Volume 31, Issue 1. Are exports and imports cointegrated in India and China? An empirical analysis

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1 Volume 3, Issue Are expors and mpors conegraed n Inda and Chna? An emprcal analyss Avral Kumar war ICFAI Unversy, rpura Absrac hs sudy analyss he susanably of he rade defcs n he wo gan economes of Asa, namely Inda and Chna wh allowance of endogenous srucural breaks. We found ha rade defc s susanable n case of Inda bu no n case of Chna. hs mples ha macroeconomc polces of Inda bu no of Chna have been effecve n leadng expors and mpors o long run seady sae equlbrum relaonshp. I am graeful o Paresh Kumar Narayan for provdng me he codes of hs paper for my analyss and wo anonyms referee for he consrucve suggesons n mprovng hs paper n consderable manner parcularly n mehodologcal aspec. Of course, any error ha remans s mne. Caon: Avral Kumar war, (0) Are expors and mpors conegraed n Inda and Chna? An emprcal analyss, Economcs Bullen, Vol. 3 no. pp Submed: Jun Publshed: March 7, 0.

2 I. Inroducon Impors and expors are wo mporan elemens of he Balance of Paymens (BOPs) of any counry. Developng counres receve a major share of her Gross Naonal Produc (GNP) from he expor of agrculural, agr-relaed and oher prmary commodes. Developng counres are also heavly dependen on he mpor of dverse capal and consumer goods o feed her ndusres and sasfy her people s consumpon needs. herefore, hese counres have o ake adequae care of he movemen of her mpors and expors and hus have o revse her rade polcy from me o me so ha he adverse rade balance may no ge elusve. A beer pcure of he foregn rade regme of a counry can be obaned f he behavor of mpors and expors s nvesgaed by examnng her me seres properes. Exernal accoun s an mporan ndcaor of a counry s economc performance as major exernal mbalances mgh predc fuure changes n a managed foregn exchange regme. here are number of facors ha may cause he exernal defcs or surpluses n he counry s exernal accoun. Emprcal sudes aemp o denfy he sources of exernal mbalances by relang he exernal accouns o key macroeconomc varables: governmen spendng, prvae consumpon, ncome ec. (Sachs, 98; Ahmed, 987; Razn, 995; Ello and Faas, 996). Some auhors (for example Ars and Bayoum, 989) argue ha fscal and moneary polces have amed o reduce he sze of exernal mbalances n a number of counres. Oher sudes have poned ou ha hese exernal balances are he oucome of bad polcy, a leas n relaon o he USA durng he 980s (Summers, 988 and Hused, 99). ha s why susanably of foregn rade defcs has become he major concern of he polcy makers, cenral banks and he marke analyss of he emergng economes. In smple foregn rade mulpler erms an ncrease n expors leads o an ncrease n domesc ncome whch ncreases mpor. herefore, a counry s mpor nensy depends on s expor ably; noneheless s no he only one deermnng facor. hs s why, he objecve of hs sudy s o examne wheher he foregn rade defcs n Inda and Chna are susanable.e., wheher Inda s and Chnas expors and mpors are conegraed. For fases growng counres lke Inda and Chna, he curren accoun defc occupes he cenre sage n polcy dscussons, as he perssen dscrepances n curren accoun and rsng levels of rade defc pose rsks o he susanably of hgh economc growh and macroeconomc sably. From he fgure s evden ha expors and mpors seres of he boh counres have sharp flucuaons n he year of 990.

