A tree-form constant market share model for growth causes in international trade based on multi-level classification

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1 A tree-form cotat maret hare model for growth caue teratoal trade baed o mult-level clafcato Yuahua Feg * Zhchao Guo hrta Petz ad Xagyog Ta 3 Faculty of Bue Admtrato ad coomc Uverty of Paderbor Germay ollege of coomc ad Maagemet ha Agrcultural Uverty ha 3 Beg Techology ad Bue Uverty ha Abtract: Th paper troduce a tree-form cotat maret hare (MS) model for aalyzg growth caue teratoal trade baed o mult-level clafcato. The treeform MS a collecto of MS model at dfferet level cludg the etre brach- ad leaf-model whch cot of a large amout of formato ad ha a wde applcato pectrum. Bac properte of th model are vetgated detal. t how that the treeform MS model uperor to other MS model the lterature. t alo how that well ow MS formulato are pecal cae of a lear cla wth two parameter whch cotrol how the teracto term dvded to the demad growth ad compettve term. Applcato to blateral trade betwee ha ad Germay how that the growth caue dfferet perod are clearly dfferet. t how that the output of the tree-form MS model ca be ued for further utable tattcal aaly. Furthermore our theoretcal fdg are alo cofrmed by thoe data example. JL clafcato: 5 F4 43 Keyword: Tree-form MS; teratoal trade; growth caue; geeral MS formulato * orrepodg author wth Tel: ; Fax: ; -mal: yuahua.feg@ww.upb.de

2 . troducto otat maret hare (MS) aaly a accoutg method for decompog a coutry export chage to the demad growth (or tructural chage ) the compettve ad the teracto compoet. Th method ow a hft-hare aaly wa frt appled the emprcal tude of tructural chage dutral ad regoal ecoomc (reamer 943). Revew o the developmet thee feld may e.g. be foud Houto (967) Steve ad Moore (98) ad Loverdge ad Seltg (998). MS aaly became popular appled teratoal ecoomc wth the poeerg wor of Tyzy (95) ad t ha bee creagly ued ad refed depte cotued crtcm both o t theoretcal ad emprcal apect (ee e.g. Rchardo 97a Jepma 986 Mere ad va der Meer 988 ad Mlaa 988). recet year addto to t applcato teratoal ecoomc (ee e.g. he et al. Smo ad apadre 6) ad regoal ecoomc (ee e.g. teba ad Ble ad Wolf ) MS or hft-hare aaly alo wdely appled other feld uch a tourm (ee e.g. Sraaya et al. 995 ad Toh et al. 4) eergy ecoomc (ee e.g. Su 998 Zhag 3 ad Mazzat ad Mot 9) ad frm performace (ee e.g. Fotopoulo 7 ad Mar ). Moreover reult of the MS decompoto ca alo be ued for further tattcal aaly (Batta 8). epte log htory ad wde applcato of the MS model there are tll may ope ueto th cotext. A tradtoal ueto wth the defto of the three bac compoet becaue they ca be defed followg the Lapeyre- or the Paache-type dex or ome mxture of both (Rchardo 97a ad Mlaa 988). Aother ueto wth the further decompoto of a bac compoet. To th ed dfferet dea are propoed the lterature (ee e.g. Jepma ). Uually the three compoet are decompoed dfferet way accordg to the purpoe of applcato. Furthermore the tradtoal MS model defed for a cro-table wth oe obervato each etry whch caot be appled drectly f mult-level clafed data for blateral trade codered. For data clafed at two level Toh et al. (4) ad Lu ad Me (7) propoe to ft a MS model frt oly ug data of the frt-level categore ad the to ft oe MS model to each frt-level category ug data of the ecod-level ub-categore. Guo et al. () call th a herarchcal MS model ad dcu t theoretcal bacgroud brefly whch oly volve data at two level ad ca be teratvely ued at each level ug data clafed at the ext level. The herarchcal MS model eay to udertad ad eay to ue. But t eem that there a lac of theoretcal foudato of th propoal. partcular for meaurg the overall chage data clafed at the ecod level or above caot be ued ad for meaurg

