The Role of Stock Markets in Current Account Dynamics: a Time-Series Approach

Transcription

1 WP/04/50 The Role of Sock Make n Cuen Accoun Dynamc: a Tme-See Appoach Benoî Meceeau

2 2004 Inenaonal Moneay Fund WP/04/50 IMF Wokng Pape Aa and Pacfc Depamen The Role of Sock Make n Cuen Accoun Dynamc: a Tme-See Appoach Pepaed by Benoî Meceeau Auhozed fo dbuon by Aleando Zanello Mach 2004 Abac Th Wokng Pape hould no be epoed a epeenng he vew of he IMF. The vew expeed n h Wokng Pape ae hoe of he auho() and do no necealy epeen hoe of he IMF o IMF polcy. Wokng Pape decbe eeach n poge by he auho() and ae publhed o elc commen and o fuhe debae. Th pape develop a mple model o udy he mpac of ock make on he cuen accoun. A cloed-fom oluon fo he cuen accoun deved fom he opmal pofolo and conumpon/avng choce of a epeenave agen. Fomally, he model can be een a a ock make-augmened veon of he fundamenal equaon of he cuen accoun populazed by effey Sach. I appea o hed lgh on ecen developmen n he U.S. cuen accoun defc. The model alo how how he cuen accoun may help pedc fuue ock make pefomance and/o endowmen eam. EL Clafcaon Numbe: F3; F32 Keywod: Cuen accoun; ock make Auho E-Mal Adde: [email protected] I am gaeful o Chophe Sm fo h pcele gudance and advce houghou h pojec. I alo would lke o hank Wllam Banad, Robeo Gaca-Salo, Pee-Olve Gouncha, Gegoy He, Shgeu Iwaa, Phlp Lane, Hélène Rey, Davd Rome, Robe Shlle, Aleando Zanello, wo anonymou efeee, and emna pacpan a he Unvey of Chcago Gaduae School of Bune, he Euopean Cenal Bank, Humbold Unveä, he IMF Inue, Pnceon Unvey, and Yale Unvey fo ueful commen and uggeon. Th pape wa undeaken dung he academc yea 2000/200 whle I wa a vng uden n he Economc Depamen of Pnceon Unvey, whoe hopaly I gealy appecaed. Thank ae alo exended o Dene Ho, Mana Dave, and Naale Baume fo knd edoal aance. The fnal pee-evewed veon of h pape appea a Beno Meceeau, 2003 The Role of Sock Make n Cuen Accoun Dynamc: a Tme See Appoach, Topc n Macoeconomc: Vol. 3: No., Acle 6, whch avalable on he web a hp://

3 - 2 - Conen Page I. Inoducon...3 II. III. The Model: A Sock Make-Augmened Fundamenal Equaon of he Cuen Accoun...4 A. The Model...4 B. Expeon of Cuen Accoun...7 C. Inepeaon...9 Some Implcaon of Model... A. Uned Sae Cuen Accoun Defc: Iaonal Exubeance?... B. Cuen Accoun a a Poenal Pedco of Fuue Sock Make Pefomance...3 C. Ohe Implcaon of Model...5 IV. Concluon...7 Appendx I. Poof of Popoon...8 II. Summay of Man Noaon...27 Refeence...28

