1247 Discussion Papers Deusches Insiu für Wirschafsforschung 212 Tesing he Marshall-Lerner Condiion in Kenya Guglielmo Maria Caporale, Luis A. Gil-Alana and Rober Mudida
Opinions expressed in his paper are hose of he auhor(s) and do no necessarily reflec views of he insiue. IMPRESSUM DIW Berlin, 212 DIW Berlin German Insiue for Economic Research Mohrensr. 58 1117 Berlin Tel. +49 (3) 897 89- Fax +49 (3) 897 89-2 hp://www.diw.de ISSN prin ediion 1433-21 ISSN elecronic ediion 1619-4535 Papers can be downloaded free of charge from he DIW Berlin websie: hp://www.diw.de/discussionpapers Discussion Papers of DIW Berlin are indexed in RePEc and SSRN: hp://ideas.repec.org/s/diw/diwwpp.hml hp://www.ssrn.com/link/diw-berlin-german-ins-econ-res.hml
Tesing he Marshall-Lerner Condiion in Kenya Guglielmo Maria Caporale Cenre for Empirical Finance, Brunel Universiy, London, UK Luis A. Gil-Alana * Navarra Cener for Inernaional Developmen, Universiy of Navarra, Pamplona, Spain and Rober Mudida Srahmore Universiy, Nairobi, Kenya Sepember 212 Absrac In his paper we examine he Marshall-Lerner (ML) condiion for he Kenyan economy. In paricular, we use quarerly daa on he log of real exchange raes, expor-impor raio and relaive (US) income for he ime period 1996q1 211q4, and employ echniques based on he concep of long memory or long-range dependence. Specifically, we use fracional inegraion and coinegraion mehods, which are more general han sandard approaches based exclusively on ineger degrees of differeniaion. The resuls indicae ha here exiss a well-defined coinegraing relaionship linking he balance of paymens o he real exchange rae and relaive income, and ha he ML condiion is saisfied in he long run alhough he convergence process is relaively slow. They also imply ha a moderae depreciaion of he Kenyan shilling may have a sabilizing influence on he balance of paymens hrough he curren accoun wihou he need for high ineres raes. Keywords: Marshall-Lerner condiion, fracional inegraion, fracional coinegraion JEL Classificaion: C22, C32, F32 Corresponding auhor: Professor Guglielmo Maria Caporale, Research Professor a DIW Berlin, Cenre for Empirical Finance, Brunel Universiy, Wes London, UB8 3PH, UK. Tel.: +44 ()1895 266713. Fax: +44 ()1895 26977. Email: Guglielmo-Maria.Caporale@brunel.ac.uk * Luis A. Gil-Alana graefully acknowledges financial suppor from he Minisry of Educaion of Spain (ECO211-214 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz projec of he Governmen of Navarra.
1. Inroducion A lo of he lieraure on he balance of rade is based on he so-called "elasiciy approach", namely on esing he exen o which rade flows are responsive o relaive price changes, more specifically wheher a devaluaion improves he rade balance, which implies ha he well-known Marshall-Lerner (ML) condiion holds. The seminal empirical paper by Houhakker and Magee (1969) found inconclusive evidence. Several subsequen sudies using leas-squares mehods o esimae price elasiciies in impor and expor equaions also produced mixed resuls (see, e.g., Khan 1974, Goldsein and Khan 1985, Wilson and Takacs 1979, Warner and Kreinin 1983, Bahmani-Oskooee 1986, Krugman and Baldwin 1987). More recenly, he evidence obained wih more advanced economeric echniques aking ino accoun non-saionariies in he daa has been more supporive of he ML condiion (see, e.g., Bahmani-Oskooee 1998, Bahmani-Oskooee and Niroomand 1998, Caporale and Chui 1999, Boyd, Caporale and Smih, 21). Also, increasingly empirical invesigaions have been based on a reduced-form equaion for he balance of rade, a mehod which allows o es direcly for he response of rade flows o relaive price movemens using he real exchange rae (as opposed o he erms of rade) (see, e.g., Rose 1991, and Lee and Chinn 1998). I is normally hough ha a nominal devaluaion or depreciaion can only reduce rade imbalances if i ranslaes ino a real one and if rade flows respond o relaive prices in a significan and predicable manner (Reinhar, 1995). A depreciaion (or devaluaion) of he domesic currency may simulae economic aciviy hrough an iniial increase in he price of foreign goods relaive o home goods: by increasing he global compeiiveness of domesic indusries i divers spending from he former o he laer (Kandil and Mirazaie, 25). 1
