Endogenous Growth Models in Open Economies: A Possibility of Permanent Current Account Deficits

Transcription

1 Endogenou Growh Model in Open Eonomie: Poibili of Permanen Curren oun Defii Taiji HRSHIM Univeri of Tuuba Cabine Offie of Japan pril 5 Verion. bra The paper explore he impa of heerogenei in degree of relaive ri averion on he balane on urren aoun in a wo-ounr endogenou growh model. I onlude ha, lie he heerogenei of demographi hange, he heerogenei in degree of relaive ri averion generae periing urren aoun defii. The defii oninue permanenl, bu i raio o oupu abilize. Wih evidene ha he degree of relaive ri averion in Japan i relaivel higher han ha in he U.S., here i a poibili ha he periing bilaeral rade defii of he U.S. wih Japan i pariall generaed b hi mehanim. JEL Claifiaion ode: F4, F, F43, O4, E Keword: Curren aoun; Trade defii; Capial flow; Endogenou growh; Ri averion Correpondene: Taiji HRSHIM: Graduae Shool of Sem and Informaion Engineering, Univeri of Tuuba, -- Tenoudai, Tuuba, Ibarai , Japan harahm@.uuba.a.jp -harahima@mve.biglobe.ne.jp *The view expreed herein are hoe of he auhor and no neearil hoe of Cabine Offie of Japan.

2 I. INTRODUCTION The large urren aoun defii in he U.S. and he large urren aoun urplu in Japan have oninued during he pa hree deade (ee Figure ), and he large bilaeral rade defii of he U.S. wih Japan ha alo peried (ee Figure ). The onvenional ineremporal approah o he urren aoun an no explain hee periing large urren aoun imbalane a Obfeld and Rogoff (995) argue, and hu i need he help of overlapping-generaion varian of he ineremporal model. The overlapping-generaion varian of he ineremporal model explain perien urren aoun imbalane b heerogeneou demographi hange. For example, he explain ha more rapidl aging Japan experiene periing urren aoun urplue while le rapidl aging US experiene periing urren aoun defii. There are voluminou wor ha ondu imulaion baed on he overlapping-generaion varian of he ineremporal model and proje he impa of heerogeneou demographi hange in he U.S., Japan and oher ounrie. lhough here are variou pe of model, he bai idea behind he explanaion of periing urren aoun imbalane i ommon and imple: naional aving move heerogeneoul under he influene of heerogeneou demographi hange while naional invemen are affeed le b he heerogeneou demographi hange beaue he are deermined baiall b he world real inere rae, and hu heerogeneou demographi hange generae heerogeneou movemen of he balane on urren aoun, i.e., heerogeneou movemen of naional aving minu naional invemen. However, alhough heoreial projeion baed on demographi hange have been numeroul arried ou, few emai empirial examinaion ino he relaionhip beween he See e.g. Kolioff, Smeer and Wallier (), Broo (3), or Faruqee (3). Mo of hee imulaion proje ha he urren aoun in Japan will urn o defii in near fuure due o he rapid demographial hange in Japan.

3 balane on urren aoun and demographi hange have repored. mong hee few udie, Poerba () onlude ha alhough heoreial model generall ugge ha equilibrium reurn on finanial ae will var in repone o hange in populaion age ruure, i i diffiul o find robu evidene of uh relaionhip in he ime erie daa. a reul, he onjeure ha urren aoun imbalane are generaed b heerogeneou demographi hange ha no been full uppored b empirial evidene and i ill merel a heoreial poibili. If explanaion baed on heerogeneou demographi hange indiae onl a heoreial poibili, heerogenei ha an be examined a he oure of perien urren aoun imbalane ma no neearil be ied onl o he heerogenei of demographi hange. Oher heerogeneou naure of eonomie ma alo heoreiall generae direpan beween naional aving and invemen. The paper explore heerogenei in degree of ri averion a anoher poible oure of perien urren aoun imbalane. The reaon wh he paper dire i aenion o he degree of ri averion i firl ha in endogenou growh model he degree of relaive ri averion pla a ruial role for growh rae and hu i heerogenei ignifianl ompliae movemen of inernaional ranaion. ume ha here are onl wo ounrie in he world, onl differene beween whih i he degree of relaive ri averion. The onvenional growh model wih exogenou ehnologie, he heerogeneou degree of ri averion in wo ounrie do no maer for ead ae growh rae beaue he are deermined b he ommon exogenou growh rae of ehnologie in boh ounrie. However, in endogenou growh model, he degree of relaive ri averion i he ruial parameer ha deermine growh rae, and hu ead ae growh pah under i heerogenei are no o imple. The familiar Euler ondiion in ae of a Harrod neural produion funion uh ha Y K i L L ( ) n where i oupu per apia,