3 Fgure : Expors and mpors plos of Inda and Chna (measured n bullons of US dollars and expressed n naural log forms. II. Leraure revew In recen mes, n he area of nernaonal rade, many emprcal sudes have been conduced o analyze he exsence and he naure of long-run or conegrang relaonshp beween expors and mpors. One of he earles poneerng works n hs area has been he sudy by Hused (99). Usng quarerly US rade daa for he perod , Hused has shown ha expors and mpors are conegraed n he long run. Hused (99) has shown ha he exsence of conegrang relaonshp beween expors and mpors mples ha counres do no volae her nernaonal budge consran and herefore suppors he effecveness of her macroeconomc polces n resorng he long-run equlbrum. Herzer and Nowak-Lehmann (006) and Erbaykal and Karaca (008) have shown he exsence of a conegraed relaonshp beween expors and mpors, whch sugges ha rade defcs are only shor-erm phenomenon herefore, susanable n he long-erm. Bahman-Oskooee and Rhee (997) used quarerly daa o model expors and mpors for Korea. hey found evdence of conegraon and he coeffcen on expors was posve. Narayan and Narayan (005) nvesgae wheher here s a long-run relaonshp (conegraon) beween expors and mpors for leas developed counres (LDCs). hey analyzed hs ssue usng he bounds esng approach o conegraon. hey found ha expors and mpors are conegraed only for sx ou of he counres, and he coeffcen of expors s less han one. In he Indan case, Upender (007) has shown ha Inda s nomnal expors and mpors were conegraed by employng daa for he perod o Arze (00) used quarerly daa for he perod from 50 OCED and developng counres o examne he same queson. He found ha for 35 of he 50 counres here was evdence of conegraon beween expors and mpors; and 3 of he 35 counres had a posve expor coeffcen. Konya and Sngh (008), by employng daa for he perod o and allowng a srucural break n 99-93, found no evdences of conegrang relaonshp beween Inda s expors and mpors. he exogenously deermned srucural break n He has also developed a heorecal model o explan hs phenomenon.

4 ncorporaes he poenal mpac of he March 993 swch from a fxed exchange rae regme o a free floang exchange rae polcy. III. Objecve, Daa source and esmaon mehodology III.I. Objecve he basc objecve se n he sudy s o examne he long-run relaonshp beween expors and mpors for he Chnese and Indan economy. o he bes of my knowledge here s no sudy n he conex of Chna and Inda whch has analyzed he conegraon relaonshp by endogenously deermned srucural break. Our conrbuon o he exsng leraure s wofold. Frs, mos of he exsng sudes have used sandard un roo ess for saonary. However, s emprcally verfed ha resuls wll be nconclusve f endogenous srucural breaks have no been ncorporaed n he analyss. Secondly, as Herzer and Nowak-Lehmann (006) have shown ha sandard conegraon ess end o falsely accep he null of no conegraon when here s a srucural break under he alernave hypohess. herefore, n hs sudy we have made an aemp o ncorporae endogenously deermned srucural breaks n conducng un roo and conegraon analyss. III.II. Daa source and varables descrpon he daa used are monhly observaons of he (nomnal) bllon Uned Saes (US) $ values of expors and mpors. he daa has been obaned from OECD webse and was exraced on 7 h June 00. me perod of he analyss s from January -99 o February Boh varables have been ransformed n naural log form n order o make daa seres of less order Auoregressve (AR).e., o mnmze flucuaons n he seres. III.III. Esmaon mehodology radonal un roo ess lke Augmened Dckey Fuller (ADF) (979) and Phllps-Perron (PP) (988) are found o gve msleadng resuls (.e., based owards he non-rejecon of null hypohess when srucural breaks are presen n he daa seres (Perron, 989). herefore, n he presen sudy we have adoped wo dfferen es of un roo es o es he saonary propery of he daa n he presence of srucural breaks. 4 Frs one s Lee and Srazcch (003, 004) es and second s Narayan and Popp (00), a novel es. Lee and Srazcch (003, 004) es of un roo allows us o es for a mos wo endogenous break and uses he Lagrange Mulpler (LM) es sascs. Le us consder he followng daa generang process (DGP): y = δz + e, e = β e + ε.