where g ˆ G( X, Z ; Ψˆ ) and = vˆ ˆ ' ' ' = [ X, X Φ( γ, θ; Z ]. Under he null hypohesis Medeiros and Veiga (23) have shown ha A9 is disribued as m = ( h + )( p + ). In our applicaion we consider only he case of h =. χ 2 ( m) saisic wih 25