4 i onumpion per apia, i apial inpu per apia, Y i oupu, K i apial inpu, L i labor inpu, i nowledge/ehnolog/idea, n L i he growh rae of populaion, i he L rae of ime preferene, i he degree of relaive ri averion, and i a onan. In mo endogenou growh model, i modeled o be onan, and hu he growh rae of onumpion beome onan. Hene, in endogenou growh model, he onan growh rae of onumpion ( ) n ruiall depend on he value of degree of relaive ri averion, and hu i heerogenei ignifianl ompliae ead ae growh pah in he world of free rade. The eond reaon wh he paper dire i aenion o he degree of relaive ri averion i beaue i ha been repored ha he degree of relaive ri averion in Japan i relaivel higher han ha in he U.S. I i anoher imporan heerogenei han demographi hange beween he U.S. and Japan, and i implie a poibili ha he large urren aoun defii in he U.S. and he large urren aoun urplue in Japan an be explained b he relaivel higher degree of relaive ri averion in Japan han ha in he U.S. In he well-nown Szpiro (986), i i repored ha of he nine indurialized ounrie udied he Japanee have he highe degree of relaive ri averion, e.g. he degree of relaive ri averion in Japan i.76 while ha in he U.S. i.9. I i a well nown fa ha ompared wih houehold in he U.S., houehold in Japan inve heir finanial ae muh le in ri invemen, whih learl indiae ha he degree of ri averion in Japan i muh higher han ha in he U.S. Furhermore, heerogenei in ri averive behavior ha reenl been repored from he medial or geneial poin of view. Ono e al. (997) and Naamura e al. (997) how ha he See e.g. Romer (99), ghion and Howi (998), or Jone (3). 3

5 genei ompoiion of he reepor for brain hemial uh a eroonin or dopamine differ widel among human rae, and ha mo Japanee have inheried a erain pe of reepor ompoiion ha produe more auiou and herefore more ri averive haraerii, while man merian have inheried he oher pe ha produe le ri averive haraerii. In addiion, Harahima (998) how ha he o-alled Japanee eonomi em or Japanee apialim originae in he higher degree of relaive ri averion in he Japanee. The model in he paper, whih i baed on he oluion in Sorger () and Ghiglino () o he problem of heerogeneou houehold raied b Beer (98), how ha here i a poibili ha heerogenei in degree of relaive ri averion generae perien, more orrel permanen, urren aoun imbalane. In ome irumane, a ounr wih lower degree of relaive ri averion experiene a permanen urren aoun defii, and in revere a ounr wih higher degree of relaive ri averion experiene a permanen urren aoun urplu. Neverhele, urren aoun defii and urplue do no explode bu he raio of defii and urplu o oupu ampoiall approah unique finie value and abilize in boh ounrie. Hene, he model predi ha if he degree of relaive ri averion in Japan i rul relaivel higher han ha in he U.S., here i a poibili ha he urren aoun urplu peri in Japan permanenl and he urren aoun defii peri in he U.S. permanenl. The paper i organized a follow. In eion II, a wo-ounr endogenou growh model ha inorporae inernaional ranaion i onrued, and he bai naure of he model i examined. I i hown ha here i a ead ae growh pah on whih he i of growh rae of onumpion, apial, nowledge/ehnolog/idea, and oupu are all equal and he are equal in boh ounrie. In eion III, he balane on urren aoun in he model i examined. I i hown ha here i a poibili ha a ounr wih lower degree of relaive ri averion experiene a permanen urren aoun defii and in revere a ounr wih higher degree of relaive ri averion experiene a permanen urren aoun urplu. In eion IV, fir, evidene ha he degree of relaive ri averion in Japan i relaivel higher han ha in he 4

6 U.S. i preened. Seondl imple imulaion wih alibraed parameer value are arried ou, reul of whih indiae a poibili of permanen rade imbalane. Finall, ome onluding remar are offered in eion V. II. THE MODEL. The bai model In mo endogenou growh model, he growh rae of onumpion i ommonl expreed a ( ) n where i ep onan b ome mehanim ha are differen aording o he pe of model, and hu in mo model, he degree of relaive ri averion pla a ruial role for ead ae growh rae. In hi ene, man pe of endogenou growh model ha inorporae inernaional ranaion ma be ued for he ae of he anali in he paper and ma lead o he ame onluion. From among variou endogenou growh model, however, he paper hooe a peifi model ha i examined in Harahima (4), beaue hi model ha he advanage of being free from ale effe and he influene of populaion growh imulaneoul, whih eem ver advanageou when a faor oher han demographi hange i examined ine we an exra he effe of he faor ha are independen from effe of populaion. 3 The produion funion i aumed o be Y F(, K, L ), where Y ( ) i oupu, K ( ) i apial inpu, L ( ) i labor inpu, and ( ) i nowledge/ehnolog/idea inpu in period. The model i baed on he following aumpion. umpion: 3 See e.g. Jone (995), ghion and Howi (998), and Pereo and Smulder (). 5