Dornbusch (1988) shows ha he effeciveness of a depreciaion in improving he balance of paymens depends on redirecing demand in he righ direcion and by he correc amoun and also on he capaciy of he domesic economy o mee he addiional demand hrough increased supply. Bird (21) argues ha here is no mechanism for keeping he real exchange rae a an equilibrium level if inflaion is rising quickly or for changing equilibrium raes in he case of permanen real shocks. In his opinion, his is he reason why many developing counries have chosen flexible exchange raes, alhough his is no an ideal soluion since demand and supply elasiciies may be relaively low: even when hey saisfy he Marshall-Lerner condiions, heir response o exchange rae changes may no be as big as in developed economies. Moreover, wih hin foreign exchange markes floaing exchange raes may be unsable and vulnerable o speculaive aacks as he Kenyan exchange rae crisis of 211 illusraed (Mudida, 212): if he exchange rae is driven down sufficienly, i can generae addiional inflaion which may offse he exra compeiiveness associaed wih a depreciaion. A relaed issue is wheher here exis J-curve effecs, i.e. wheher following a currency depreciaion or devaluaion he balance of rade will worsen in he shor run, bu hen, as elasiciies increase over ime, i will begin o improve (Kulkarni and Clarke, 29). Case sudies on several African counries such as Zambia and Nigeria seem o suppor empirically he exisence of a J-curve. However, no sudies have been carried ou ye o es he Marshall-Lerner condiion in Kenya, which represens an ineresing case since is expors are relaively more diversified han hose of he sub-saharan African economies. The presen paper is he firs o provide evidence for his counry; moreover, i uses advanced echniques in ime series analysis, based on he conceps of fracional inegraion and coinegraion, which are more general han he sandard mehods based 2
exclusively on ineger degrees of differeniaion and have no been previously used o analyse he Marshall-Lerner condiion in an African conex. The layou of he paper is as follows. Secion 2 discusses he imporance of he Marshall-Lerner condiion in he Kenyan case. Secion 3 briefly describes he heoreical framework, whils Secion 4 presens he economeric analysis. Finally, Secion 5 summarises he main findings and offers some concluding remarks. 2. The Marshall-Lerner condiion and he Kenyan economy The Inernaional Moneary Fund (IMF) classifies Kenya as having operaed an independen floa beween 1992 and 1997 and a managed floa since 1998. Prior o ha, he Kenyan shilling was pegged firs o he Briish pound, hen o he US dollar, and finally o he IMF s Special Drawing Righs (SDRs) before a crawling peg based on a rade-weighed baske was inroduced. The Marshall-Lerner condiion should herefore be analysed in Kenya in he conex of he curren exchange rae sysem, which is a managed floa sysem, and indeed he daa se used in his sudy covers he floaing period. Consequenly, we consider a depreciaion raher han a devaluaion of he Kenyan shilling since his is wha is relevan for he period under invesigaion. The exising empirical evidence on he operaion of Kenya s managed floa sysem suggess ha a imes of relaive ranquilliy in foreign exchange markes he Cenral Bank of Kenya can smooh ou exchange rae volailiy wih relaively modes inervenions; by conras, more acive policies are required in he presence of more volaile exchange raes (O Connell e. al, 21). Tesing he Marshall-Lerner condiion is paricularly imporan in he Kenyan case because, as in many oher developing counries, he curren accoun of he Kenyan balance of paymens is persisenly in defici. The issue of wheher a depreciaion of he 3