() where Z s a vecor of exogenous varables, δ s a vecor of parameers and ε s a whe nose process, such ha ε ~ NIID (0, σ ). Frs we wll consder he case when break here s evdence of one srucural break. he Crash model ha allows shf n level only s descrbed by Z =,, D ], and he break model ha allows for changes n boh level and rend s descrbed as [ Z = [,, D D ], where D and D =,f + B D are wo dummes defned as: I should be noed ha f we ake real values of expors and mpors he resuls may ge change. herefore, for he polcy purpose he use of he resuls drawn n hs paper should be carefully examned. 3 I should also be noed ha snce we are usng monhly observaons herefore, even hough sample sze s large bu me span of he sudy s small whch may also affec our resuls so careful examnaon of resuls s requred s for polcy purposes. 4 I s mporan o no ha we have also used un roo es proposed by Sakkonen and Lükepohl (00) and resuls of Sakkonen and Lükepohl (00) un roo es are repored n able of Appendx. Snce we do no fnd any dfference n fndngs when we adop he seasonal dummes and when we do no ncorporae he seasonal dummes herefore, we have repored resuls of he models whch do no ncorporae seasonal dummes only. However, resuls of he model whch ncorporaes seasonal dummes are avalable from he auhor upon reques. 3

5 = 0, oherwse and D = B, f B + = 0, oherwse where B s he me perod of he break dae. Nex, le us consder he framework ha allows for wo srucural breaks. he crash model ha consders wo shfs n level only s descrbed by Z = [,, D, D ], and he break model ha allows for wo changes n boh level and rend s descrbed as Z = [,, D D D D ], where D j and D j for j =, are approprae dummes defned as above, vz., D j =,f + and D Bj = 0, oherwse = f + j Bj, Bj = 0, oherwse where Bj s he j h break dae. he man advanage of (Lee and Srazcch, 003, 004) approach o un roo es s ha allows for breaks under he null (β = ) and alernave (β < ) n he DGP gven n equaon (). hs mehod uses he followng regresson o oban he LM un roo es sascs k ~ ~ y = δ Z + φs + γ S j + u...() = ~ ~ ~ ~ where S = y Ψ Zδ, =,..., ; δ denoes he regresson coeffcen of y on Z and ~ ~ Ψ = y Z δ, y and Zbeng frs observaons of y and Z respecvely. he lagged erm ~ are ncluded o correc for lkely seral correlaon n errors. Usng he above equaon, he S j null hypohess of un roo es ( φ = 0) s esed by he LM -sascs. he locaon of he srucural break or srucural breaks s deermned by selecng all possble breaks for he mnmum -sasc as follows: ln f ~ τ ( λ ) ln ~ = λ fτ ( λ), where λ = B /. he search s carred ou over he rmmng regon (0.5, 0.85), where s sample sze and B denoes dae of srucural break. We deermned he breaks where he endogenous wo-break LM -es sasc s a a mnmum. he crcal values are abulaed n Lee and Srazcch (003, 004) for he wo-break and one-break cases respecvely. Second es adoped n hs sudy s suggesed by Narayan and Poop (00). he procedure of he es of Narayan and Poop (00) can be explaned as follows. Suppose, we consder an unobserved componens model o represen he DGP and he DGP of a me seres y has wo componens, a deermnsc componen (d ) and a sochasc componen (u ), as follows: y = d + u,...(3) u = ρ u + ε = Ψ * ( L) e ε,...(4) = A * ( L) B( L) e, (5) 4

6 e s a whe nose process, such ha e ~ NIID (0, σ ). By assumng ha he roos of he lag polynomals A*(L) and B(L) are of order p and q, respecvely, le ousde he un crcle NP (00) consdered wo dfferen specfcaons for rendng daa- one allows for wo breaks n level (denoed as model.e., M) and he oher allows for wo breaks n level as well as slope (denoed as model.e., M). he specfcaon of boh models dffers n erms of he defnon of he deermnsc componen, d, : M d = α + β + Ψ * ( L)( θ DU + θ DU ),...(6) d M, = α + β + Ψ *( L)( θ DU + θ DU + γ D + γ D,,,,, ),...(7) Wh DU, = ( > B, ), D, = ( > B, )( DB, ), =,..