7 () umulaion of apial and nowledge/ehnolog/idea are K Y C ν K, where ν ( > ) i a onan and a uni of K and of a uni of are produed uing he ame ν amoun of inpu, and i he rae of depreiaion. 4 () Ever firm i idenial and ha he ame ize, and for an period, M m L ρ onan where M i he number of firm and ρ ( > ) i a onan. (3) Y K M ρ Y ( ν) and hu. umpion () i andard one in he lieraure of endogenou growh. umpion () impl aume ha he number of populaion and he number of firm in an eonom are poiivel relaed, whih eem inuiivel naural. In aumpion (3), he paper aume ha reurn on inveing in K and inveing in for a firm are ep equal. However i i alo aumed in (3) ha a firm ha inven a new ehnolog an no obain all he reurn on inveing in. Thi mean ha inveing in inreae Y bu reurn of an individual firm ha inve in i onl a fraion of he inreae of Y uh ha M ρ Y ( ν) ml ( ν) Y. The reaon wh onl a fraion of he inreae in Y he reurn of an individual firm i, i unompenaed nowledge pillover o oher firm. More peifiall, he produion funion i aumed o have he following funional form: Y F(,K,L ) f( K ), where ( < <),L i a onan. Le Y, L K, L C and L n L and aume ha ( K L ) L f, i homogenou of degree one. Thereb 4 Hene, lie Jone (995) non-ale model,, a well a K, i produed le a and L inreae if he uual produion funion of homogeneou of degree one i aumed. 6

8 ( ) ν f, and n L. B aumpion () and (3), ( ) ( ) f beaue m νf f ( ) f ( ). Sine f, hen f f f f and f f. f. The model in open eonomie For implii, i i aumed ha in he world here are onl wo ounrie, i.e., ounr and ounr, in whih parameer a well a populaion are idenial exep he degree of relaive ri averion, and he growh rae of populaion i zero, i.e., n. Le he degree of relaive ri averion in he ounr be and ha in he ounr be. Good and ervie and apial are freel raded bu labor i immobilized in eah ounr. The produion funion in he ounr i f( ) f( ) where i i oupu, i i apial inpu (,), and ha in he ounr i i in eah ounr. In he paper, onl he ae of Harrod neural ehnologial progre uh ha Y ( L ) ( i,) i Ki i examined. 5 i i and hu Here, ine boh ounrie are free open eonomie, reurn on invemen in boh ounrie are ep equal hrough inernaional arbiraion uh ha ( ). n inreae in enhane oupu in boh ounrie beaue of nowledge pillover and hu reurn on inveing in ( ) i deribed a [ f( ) ]. Thereb, f f ( ) 5 i well nown, onl Harrod neural ehnologial progre mahe he lized fa preened b Kaldor (96). 7

9 [ f( ) f ] f ( ). Beaue hi equaion i alwa held hrough inernaional arbiraion, he following equaion are alo held:, and f( ). Hene, f ( ) ( ) f. f Here, he balane of pamen i inrodued in he model. The balane on urren aoun in he ounr i and he balane on urren aoun in he ounr i. The equene of i deermined b he ineraion of raegi behavior of boh ounrie houehold a Ghiglino () and Sorger () argue and hu eah ounr an no onrol he equene of independenl. How he equene of i deermined i explained laer. The opimizaion problem in he ounr i; Max ( ) exp( )d, E u ubje o () ν d, L and he opimizaion problem in he ounr i; Max ( ) exp( )d, E u ubje o () ν d, L where u i ( i,) i he uili funion in eah ounr, L i he populaion, and i (,) i i he inreae of b RD in eah ounr and. The aumulaed urren aoun balane d mirror inernaional apial flow due o urren aoun imbalane, i.e. a 8

10 9 ounr wih urren aoun urplue inve hem in he oher ounr. Sine are reurn on invemen, d and d repreen inernaional inome reeip on ae or inome pamen on ae. Hene, d i he balane on good and ervie in he ounr, and d i he balane on good and ervie in he ounr. Equaion () and () impliil aume ha a eah ounr doe no have an foreign ae. Beaue he produion funion i Harrod neural uh ha i i and hu i i L K Y, and beaue f f f f and i f, hen i, f f f and i i. Sine and, L ν d L ν d f f f ml d f f mv. Hene, f f f ml d f f

11 d ml ml. Therefore he opimizaion problem in he eonom an be rewrien a Max d u E exp, ubje o d ml ml. Le Hamilonian H be d ml ml λ u H exp where λ i a oae variable, hu he opimali ondiion for he eonom are (3) [ ] λ ml ml u exp, (4) H λ, (5) d ml ml, (6) λ. Similarl, le Hamilonian H be d ml ml u H exp λ where λ i a oae variable, hu he opimali ondiion for he eonom are (7) [ ] λ ml ml u exp,

12 (8) H λ, (9) d ml ml, () λ. Sine he problem of ale effe in endogenou growh model i no a foal poin in he paper, i i aumed for implii ha L i uffiienl large and hu ml ml in he following eion. Hene, b he opimali ondiion (3), (4) and (5), and b he opimali ondiion (7), (8) and (9), he growh rae of onumpion are () d and () d. 3. The bai naure of he model Before examining he balane of urren aoun in he model, he bai naure of he model i inveigaed. The mo imporan poin ha mu be made lear beforehand i wheher he model i an endogenou growh model ha an ahieve ead ae growh pah and if i i uh a model, in wha ondiion ead ae growh pah are ahieved. To begin wih, he ranverali ondiion are examined. Lemma : The ranverali ondiion (6) λ and () λ are no