exchange rae can reduce his defici herefore becomes criical. A large share of Kenyan expors is represened by agriculural producs wih low price elasiciies of demand. However, horiculural producs and manufacured goods are also expored. Indeed, Kenya s larges rading parner is Uganda which impors primarily manufacured goods from Kenya. On he oher hand, Kenyan impors are primarily made up of agriculural machinery, peroleum and manufacured goods which one would expec o have a low price elasiciy of demand for impors owing o heir criical role in he developmen process. This raises he ineresing quesion of he size of real exchange depreciaion required o eliminae Kenya s balance of paymens curren accoun defici. The broader issue relaed o he Marshall-Lerner condiion in Kenya is ha of real exchange arges for he Cenral Bank of Kenya, namely is here an opimal real exchange rae ha should be argeed? A real exchange rae appreciaion redirecs resources from he expor-producing secor penalizing i and causing poenially severe welfare losses (Rodrik, 28). Pollin and Heinz (27) have advocaed he adopion of a new moneary policy framework in Kenya in order o achieve a more sizeable depreciaion of he shilling in real erms. They sress ha he conribuion of he expor secor, which is favoured by a real exchange depreciaion, is unique from a developmen perspecive owing o he number and qualiy of jobs creaed and also o he produciviy spillovers o oher secors of he economy. The challenge of an excessively weak Kenya shilling, however, was illusraed in 211 when a vicious cycle was creaed beween inflaion and depreciaion (Mudida, 212). This paper herefore also aims o conribue o he debae on he arge for he real exchange rae of he Kenya shilling, which is a paricularly ineresing one because he primary ask of he Cenral Bank of Kenya is price sabiliy, a presen being pursued hrough inflaion argeing, wih expeced inflaion as he nominal anchor. I is well known ha inflaion argeing may be counerproducive in he presence 4
of supply-side shocks, which are prevalen in he Kenyan economy (Adam e. al, 21). Therefore analysing he Marshall-Lerner condiion in Kenya is also imporan in view of he concerns facing he Kenyan moneary auhoriies. 3. Theoreical Framework The balance of rade can be expressed as he raio of nominal expors o nominal impors, B, which is equal o he raio of he volume of expors, X, muliplied by domesic prices, P, o he volume of impors M, muliplied by foreign prices, P *, and he nominal spo exchange rae S: B = P X, * P S M or using lower case leers for logarihms: b ( s p + p ) = x m e, * = x m (1) where e s p + * p = is he real exchange rae. Long-run impor and expor demand are given by: x m * * = α + β y + η e + γ, (2) x x = α + β y η e + γ. (3) m m x m where y and y * sand for domesic and foreign real income respecively, he rends capure erms of rade effecs, and η x and η m represen he expor and income elasiciies respecively. The long-run balance of rade is b = ( α x α y ) + β * y * β y + ( η x + η m 1)e + ( γ x γ m ). (4) The coefficien on e gives he familiar Marshall-Lerner condiion for a devaluaion (increase in e ) o improve he balance of paymens (i.e., his coefficien 5
needs o be saisically significan and posiive for he ML condiion o be saisfied, which means ha he sum of he demand elasiciy for impors and he foreign demand elasiciy for he naion s expor exceeds uniy). Solvency requires b = in he long run, whils Purchasing Power Pariy (PPP) requires e = e, for all. The long-run relaionship (4) can be wrien as b * * = α + β y β y + ηe + γ, (5) where α = (α x - α m ); η = (η x η m - 1), and γ = (γ x γ m ), and he deviaions from he longrun equilibrium can be defined as z * * = α + β y β y + ηe + γ b. (6) 4. Economeric Analysis We use quarerly daa on he log of real exchange raes, expor-impor raio and relaive (US) income for he ime period 1996q1 211q4. All series were obained from he Cenral Bank of Kenya. The base period for he real effecive exchange rae is January 23. The real effecive exchange rae is consruced using a baske including he eigh counries which are Kenya s mos imporan rading parners, and is defined in such a way ha an increase represens a depreciaion, i.e. a direc quoe is used as common in developing counries. Figure 1 displays he hree series (in logs) in boh levels and firs differences. The expor/impor raio and he real exchange rae decline over he sample period, whils relaive income increases. The firs differenced series daa show ha seasonaliy is an imporan feaure of hese daa, especially for he expor/impor raio and relaive income. [Inser Figures 1 3 abou here] Figure 2 displays he firs hiry sample auocorrelaions for he original series and heir firs differences. The slow decay for he series in levels indicaes ha hey may be 6