(8) were,, =,, denoe he rue break daes, θ and γ, ndcae he magnude of he level and B, slope breaks, respecvely. he ncluson of Ψ *( L) n Equaons (6) and (7) enables breaks o occur slowly over me.e., assumes ha he seres responds o shocks o he rend funcon he way reacs o shocks o he nnovaon process e (Vogelsang and Perron, 998). hs process s known as he Innovaonal Ouler (IO) model and he IO-ype es regressons o es for he un roo hypohess for M and M can be derved by mergng he srucural model (3) (8). he es regressons can be derved from he correspondng srucural model n reduced form as follows: y M Wh = ρ y + α + β * + θd( B ), + θd( B ), + δdu, + δdu, + β j y j + e,...(9) α * β = Ψ *() y + M k j= = ρy = Ψ *() [( ρ) α + ρβ] + Ψ*() ( ρ) β, Ψ*() ( ρ) β, φ = ρ, δ = φθ andd( B ), = ( = B, β y j j + α * + β * + κ D( + e,...(0) ) B, + κ D( B ), + δ DU *, * k j= + δ DU beng he mean lag, + ), =,., + γ D *, + γ D where equaon (9) and (0) are Innovaonal Ouler (IO)-ype es regresson for M and M * * respecvely, κ = ( θ + γ ), δ = ( γ φθ ), and γ = φγ, =,. In order o es he un roo null hypohess of ρ = agans he alernave hypohess of ρ <, we use he -sascs of ρˆ, denoed ρˆ, n Equaons (9) and (0). Snce s assumed ha rue break daes are unknown, subsued by her esmaes ˆ B, B, *, n equaons (9) and (0) has o be, =,, n order o conduc he un roo es. he break daes can be seleced smulaneously followng a grd search procedure or a sequenal procedure comparable o Kapeanos (005). Narayan and Poop (00) have preferred sequenal procedure as because s far less compuaonally demandng herefore; we have also followed sequenal procedure. In hs case n he frs sep search for a sngle break whch we selec accordng o he maxmum absolue -value of he break dummy coeffcen θ for M and κ for M. hereafer, we mpose he resrcon θ = δ = 0 for M and κ = δ= γ= 0 for M and hence, we have: 5

7 arg max ˆ ( B ), for θ, B, M, B, = () arg max ˆ ( B,), for M κ B, So, n he frs sep, he es procedure reduces o he case descrbed n (Popp, 008). Imposng he frs break ˆB, n he es regresson, we esmae he second break dae ˆB,. Agan we maxmze he absolue -value; hs me θ for M and κ for M. Hence, we have: arg max ˆ ˆ ( B, B ), for θ,, B, M, B, = () arg max ( ˆ ˆ B,, B,, for M κ B, Afer deermnng he order of negraon of each varable, we esed for conegraon o fnd ou wheher any long-run relaonshp exss among he varables (f conegraon exss wll mply he susanably of rade). Sandard conegraon echnques are based owards accepng he null of no conegraon and f here s a srucural break n he relaonshp as Kunomo (996) menoned ha hese ess may produce spurous conegraon resuls. Furher, es based on exogenously deermned srucural breaks also may no provde fruful resuls herefore; we apply he Gregory and Hansen (996) conegraon procedure ha allows for an endogenously deermned srucural break n sngle equaon framework. he es presens hree models, whereby he shfs can be n eher he nercep alone (C): y = µ + µ ϕτ + α y + e...(3) where =, n. In boh rend and level shf (C/) y = µ + µ ϕτ + β + α y + e...(4) And a full shf of he regme shf model (C/S) y = µ + µ ϕτ + α y + α yϕτ + e...(5) where =, n and µ, β and α are he nercep, rend and slope coeffcens respecvely before he regme shf and µ, β and α are he correspondng changes afer he break. he dummy varable ϕ τ s defned as: 0, f { ητ } ϕ τ =, f > { ητ } Where unknown parameer τ (0,) denoes he (relave) mng of he change pon, and { } denoes neger par. Followng he procedure suggesed by Herzer and Felcas (006), all he models we esmaed for each possble break dae n he daa se (for eachτ ). hen we perform a un roo es on he esmaed resduals ê τ and he smalles value of he un roo es sascs are used for esng he null hypohess of no conegraon beween expors and mpors, agans he alernave hypohess of conegraon n he presence of an endogenous srucural break. he asympoc crcal values are abulaed n Gregory and Hansen (996) Lag-lengh n conegraon equaon s based on SIC and AIC. III. Daa analyss and resuls nerpreaon Frs, we presen he resuls of un roo analyss based on endogenously deermned srucural breaks n Lee-Srazcch un roo es (003, 004) and Narayan and Poop es (00) procedure n able. 6

