Indan Journal of Scence and echnology, Vol 0(9), DOI: 0.7485/js/07/v09/58, May 07 ISSN (Prn) : 0974-6846 ISSN (Onlne) : 0974-5645 Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade Musofa Usman *, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak 3 and Wdar Deparmen of Mahemacs, Faculy of Scences and Mahemacs, Unversy of Lampung, Indonesa; usman_alfha@yahoo.com Deparmen of Managemen, Unversas Bandar Lampung (UBL), Indonesa; Yusuf.barusman@yahoo.com 3 Deparmen of Mahemacs, Sascs and Physcs, College of Ars and Scences, Qaar Unversy, Doha, Qaar; fazelfak@yahoo.com Absrac Objecves: o deermne he relaonshp among Prce Index Receved by Farmer (PIR), Prce Index Pad by he Farmers (PIP) and he Farmers erms of rade (F) by usng he model VECM, and o aemp o know he behavor of (F) f here s a shock n varables PIR and PIP. Mehods/Sascal Analyss: Vecor Error Correcon Model (VECM) s a model Vecor Auoregressve (VAR) whch can be used for daa seres whch are non saonery and have conegraon relaonshp (long erm relaonshp). he model VECM can also be used o see he movemen n one varable o gve a response regardng he shock produce by anoher varable hrough he graph of Impulse Response Funcon (IRF). Fndngs: Based on he daa of Farmers erms of rade n Indonesa over he perods from January 008 o November 03, we have deermned ha he bes model VECM s VECM order (VECM ()). Applcaons: Based on he graph of he Impulse Response Funcon (IRF) we have esablshed ha he response of F oward he shock of a prce boh receved and pad by he farmers s flucuave and emporary over me. Keywords: Farmers erms of rade (F), Impulse Response Funcon, Prce Index Receved by Farmer (PIR), Prce Index Pad by he Farmers (PIP), VAR, VECM. Inroducon hs sudy nvolved hree varables and he model VAR (Vecor Auoregressve) has been used 6. Before he model can be chosen, he saonary daa mus be check. In esng he saonary daa, a combnaon of me seres plo, correlogram of ACF and un roo es can be used. he nex sep s o es he conegraon o analyze he long erm relaonshp among he varables used n hs sudy. When he daa are saonary as a ordered and here s a conegraon relaonshp as large as r, hen he model VAR whch s gong o be used s Vecor Error Correcon Model (VECM),3,5 0. In hs sudy he daa whch are gong o be analyzed are Prce Index Receved by Farmer (PIR), Prce Index Pad by he Farmers (PIP), and Farmers erms of rade (F). he daa used n hs sudy was obaned from BPS Sascs Indonesa (04) over he perod from 008 o 03.. he Concep of Farmers erms of rade (F) he F s an ndcaor of he prospery of farmers. One of he elemens of he prospery of farmers s he ably o ensure ha her farm earnngs can fulfl her house hold needs. he ncremen of prospery can be measured from he ncremen ably o purchase her house hold needs. he hgher he ably o purchase oward con- *Auhor for correspondence
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade sumpon needs, hen he hgher he Farmers erms of rade (F).hs means ha he farmers wll be more prosperous. Furher, as an ndcaor of prospery, accordng o Cenral Bureau of Sasc Indonesa (BPS), F can also be used n he followng way:. o measure he change ably (erms of rade) of produc sold by he farmers agans he produc requred by he farmers n her producon and household consumpon needs.. o deermne he developmen of he farmers earnng levels from me o me whch can be used as a bass for makng a polcy o mprove and ncrease he level of prospery of farmers. 3. o demonsrae he level of compeveness of farm producs compared o oher producs.. he Farmers n he Concep of F by BPS he farmers n he concep of F as defned by BPS are hose farmers who work n specfcally: Subsecor food crops (paddy and secondary food crops; maze, soybeans, peanus, cassava, and swee poaoes); horculure (vegeables, frus plan, ornamenal plans, and medcnal plans); people esae plans (coconu, coffee, clove, and obacco); lvesocks (large lvesock, small lvesock, and he producon of lvesocks n addon o fshery subsecor (eher capure fshery or aquaculure). F ndces can be classfed no wo pars, ndces of prces receved by farmers (PIR) and ndces of prces pad by farmers (PIP)..3 Measuremen of Farmers erms of rade (F) F s he comparson or rao beween he Prce Index Receved by Farmer (PIR) and Prce Index Pad by he Farmers (PIP) whch s represened n percenage. F s defned as