nonsaionary, while he sample auocorrelaions for he firs differences sugges once more he presence of seasonaliy, especially in he case of relaive income. Finally, Figure 3 displays he periodograms. For he series in levels he highes value corresponds o he smalles frequency, which indicaes ha hey may require differencing. However, he periodogram of he firs differenced expor/impor raio series has a value close o zero a he smalles frequency, suggesing ha his series may now be overdifferenced. As a firs sep we check he order of inegraion of he hree series by means of sandard mehods such as ADF (Dickey and Fuller, 1979), Phillips and Perrron (PP, 1988), Kwiakowski e al. (KPSS, 1992), Ellio e al. (ERS, 1996) and Ng and Perron (NG, 21) ess. The resuls (no repored) are conclusively in favour of uni roos for he real exchange rae and relaive income, whils mixed evidence is found in he case of he expor/impor raio. However, hey should be aken wih cauion, since he above mehods have limiaions such as very low power if he rue Daa Generaing Process (DGP) is fracionally inegraed (see, e.g., Diebold and Rudebusch, 1991; Hassler and Wolers, 1994; Lee and Schmid, 1996 among ohers). Thus, in wha follows we consider models ha allow for boh ineger and fracional orders of differeniaion. We esimae d (he differencing parameer) using he While funcion in he frequency domain (Dahlhaus, 1989) and also employ a esing procedure developed by Robinson (1994) which has been shown o be he mos efficien in he conex of I(d) models. The laer mehod is parameric, so a parameric model for he disurbances erm has o be specified. A semiparameric mehod, also based on he While funcion (Robinson, 1995, Abadir e al., 27) will also be employed. We repor in Table 1 he esimaed values of d in a model given by d y = α + β + x (1 L) x = u, (7) ; 7
where y is he observed (univariae) ime series; α and β are he coefficiens on he inercep and a linear rend respecively, and x is assumed o be an I(d) process. Thus, u is I() and given he parameric naure of his mehod is funcional form mus be specified. We assume ha u is a whie noise, auocorrelaed and seasonally auoregressive respecively. In he case of auocorrelaed errors, we use he exponenial model of Bloomfield (1973). This is a non-parameric approach for modelling u ha produces auocorrelaions decaying exponenially as in he AR(MA) case. The model is implicily deermined by is specral densiy funcion, which is given by: 2 σ m f ( λ ; τ ) = exp 2 cos( ), 2 τ r λ r (8) π r = 1 where σ 2 is he variance of he error erm, and m is he number of parameers required o describe he shor-run dynamics of he series. Bloomfield (1973) showed ha he logarihm of an esimaed specral densiy funcion is ofen a fairly well-behaved funcion and can hus be approximaed by a runcaed Fourier series; in paricular, he specral densiy of an ARMA process can be well approximaed by (8). Moreover, his model is saionary across all values of τ, and works exremely well in he conex of Robinson s (1994) ess (Gil-Alana, 24). [Inser Table 1 abou here] Table 1 displays he esimaes of d (along wih he 95% confidence bands corresponding o he non-rejecion values of d using Robinson s (1994) ess) for he hree ypes of disurbances (whie noise, Bloomfield, and seasonal AR) and for he hree sandard cases of: i) no regressors (i.e., α = β = a priori in (7)), an inercep (α unknown and β = a priori), and an inercep wih a linear ime rend (i.e., α and β unknown). The -values (no repored) for he deerminisic erms indicae ha he ime rend is required 8
in all cases. The upper par of he able refers o he case of whie noise disurbances. Focusing on he case of a linear rend, we see ha he esimaed value of d for he log(expor/impor) raio is.373, and he confidence inerval excludes he cases of saionariy I() (d = ) and nonsaionary uni roos (d =1). For he real exchange rae, he esimaed d is.888 and he uni roo null hypohesis canno be rejeced a he 5% level. Finally, for relaive income, he esimaed value of d is.664 and he I(1) case is rejeced in favour of mean reversion (d < 1). The resuls based on he assumpion of auocorrelaion as in he model of Bloomfield (1973) (wih m = 1) 1 are displayed in Table 1(ii). The esimaed values of d (for he case of a linear