13 aified if and onl if d d or d d. Proof: See ppendix. Uing lemma, an imporan naure of he model ha he onl growh pah ha aifie all he opimali ondiion i he pah uh ha onan i proved in he following lemma. Lemma : If and onl if onan, all he opimali ondiion are aified. Proof: See ppendix. Taing lemma ino onideraion, i i highl liel ha raional houehold behave o a o ahieve a ead ae growh pah uh ha onan. However, we mu onider, beforehand, how he equene of i deermined. In he well-nown paper of Beer (98), i i proved ha if houehold are purel prie aer, he mo paien houehold own all wealh in he onvenional Rame model if houehold have heerogeneou rae of ime preferene. Ghiglino () predi ha i i liel ha under

14 appropriae aumpion he reul in Beer (98) ill hold in endogenou growh model. Farmer and Lahiri (4) how ha in general, balaned growh equilibria do no exi in a muli-agen eonom exep for he peial ae where all agen have he ame onan rae of ime preferene. The above reul in he ae of heerogeneou rae of ime preferene rae ma hold in he ae of heerogeneou degree of relaive ri averion. Propoiion : If eah ounr e wihou regarding he oher ounrie opimali, hen if and onl if, all he opimali ondiion for he repreenaive houehold in he ounr an be aified imulaneoul. Proof: See ppendix 3. Propoiion ma provide a poibili ha he ounr an eape he onrain of Beer (98) if ondiion i aified. However, i i exremel diffiul ha he ondiion i aified beaue and are exogenoul and independenl given a hown in he proof, i.e., and. Onl in exremel lu ae wih he ombinaion of exogenou parameer ha aifie he nife-edge ondiion [ ] ( ), he ondiion i aified, whih will be exeedingl rare. a reul, propoiion onend ha viruall all he opimali ondiion for he repreenaive houehold in he ounr an no be aified imulaneoul. Thi reul orrepond o he well-nown reul in ae of Rame model wih 3

15 exogenou ehnologie and heerogeneou houehold hown in Beer (98). However, Sorger () how ha in he ae where a governmen levie a progreive inome ax, or in he ae where here are few houehold of eah pe and hu he are no imple prie aer bu pla a Nah equilibrium, he reul hown in Beer (98) do no hold anmore. Ghiglino () argue ha he laer ae in Sorger () an be inerpreed a a model of inernaional rade wih a ommon mare impl b aoiaing eah houehold pe o a ounr wih a naional enral planner or a repreenaive houehold. Baed on he argumen in Sorger () and Ghiglino (), in he model of wo non-mall ounrie wih heerogeneou houehold in he paper, i i poible o aume ha eah repreenaive houehold in wo ounrie pla a Nah equilibrium wih regard o he equene of in he opimizaion problem deribed in he previou ub-eion. Beaue, b lemma, if and onl if onan all he opimali ondiion in eah ounr are aified, whih i a ondiion for a Nah equilibrium, hen i i a lea poible o aume he following behavior of houehold. umpion: For he iniial apial o and nowledge/ehnolog/idea, houehold in boh ounrie ele a equene of and e he iniial onumpion o a o ahieve a growh pah ha aifie all he opimali ondiion, i.e. a growh pah of onan, while firm in boh ounrie adju o a o ahieve ( ). 6 6 Beaue, hen ( ) i. i ( ) 4

16 If houehold in boh ounrie behave aording o he above aumpion, ahieved ead ae growh pah have he following imporan feaure. Propoiion : onan. Proof: See ppendix 4. Beaue will no dereae, in he paper onl he ae uh ha > i examined. Therefore, i i aumed ha ( ) >, whih mean ha he rae of reurn on apial exeed he rae of ime preferene plu he growh rae of populaion and i quie naural eonomiall. III. THE TRDE BLNCE In hi eion, he balane on inernaional ranaion in he model i examined. Sine rade imbalane will grow infiniel, wha hould be diloed firl i wheher heir raio o oupu explode or abilize. Thi queion i anwered b he following orollar. Corollar : d d d d a poiive onan. 5

17 Proof: See ppendix 5. Beaue urren aoun imbalane grow a he ame rae wih oupu, onumpion, or apial evenuall, he raio of he balane on urren aoun o oupu do no explode bu abilize, i.e., i approahe o a unique finie value. Corollar how ha one ounr experiene a permanen urren defii and he oher ounr experiene a permanen urren aoun urplu. The nex naural queion i whih ounr experiene urren aoun defii and whih ounr experiene urren aoun urplue; he ounr wih lower degree of relaive ri averion or he oher. Thi queion i anwered b he following propoiion 3. Propoiion 3: If < and oher parameer are equal, hen if > ( ) ( ), he ounr experiene a permanen urren aoun defii uh ha a negaive onan, and he ounr experiene a permanen urren aoun urplue uh ha a poiive onan. Proof: See ppendix 6. Propoiion 3 indiae ha, in ome irumane, he ounr wih lower degree of relaive ri averion will experiene a permanen urren aoun defii, and in revere he ounr wih higher degree of relaive ri averion will experiene a permanen urren aoun urplu. Beaue in general ( ) >, and beaue he oeffiien of ( ) 6