follows: PIR F = 00% PIP Calculaon of he Prce Index, nvolved four componens, namely commodes, quany, based year, and daa prce. Prce Index Receved by Farmer (PIR) PIR s an ndex whch measures he average change of prce n a ceran perod. I s work ou from a knd of package of agrculure producon a he level prce of producer of farmers over ceran perods.pir s calculaed by usng a modfed Laspeyres mehod 4 and s defned as follows: m P P Q P PIR = 00% where: ( ) 0 ( ) m P 0Q = 0 PIR = Prce Index receved by farmers a he -h monh. P l = Prce receved by farmers a he -h monh for he -h knd of goods. P (-)l = Prce receved by farmers a he (-)h monh for he -h knd of goods. P P ( ) = Relave prce receved by farmers a he -h monh compared wh he (-) h monh for he -h knd of goods. P 0 = Prce receved by farmers a he based year for he -h knd of goods. Q 0 = Quany a he based year for he -h knd of goods. m = Number of knds of goods ha are ncluded n he Commodes packages. Prce Index Pad by he Farmers (PIP) s an ndex ha measures he average change of prce n a ceran perod from a parcular package commody. I s an ndex whch measures he average change of prce durng a ceran perod from a package commody of goods and cos producon servces and ncremen of capal goods. In addon, s measures household consumpon expendure n a vllage over parcular perod. PIP s defned as follows: PIP Pb l m Pb Pb ( ) Q 0 Pb( ) PIP = 00% Pb Q where: m 0 0 = Prce Index pad by farmers a he -h monh. = Prce pad by farmers a he -h monh for he -h knd of goods. Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar Pb (-) = Prce pad by farmers a he (-) h monh for he -h knd of goods. = Relave prce pad by farmers a he -h monh compared wh he (-) h monh for he -h knd of goods. Pb 0 = Prce receves by farmers durng he based year for he -h knd of goods. Q0 goods. = Quany a he based year for he -h knd of m = Number of knds of goods ha ncluded n he Commodes packages Saonary Many daa analyses of me seres are based on he assumpon ha he me seres s saonary. he process beng saonary ndcae ha he mean, varance and auocorrelaon funcons are essenally consan and do no depend on me 5 ha s he frs wo momen are me nvaran 6. If he daa are nonsaonary, hen we need o modfy he daa by a ceran mehod o make saonary and hs modfcaon has o be done before he daa are analyzed. We can modfy daa whch are non-saonary n varance o become saonary by a parcular ransformaon. For example,. If he sandard devaon of a seres s proporonal o s level, akng he naural logarhms yelds a new seres wh a consan varance; or. If he varance of he orgnal seres s proporonal o s level, akng he square roo nduces a consan varance. Many oher ransformaons are possble, bu hese wo (especally he log ransformaon) are ofen useful n pracce. he log ransformaon s boh common and nerpreable; he changes n a log value are relave (percen) changes n he orgnal merc 6. he logarhmc and square roo ransformaon are a member of he famly of power ransformaons called Box-Cox ransformaon 7,8. By hs ransformaon we defne a new seres Z' as follows: λ Z Z = λ where s a real number. Please noe ha Z mus no be negave. If some values of Z negave, hen addng a posve consan Z so wll ensure ha all he values wll be posve 6. In relaon o a seres whch s no saonary n mean, we can usually make he daa saonary by a mehod of dfferencng he daa. ha s, we compue he successve changes n he seres for all, as follows: w = Z Z (If a varance sablzng ransformaon has been used, we can ulze dfference seres Z' nsead of Z.) Performng hs calculaon once, for all, s known as called frs dfferencng. If he resulng seres does no ye have a consan overall mean, we hen compue he frs dfferences of he frs dfferences for all. ha s, denoe he frs dfferences of z as w *. hus, he frs dfferences of he w * seres are.. w = w w = Z Z Z Z ( ) ( ) he resulng seres s called he second dfferences of z. Le d denoe he degree of dfferencng. For frs dfferencng d=. For second dfferencng d =. If he orgnal daa lack a consan mean, usually seng d = wll creae a new (dfferenced) seres wh a consan mean; seng d > s almos never needed 6..5 Conegraon Modelng mulvarae me seres daa s complcaed by he presence of non-saonary facors, parcularly wh economc daa. hs s due n par o he possbly of conegraon among he componen seres X of a nonsaonary vecor process X 