3 the chage of a frt-level category data clafed at the thrd level or above caot be ued. To olve the above ueto we wll troduce a tree-form MS model baed o multlevel clafed data. t pecal cae for three-level clafed data a modfcato of the tradtoal MS model the curret cotext. The frt- ad ecod-level brach-model ad leaf-model are alo defed by tag correpodg term out of the etre tree-form MS model whch clude ueful ad detaled formato. Theoretcal properte of th model are dcued detal. teretg fdg o the meag ad ource of the effect caued by clafcato at a gve level called the level-effect are acheved whch how that uder certa uffcet codto ome or all of the level-effect vah. Partcularly the pecal cae wth oly two categore the obtaed uffcet codto uch that the level-effect vah are alo eceary at the ame tme. Relatohp betwee the curret propoal ad related dea the lterature alo dcued. ocerg the defto of the decompoto of the MS compoet at a gve level t how that all of the well ow MS formulato are pecal cae of a lear combato of the three term followg the Lapeyre-dex wth two parameter whch cotrol how the teracto term dtrbuted to the other two. The choce of a MS formulato hece reduce to the ueto how we hould (or would le to) dvde the teracto term. Baed o th fdg we propoe to decompoe each of the three compoet the ame way over all clafcato level. Th mea that the demad growth ad compettve compoet are treated eually. Moreover a mlar decompoto of the teracto term mae ure that the reult ca tll be ummarzed accordg to ay other pecfed MS formulato. Further tattcal aaly of ome output of the tree-form MS model how that the propoal very meagful ad ueful practce. ummary th paper provde a ytematc methodologcal dcuo o ome problem related to the MS model ad may ope ome further reearch topc. The paper orgazed a follow. Secto defe the (etre) tree-form MS model ad t brach- ad leaf-model. The the properte of effect caued by each level of clafcato are dcued Secto 3. Secto 4 relatohp betwee the tree-form MS model ad extg dea the lterature compared ad a geeral MS formulato for the bac MS decompoto troduced. Reult of applcato to ha-germay trade are reported Secto 5. Fal remar Secto 6 coclude the paper. Proof of the reult are put the Appedx.. The tree-form MS model th ecto we wll defe the tree-form MS model for decompog chage of total export for mult-level clafed data by modfyg the defto of commo MS model 3

4 the lterature. Poble exteo of th model wll alo be dcued brefly.. ecompog the export chage at dfferet clafcato level oder the teratoal trade betwee a focu coutry (outry A) ad a gle detato (outry B). th paper we wll maly dcu the ue of the MS model baed o data clafed at three level. That outry A aggregate export are frt dvded to frtlevel categore the -th frt-level category cot of ecod-level ub-categore ad the ( )-th ecod-level category aga compoed of thrd-level ub-categore. outry B total mport from the world are alo clafed the ame way. eote the uatte of outry A export at thoe clafcato level the tal ad fal year by ; ; ad = = ad =. The correpodg uatte of outry B mport from the world wll be deoted by ; ; ad repectvely. Ad outry A correpodg maret hare are deoted by ; ; ad repectvely. Here we have where ad deote double ad trple um over ad ad over ad repectvely. Let deote the chage betwee the tal ad fal year. The chage of outry A aggregate export ca be decompoed baed o data at dfferet level of clafcato ug the Lapeyre-type dex (ee e.g. Jepma 986): overall decompoto frt level decompoto ecod level decompoto thrd level decompoto () where the three term each row o the rght-had-de (rh) of Model () are called the demad growth compoet ( l ) compettve compoet ( l ) ad teracto compoet ( l ) l = 3 repectvely calculated at the overall to the thrd-level ug the aggregated the frt- ecod- ad thrd-level clafed data. Thee term are bac decompoto of the total export chage.. The etre tree-form model Now we propoe to decompoe each of the three MS compoet further a ymmetrcal way. Baed o Model () the etre (three-level) tree-form MS model defed by 4

5 5 () where the three term the frt row o the rh of Model () are the overall compoet ( ad ) ad thoe the ecod thrd ad fourth row are the frt- ecod- ad thrd-level effect called the demad growth effect ( l ) compettve effect ( l ) ad teracto effect ( l ) (l = 3) repectvely. th paper the cocept compoet tad for a ma term accordg to the MS decompoto ad the cocept effect for the dfferece betwee ame-amed compoet at two level over each other. Alo ote that the um of the leveleffect at each level or wth ay (ub-) category alway zero. ue to the data tructure uder coderato the order of the dce ad for each um fxed ad the dce are ot exchageable. Th fact roll out a poble problem a MS formulato caued by the order of decompoto becaue th ow determed by the ature of the data. Model () clude all level-effect due to the clafcato ad provde u detaled ource that caue the chage of export..3 The brach- ad leaf-model Furthermore the -th frt-level brach-model defed by tag the -th elemet out of Model () whch baed o two-level of further categore: (3) where the three term the frt row o the rh of Model (3) are the frt-level compoet ( ad ) ad thoe the ecod ad thrd row are the ecod- ad thrd-level effect deoted by ad repectvely. Aalogouly the ( )-th ecod-level brach-model defed by tag the ( )-th elemet out of Model () whch baed o oe-level of further categore:

6 (4) where the three term the frt row o the rh of Model (4) are the ecod-level compoet ( ad ) ad thoe the ecod row are the thrd-level effect deoted by 3 3 ad 3 repectvely. Fally a o-called leaf-model ca be defed for each fal (leaf-) category. The ( )-th leaf-model.e. the ( )-th elemet of Model () gve by: (5) where the three term o the rh of Model (5) are the thrd-level compoet ( 3 3 ad 3 ). Note that all of the brach- ad leaf-model are part of Model (). Partcularly each model at a gve level loo le aother tree-form MS model defed baed o data from that level to the fal categore. ummary Model () through (5) cottute a collecto of MS model defed at dfferet level whch cot of a large amout of formato ad ha a wde applcato pectrum..4 Poble exteo The tree-form MS model above decrbed baed o data clafed at three level. practce teratoal trade data clafed at four or more level are avalable. The tree-form MS model ca be ealy exteded to aalyze thoe more detaled data. Furthermore the tadard MS model propoed for modelg teratoal trade of a focu coutry to more tha oe detato. f export to more tha oe detato clafed at mult-level are tuded a combato of the tadard ad the tree-form MS model ca be defed ad appled. addto f mothly or eaoal data are collected the the eaoal or mothly export ca be codered a ub-categore of yearly export. Now t poble to apply the dea of the tree-form MS model for aalyzg the effect caued by eaoal fluctuato. Th wll lead to a o-called eaoal MS model. Here the eao are treated a a further clafcato over tme. Alo ote that the eao are depedet of the clafcato baed o the product. Such a eaoal MS model hece mlar to the combato of the treeform ad the tadard MS model. Fally the tree-form MS model ca alo be appled to aalyze the chage of maret hare ( ) relatve export growth ( / ) ad relatve maret hare ( / ). Th ca be doe e.g. followg Formulato (5) (3) ad (4) Mlaa (988). To th ed ee alo Fagerberg ad Solle (987) for a aaly of the maret hare growth a ample of O coutre. 6

7 3. Properte of the tree-form MS model Followg Model () ad () we ca ee that the l-th level-effect tad for a redtrbuto of the MS compoet calculated by data clafed at level l tead of thoe at level l. f all of the level-effect are about zero t mea that the three compoet calculated ug data clafed at level l or level l roughly cocde wth each other. Otherwe the MS compoet calculated ug data clafed at dfferet level may be ute dfferet to each other. Now we wll dcu the ource of the level-effect detal. The followg theorem provde codto uder whch ome or all of the level-effect Reult o the level-effect at other level may be foud Secto 4.. Theorem : Uder the regularty codto ad we have ad vah. ae : a) f b) f the the vahe; vahe ad c) f both codto a) ad b) are fulflled the ad all vah. ae : f : : : the all of the three frt-level effect vah. Proof of Theorem gve the Appedx. Theorem reveal a more deep relatohp betwee dfferet varable o that the level-effect vah. All codto ae ad are uffcet but may be ueceary. the followg we wll call ad edogeou ad ad exogeou uatte whch reflect outry A export tructure ad t chage ad outry B maret tructure ad t chage repectvely. odto ae how that f the maret hare are the ame for all commodte the tal ad fal perod repectvely all of the three level-effect caued by the clafcato wll vah. Thee codto ca be regarded a utable mxed codto becaue maret hare deped o ad ad ad multaeouly whch dcate that the homogeety of outry A maret hare dfferet commodte oe of the ource of the level-effect. The homogeety aumpto o outry A maret hare rrelevat practce. odto ae are utable exogeou codto oly depedg o the detato maret tuato whch demotrate that f the maret growth each of the categore (about) the ame all of the three level-effect wll be (about) zero. Now the chage of export maly reflected by the overall compoet. The homogeety of the maret growth dfferet 7

8 commodte aother ource of the level-effect. ata example Secto 6 how that the maret growth ometme roughly homogeeou. orollary : f the codto of Theorem hold for everal categore at the ame level the correpodg level-effect wll ot be chaged f ome of thoe categore are combed together. Proof of orollary traghtforward ad hece omtted. The pecal cae wth = tae to how ome detal. Note that ow the uffcet codto ae of Theorem become. Let ff tad for f ad oly f. orollary : Aume that the regularty codto of Theorem hold. For = we have a) b) c) > (= or <) ff or ; > (= or <) ff or ; > (= or <) ff or ad d) The effect ad all vah ff or ad. Proof of orollary gve the Appedx. orollary d) how that for = the codto Theorem uch that the three term all vah are alo eceary. orollary a) to c) dcate further whe the level-effect ad wll be potve or egatve repectvely. Oce oe of the three term vahe the other two are eual abolute value ad oppote g. Furthermore f but ad the the frt-level teracto effect completely dvded to ad. For > eceary codto uch that complex ad wll ot be dcued. ad all vah become more 4. Some further reult Now we wll dcu the relatohp betwee the tree-form MS model ad related propoal the lterature exted the above reult to mult-level tree-form MS model ad dcu the relatohp betwee dfferet well ow MS formulato the lterature more detal. 4. Relatohp betwee dfferet MS model the lterature there ext much debate about whch level of clafed data hould be ued whe applyg the MS model. Ad mot of them admt that f employg data at dfferet level the the reult are alo clearly dfferet. Rchardo (97b) dcue th problem 8