18 and he oeffiien of i i ( ) in he ondiion > ( ) ( ), hen in he reaonable range of i, he larger and are, he more eail he ondiion will be aified. I hould be noed ha propoiion 3 need he upplemenar ondiion uh ha i and and are no o differen in order o a in he iuaion uh ha d d <. I i hown more orrel in he following orollar. Corollar : If < and oher parameer are equal, hen if <, hen d d <. Proof: See ppendix 7. Nex, he balane on good and ervie i examined. Corollar 3: If < and oher parameer are equal, hen he ounr experiene a permanen urplu in good and ervie rade uh ha ( ) d a poiive onan, and he ounr experiene a permanen defii in good and ervie rade 7

19 uh ha ( ) d a negaive onan. Proof: See ppendix 8. The reaon of hi reul i beaue here i differene beween he reurn on d, i.e., ( ) and he growh rae of. 7 VI. DISCUSSION. The degree of ri averion wa menioned in inroduion, during he la hree deade, he U.S. ha experiened periing urren aoun defii and in onra Japan ha experiened periing urren aoun urplue. Sine he U.S. eonom i he world large and he Japanee eonom i he eond large, he model in he paper will be applied well o he inernaional ranaion beween he U.S. and Japan. The model in he paper predi ha, in ome irumane, if he degree of relaive ri averion in Japan i higher han ha in he U.S., he U.S. will experiene a permanen urren aoun defii and Japan will experiene a permanen urren aoun urplu. 7 lhough evenuall a ounr wih relaivel lower degree of relaive ri averion experiene rade urplue a orollar 3 how, i i eail underood b he proof of orollar 3 ha, if he ondiion in propoiion 3 are aified, in revere a ounr wih relaivel lower degree of relaive ri averion experiene rade defii and a ounr wih relaivel higher degree of relaive ri averion experiene rade urplue in earl raniion period uh ha >>. d 8

20 re he Japanee reall more ri averive han people in he U.S.? In he well-nown Szpiro (986) ha arried ou a omprehenive eimaion of degree of relaive ri averion around he world, of he nine indurialized ounrie udied he Japanee have he highe degree of relaive ri averion. Szpiro (986) repor ha he degree of relaive ri averion in Japan i.76 while ha in he U.S. i.9, i.e., he degree of relaive ri averion in Japan i double ha in he U.S. 8 I i a well nown fa ha ompared wih houehold in he U.S. he Japanee inve heir finanial ae le in ri invemen, whih learl indiae ha he degree of ri averion in Japan i muh higher han ha in he U.S. 9 Wih hee daa, Naagawa and Shimizu (999) onlude ha he degree of relaive ri averion in Japan i wo or hree ime higher han ha in he U.S. lhough here are variou eimae of he degree of relaive ri averion in he U.S. and Japan and hu heir abolue value are ill inonluive, he reul in Szpiro (986) or Naagawa and Shimizu (999) a lea indiae ha if he ame eimaion mehod i ued in boh ounrie, he eimae of he degree of relaive ri averion in Japan will be relaivel higher han ha in he U.S. Furhermore, here i indire evidene ha he Japanee are highl ri averive. Firl heerogenei in ri-avere behavior ha reenl been repored from he medial or geneial poin of view. See e.g. Ono e al. (997) and Naamura e al. (997). Thoe reearhe have 8 The eimae of degree of relaive ri averion repored in Szpiro (986) are a follow: minimum mean maximum The U.S Japan ording o he daa on flow of fund publihed b FRB and he Ban of Japan, houehold in he U.S. alloae abou half of heir peronal finanial ae o ri ae lie equiie, bu in onra houehold in Japan alloae onl abou % of heir peronal finanial ae o ri ae and inead alloae abou 6 % of hem o afe ae lie depoi and ru. Lua (987) argue, he degree of relaive ri averion in he U.S. ma be muh higher han bu le han. 9

21 hown ha he genei ompoiion of he reepor for brain hemial uh a eroonin or dopamine differ widel among human rae. The alo how ha mo Japanee have inheried a erain pe of reepor ompoiion ha produe more auiou and herefore more ri averive haraerii, while man merian have inheried he oher pe ha produe le ri averive haraerii. Thee reen reul from medial reearhe renghen he appropriaene of he reul from pa reearhe on eimaion of degree of ri averion. Seondl, Harahima (998) how ha he o-alled Japanee eonomi em or Japanee apialim originae in he higher degree of ri averion in he Japanee. The Japanee eonomi em an be regarded a a oie wih le open-minded onvenion in whih relaivel longer-erm relaionhip wihin agen who are well-nown eah oher, e.g. Keireu, are eablihed and unnown agen are evaded. If he degree of ri averion i higher, people will prefer mainaining he au quo o hallenging new relaionhip, and hu exiing relaionhip will oninue relaivel longer period. In um, we an a lea onlude ha he Japanee are more auiou and have he relaivel higher degree of ri averion ompared o he merian, alhough he abolue value of degree of relaive ri averion in boh ounrie are ill inonluive. The fa ha wo non-mall ounrie have heerogeneou degree of relaive ri averion i imporan, beaue he mehanim of rade imbalane hown in he paper ma have wored beween he U.S. and Japan.. Impa on rade balane The magniude of impa of heerogenei in ri averion on rade balane depend on More preiel, he onluion of Ono e al. (997) and Naamura e al. (997) are a follow. There are wo genei pe of eroonin ranporer (5HTT): -pe and l-pe. peron who inheri -pe end o feel anxie more and beome more ri averive. ording o Ono e al. (997), mo Japanee have inheried onl -pe and ver few have l-pe, bu few merian have inheried onl -pe and over 3% have inheried onl l-pe.