rend) are.574,.728 and.865 respecively for he expor/impor raio, real exchange raes and relaive income, and he uni roo null canno be rejeced in he las wo cases. Finally, when imposing seasonal (quarerly) auoregressions, hese values are.376,.899 and.963 and similarly o he previous case he I(1) hypohesis canno be rejeced for real exchange raes and relaive income, while i is rejeced in favour of mean reversion for he expor/impor raio. The above resuls are corroboraed by hose based on he semiparameric mehod of Robinson (1995). This is essenially a local While esimaor in he frequency domain, which uses a band of frequencies degeneraing o zero. The esimaor is implicily defined by: ˆ m 1 d = arg min log ( ) 2 log d C d d λ s, (9) m s = 1 C( d) = 1 m m 2d 2 π s 1 m I( λ s) λ s, λs =, + s = 1 T m T, where I(λ s ) is he periodogram of he raw ime series, and d (-.5,.5). Under finieness of he fourh momen and oher mild condiions, Robinson (1995) proved ha: 1 Oher values of m produced essenially he same resuls. 9
ˆ * m ( d d ) db N(, 1/ 4) as T, where d * is he rue value of d. This esimaor is robus o a cerain degree of condiional heeroscedasiciy (Robinson and Henry 1999) and is more efficien han oher semiparameric compeiors. 2 [Inser Figure 4 abou here] Figure 4 display he esimaes of d in (9) along wih he 95% confidence inerval corresponding o he I() and I(1) cases. The horizonal axis repors he bandwidh parameer while he verical one he esimaes of d. For he expor/impor raio some of he esimaes are wihin he I(1) inerval bu mos are below i alhough above he I() one. For he real exchange rae, mos of he esimaes of d are wihin he I(1) inerval. Finally, for relaive income, hey are above he I(1) inerval if he bandwidh parameer is low, whils are wihin i if i is large. This may be a consequence of he srong seasonal paern observed in his series. 3 I is also consisen wih he resuls repored for he parameric case above where he uni roo canno be rejeced in case of he exchange rae (and in some cases for relaive income) and is rejeced in favour of mean reversion for he expor/impor raio. Considering again he resuls presened in Table 1, we nex selec he bes model specificaion for each series. We conduced several diagnosic ess on he residuals of he esimaed models, and, in paricular, we used Box-Pierce and Ljung-Box-Pierce saisics (Box and Pierce, 197; Ljung and Box, 1978) o es for no serial correlaion, as well as LR ess and oher likelihood crieria. 4 The seleced models for each variable are he following: 2 This mehod has been furher refined by Velasco (1999), Velasco and Robinson (2), Phillips and Shimosu (24, 25), Abadir e al. (27) and ohers. When using hese approaches he resuls were pracically idenical o hose repored in he paper. 3 The bandwidh deermines he rade-off beween he bias and he variance in he esimaion of d. 4 Specifically, he AIC and he SIC. Noe, however, ha hese crieria migh no necessarily be he bes ones in applicaions involving fracional differences, as hey focus on he shor-erm forecasing abiliy of he 1
y =.473.81 + x, (1 L).573 x = u, ( 5.9) ( 3.) u Bloomfield ( τ =.291) for he expor/impor raio. (-values in parenhesis). For he real exchange rae, he seleced model is y = 4.6981.64 + x, (1 L).728 x = u, (135.12) ( 3.71) u Bloomfield ( τ =.28) Finally, for relaive income, y = 3.8257.16 + x, (1 L).963 x = u, ( 24.33) ( 5.19) u =.893u 4 + ε. The fac ha he confidence inervals for he fracional differencing parameers in he seleced models overlap for he hree series 5 implies ha he null of equal orders of inegraion canno be rejeced. This is imporan since i makes i legiimae o run an OLS regression wih he hree variables o check if he esimaed errors are I() or a leas mean-revering wih a smaller order of inegraion han he hree paren series. 6 We follow a wo-sep procedure, similar o ha of Engle and Granger (1987), bu specifically designed o allow for fracional inegraion. In he firs sep, we compue he following regression, y = α + β1z1 + β2z2 + x, (1) fied model and may no give sufficien aenion o heir long-run properies (see, e.g. Hosking, 1981, 1984). 5 These inervals are (.267,.975) for he expor/impor raio, (.441, 1.124) for he real exchange rae, and (.763, 1.247) for relaive income (see Table 1). 6 We also compue an adapaion of he Robinson and Yajima (22) saisic Tˆ xy for log-periodogram esimaion in pairwise comparisons of he hree series; he resuls suppor he hypohesis of homogeneiy in he orders of inegraion. 11