9 detal ue the clafcato of commodte over four opto ad pot out The varou compoet wll vary wth the level of commodty aggregato. Alterg the commodty clafcato led to ubtatal varato the value of MS effect. The tree-form MS model how that the level-effect tad for the dfferece betwee the MS compoet baed o data clafed at two level. Whether thee dfferece are clear or ot deped o the ueto f the codto uch that all of the level-effect vah are about fulflled or ot. The followg example provde a further explaato for the dfferece betwee the leveleffect caued by the ue of data at dfferet level of clafcato. Aume that data are clafed at two level ad coder the ue of two type of model. Oe ue oly the data the frt-level categore called Model A the other ue oly the data all of the ecodlevel categore called Model B. The overall compoet ad the frt-level effect gve by Model A are exactly the ame a thoe gve by the tree-form MS model. However Model A caot provde the formato of the ecod-level effect. The overall compoet gve by Model B are alo the ame a thoe gve by the tree-form MS model. ach of the further effect of Model B the um of the two correpodg frt- ad ecod-level effect of the tree-form MS model. A further decompoto of thoe two level-effect oly ug the data at the ecod-level however mpoble. We ee that the tree-form MS model uperor to the two type of wdely ued MS model.e. Model A ad B. 4. Properte of the level-effect at ay level Reult of Theorem ad orollary alo hold for the level-effect of a mult-level tree-form MS model at each level. orollary 3: oder data clafed at level. Uder the ame regularty codto of Theorem let l =. The followg hold a) f the correpodg codto of ae ad Theorem or thoe of orollary hold for the commodte at level l of a ub-model at level l the the correpodg level-effect of th ub-model vah ad b) f the correpodg codto of ae ad Theorem or thoe of * orollary hold for all ub-model at level l the the correpodg leveleffect at ay level l vah l l * l *. Proof of orollary 3 traghtforward ad hece omtted. The meag of orollary 3 a) mlar to that of Theorem or orollary. odto of orollary 3 b) dcate that the etre level-effect at each level are caued ether by the homogeety of the maret hare 9

10 or the maret growth all ub-categore. 4.3 Relatohp betwee well ow MS formulato To our owledge mot dpute about well ow MS formulato ca be attrbuted to how to decompoe the three MS compoet reaoably ad valdly. The followg ecto maly focue o the decompoto of the overall compoet. We wll explore the relatohp betwee the well ow decompoto propoed the lterature. Ug the Lapeyre- ad Paache-type dce two bac MS formulato are (6) wth ad ad (7) wth ad. Note that ca be repreeted baed o Model (6) or (7) a follow ( ) ( ) ( ) or ( ) ( ) ( ) (8) (9) where ad are two parameter. pecally Model (8) ad (9) are euvalet wth. deed the retrcto ad are ueceary whch are oly ued for mplcty. The relatohp betwee mot well ow decompoto the lterature ca be ummarzed a follow: Theorem : Mot of the MS formulato the lterature are pecal cae of Model (8) wth certa value of ad. Smlar tatemet hold for Model (9). The above fact alo hold for other compoet ad level-effect of the tree-form MS model. To clarfy the meag of Theorem we wll how that all of the Formulato (6) to () Mlaa (988) (ee alo Formulato (6) to (9) Rchardo 97a) are all pecal cae of Model (8) wth dfferet choce of ad. f ad the Model (8) become Formulato (6) there.e. ; f ad the Model (8) become Formulato (7) there.e. ; Formulato (9) there the ame a Model (6) ad Formulato () there the ame a * * Model (7).e. Model (8) wth ad Model (9) wth.