9,0. One possble mehod o deal wh hs problem s o dfference each seres unl s saonary and hen f a vecor ARIMA model. However, hs does no always lead o sasfacory resuls 9. An alernave approach s o look for wha s called conegraon 3,6,7,9,. For example, le us suppose ha X and X are me seres daa and boh nonsaonary; however, a parcular lnear combnaon of he wo varables, say X - c X, s saonary. he wo varables are hen sad o be co-negraed 3,6,7,9,9. A more general defnon of conegraon s as follows. A seres X s sad o be negraed wh order d, wren I(d). I needs o be dfferenced d mes o make saonary. If wo seres X and X are boh I(d), hen any lnear combnaon of he wo seres wll usually be I(d) as well 9. However, f a lnear combnaon exss for whch he order of negraon s less hen d, say I(d-b), hen he wo seres are sad o be conegraed wh order (d,b) and be wren as CI(d,b) 3,6,7,9. If hs lnear combnaon can be wren n he form α X, where X = (X,X ), hen Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology 3
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade he vecor α s called a conegrang vecor 7,9. Suppose ha here are n varables seres X, X,..., X n as he componens of vecor process X. here s eher no conegraon a all, nor s here one or wo up o n- vecor conegraon. If we have more han wo varables, hen he frs sep ha we mus carry ou s o fnd he rank of conegraon r, namely he number of vecor conegraon. o do hs we can used he procedure whch has been developed by Johansen. he procedure leads o wo es sascs for conegraon. he frs s called he race es, and ess he hypohess ha here are a mos r conegraon vecors. he second s called he maxmum Egen value es. hs procedure ess he hypohess ha here are r+ conegraon vecors versus he hypohess ha here are r conegraon vecors 3. () race es H 0 : here exs a mos egen values whch are posve. H : here exs more han egen values whch are posve. k ( ) = In ( ˆ ) r r λ r+ () es wheher here are or vecors conegraon. H 0 : here exs exacly r egen values whch are posve. H :here exs exacly r + egen values whch are posve. λ ( rr, + ) = ln ( λ ) max where : : he esmaon of Egen values : Number of observaons. : Number of endogenous varables. hs es sars from r = 0 and up o he frs me we noe ha he null hypohess s no rejeced. Rank conegraon s found from he value of r. he null hypohess s rejeced for he values ha are larger han he es sascs 8..6 Vecor Auo Regressve (VAR) For he analyss of daa me seres whch nvolve more han one varables (mulvarae me seres), he Vecor Auoregressve (VAR) s used,4. he srucure s ha each varable comprses a lnear funcon of pas lags of self and pas lags of he oher varables. For example suppose ha we measure hree dfference me seres varables, say y,, y,, and y,3 VAR model for order, VAR() s as follows: y c + φ y + φ y + φ y + ε, =,, 3,3 y, = c + φ y, + φ y, + φ3 y,3 + ε y,3 = c3 + φ3 y,3 + φ3 y,3 + φ3 y,3 + ε,3 In general, model VAR(p) for m dfference me seres varable scan be defned as follows: y p, = c + j = φj y j, p y = c+ y + ε where: : he elemen vecor of a me,, (.) : Marxorder n n whch he elemens are he coeffcen of he vecor y -, for,,...p. : he lengh of lag : Vecor nercep : Random vecor of shock. When he daa used are saonary a he same level of dfferencng and here s a conegraon, hen he model VAR wll be combned wh Error correcon model o become Vecor Error Correcon Model (VECM)..7 Vecor Error Correcon Model (VECM) Vecor Auoregressve (VAR) s one of he specal forms of sysem smulaneous equaon. Model VAR can be appled f all he varables are saonary. However, f he varables n vecor are nonsaonary, hen he model used s Vecor Error Correcon Model (VECM) f here exs a leas one or more conegraon relaonshp exss among he varables. VECM s VAR whch has been desgned for use wh nonsaonary daa havng conegraon relaonshp 3. VECM s one of he me seres modelngs whch can drecly esmae he level o whch a varable can be brough back o equlbrum condon afer a shock on oher varables. VECM s very useful by whch o esmae he shor erm effec for boh varables and he long run effec of he me seres daa. he VECM(p) wh he conegraon rank r ks as follows: 4 Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar p y = c+π Y + Γ Y + ε (.) where: Δ : Operaor dfferencng, where Δy = y - y - y - : Vecor varable endogenous wh he -s lag. : Vecor resdual. : Vecor