where y sands for he balance of rade, z 1 for he real exchange rae and z 2 for relaive income. Then, in he second sep, we esimae he order of inegraion of he residuals from (1) using he mehods employed above for he univariae analysis. Performing he OLS regression in (1) we obain y = 3.487 ( 6.84) +.942 z1 (1.77).6643 z2 ( 4.89) + xˆ. (11) The esimaed residuals are ploed in Figure 4. The posiive (and saisically significan) coefficien on he real exchange rae indicaes ha he ML condiion is saisfied in Kenya. [Inser Figure 4 and Table 2 abou here] Table 2 displays he esimaed values of d for he OLS residuals. We consider again he hree sandard cases of no regressors, an inercep and a linear rend, for whie noise, Bloomfield, and seasonal AR disurbances. The esimaes are all in he range (.23,.25) being subsanially smaller han hose for he individual series and hus supporing he exisence of mean reversion in he long-run equilibrium relaionship. If we focus now on he confidence inervals we see ha he null hypohesis of I() errors is rejeced for he cases of whie noise and seasonal AR disurbances in favour of posiive orders of inegraion, while his hypohesis canno be rejeced wih auocorrelaed (Bloomfield) disurbances. The mos adequae specificaion for he esimaed residuals in he coinegraing regression (1) appears in bold in Table 2. This model includes an inercep and seasonal AR disurbances. We also perform he Hausman-ype es of no coinegraion agains he alernaive of fracional coinegraion proposed by Marinucci and Robinson (21); he resuls (no repored) srongly rejec he null for differen bandwidh parameers given furher suppor o he hypohesis of coinegraion among he variables examined. 12
5. Conclusions and Policy Recommendaions Our findings suppor he exisence of a well-defined coinegraing relaionship beween he balance of paymens, he real exchange rae and relaive income and indicae ha he Marshall-Lerner condiion holds in Kenya. Our analysis is based on fracional inegraion and coinegraion mehods, which are more general han he sandard mehods allowing only for ineger degrees of differeniaion. Sudies using he laer o es he Marshall- Lerner condiion in many African counries are eiher inconclusive or end o sugges ha i does no hold in he shor run alhough i may hold in he long run. The evidence (based on more general mehods) ha i holds in Kenya has imporan policy implicaions for his counry. I implies ha he exchange rae is an imporan ool for aemping o address persisen balance of paymens curren accoun deficis in Kenya and can herefore conribue o achieving an exernal balance. The fac ha he Marshall-Lerner condiion holds means ha a depreciaion of he exchange rae leads o a reducion in impor expendiure and an increase in expor sales. This reflecs an imporan ransiion made in Kenya in erms of he composiion of expors: from radiional agriculural expors exhibiing low expor elasiciies of demand o more diversified non-radiional expors such as horiculure and manufacured goods ha exhibi a higher elasiciy of demand. Our resuls indicae ha a depreciaion in he Kenya shilling can herefore have poenially beneficial effecs on Kenya s curren accoun defici. These, however, have o be weighed agains he higher inflaion rae associaed wih such an exchange rae movemen. Inflaionary effecs were eviden during he 211 foreign exchange crisis in Kenya when a depreciaion of 3% of he Kenya shilling agains he US dollar led o monh-on-monh inflaion of 19% by he end of 211 (Mudida, 212). 13