11 partcular t ca be how that Formulato (8) there.e. ~ ~ ~ ~ ~ alo a pecal cae of Model (8) wth ~ ~ ad. Uder the further retrcto cludg Formulato (6) ad (7) the teracto term wll be completely dvded to the other two term. The value of ad ca be choe baed o dfferet purpoe. For tace ad or ad are two commoly ued choce. Mlaa (988) propoe to ue.5. Th decompoto ue the Törpvttype dex whch tae the average of the Lapeyre- ad Paache-type dce umber. Thee choce are all depedet of the data. We fd that determg ad accordg to the rato of the abolute value of ad may be a more reaoable choce..e. The dea to decompoe each of the three MS compoet further ymmetrcally ha a clear advatage becaue t allow u to ummarze the decompoto reult of Model () accordg to ay other choce of ad. Th how ug data clafed at two level wth. 5. Now we have.5 ad.5 () where the frt term o the rh of Model () tad for the tructure compoet or demad growth compoet ad the ecod for the compettve compoet. The teracto term completely dvded to thoe two compoet a dcated before. f the demad growth compoet ad the compettve compoet are treated a mlar way Model () ca be further decompoed ymmetrcally a follow: Model () the demad growth compoet dvded to the overall demad growth compoet ad the frt-level ad ecod-level demad growth effect correpodg to the three term the frt colum o the rh repectvely ad the three term the ecod colum o the rh are the overall compettve compoet ad the frt-level ad ecodlevel compettve effect. We wll alo call Model () a tree-form MS model due to the data tructure uder coderato. Although Model () modfed from Formulato (9) ()

12 Mlaa (988) t tll dffer from that formulato everal way. f the teracto compoet the thrd row of Model () aged to the other two compoet ug eual weght t wll be coverted to Model (). Th relatohp alo hold for the frt three row of Model () ad Model (): ~ ~ ~ orollary 4: eote the x compoet ad effect Model () by ad ad ~ ~ ~ ad repectvely. The we have the followg relatohp wth the correpodg term Model (): ~ ~ ~ ~ ad ~ ~ Proof of orollary 4 omtted. Thee reult mea that gve the decompoto reult of Model () we ca obta thoe of Model () but ot vce vera. Reult of orollary 4 wll be cofrmed ug data example Secto 5.. Smlar reult apply to ay other choce of ad. 5. Applcato to ha-germay trade ata dowloaded from the Uted Nato ommodty Trade Stattc atabae (UN omtrade) from 993 to 9 are ued a example. Both ha export to Germay ad Germay export to ha wll be tuded. Accordg to the Stadard teratoal Trade lafcato (ST Rev. 3 hortly ST) the total export are frtly dvded to two frtlevel categore.e. agrcultural ad dutral product. Baed o the -dgt ST agrcultural product are compoed of four categore (ST ad 4) ad dutral product alo cot of four categore (ST 5-8). Thee are the eght ecod-level categore codered here. ST 3 ad 9 are excluded due to may mg value. The baed o the -dgt ST each of the four agrcultural categore compoed of te two e ad three ub-categore ad each of the four dutral categore dvded to e e e ad eght ub-categore repectvely. Thee are codered a the thrd-level categore. Hece the data uder coderato are clafed at three level. th paper the decompoto carred out yearly o that the ed of the perod each decompoto alo the begg of the ext perod. Note that the output of each compoet or effect of a MS model wth the obervato perod form a tme ere. Here t worthy to aalyze thoe output further.

13 5. xploratve aaly of the MS output We wll gve ome exploratve aaly of elected reult to how th. The demad growth compettve ad teracto compoet ad ther correpodg level-effect of the threelevel tree-form MS model ha total export to Germay ad Germay total export to ha from 994 to 9 are dplayed Fgure ad repectvely. Frtly the three compoet are dcued. For ha export to Germay (ee the frt row Fgure ) both the demad growth ad teracto compoet exhbted a great drop.e. a tructural brea 9 due to the facal cr whch however dd ot happe the compettve compoet. That the compettvee of ha export to Germay wa ot affected by the facal cr. Furthermore there a clear potve ump the teracto compoet betwee ad 3 whch may dcate the mpact of ha acceo to WTO o the growth caue of t export to Germay. To vetgate th detal a mple lear ad a cotat regreo model wth a rollg dummy varable ether the tercept or the lope appled to the three ere (wthout the value 9). See alo Guo et al. () for a related propoal. The the A ued to detect a poble tructural brea. t foud that all of the three ere exhbt a hghly gfcat potve tructural brea betwee ad 3. Ad the tructural brea the demad growth ad compettve compoet a rate-hft (a ump the growth rate) whle the teracto compoet exhbt a level-hft (a ump the tercept). Jump the teracto compoet otly caued by thoe the demad growth ad compettve compoet ad hece much clear. We ca alo ee that the developmet of the demad growth compoet betwee 994 ad 8 relatvely regular the varato the teracto compoet betwee 3 ad 8 clearly larger tha before ad that the compettve compoet very large. Moreover the compettve compoet eem to correlate to each other a egatve way. Th mea that f ha compettvee trogly creae oe year t cremet the ext year ted to be maller. Reult of the urb- Wato tet ad the correlogram how that th egatve correlato however gfcat at the 5%-level. For Germay export to ha (ee the frt row Fgure ) the commo feature that the developmet of the three compoet are relatvely table betwee 994 ad whch however exhbt large fluctuato betwee 3 ad 9. The reao could be the offcal lauch of the uro the U AP (ommo Agrcultural Polcy) reform 999 ad further reform thereafter. Smlarly to the compoet Fgure the demad growth ad teracto compoet alo howed a clear reducto 9 maly caued by the facal cr. But the compettve compoet tll had a ga tead of lo whch ugget that Germay export compettvee mproved ad t maret hare ha 3