8 . able : Unvarae un roo ess: Consan and rend ncluded n he model wh srucural breaks Lee-Srazcch s LM un Roo es Seres n level form Seres n frs dfference form B B k es sascs B B k es sascs Resuls for unvarae LM un roo es wh one and wo srucural break n nercep/consan only Inda s 004: : expors 998:08 004: : 004: Inda s 996: : *** mpors 996:0 007: :05 007: *** Chna s 999: : expors 997: 00: :0 003: Chna s 996: : mpors 997:0 004: :0 00: Resuls for unvarae LM un roo es wh one and wo srucural break n nercep/consan and rend boh Inda s 00: : *** expors 00: 008: :05 995: *** Inda s 00: : *** mpors 00:06 008: :0 008: *** Chna s 999: : *** expors 00:0 007: :04 008: *** Chna s 00: : *** mpors 997:0 003: : 998: *** NP (00) resuls of un roo wh srucural breaks for model M and M Model M Inda s 00:M 004:M :4 005: *** expors Inda s 996:M6 00:M :4 005: *** mpors Chna s 997:M 00:M :4 005: *** expors Chna s 00:M 004:M :4 005: *** mpors Model Inda s 00:M 004:M expors Inda s 996:M 996:M mpors Chna s 997:M 00:M expors Chna s mpors 999:M 00:M Noe: () Crcal values for NP (00) are: -4.73, and a %, 5% and 0% level of sgnfcance respecvely for model M and -538, and a %, 5% and 0% level of sgnfcance respecvely for model M; Model M for frs dfference we could no esmae because of he problem of near sngular marx n he daa seres; (3) B and B are he daes of he srucural breaks; (4) k s he lag lengh; (5) Crcal values of boh es sascs (ha s when breaks occur n nercep only and nercep and rend jonly are repored n Lee-Srazcch (003, 004) wo-break and one-break cases respecvely; (6) * (**) *** denoe sascal sgnfcance a he 0%, 5% and % levels respecvely; (7) M (where =,,,) repored under B and B es sascs denoes number of monhs. Source: Auhor s calculaon 7

9 I s evden from able ha n case of LM un roo es of Lee-Srazcch expors and mpors of he boh counres are frs dfference saonary when model nclude one or wo breaks whch occurs n he model of nercep and rend. Model M of NP (00) es also repors he same resuls and hence confrms he concluson whch we can draw from he LM un roo es of Lee- Srazcch (003, 004) 5. Afer confrmng ha boh varables of boh counres follows frs order auoregressve scheme (.e., AR()) we have proceeded o carry ou conegraon analyss wh Gregory-Hansen conegraon es 6. Resuls of conegraon analyss are repored n he followng able. able : Conegraon analyss Conegraon es : Gregory-Hansen Conegraon ess Chna Inda Break n Inercep. No rend es sascs (k) Break n Inercep. No rend es sascs (k) (994:M) (000:M07) Yes () Yes () Break n Inercep. rend Included (000:M04) Break n Inercep. rend Included (998:M0) Yes () Yes () Full Srucural Break () Full Srucural Break (000:M03) (000:M06) Yes ---- Yes () Noe: () k Denoes lag lengh; () Crcal values are -5.3 and -4.6 a % and 5% respecvely for Break n Inercep and no rend model; () Crcal values are and a % and 5% respecvely for break n nercep when rend s ncluded n he model and crcal values are and a % and 5% respecvely for full srucural break model; (3) M (where =,,,) denoes number of monhs. Source: Auhor s calculaon I s evden from able ha n all he cases here are srong evdences for he presence of a conegrang vecor beween expors and mpors seres of Inda bu no for Chna. o pu dfferenly, we fnd ha here s srong evdence for susanably of BO defcs n he Indan conex bu no he Chnese conex. IV. Concluson hs sudy examnes he naure of he long-run relaonshp beween expors and mpors for he Chnese and Indan economy from he perod January -99 o February-00. I employs recen me seres economerc mehods lke un roo es n he presence of endogenous srucural breaks and seasonal adjusmens and conegraon echnques ha allow for srucural breaks and seasonal adjusmens for he analyss. he resuls sugges ha ndvdually expors and mpors (evaluaed n nomnal bllon US $ and expressed n logarhms) have mulple breaks. Conegraon analyss based on Gregory-Hansen conegraon es reveals ha expors and mpors of Inda are conegraed whle ha of Chna no. However, conegraon resuls based on Sakkonen and Lükepohl (000a,b,c) reveals ha expors and mpors of boh counres are conegraed. Hence, we can say ha we have srong evdence of conegraon relaonshp of Inda s expors and mpors seres whle weak evdence for Chnas expors and mpors seres. hs ndcaes ha Indan governmens have been playng a crucal role n srongly sablzng he rade balance and all of Inda s macroeconomc polces 5 Resuls of Sakkonen and Lükepohl (00) un roo es also confrm he same fndngs. 