Given ha a presen he primary objecive of he Cenral Bank of Kenya is price sabiliy, he focus recenly has been on mainaining high ineres raes so as o reduce he inflaion rae and also o avoid a significan depreciaion of he Kenya shilling. This igh moneary policy sance is hough o reduce inflaionary pressure and also o promoe porfolio invesmen inflows ino Kenya, hus improving he capial accoun. High ineres raes end o have a derimenal effec on economic growh. Our findings, however, sugges ha a moderae depreciaion of he Kenyan shilling may in fac have a sabilizing influence on he balance of paymens hrough he curren accoun wihou he need for high ineres raes. Thus a less conracionary moneary policy by he Cenral Bank of Kenya could in fac be combined wih an appropriae exchange rae policy o achieve more effecively he objecives of inernal and exernal balance in Kenya. This would be a beer opion han he curren high ineres rae policy being pursued by he Cenral Bank ha achieves exernal balance bu only a he high cos of sifling economic growh. Oher recenly developed bivariae or mulivariae fracional coinegraion esing mehods (e.g. Johansen, 21; Nielsen, 21; Nielsen and Frederiksen, 211) could also be applied. This could be very useful o invesigae possible J-curve effecs in he conex of a much richer srucure including oher underlying dynamics and shor-run componens. Srucural breaks and non-lineariies could also be examined in he conex of fracional inegraion. These issues will be invesigaed in fuure papers. 14
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Figure 1: Original series and firs differences LOG(EXP/IMP) = x 1 (1 L)x 1,4 -,2 -,4,2 -,6 -,8-1 -,2-1,2 1996q1 211q4 -,4 1996q2 211q4 LOG(REER) = x 2 (1 L)x 2 4,8,15 4,6 4,4,5 4,2 4 -,5 3,8 1996q1 211q4 -,15 1996q2 211q4 LOG(NOMGNP/USGNP) = x 3 (1 L)x 3-3,15-3,2-3,4,5-3,6 -,5-3,8-4 1996q1 211q4 -,15 1996q2 211q4 EXP/IMP = Expor/Impor raio; REER = Real Effecive Exchange Rae; NOMGNP = Nominal GNP and USGNP= US GNP. 19
Figure 2: Correlograms of he original series and firs differences LOG(EXP/IMP) = x 1 (1 L)x 1 1,2,8,8,4,4 -,4 -,4 1 4 7 1 13 16 19 22 25 28 31 -,8 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 LOG(REER) = x 2 (1 L)x 2 1,2,3,8,1,4 -,1 -,4 1 4 7 1 13 16 19 22 25 28 31 -,3 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 LOG(NOMGNP/USGNP) = x 3 (1 L)x 3 1,2,8,7,4,3 -,1 -,4 1 4 7 1 13 16 19 22 25 28 31 -,5 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 The hick lines give he 95% confidence band for he null hypohesis of no auocorrelaion. 2
Figure 3: Periodograms of he original series and firs differences LOG(EXP/IMP) = x 1 (1 L)x 1,8,16,6,12,4,8,2,4 1 4 7 1 13 16 19 22 25 28 31 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 LOG(REER) = x 2 (1 L)x 2,1,2,8,15,6,4,2,1,5 1 4 7 1 13 16 19 22 25 28 31 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 LOG(NOMGNP/USGNP) = x 3 (1 L)x 3,2,4,15,3,1,2,5,1 1 4 7 1 13 16 19 22 25 28 31 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 The horizonal axis refers o he discree Fourier frequencies λ j = 2πj/T, j = 1,, T/2. 21
Table 1: Esimaes of d and 95% confidence bands for he hree individual series i) Whie noise disurbances No regressors An inercep A linear ime rend LOG(EXP/IMP).511 (.372,.714).493 (.413,.65).373 (.258,.536) LOG(REER).934 (.787, 1.148).883 (.742, 1.129).888 (.74, 1.129) LOG(NOM/USGNP).949 (.792, 1.174).755 (.691,.856).664 (.569,.82) ii) Bloomfield-ype disurbances No regressors An inercep A linear ime rend LOG(EXP/IMP).728 (.394, 1.144).643 (.422,.971).574 (.267,.975) LOG(REER).842 (.552, 1.234).83 (.637, 1.117).728 (.441, 1.124) LOG(NOM/USGNP).824 (.543, 1.173).892 (.741, 1.74).865 (.673, 1.93) iii) Seasonal (quarerly) AR disurbances No regressors An inercep A linear ime rend LOG(EXP/IMP).495 (.321,.734).495 (.361,.626).376 (.223,.569) LOG(REER).857 (.546, 1.155).896 (.745, 1.134).899 (.723, 1.137) LOG(NOM/USGNP).885 (.574, 1.173).969 (.82, 1.262).963 (.763, 1.247) 22
Figure 4: Esimaes of d and 95% confidence bands for he hree individual series i) LOG(EXP/IMP) 2 1,5 1,5 -,5-1 1 4 7 1 13 16 19 22 25 28 31 ii) LOG(REEF) 2 1,5 1,5 -,5-1 1 4 7 1 13 16 19 22 25 28 31 iii) Log(NOM/USGNP) 2 1,5 1,5 -,5-1 1 4 7 1 13 16 19 22 25 28 31 The horizonal axis concerns he bandwidh parameer while he verical one refers o he esimaed value of d. The hick lines give he 95% confidence bands for he I() and I(1) hypoheses. 23
Figure 4: Esimaed residuals from he coinegraing regression,4,2 -,2 -,4 1966q1 211q4 Table 2: Esimaes of d and 95% confidence bands for he hree individual series i) Whie noise disurbances No regressors An inercep A linear ime rend Whie noise.239 (.89,.435).239 (.89,.434).241 (.91,.436) Bloomfield.255 (-.46,.575).258 (-.5,.579).259 (-.48,.579) Seasonal AR.244 (.72,.453).244 (.71,.452).246 (.72,.455) 24