14 creaed durg the facal cr. The we loo at the level-effect from the frt- to the thrd-level. For both coutre there o obvou rule ther developmet. Fgure : The three-level tree-form MS model for ha total export to Germay. Now coder the behavor of the frt-level brach-model. Sce dutral product accout for about 97% of the total export for both coutre the reult of the frt-level brach-model for th category are very mlar to the frt thrd ad fourth row Fgure ad repectvely. Thee two brach-model are hece omtted. From the two frt-level brach-model for agrcultural product oly that of ha export to Germay choe ad dplayed Fgure 3. Here the three compoet (the frt row) are maly codered. We ee that the demad growth compoet ept potve from to 8 whch dcate Germay mport demad wa expadg durg that perod. But 9 t decreaed gfcatly ad became egatve becaue of the facal cr. For the compettve 4

15 Fgure : The three-level tree-form MS model for Germay total export to ha. compoet t how that the developmet wa very rregular wthout clear tructural brea. cotrat the compettve compoet of ha export to Germay dutral product had a clear tructural brea betwee ad 3 ad ept a relatvely hgh level from the o (compare wth Fgure (b)). Th ugget that ha acceo to WTO exhbted a more clearly potve mpact o t export of dutral product tha agrcultural product. Smlarly to Fgure (b) the compettve compoet alo appear to correlate to each other a egatve way whle the correlato gfcat at the %-level. The teracto compoet had a udde reducto durg 8 to 9 whch alo reflect the mpact of the facal cr. Fally ome choe ecod-level brach-model ad leaf-model are dplayed Fgure 4. For ha export to Germay machery ad traport eupmet (ST 7) ad oe of t bgget ub-categore electrcal machery etc. (ST 77) are how the frt ad thrd 5

16 Fgure 3: The frt-level brach-model for ha export to Germay agrcultural product. row of Fgure 4 repectvely. For Germay export to ha food ad lve amal (ST ) ad t mot repreetatve ub-category vegetable ad frut (ST 5) are gve the ecod ad fourth row of Fgure 4 repectvely. For the ecod-level brach-model oly the three compoet are provded ad the thrd-level effect are omtted to ave pace. Smlarly to Fgure (b) the compettve compoet of machery ad traport eupmet (ee Fgure 4 (b)) alo exhbt a clear potve ump betwee ad 3. Ad we ee that the varato of th compoet betwee 3 ad 8 very large. cotrat to the correpodg reult Fgure (b) the egatve hort-term mpact of the facal cr o the compettvee of ha export th category clearer wth a great drop 9. The demad growth compoet of food ad lve amal (ee Fgure 4 (d)) wa potve 9 whch dcate that ha mport demad th category tll creaed depte the facal cr. Furthermore vegetable ad frut the oly oe ub-category that t demad growth compoet (ee Fgure 4 ()) had a clear cremet 9. Lat but ot leat the teracto compoet dffcult to expla ad ofte wth large fluctuato. f the compettve compoet potve ad t developmet table the the hape of the teracto compoet loo le the demad growth compoet (ee Fgure 4 ()). Smlarly f the demad growth compoet potve ad t developmet table the the hape of 6

17 the teracto compoet loo le the compettve compoet. Th e.g. true for the category of geeral dutral machery ad eupmet etc whch omtted to ave pace. Fgure 4: Some choe ecod-level brach-model ad leaf-model for both coutre. 5. Numercal evdece of the theoretcal reult th ub-ecto we wll ue ome example to cofrm the theoretcal reult Secto 3 ad 4 detal. The perod from 4 to 8 codered becaue the trade developmet betwee ha ad Germay wth th perod more table wthout tructural brea (ee Guo et al. ). At frt reult of the three-level tree-form MS model are lted Table whch correpod to the term of Model (). From Table we ca ee that each um of the effect at the frt- ecod- ad thrd-level zero. For tace Germay export to ha from 4 to 5 the three thrd-level effect are ad 387 mllo US dollar repectvely whch um up to zero. Reult of orollary ca be ow cofrmed 7