6 Apar from Gregory-Hansen conegraon es we have also conduced conegraon es proposed by Sakkonen and Lükepohl (000a,b,c) and resuls are repored n able of Appendx. Conegraon es of Sakkonen and Lükepohl (000a,b,c) reveals ha expors and mpors of boh counres are conegraed, conrary resuls as obaned from Gregory-Hansen conegraon es. 8

10 have been srongly effecve n leadng expor and mpor o long run seady sae equlbrum relaonshp. Whle Chnas governmen have been playng a role n sablzng he rade balance and all of Chna s macroeconomc polces have been jus effecve n leadng expor and mpor o long run seady sae equlbrum relaonshp. Long run convergence beween expor and mpor also mples ha he shor run flucuaon beween expor and mpor are no a all susanable n he conex of Inda whle n he conex of Chna hey have a lle effec. In he sense of Hused (99), Inda does no volae her nernaonal budge consran n srong sense and herefore, suppors he effecveness of her macroeconomc polces n resorng he long-run equlbrum. Reference Arze, A.C. (00) Impors and expors n 50 counres: ess of conegraon and srucural breaks Inernaonal Revew of Economcs and Fnance, 0-5. Bahman-Oskooee, M. and H-J. Rhee (997) Are Expors and Impors of Korea Conegraed? Inernaonal Economc Journal, Caner, M. (998) A local opmal seasonal un roo Journal of Busness and Economcs Sascs 6, Canova, F. and B. E. Hansen (995) Are seasonal paerns consan over me: A es for seasonal sably. Journal of Busness and Economcs Sascs, 3, Dckey, D.A., D. P. Hasza and W. A. Fuller (984) esng for un roos n seasonal me seres. Journal of he Amercan Sascal Assocaon 79, Erbaykal, E. and O. Karaca (008) Is urkey s foregn defc susanable? Conegraon relaonshp beween expors and mpors. Inernaonal Research Journal of Fnance and Economcs 4, Franses, P. H. (990) esng for Seasonal Un Roos n Monhly Daa Economerc Insue Repor 903A Erasmus Unversy Roerdam. Franses, P. H. and B. Hobjn (997) Crcal Values for Un Roo ess n Seasonal me Seres Journal of Appled Sascs 4, Gregory, A. and B. Hansen (996) Resdual-Based ess for Conegraon n Models wh Regme Shfs. Journal of Economercs 70, Herzer, D. and Nowak-Lehmann D. Felcas (006) Is here a Long-run Relaonshp Beween Expors and Impors n Chle? Appled Economcs Leers 3, Hused, S. (99) he emergng US curren accoun defc n he 980s: a conegraon analyss Revew of Economcs and Sascs 74, Hylleberg, S., R. F. Engle, C. W. J. Granger and B. S. Yoo (990) Seasonal Inegraon and Conegraon. Journal of Economercs 44, Johansen, S., R. Moscon and B. Nelsen (000) Conegraon Analyss n he Presence of Srucural breaks n he Deermnsc rend. Economercs Journal 3, Kapeanos, G. (005) Un-roo esng agans he alernave hypohess of up o m srucural breaks Journal of me Seres Analyss 6(), Konya, L. and J. P. Sngh (008) Are Indan Expors and Impors Conegraed? Appled Economercs and Inernaonal Developmen 8, Kunomo, N. (996) ess of un roos and conegraon hypoheses n economerc models Japanese Economc Revew 47,

11 Lanne, M., H. L ukepohl and P. Sakkonen (00) es Procedures for Un Roos n me Seres wh Level Shfs a Unknown me Dscusson paper, Humbold-Unvers a Berln. Lanne, M., H. Lükepohl and P. Sakkonen (00) Comparson of Un Roo ess for me Seres wh Level Shfs. Journal of me Seres Analyss 7, Lee, J. and M. C. Srazcch (003) Mnmum Lagrange Mulpler Un Roo es wh wo Srucural Breaks. Revew of Economcs and Sascs 85(4), Lee, J. and M. Srazcch (004) Mnmum LM Un Roo es wh One Srucural Break Workng Paper, Deparmen of Economcs, Appalachan Sae Unversy. Narayan, Paresh Kumar and Sephan Popp (00) A New Un Roo es wh wo Srucural Breaks n Level and Slope a Unknown me. Journal of Appled Sascs 37(9), Narayan, Paresh Kumar and Seema