nercep. : Marx coeffcen of conegraon ; vecor adjusmen, marx wh order (k r) and vecor conegraon (long-run parameer) marx k r) : Marx wh order k k of coeffcen Endogenous of he -h varable. he lengh of he lag Opmal o deermne he lengh of he lag o be chosen, we can use he mnmum values of he crera. Some commonly used crera are as follows: () Fnal Predcon Error (FPE) + m ( p) FPE = ( u ) m = () Akake Informaon Creron (AIC) ( p) ( ) AIC = In uˆ + m () Bayesan Creron of Gdeon Schwarz ( ) In SC = In ( uˆ ) + m (v) Hannan-Qunn Creron ( p) In ( In ) HQ = In ( uˆ ) + m = ( ) Where u ˆ p are denoes he resduals esmaon from he model VAR(p), ms number of dependen varables, s number of observaons and p s he lengh of model VAR 8..8 esng for Normaly I s a sandard ool o conduc a dagnosc check o denfy a model before can be used for forecasng 5, 6. esng for normaly of resdual s a es desgned o deermne he normaly resdual of daa.he purpose of hs es s o asceran wheher he resduals from he daa are normally dsrbued or no.o esng for normaly, we can use he Jarque-Bera (JB) es of Normaly. hs es used he measure of skewness and kuross. In s applcaon o decde wheher he null hypohess s rejeced or no, we compare he value of Jarque-Bera (JB) wh he value of ch-square wh degrees of freedom. he calculaon of JB s as follows: ( k ) n 3 JB = s + 6 4 where : : Number of sample : Expeced Skewness = n n n n ( X X) ( X X) 3 3 k : Expeced Excess Kuross n 4 ( X ) X = n n ( X ) X = n Jarque-Bera (JB) (whch s used n esng for normaly for resduals) deermned ha he calculaon used s as follows: ( K ) n k 3 JB = S + 6 4 where : k : Number of ndependen varables..9 esng for Sably he sably sysem VAR can be from he nverse roos characerscs polynomal of AR. A VAR sysem s sad o be sable (saonary) f all roos have a modulus of less han one and all are conaned whn he un crcle. Accordng o Lukepohl 9 ha he model VAR(p) gven n Equaon (.) can be wren as follows: y = c+ y + + y + ε p p (.3) Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology 5
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade If hs mechansm s sared a ceran me, for example a =, hen we have : y = c+ y + ε ; 0 y = c+ y + ε c ( c y ε ) ( I ) c y = + + + + ε k 0 = + + + ε + ε 0 ( k ) 0 ε 0 y = I + + + c+ y + ( ) = k + + + + 0 + 0 y I c y ε () herefore vecor ( y, y,..., y ) can be deermne by vecor y, ε,..., ) and he jon dsrbuon of s ( 0 ε deermned by jon dsrbuon of ( y, y,..., y ) s ( y,,..., ) deermned by jon dsrbuon of 0 ε ε. + ( ) j j j = + + ε= K+ + + + + ε 0 y c y I c (.5) If all he egen values of Ø are less han n absolue values, hen he order of Ø, 0,,...s summable. And he model y s sochasc process and defned as: y = µ + ε, =, 0,, 0 (.6) Gven he defnon of characerscs polynomal of a marx we call hs polynomal he reverse characersc polynomal of he VAR(p) process. Hence, he Process (.3) s sable f he reverse characerscs polynomal has no roos n or on he complex un crcle. Formally Y can be sad o sable f de( I ) de(... p Kp ϕz = IK ϕ z ϕpz ) 0 for z (.7) hs condon s called he sably condon 9. Impulse Response Funcon (IRF) In 7 sae ha he IRF s a mehod ha can be used o deermne he response of an endogenous varable oward a shock from he oher varables. A Vecor Auoregressve can be wren as he form of Vecor Movng Average (VMA). he represenaon of VMA s an mporan feaure whch enables us o see he varous shocks on varable n he VAR model. As an llusraon, we used wo varables n he form of marx VAR 3 as follows: y = b b z + α y + α z + ε 0 y z = b b y + α y + α z + ε 0 z (.8) In marx noaon can be wren as b y b0 α α y ε y = + + b z b0 α α z ε z or Bx Γo + Γ x + ε = (.9) where b y b0 B =, x =, Γ o b z =, b0 α α ε y Γ =, and ε = α α ε z By usng he equaon model VAR gven n (.)he general form whch s assumed has a sable condon s as follows: X 0, where: y y a a X =, µ and A Z = Z = a a We have: y y a a e Z = Z + 0 a a e () Equaon () saes ha and n erms of he order and whch can be wren as and. Premulplcaon Equaon (.9) by whch enables us o have he model VAR n he form X = A0 + AX + e where = µ + Ae A = B Γ, A = B Γ and e = B ε. 0 0 I s noed ha he erm error (error e ) refers o he combnaon ofshocks (c ). By usng he Equaon e =B- ε, hen e and e a he Equaon (.3) can be wren as: 6 Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar ( b ) ( b ) y Z Z y = and e = ( bb ) e ε ε ε ε ( bb ) he equaon above can be wren n he marx form as follows: e τ b ε yτ e = τ bb b ε yτ (.) he Equaons () and (.) can be combned n he followng form: y y a a b ε z a a b y = + z bb 0 ε z he noaon above can be smplfed by defned marx of order. hen he represenaon of VMA a he Equaons () and (.) can be wren n he form {ε y } and {ε z }: ( ) ( ) ( ) ( ) y y ε y z = z + 0 ε z wh he elemen a a b bb a a b = Equaon (.) can be wren n he formx as: x τ = µ + ε τ (.) 