18 umercally. Frtly the three frt-level effect of ha export to Germay from 5 to 6 are all about zero. Accordg to orollary d) th ca oly happe f : : or ad. After checg the detal we fd ad but : 9.6: : ad : : : ad codto of orollary d) are roughly fulflled. By Germay export to ha from 7 to 8 the frt-level demad growth effect ( ) egatve ad the frt-level compettve effect ( The reao for th are ad ) potve. accordg to orollary a) ad b). Reult Table alo how that the abolute value of the ecodor thrd-level effect may alo be larger tha that of the correpodg frt-level effect. Table : Reult of the three-level tree-form MS model from 4 to 8 ($US mllo) Year Level ha export to Germay Overall Level Germay export to ha Overall Now we wll aalyze the reult of the frt-level brach-model ad wll oly focu o agrcultural product. Reult of the frt-level brach-model for agrcultural product are gve Table whch correpod to Model (3) wth =. Baed o Model () ad (3) the reult for dutral product ca be obtaed by mple calculato of correpodg term Table ad ad are hece omtted. Table cofrm aga that ad t foud that all of the three ecod-level effect of Germay export to ha agrcultural product from 7 to 8 are relatvely very mall becaue ha

19 maret growth the four ub-categore of agrcultural product durg that perod wa roughly homogeeou wth : : :.:.3:.65 ad : : 3 : 4 3 : :.4:.9:.76. That the codto of ae Theorem approxmately fulflled. Table : Reult of the frt-level brach-model for agrcultural product ($US mllo) Year ha export to Germay Year Germay export to ha Furthermore reult for ome choe ecod-level brach-model are how Table 3 whch correpod to Model (4) wth certa ad. Both agrcultural ad dutral product are compoed of four ecod-level categore o the umber of correpodg ecod-level brach-model eght. t dcate that for = ad = 3 4 all cae. Accordg to the -dgt ST we chooe food ad lve amal () ad machery ad traport eupmet (7) a example to how th. Fally reult for ome choe leaf-model are lted Table 4 whch correpod to Model (5) wth gve ad. For ha export to Germay two repreetatve -dgt ST commodte.e. fh etc. (3) ad offce mache etc. (75) are choe. For Germay export to ha aother two typcal -dgt ST commodte.e. coffee tea cocoa etc. (7) ad road vehcle (78) are elected. The reult are very dfferet amog thoe thrd-level categore. ach leaf-model baed o each thrd-level category could provde u ome detaled formato that caue the chage of export partcular the growth caue for that category. 9

20 Table 3: Reult of the choe ecod-level brach-model ($US mllo) Name Food ad lve amal Machery ad traport eupmet Year ha export to Germay Year Germay export to ha Table 4: Reult of the choe leaf-model ($US mllo) ha export to Germay Germay export to ha Name Name Fh etc offee tea cocoa Offce Road mach- e vehcle etc Reult of the MS model ug dfferet type of dex are gve Table 5 whch tae 5 to 6 ad 7 to 8 at the overall-level a example. The followg fact ca be exteded to the frt- ecod- ad mult-level correpodgly. Table 5 the abbrevato N for ha ad for Germay are ued. Baed o Theorem ad orollary 4 the relatohp betwee dfferet type of the MS model that they ca be traformed to each other uder ome codto. t clear that f the Paache-type dex ued the

21 ; f the Törpvt-type dex ued the ~ ~. 5 ad. 5 ; ad f the rato of the abolute value of ad ued a weght the ad the teracto compoet alo vahe. Table 5 how that e.g (Table ) for ha export to Germay from 5 to 6. addto ad ca alo be defed dfferetly at dfferet level. Table 5: Reult of the MS model ug dfferet type of dex ($US mllo) Year Type ompoet N to to N N to to N Paache Törpvt Relatve 569(. 73) 477(. 6) 57(. 49) 53(. 6) Weght 85(. 7 ) 37(. 4 ) 5(. 5) 358(. 38) 6. Fal remar Th paper provde a deep ght to the MS aaly by troducg a tree-form MS model. t how that the tree-form MS model ca be exteded to mult-level clafed data ad other way. t alo dcated that whe ug the MS model ot oly the fal but alo the termedate reult cota ueful formato for deco mag. Furthermore t how that the well ow MS formulato deed form a lear cla wth two parameter whch cotrol how the teracto term dvded to the demad growth ad the compettve term. A ymmetrc further decompoto of the three compoet uggeted. Th allow u to report the reult accordg to dfferet MS formulato after the decompoto. Source of effect caued by each level of clafcato are dcued detal. Advatage of the ew MS model to related oe the lterature are clarfed. Applcato to trade betwee ha ad Germay how that the propoal are very ueful ad flexble. Aaly of the output of the three-level tree-form MS model how that ha acceo to WTO ha had a potve log-term mpact o all of the three MS compoet ha

22 export to Germay. t foud that the growth caue before ad after ome remarable ecoomc evet are clearly dfferet. Furthermore our theoretcal fdg are alo cofrmed by data example. We ee that depte a huge umber of theoretcal tude o the MS model ad t wde applcato there tll eem to be a bg play room for further developmet of theory ad practce of the cotat maret hare aaly. Hece the curret paper may ope a ew reearch drecto th area. Acowledgemet The paper wa a part of a cooperatve reearch proect betwee the Uverty of Paderbor ad the ha Agrcultural Uverty. We are grateful to the facal upport of the Faculty of Bue Admtrato ad coomc Uverty of Paderbor Germay. We would le to tha UN omtrade for publhg the data.