Narayan (005) Are Expors and Impors Conegraed? Evdence from Leas Developed Counres. Appled Economcs Leers, Perron, P. (989) he grea crash, he ol prce shock and he un roo hypohess Economerca 57, Phllps, P. C. B. and P. Perron (988) esng for a Un Roo n me Seres Regresson. Bomerka 75(), Popp, S. (008) New nnovaonal ouler un roo es wh a break a an unknown me Journal of Sascal Compuaon and Smulaon 78(), Sakkonen, P. and H. L ukepohl (00) esng for a Un Roo n a me Seres wh a Level Shf a Unknown me. Economerc heory 8, Sakkonen, P. and H. Lükepohl (000a) esng for he Conegrang Rank of a VAR Process wh an Inercep. Economerc heory 6(3), Sakkonen, P. and H. Lükepohl (000b) esng for he Conegrang Rank of a VAR Process wh Srucural Shfs Journal of Busness and Economc Sascs 8(4), Sakkonen, P. and H. Lükepohl (000c) rend Adjusmen Pror o esng for he Conegrang Rank of a Vecor Auoregressve Process. Journal of me Seres Analyss, Shn, D.W. and B. S. So (000) Gaussan ess for Seasonal Un Roos based on Cauchy Esmaon and Recursve Mean Adjusmens. Journal of Economercs 99, Upender, M. (007) Long run equlbrum beween Inda s expors and mpors durng Appled Economercs and Inernaonal Developmen 7, Vogelsang,. and P. Perron (998) Addonal ess for a Un Roo Allowng for a Break n he rend Funcon a an Unknown me. Inernaonal Revew of Economcs 39(4),

12 Appendx o es he saonary propery of he daa we have also carred ou un roo analyss followng Sakkonen and Lükepohl (00) and Lanne e al. (00) for he equaon y = µ 0 + µ + f ( θ ) γ + x....(). Where f ( θ ) γ s a shf funcon andθ and γ are unknown parameers or parameer vecors and x s generaed by AR(p) process wh possble un roo. We used a smple shf dummy varable wh shf dae B. 0, < B f = d : he funcon does no nvolve any parameer θ n he shf erm f θ ( ) γ, he, B parameer γ s scalar. Dfferencng hs shf funcon leads o an mpulse dummy. Daes of srucural breaks have been deermned by followng Lanne, Lükepohl and Sakkonen (00). hey recommended o chose a reasonably large AR order n a frs sep 7 and hen pck he break dae whch mnmzes he Generalzed Leas Square (GLS) objecve funcon used o esmae he parameers of he deermnsc par. Afer checkng ha all varables are nonsaonary by ncorporang he poenal srucural breaks he nex sep s o go for conegraon. here are wo dfferen ess proposed by Johansen e al. (000) and Sakkonen and Lükepohl (000a,b,c). Sakkonen and Lükepohl (000a,b,c) have proposed a es for conegraon analyss ha allows for possble shfs n he mean of he Daa- Generang Process (DGP). Snce many sandard ypes of DGP exhb breaks caused by exogenous evens ha have occurred durng he observaon perod, hey sugges ha s necessary o ake no accoun he level shf n he seres for proper nference regardng he conegrang rank of he sysem. herefore n hs sudy we have aken no accoun he level shf n carryng ou conegraon analyss. he Sakkonen and Lükepohl (SL) es nvesgaes he consequences of srucural breaks n a sngle equaon framework. Accordng o Sakkonen and Lükepohl (000b) and Lükepohl and Wolers (003), an observed n-dmensonal me seres y = (y,., y n ), y s he vecor of observed varables (=,, ) whch are generaed by he followng process: y = µ 0 + µ + γd + γ d + γ 3d3 + δdo + δ DU + x...() where D 0 and DU are mpulse and shf dummes respecvely, and accoun for he exsence of srucural breaks. D 0 s equal o one, when = 0, and equal o zero oherwse. Sep (shf) dummy (DU ) s equal o one when (> ), and s equal o zero oherwse. he parameers γ (=,, 3), µ 0,, µ, δ and δ are assocaed wh he deermnsc erms. he varable d, d, and d 3, are seasonal dummy varables. Accordng o SL (000b), he erm x s an unobservable error process ha s assumed o have a VAR (p) represenaon as follows: x A x A x + ε...(3) = p p where ε s assumed o follows N.I.D. ( 0, Ω ). By subracng x - from boh sdes of he above equaon and rearrangng he erms, he usual error correcon form of he above equaon s gven by 7 Here, we have fxed larges lag lengh 3 as me duraon s oo shor noneheless he sample sze s large snce n me seres analyss sample sze does no maers whle me perod/span maers.