22 parameer value, and whih ounr experiene urren aoun defii i alo deermined b parameer value. In hi ub-eion, imple imulaion wih alibraed parameer value are arried ou. B equaion (7) and (8) in he proof of propoiion 3 hown in ppendix 6, (3) ( ) ( ). The i of onumpion growh rae an be alulaed b he relaion uh ha ( ). Thereb, wih he appropriae alibraed parameer, i.e. he degree of relaive ri averion in boh ounrie and, he rae of ime preferene, he rae of depreiaion rae, he hare of labor inpu, and he oupu/apial raio ( ), he i of he balane on urren aoun/apial raio and hu he i of he balane on urren aoun/oupu raio alulaed b equaion (3). an be Here, he pial alibraed value of he deep parameer uh ha. 5,. 5,.6 and he apial/oupu raio i 3 are eleed. The eimae of he i of he balane on urren aoun/apial raio and hu he i of he balane on urren aoun/oupu raio for hree ombinaion of and, i.e., (a)., (b). 5, and ()., are hown in Table. The value are roughl ame a hoe ued for he alibraion of he U.S. eonom in Coole and Preo (995).

23 The reul mae luid ome imporan feaure of he model. Firl, if i le han 3 in he ae of (a) and (b) and le han in he ae of (), he ounr experiene a permanen urren aoun urplu, however, if i 3 or more han 3 in he ae of (a) and (b) and or more han in he ae of (), he ounr experiene a permanen urren aoun defii. Hene, wheher he ounr experiene a permanen urren aoun urplu or defii depend on he abolue value of he degree of relaive ri averion, whih wa predied b propoiion 3. In oher word, here i a poibili ha a ounr wih relaivel lower degree of relaive ri averion experiene a permanen urren aoun defii. Seondl, everal ombinaion of and reul in unrealii onequene: firl, if he differene beween and i large, e.g. he ae of (), aumulaed balane on urren d d aoun exeed apial o, i.e., >, whih wa predied b orollar, and eondl, if i mall, e.g. i 3 or le han 3 in he ae of (a), he growh rae of onumpion i unrealiiall high. a reul, realii reul are oberved in ae ha i more han 6 in he ae of (a) and (b). However, even in hee ae, he magniude of rade imbalane i everal peren of GDP and hu larger han auall oberved daa, i.e., roughl % of GDP (ee figure ). Hene, alhough he model how a heoreial poibili of a permanen urren aoun defii, quaniaivel he model ma need ome modifiaion o fi more loel wih he aual daa. There are everal poibiliie ha ma olve hi quaniaive problem. Firl, beaue here are man oher faor ha have influene on he rade balane and hu he oberved aual daa are he mix of effe of hee man faor, here i a poibili ha effe of heerogeneou degree of relaive ri averion are mol aneled ou b effe of oher faor. Seondl, here i a poibili ha he inernaional finanial mare i no neearil well

24 inegraed a he Feldein-Horioa puzzle indiae. 3 In hi iuaion, he volume of inernaional finanial ranaion will be muh maller han ha predied in he model and hu rade imbalane will alo be muh maller. Thirdl, here i a poibili ha he differene of degree of relaive ri averion beween he U.S. and Japan i no o large, e.g. ha in Japan i.5 ime ha in he U.S. Hene rade imbalane ma be muh maller beaue he model predi ha a he differene of degree of relaive ri averion beome maller, he rade imbalane beome maller. Fourhl, here i a poibili ha here are oher ignifian heerogeneiie in deep parameer han he degree of relaive ri averion beween he U.S. and Japan. V. CONCLUDING REMRKS The large urren aoun defii in he U.S. and he large urren aoun urplu in Japan have oninued during he pa hree deade, and he large bilaeral rade defii of he U.S. wih Japan ha alo peried. The onvenional ineremporal approah o he urren aoun an no explain hee periing large urren aoun imbalane a Obfeld and Rogoff (995) noe, and hu i need he help of overlapping-generaion varian of he ineremporal model wih heerogeneou demographi hange. However, he onjeure ha urren aoun imbalane are generaed b heerogeneou demographi hange ha no been full uppored b empirial evidene and i ill merel a heoreial poibili. The paper explore heerogenei in degree of ri averion a anoher poible oure of perien urren aoun imbalane. The reaon wh he paper dire i aenion o he degree of ri averion i ha in endogenou growh model he degree of relaive ri averion pla a ruial role for growh rae, and hu i heerogenei ignifianl ompliae movemen of inernaional 3 See Feldein and Horioa (98). 3