0 (.3) he coeffcens Ø (), Ø (), Ø () and Ø () are called mpulse response funcons. he plo of mpulse response funcon (s he plo of Ø jk () and) s a praccal saonary n varance we can use Box- Cox ranformaon 6,6. If he saonary n varance has been aaned, bu he daa sll has a rend, hen we can use he dfferencng process o make he daa saonary n mean 6,6. Sep : Esmaon of he Model If he daa fulfl he assumpon of saonary n mean and varance, hen we can es he order of conegraon by usng Johansen s es 5,6,0,6. hen we can perform calculaons o deermne he lengh of opmal lag p by usng he mnmum values of he nformaon crera gven n,8,6. A hs sep we wll fnd he esmaor of parameers by usng he maxmum lkelhood mehod. Sep 3: esng for Resdual he model we found n Sep needs o be checked agans he normaly of he resduals and esng he sably. If he resduals are normally dsrbued and have hgh sably, hen he model can be used 9. Sep 4: IRF Analyss Impulse Response Funcon (IRF) s used o depc how he rae of a shock for a varable reacs oward he response of ohers varables. I also aemps o deermne he lengh of he mpac of he shock from one varable o he oher varables,6,8. 3. Resuls and Dscusson 3. Idenfcaon he frs sep of modelng me seres s o check wheheror no he me seres daa are saonary. o check he saonary of he daa we can use me seres plo, correlogram ACF and un roo es. Plo me seres way o vsualze he behavour of {y} and {z} n response oward he shocks (shocks) 3.. Mehod Sep : Idenfcaon A hs sep, we denfy and check wheher he me seres daa are saonary. If he plo of me seres daa moves around a consan and has no rend, hen we can say ha he daa are saonary n mean. Bu f he daa are movng flucuavely and are no consan, hen we say ha he daa are no saonary n varance. o make he daa Fgure. Plo me seres daa F. Fgure shows ha he hree varables are saonary n varances, bu no n means because he graph shows ha here are rends. Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology 7
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade Correlogram ACF Un roo es Fgure. ACF for varable PIR. Fgure 5. Un roo es varable PIR. Fgure 3. ACF for varable PIP. Fgure 6. Un roo es varable PIP. Fgure 4. ACF for varable F. Fgure, 3 and 4 shows ha from lag o lag, here s a slow decrease endng o zero. hs means ha he coeffcen of correlaon dfference sgnfcanly from zero. Accordngly, hen we can conclude ha, based on correlogram ACF, he hree varables of daa F are no saonary. Fgure 7. Un roo es varable F. Hypohess: H 0 = Daa F s nonsaonary H = Daa F saonary Fgure 5, 6, and 7 shows ha, a any lag, he hree varables do no pass hrough he sgnfcance α = 05, 8 Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
. Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar hs means ha he p-values of lag 0 o lag 5 are greaer han 05. hus, s no suffcen evdence o rejec Ho, so we can conclude ha he daa F are nonsaonary. From he plo of me seres, we know ha he daa F s saonary n varance. hs also can be shown hrough Box-Cox ransformaon o deermne ha he bes value (lambda). By usng SAS program, he bes value of s as follows: able 3. he value of λ from Box-Cox ransformaon for varable F able. he value of λ from Box-Cox ransformaon for varable PIR able. he value of λ from Box-Cox ransformaon for varable PIP Fgure 8. Plo me seres PIR afer he frs dfferencng. ables, and 3 show ha he values of λ whch can be used are =, for Z ransformaon. Wh he level of sgnfcance of 95% can be concluded ha he daa are saonary n varances. Nex, n order o make he daa are saonary n means, we need o perform dfferencng on daa whch have been ransformed by Box-Cox ransformaon wh λ =. Afer he frs dfferencng, hen he saonary daa can be rechecked hrough me seres plo, correlogram ACF and un roo es. Plo me seres Fgure 9. Plo me seres PIP afer he frs dfferencng. Fgures 8, 9 and 0 are me seres plo daa whch have been ransformed by usng Box-Cox ransformaon wh λ = he frs dfferencng shows ha he daa are saonary. Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology 9