13 x = Πx p + Γj x j + j= u...(4) where u s assumed o follows N.I.D. ( 0, Ω ).hs equaon specfes he conegraon properes of he sysem. In hs equaon, u s a vecor whe nose process; x = y -D and D are he esmaed deermnsc rends, seasonaly and oher dummes. he rank of Π s he conegrang rank of x and hence of y (SL, 000b). here are hree possble opons n he SL procedure, as n Johansen, a consan, a lnear rend erm, or a lnear rend orhogonal o he conegraon relaons. In hs mehodology, he crcal values depend on he knd of he above-menoned deermnsc rend ha ncluded n he model. SL have menoned ha he crcal values reman vald even f dummy varables are ncluded n he model, whle n he Johansen es; he crcal values are avalable only f here s no shf dummy varable n he model. he SL approach can be adoped wh any number of (lnearly ndependen) dummes n he model. I s also possble o exclude he rend erm from he model; ha s, µ =0 maybe assumed a pror. In hs mehodology, as n Johansen s, he model selecon crera (SBC, AIC, and HQIC) are avalable for makng he decson on he VAR order. In he followng secon, we have appled SL ess for he conegraon rank of a sysem n he presence of srucural breaks. Sakkonen and Lükepohl (000b) derved he lkelhood rao (LR) es n order o deermne he number of conegrang relaons n a sysem of varables, by allowng for he presence of poenal srucural breaks. We now apply a maxmum lkelhood approach, based on SL, for esng and deermnng he long-run relaonshp n he model under nvesgaon. As menoned earler, n hs procedure SL assumed ha he break pon s known a pror herefore, by usng hose srucural breaks daes as was obaned n he un roo analyss we have proceeded o carry ou conegraon analyss. Snce here s no lag srucure for he dummy seres, herefore dummy varable s ncluded n he sysem, bu no n he conegraon space. For hs reason, he dummy resul s no presen n he conegraon resuls. Followng he SL procedure we consder he case of shf dummy and mpulse dummy for dfferen break daes when rend, nercep and when orhogonal rend ncluded. In hs case also opmum number of lags has been based on AIC.

14 Varables Chna able : SL Un roo analyss Un Roo es wh srucural break {searched range: [99 M6, 009 M]} Inda me rend (mpulse me rend ncluded Sakkonen me rend (mpulse dummy and used (shf dummy and and dummy and used break dae s 993 used break dae s Lükepohl break dae s 00 M) 993 M) (k) M) me rend (shf dummy and used break dae s 008 M9) Sakkonen and Lükepohl (k) Ln(Expor) Yes () () Ln(Expor) Yes -.64() () DLn(Expor) Yes () () DLn(Expor) Yes () () me rend (mpulse dummy and used break dae s 993 M) me rend (shf dummy and used break dae s 008 M0) Sakkonen and Lükepohl (k) me rend (mpulse dummy and used break dae s 993 M) me rend (shf dummy and used break dae s 008 M0) Ln(Impor) Yes () Yes () Ln(Impor) Yes () Yes () DLn(Impor) Yes () Yes (0) DLn(Impor) Yes -7.8 () Yes (0) Noe: () k Denoes lag lengh. () Crcal values -3.55, and -.76 are obaned from Lanne e al. (00) a %, 5%, and 0% respecvely. (3) M (where =,,,) denoes number of monhs. Source: Auhor s calculaon able : Resuls of conegraon analyss Sakkonen and Lükepohl conegraon es Chna Inercep {mpulse: 993 M and Inercep and rend {mpulse: 993 M Orhogonal rend {mpulse: 993 M and shf : 993 M} (3) shf : 993 M} (3) and shf : 993 M} (3) r LR P-value r LR P-value r LR P-value Inercep {mpulse: 993 M and shf: 008 M0} (3) Inercep and rend {mpulse: 993 M and shf: 008 M0} (3) r LR P-value r LR P-value r LR P-value Inda Inercep {mpulse: 00 M and shf: 008 M9} (3) Inercep and rend {mpulse: 00 M and shf: 008 M9} (3) Orhogonal rend {mpulse: 993 M and shf : 008 M0} (3) Orhogonal rend {mpulse: 00 M and shf: 008 M9} (3) r LR P-value r LR P-value r LR P-value Inercep {mpulse: 993 M and shf: [008 M0} (3) Inercep and rend {mpulse: 993 M and shf: 008 M0} (3) Orhogonal rend {mpulse: 993 M and shf : 008 M0} (3) R LR P-value r LR P-value r LR P-value Noe: () r and LR denoes number of conegrang relaons/vecors and log lkelhood rao respecvely. () Values n ( ) denoes he number of lag lengh used n conegraon analyss. (3) M (where =,,,) denoes of number monhs. Source: Auhor s calculaon 3