25 ranaion. noher reaon i beaue i ha been repored ha he degree of relaive ri averion in Japan i relaivel higher han ha in he U.S., whih implie a poibili ha he large urren aoun defii in he U.S. and he large urren aoun urplue in Japan an be explained b he relaivel higher degree of relaive ri averion in Japan han ha in he U.S. The model in he paper, whih i baed on he oluion in Sorger () and Ghiglino () o he problem of heerogeneou houehold raied b Beer (98), how ha he heerogenei in degree of ri averion generae perien, more orrel permanen, urren aoun imbalane. In ome irumane, a ounr wih relaivel lower degree of relaive ri averion experiene a permanen urren aoun defii, and in revere a ounr wih relaivel higher degree of relaive ri averion experiene a permanen urren aoun urplu. Neverhele, urren aoun defii and urplue do no explode bu he raio of defii and urplue o oupu ampoiall approah unique finie value and abilize in boh ounrie. Hene, he model predi ha if he degree of relaive ri averion in Japan i rul relaivel higher han ha in he U.S., here i a poibili ha he urren aoun urplu peri in Japan permanenl and he urren aoun defii peri in he U.S. permanenl. The reul of imple imulaion wih alibraed parameer value indiae ha a ounr wih relaivel lower degree of relaive ri averion experiene a permanen urren aoun defii for ome ombinaion of degree of relaive ri averion. However, he reul alo indiae ha he magniude of rade imbalane i larger han auall oberved daa, and hu alhough he model how a poibili of a permanen urren aoun defii, quaniaivel he model ma need ome modifiaion o fi more loel wih he aual daa. There are everal poibiliie ha ma olve hi quaniaive problem: ) a poibili ha effe of heerogeneou degree of relaive ri averion are mol aneled ou b effe of oher faor, ) a poibili ha he inernaional finanial mare i no neearil well inegraed a he Feldein-Horioa puzzle indiae, 3) a poibili ha he differene of degree of relaive ri 4

26 averion beween he U.S and Japan i no o large, and 4) a poibili ha here are oher ignifian heerogeneiie in deep parameer han he degree of relaive ri averion beween he U.S. and Japan. Finall, he mehanim of rade imbalane preened in he paper of oure doe no den he poibili of rade imbalane aued b heerogeneou demographi hange. Boh mehanim have probabl wored imulaneoul. Furhermore, here ma be oher heerogeneou parameer ha pla imporan role for inernaional ranaion beween oher ounrie, e.g. heerogeneou ehnologie. 5

27 6 PPENDIX. Proof of lemma B he opimali ondiion (5), d, and hu d. On he oher hand, b he opimali ondiion (4), d λ λ, and hu d λ λ. Here, λ λ d d d d.

28 7 Thereb if < d d, hen < λ λ. Similarl if < d d, hen < λ λ. Hene, he ranverali ondiion (6) λ and () λ are no aified if and onl if d d or d d. Q.E.D.. Proof of lemma (Sep ) B equaion () and (), d and d.

29 On he oher hand, d ( ) ( ) and d ( ) ( ). (Sep ) B equaion () and (), n d. Hene, if onan, hen d d d. Thu, b lemma he ranverali ondiion (6) and () are d aified, and alo all he oher opimali ondiion are aified. However, if, hen d d d. Thu b lemma, for boh d ounrie o aif he ranverali ondiion, i i neear ha or, whih violae he opimali ondiion (5) or (9). If or, he ranverali ondiion (6) or (), or he opimali ondiion (5) or (9) i violaed. a reul, if and onl if onan, all he opimali ondiion are aified. Q.E.D. 8

30 9 3. Proof of propoiion (Sep ) In hi ae, an be een a a onrol variable for eah ounr. Hene, he opimali ondiion (4) d i added o he opimali ondiion for he ounr, and he opimali ondiion (5) d i added o he opimali ondiion for he ounr. The opimali ondiion (4) and (5) are idenial, and b hem, d and hu he opimal onumpion growh rae are and. Thereb >. On he oher hand, b he opimali ondiion (4) and (5), d d and hu. (Sep ) For he ounr, i i neear o hold for he opimali ondiion (3), (4), (5) and (6) o be aified, and for he ounr, i i neear o hold for

31 he opimali ondiion (7), (8), (9) and () o be aified. Here, beaue he equaion uh ha, and are ep b firm a an ime, he houehold in he ounr mu e he higher iniial onumpion level han ha in he ounr b imporing good and ervie from he ounr o hold >. Therefore i mu be ha > and. (Sep 3) There are hree ae: i) >, ii), and iii) <. d In he ae of i), evenuall > and hu he opimali ondiion (7) or (5) i violaed. In he ae of iii), beaue, hen, and hu he raio > of o diminihe o zero a ime pae and he rade balane beome negligible for he ounr. In hi iuaion he ounr ele a pah uh ha, hereb i i no poible for he ounr o hold >. In he ae of ii), beaue he ounr mu hold for he opimali ondiion (7), (8), (9) and () o be aified, onl and onl if, i i poible for he ounr o aif all he opimali ondiion b eing appropriae iniial value of and. Q.E.D. 3