23 Referece Batta J.. (8). ompetto betwee Bral ad other exportg coutre the US mport maret: a ew exteo of cotat-maret-hare aaly Appled coomc Ble U. ad Wolf K. (). Regoal developmet of employmet eater Germay: a aaly wth a ecoometrc aalogue to hft-hare techue Regoal Scece he K. Xu L. ad ua Y.F. (). x-pot compettvee of ha export agrfood product: Agrbue reamer. (943). Shft of maufacturg dutre dutral Locato ad Natoal Reource Wahgto..: U.S. Govermet Prtg Offce. teba J. (). Regoal covergece urope ad the dutry mx: a hft-hare aaly Regoal Scece ad Urba coomc Fagerberg J. ad Solle G. (987). The method of cotat maret hare aaly recodered Appled coomc Fotopoulo G. (7). tegratg frm dyamc to the hft-hare framewor Growth ad hage Guo Z.. Feg Y.H. ad Ta X.Y. (). Short- ad log-term mpact of remarable ecoomc evet o the growth caue of ha-germay trade agr-food product coomc Modellg Houto.B. (967). The hft-hare aaly of regoal growth: a crtue Souther coomc Joural apadre P.L. (6). Structural factor ad compettvee teratoal trade: a ew formulato of the cotat-maret-hare-aaly method upublhed maucrpt July 6. Jepma.J. (986). xteo ad applcato poblte of the cotat maret hare aaly: the cae of the developg coutre export Uverty Pre Groge Hollad. Jepma.J. (989). xteo of the cotat-maret-hare aaly wth a applcato to log-term export data of developg coutre. The Balace betwee dutry ad Agrculture coomc evelopmet Wllamo J.G. ad Pachamuh V.R. (ed) The Macmlla Pre Ltd Lodo Loverdge S. ad Seltg A.. (998). A revew ad comparo of hft-hare dette teratoal Regoal Scece Revew Lu W.. ad Me Y. (7). The caue of ha-u agrcultural trade growth: baed o the 3

24 emprcal aaly of the MS model ue Agrcultural coomy 5-9. Mar G. (). A applcato of cotat maret hare aaly for the tudy of frm proftablty MPRA Paper No. 584 September. Mazzat M ad Mot A. (9). Regoal ad ector evrometal effcecy emprcal evdece from tructural hft-hare aaly of NAMA data Fodazoe rco Matte Worg Paper November 9. Mere A.H..M. ad va der Meer T. (988). A theoretcal foudato for cotat maret hare aaly mprcal coomc Mlaa. (988). otat-maret-hare aaly ad dex umber theory uropea Joural of Poltcal coomy Rchardo J.. (97a). otat maret hare aaly of export growth Joural of teratoal coomc Rchardo J.. (97b). Some etvty tet for a cotat maret hare aaly of export growth Revew of coomc ad Stattc Smo. (). Belgum export performace: a cotat maret hare aaly Federal Plag Bureau WP -. Sraaya. Uyal M. ad Toepper L. (995). Meaurg tourm performace ug a hfthare aaly: the cae of South arola Joural of Travel Reearch Steve B.H. ad Moore.L. (98). A crtcal revew of the lterature o hft-hare a a forecatg techue Joural of Regoal Scece Su J.W. (998). hage eergy coumpto ad eergy tety: a complete decompoto model ergy coomc 85-. Toh R.S. Kha H. ad Lm L.L. (4). Two-tage hft-hare aalye of tourm arrval ad arrval by purpoe of vt: the Sgapore experece Joural of Travel Reearch Tyzy H. (95). World trade maufactured commodte The Macheter School Zhag Z.X. (3). Why dd the eergy tety fall ha dutral ector the 99? The relatve mportace of tructural chage ad tety chage ergy coomc

25 5 Appedx: Proof of the reult Proof of Theorem ae : a). Th reult we have Sce. b). Th relut we have Sce. c) Uder the codto of a) ad b) we have. ad Hece becaue. ae : have we :: : :: : :: : Sce.

26 6. Ad. Hece Furthermore. ad. Hece. becaue have Fally we

27 7 Proof of orollary a) Whe = we have. Hece potve (zero or egatve) ff. or b) Furthermore we have. Hece potve (zero or egatve) ff. or c) For we have. potve (zero or egatve) ff. or d) t clear that the term ad all vah f. ad or O the other had f or ad at leat oe of ad o-zero. Th fhe the proof.