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade Correlogram ACF Fgure 0. Plo me seres F afer he frs dfferencng. Fgure 3. ACF varable F Box-Cox() afer frs dfferencng. Fgures, and 3 shows ha from lag o lag and up o lag 4 decreases end o zero. hus, we can conclude ha based on correlogram ACF, he hree varables daa F afer he dfferencng are saonary. Un roo es Fgure. ACF varable PIR Box-Cox() afer frs dfferencng. Fgure 4. Un roo es varable PIR Box-Cox() afer frs dfferencng. Fgure. ACF varable PIP Box-Cox() afer frs dfferencng. Fgure 5. Un roo es varable PIP Box-Cox() afer frs dfferencng 0 Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar Fgure 6. Un roo es varable F Box-Cox() afer frs dfferencng. Hypohess : H 0 = Daa F s no saonary afer frs dfferencng H = Daa Fs saonary afer frs dfferencng Fgures 4, 5 and 6 show ha for any lag for he hree varables F afer he frs dfferencng passes hrough he sgnfcan level α = 05'. hs means ha he p-value a lag 0 o lag 5 s less han 05. he Ho s hen rejeced and we conclude ha he daa are saonary. 3. Conegraon es If he nonsaonary daa become saonary a he frs dfferencng, hen here s a hgh probably ha hey have a conegraon relaonshp (long erm relaonshp) among he varables. o esablsh wheher or no here s a conegraon relaonshp or no we can use Johansen s es 8,9. able 4. Resuls of conegraon es by usng Johansen es H 0 : Rank=r Conegraon Rank es Usng race H : race (λ) Rank>r 5% Crcal Value 0 0 64.7570 48 886. 3.7395 4 H 0 s no rejeced f he value λ race < crcal values. able 4. λ race < Crcal values when r =. hus, we can conclude ha he varables a F have conegraon a rank =. VAR model s used when one or all of he varables of me seres daa are saonary, whle VECM model s used when all he varables used are nonsaonary. If he varables PIR, PIP and F n he daa F are nonsaonary has also been proved ha hey have a conegraon relaonshp among he varables. In hs nsance he model VAR (p) whch s used s VECM (p) model 9,30. 3.3 Model Esmaon he frs sep o be aken s he VECM model o deermne he opmum lag by comparng every lag o he crera used. In able 5 he mnmum values from each of he nformaon crera are gven wh sar sgn (*). he able above ndcae ha he lag opmal s a lag, hence, he VECM(p) model whch s used s VECM(). he nex sep s o esmae he parameers n he model. he esmaon parameers are gven n he able 6. 4 0 8 6 4 Seres: Resduals Sample 008M0 03M Observaons 7 Mean.9e-4 Medan -00085 Maxmum 0.36657 Mnmum -0.53009 Sd. Dev. 0.7370 Skewness -0650 Kuross 3.33385 0-0.5-0 -0.3-0. -0. 0 0. 0. 0.3 0 Jarque-Bera.70035 Probably 0.56656 Fgure 7. Hsogram resdual and he value of Jarque-Bera es of normaly. Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade able 5. he resul of VAR order selecon crera VAR Lag Order Selecon Crera Lag LR FPE AIC SC HQ 0 NA 3.74 9.88 9.97 9.867 57.97 00055 04.3970*.5839 4.80* 00047* 0.85736*.54838.3079* 3 8.800 00053 0.9763.95880.366 4 5 00064 557 890.65339 able 6 demonsraes ha he model VECM () s as follows: 0.83 0.869 08 ΔY = 637 + 3.96.386 YY + 06 0.5 09 0 0.35 0.505 0.3 0.9 0.6 ΔY + εε 0.33 0.83 098 Resdual es Normaly es Hypohess: H 0 = resduals are normally dsrbued H = resdual are no normally dsrbued If he sasc JB < x orp-value > α, hen Ho s no (α,) rejeced whch means ha he assumpon normaly s sasfed. Based on Fgure 7, JB =.70035and he crcal value of ch square wh degrees of freedom and he level of sgnfcan 05 s x = 5.99. SnceJB < (05,) x, hen we (α,) do no rejec Ho. herefore, we conclude ha he resdual are normally dsrbued wh level of sgnfcance of 95%. Sably es Model VECM s sad o have hgh sably when he characersc polynomal of AR has modulus. able 7 shows ha he modulus of he characerscs roos a all lag are. hus, we can conclude ha he model VECM () s approprae o be used snce has hgh sably. 4. Impulse Response Funcon One of he advanages of he applcaon of VAR model s he ably o analyze he response of a varable oward a shock or a change n he oher varable o he varable self. o deermne he behavor of a varable n response able 6. Esmaon parameers for model VECM() Model Parameer Esmaes Model Parameer Esmae Parameer Esmae Error -value Varable D_ PIR CONS AR AR AR 3 AR AR AR 3 05.98548 0.83068-0.8695-000 0.395 0.3530 0.50537 67.3945 0.5308 0.55563 0.6443.7368.7 6749 3.57 07 08 0 PIR(-) PIP(-) F(-) D_PIR(-) D_PIP(-) D_F(-) D_ PIP CONS AR AR AR 3 AR AR AR 3 45484 58 -.9599 -.38650 0.77 0.93 0.648 50.35968 0.39664 058 083.947.865.5449.89 0.6 09 08 PIR(-) PIP(-) F(-) D_PIR(-) D_PIP(-) D_F(-) D_ F CONS AR_3_ AR_3_ AR_3_3 AR_3_ AR_3_ AR_3_3-63753 -0583 0.545 0976-0.39 0.8344 09797 499 0.3353 0.3470 0030 87 7500.98-0.6-0. 0.7 0.39 PIR(-) PIP(-) F(-) D_PIR(-) D_PIP(-) D_F(-) Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology
0.5 0-0.5.8.6. -. -. -. - -.6 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 0.5 0-0.5.8.6. -. -. -. - -.6 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 0.5 0-0.5.8.6. -. -. -. - -.6 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 5 0 5 0 5 30 35 40 Musofa Usman, Dha Fadhlah Fan, M. Yusuf S. Barusman, Faz A. M. Elfak and Wdar o a shock we can use he graph of Impulse Response Funcon (IRF). Analyss of IRF s conduced by provdng a plo from mpulse response funcon (namely he coeffcen ) o vsualze he change of response of farmers exchange values oward he shock experenced due o he change of prce receved and prce pad by farmers. able 7. Characerscs roos of AR Index 3 4 5 6 Roos of AR Characerscs Polynomal Real 0000 0000 0.80447 0.30539 0.579 0.579 Imagnary 00000 00000 00000 00000 09-09 Modulus 000 000 0.8045 0.3054 0.849 0.849 Radan 0000 0000 0000 0000 0384-0384 Degree 00000 00000 00000 00000 5.94-5.94 he reasons for change n prces pad by he farmers are due o a number of facors ncludng change n governmen polcy oward he producon coss, polcal facors as well as change n currency values. Based on Fgure 9, can be seen ha when here s a change n prce pad by farmers, he varable farmers exchange values provde negave responses. A shock n he frs monh wh he varable farmers exchange values provde a response as large as -0.37604. hs negave mpac has peaked n he second perod and slowly change o ncrease up o he 9-h perod and move o he equlbrum condon. Response of I o I Response of IB o I Response o Cholesky One S.D. Innovaons Response of I o IB Response of IB o IB Response of I o NP Response of IB o NP Response of NP o I Response of NP o IB Response of NP o NP 40 F µ ϕε = + he changes n prces whch are receved by farmers can be arbued o varyng facors, namely he prce of ferlzer and pescde, he quany of producon or he season. Fgure 8 shows ha when a shock occurs of one sandard devaon a he frs monh from he varable prce receved by farmers has a posve mpac as large as 0.30650 oward he change of farmers exchange values. hs posve mpac connues up o he peak a he second monh and proceeds o move up and down up o he 3-h monh. Followng hs he movemen becomes an equlbrum condon. 0.5 0-0.5.8.6. -. -. -. - -.6 Response of I o I 5 0 5 0 5 30 35 40 Response of IB o I 5 0 5 0 5 30 35 40 Response of NP o I 5 0 5 0 5 30 35 40 0.5 0-0.5.8.6. -. -. -. - -.6 Response o Cholesky One S.D. Innovaons Response of I o IB 5 0 5 0 5 30 35 40 Response of IB o IB 5 0 5 0 5 30 35 40 Response of NP o IB 5 0 5 0 5 30 35 40 0.5 0-0.5.8.6. -. -. -. - -.6 Response of I o NP 5 0 5 0 5 30 35 40 Response of IB o NP 5 0 5 0 5 30 35 40 Response of NP o NP 5 0 5 0 5 30 35 40 Fgure 8. Graph of response of farmers exchange values oward he change of prce receved by farmers (PIR). Fgure 9. Graph of response farmers exchange values oward he change of prce pad by farmers (PIP). Based on Fgure 9, he response owards farmers exchange values receved and pad by farmers shows he equlbrum movemen, bu ends o be no close o zero. hs means ha afer aans he level of equlbrum, he changes beween he prce receved by farmers and he prce pad by farmers wll be responded o by permanen changes o he farmers erms of rade values. 5. Concluson Based on he dscusson and resuls dealed above, we can conclude ha he daa for Farmers erms of rade (F), Prce Index Receved by farmers (PIR), and he Prce Index Pad by farmers (PIP) can be modeled by usng Vecor Error Correcon Model (), VECM (). By usng hs model, was found ha he Farmers erms of rade (F), Prce Index Receved by farmers (PIR), and Prce Index Pad by farmers (PIP) hey have a conegraon relaonshp a rank =. By usng Impulse Response Funcon (IRF) was found ha when he prce pad by farmers changed, hen he Farmers erms of rade provde negave responses (he oppose drecon). On he oher hand, f he prce receved by farmers changed, hen he farmers erms of rade offers a posve response (he same drecon). hus, he proporon of shock for Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology 3