32 3 4. Proof of propoiion (Sep ) for, beaue, (6). Sine, f f f, hen, and hu. Beaue, [ ]. Hene >. Beaue, hen. (Sep ) for, b equaion (6) and, and hu. Beaue, hen. Hene, and hu. Sine, hu. Q.E.D. 5. Proof of orollar B (ep ) in he proof of lemma, d d d d. Hene, b

33 3 propoiion, d d d d a poiive onan. Q.E.D. 6. Proof of propoiion 3 (Sep ) Beaue, hen b equaion () and (), d d d d. Hene, beaue > b aumpion, hen (7) d a poiive onan. (Sep ) B orollar, d d a poiive onan. Hene, for uffiienl

34 33 large, exp and hu d d d a poiive onan. Here, beaue d d b orollar, (8) d d d d d a poiive onan. Here,. Hene, if

35 34 > and hu if >, hen <. Therefore if < and if >, a negaive onan, and hu a negaive onan and onan poiive a. Q.E.D. 7. Proof of orollar B equaion (7) and (8),. Beaue d and, d

36 35 d. Sine, d. Hene, if <, hen < d. Q.E.D. 8. Proof of orollar 3 B equaion (8), d a poiive onan. Hene,

37 36 d a poiive onan, and d a negaive onan. Q.E.D.

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39 Jone, Charle I. (3). Populaion and Idea: Theor of Endogenou Growh, in P. ghion, R. Frdman, J. Sigliz and M. Woodford, ed., Knowledge, Informaion, and Expeaion in Modern Maroeonomi: In honor of Edmund S. Phelp, Prineon Univeri Pre. Kaldor, N. (96). Capial umulaion and Eonomi Growh, Cap. of. Luz and D. C. Hague (ed.), The Theor of Capial, S. Marin Pre, New Yor. Koolioff, Laurene J., Ken Smeer, and Jan Wallier. (). Finding a Wa Ou of meria Demographi Dilemma, NBER Woring Paper 858. Lua, Rober E. (987). Model of Buine Cle, Bail Blawell, London. Naagawa, Shinobu and Tomoo Shimizu. (). Porfolio Seleion of Finanial e b Japan' Houehold- Wh re Japan' Houehold Reluan o Inve in Ri e? Ban of Japan Reearh Paper (). Naamura T, Muramau T, Ono Y, Mauhia S, Higuhi S, Mizuhima H, Yohimura K, Kanba S, ai M. (997). Seroonin ranporer gene regulaor region polmorphim and anxie-relaed rai in he Japanee, merian Journal of Medial Genei 74 (5), P Obfeld, Maurie and Kenneh Rogoff. (995). The Ineremporal pproah o he Curren oun, in G. Groman and K. Rogoff (ed.), Handboo of Inernaional Eonomi, Vol. 3, merdam, Norh Holland. Ono Y, Mani H, Yohimura K, Muramau T, Mizuhima H, Higuhi S, Yagi G, Kanba S, ai M. (997). oiaion beween dopamine D4 reepor (D4DR) exon III polmorphim and novel eeing in Japanee ubje, merian Journal of Medial Genei 74 (5), P5-53 Pereo, Piero and Sja Smulder. (). Tehnologial Diane, Growh and Sale Effe, The Eonomi Journal, Vol., pp Poerba, Jame M. (). Demographi Sruure and e Reurn, The Review of Eonomi and Saii, Vol. 83, No.,

40 Romer, P. S. (99). Endogenou Tehnologial Change, Journal of Poliial Eonom, Vol. 98, pp. S7-S. Sorger, Gerhard. (). On he Long-run Diribuion of Capial in he Rame Model, Journal of Eonomi Theor, Vol. 5, Szpiro, George G. (986). Relaive ri averion around he world, Eonomi leer, Vol., No.,

41 Figure : Trade Imbalane.6 N e expor/ G D P I 97-IV 973-III 974-II 975-I 975-IV 976-III 977-II 978-I 978-IV 979-III 98-II 98-I 98-IV 98-III 983-II 984-I 984-IV 3-III 4-II -.6 US Japan 985-III 986-II 987-I 987-IV 988-III 989-II 99-I 99-IV 99-III 99-II 993-I 993-IV 994-III 995-II 996-I 996-IV 997-III 998-II 999-I 999-IV -III -II -I -IV Soure: US Bureau of Eonomi nali, and Cabine Offie of Japan Figure : The US Curren oun Defii wih Japan.5 C urren oun D efii / GD P I 97-IV 973-III 974-II 975-I 975-IV 976-III 977-II 978-I 978-IV 979-III 98-II 98-I 98-IV 98-III 983-II 984-I 984-IV 985-III 986-II 987-I 987-IV 988-III 989-II 99-I 99-IV 99-III 99-II 993-I 993-IV 994-III 995-II 996-I 996-IV 997-III 998-II 999-I 999-IV -III -II -I -IV 3-III 4-II Soure: US Bureau of Eonomi nali 4

42 Table (a)., d (b). 5, d

43 ()., d