Applcaon of Vecor Error Correcon Model (VECM) and Impulse Response Funcon for Analyss Daa Index of Farmers erms of rade he changed n prces pad by farmers dd no have a hgh conrbuon (effec) upon he farmers erms of rade. On he oher hand, he proporon of shock owards he changed n he prce receved by farmers has a hgh conrbuon (effec) upon he farmers erms of rade. 6. Acknowledgemen he auhors would lke o hank BPS Sascs Indonesa for provdng he daa used n hs sudy. 7. References. Aserou D, Hall SG. Appled economercs: A modern approach. Revsed ed. New York: Palgrave Macmllan; 007. PMCd:PMC868797.. Brand P, Wllams J. Mulple me seres models. housand Oaks, Calforna: Sage Publcaons Inc; 007. p. 7 48. Crossref 3. Enders W. Appled economerc me seres. New York: John Wley and Sons; 05. p. 63. 4. Gujara D. Basc economercs. 4h ed. Sngapore: McGraw- Hll Inernaonal Edons; 003. 5. Pala A. Srucural breaks, conegraon and causaly by VECM analyss of crude ol and food prce. Inernaonal Journal of Energy Economcs and Polcy. 03 Jul; 3(3):38 46. 6. say RS. Mulvarae me seres analyss wh R and fnancal applcaons. New Jersey: John Wley and Sons; 04. p. 457. 7. Engle FR, Granger CWJ. Conegraon and error correcon: Represenaon, esmaon and esng. Economerca. 987 Mar; 55():5 76. hps://do.org/0.307/9336 8. Krchgassner G, Wolers J. Inroducon o modern me seres analyss. Berln: Sprnger-Verlag; 007. p. 77. Crossref 9. Lukepohl H. New nroducon o mulple me seres analyss. Berln: Sprnger-Verlag; 005. p. 764. Crossref 0. Harrs R, Rober S. Appled economercs me seres. nd ed. Canada: John Wley and Sons; 005.. BPS sascs Indonesa. Sascs of Farmers erms of rade by Monh n Indonesa. Jakara: Cenral Bureau of Sascs; 04. p. 30.. BPS sascs Indonesa. Sascal Yearbook Indonesa 04. Jakara: BPS Sascs Indonesa; 04. p. 70. 3. Khan AA, Ahmed QM. Agrculure erms of rade n Paksan: Issues of profably and sandard of lvng of he farmers. Proceedngs PSDE Conference; Islamabad. 005. p. 3. 4. Loreo R. Calculaon and srucure of he consumers prce ndex, consumer prce ndex revson advsory commee. New Zealand: Sascs New Zealand; 997. p. 8. 5. Pankraz A. Forecasng wh unvarae box- jenkns Models: Conceps and cases. New York: John Wley and Sons; 983. p. 587. 6. Pankraz A. Forecasng wh dynamc regresson models. New York: John Wley and Sons Inerscence Publcaon; 99. PMCd:PMC0848. Crossref 7. Box GEP, Cox DR. An analyss of ransformaon. Journal of he Royal Sascal Socey (Seres B). 964; 6(): 43. 8. Mongomery D, Jennngs C, Kulahc M. Inroducon o me seres analyss and forecasng. New York: John Wley and Sons Inerscence Publcaon; 008. 9. Chafeld C. he analyss of me seres: An nroducon. 5h ed. Boson: Chapman and Hall; 995. 0. Rensel GC. Elemens of mulvarae me seres analyss. New York: Sprnger-Verlag; 993. Crossref. Lukepohl H. Inroducon o mulple me seres analyss. Berln: Sprnger-Verlag; 99. Crossref. Johansen S. Sascal analyss of conegraon vecors. Journal of Economc Dynamc and Conrol. 988 June; (-3):3 54. Crossref 3. Maddala GS, Km IM. Un roos conegraon and srucural change. UK: Cambrdge Unversy Press; 004. 4. We WS. me seres analyss unvarae and mulvarae mehods. nd ed. Canada: Pearson Educaon Inc; 006. 5. Sekar P. Dagnosc checkng of me seres models. Indan Journal of Scence and echnology. 00 Sep; 3(9):06 3. 6. Sekar P. Applcaon of me seres models. Indan Journal of Scence and echnology. 00 Sep; 3(9):03 7. 7. Pyndck R, Rubnfeld D. Economerc models and economc forecas. 4h ed. Sngapore: McGraw Hll Book Co; 998. 8. Johansen S. Esmaon and hypohess esng of conegraon vecors n Gaussan vecor auoregressve models. Economerca. 99 Nov; 59(6):55 80. Crossref 9. Gunes S. Funconal ncome dsrbuon n urkey: A conegraon and VECM analyss. Journal of Economc and Socal Research. 007 Jul; 9():3 36. 30. Sadegh M, Alav SY. Modellng he mpac of money on GDP and nflaon n Iran: Vecor Error Correcon Model (VECM) approach. Afrcan Journal of Busness Managemen. 03 Sep; 7 (35):343 34. Crossref 4 Vol 0 (9) May 07 www.ndjs.org Indan Journal of Scence and echnology