4 - 3 - I. INTRODUCTION How mpoan he pefomance of he ock make o he cuen accoun? Gven he exaodnay developmen of fnancal make, one would expec ock make even o play an mpoan ole n he dynamc of he cuen accoun. Fo example, wdely beleved ha he lage and unpecedened U.S. cuen accoun defc n he econd half of he 990 wa a lea paally caued by he damac ock make boom. Ye hee ae upngly few model udyng how ock make can affec cuen accoun dynamc. 2 The am of h pape o exploe h ue heoecally. In a companon pape, Meceeau (2003), I alo udy he ubjec empcally. Th pape develop a mple model o udy he mpac of ock make on he cuen accoun. The bac mechanm a ock make-augmened veon of a conumponmoohng oy. A couny epeenave agen eceve a ochac endowmen a each peod. The agen wll hen ue all he avalable fnancal numen o maxmze he expeced neempoal uly. Thee fnancal numen nclude an abay numbe of ky ae (boh foegn and domec), whch fom an ncomplee make, a well a a kfee bond. A cloed-fom oluon fo he cuen accoun hen deved fom he opmal pofolo and conumpon/avng choce of he agen. Th oluon elae he cuen accoun o he peen and expeced fuue pefomance of he ock make, a well a o he evoluon of he ucue of k aco make and ae. Fomally, he model can be een a a ock make-augmened veon of he o-called fundamenal equaon of he cuen accoun populazed by effey Sach (Sach, 982). Th fundamenal equaon of he cuen accoun whou doub he mo popula model of he la weny yea. Fo example, Obfeld and Rogoff (995) devoe mo of he pape o a uvey of h lne of leaue. The fuhe wok n he gaduae exbook (Obfeld and Rogoff, 997) alo ummaze he leaue. Th fundamenal equaon model baed on conumpon moohng. One of man lmaon, hough, ha feaue a k-fee bond a he unque fnancal numen. I, heefoe, pooly ued o udy he mpac of ock make on he dynamc of he cuen accoun. In ode o make he man pon of he model clea, I f olve akng pce a gven. In Meceeau (2002), I develop a geneal-equlbum veon of he model n whch ky ae pce ae deved endogenouly. One can hen ue he equaon of he cuen accoun found n h pape o gan ngh on he ole of ock make n he dynamc of he cuen accoun. Fo example, a wll be een, he model hed lgh on ecen developmen n he U.S. cuen accoun defc. 3 Some clam ha h cuen accoun defc efleced ove- 2 Impoan excepon nclude he wok by Kaay and Venua (2000), and Venua (200). 3 The mo dec nepeaon of a paal-equlbum model n whch ae pce ae exogenou a mall-couny model. Nevehele, I hnk ha he model can help one o analyze he U.S. uaon. Gven he amoun of U.S. ae owned by foegne, U.S. ock pce hould be ubanally nfluenced by foegn hf n demand fo U.S. ae ha ae no ongly elaed o fundamenal n he U.S. economy elf. A hown n he genealequlbum veon of he model, n Meceeau (2002), he poble caue of uch hf (connued )

5 - 4 - opmc, even aonally exubean expecaon of fuue ock make pefomance. The model, on he ohe hand, ugge ha opmal fo a couny o un a cuen accoun defc even f people do no expec a ock make boom o la. (Expecaon of a connung boom would only eul n a defc of a lage magnude.) Anohe ngh affoded by he model ha he cuen accoun may help pedc fuue ock make pefomance and/o fuue endowmen eam. The eaon ha he cuen accoun deved fom he opmal pofolo and conumpon/avng choce of he agen. A a conequence, he cuen accoun hould boh ncopoae and eflec all he elevan nfomaon agen have abou fuue ock make pefomance and fuue endowmen, ncludng he pece of nfomaon whch ae no obeved by economecan. Th foecang popey can be fomally expeed by a e of Gange caualy and Gange caual poy popoon. Snce ock make pefomance vey dffcul o pedc, one hould egad he above popoon wh cauon. Th pape wll nevehele dcu why h popey may be le upng han eem. Ohe mplcaon of he model ae alo befly analyzed. In a companon pape, Meceeau (2003), he model pu o he e ung U.S. daa. The adonal Sach model (Sach, 982) had been eed fo lage majoy of coune ung a mehodology developed by Campbell and Shlle (987) n a dffeen conex (ee Obfeld and Rogoff, 995 and 997 fo a uvey). 4 The model developed n h pape pefomed bee han he ame model whou ock make. The foecang popey of he cuen accoun a a pedco of fuue ock make pefomance alo eceved pelmnay empcal confmaon. The emande of he pape oganzed a follow: Secon II peen he model; Secon III dcue man mplcaon; and Secon IV conclude he analy. II. THE MODEL: A STOCK MARKET-AUGMENTED FUNDAMENTAL EQUATION OF THE CURRENT ACCOUNT A. The Model The bac mechanm of he model a ock-make-augmened veon of a conumponmoohng oy. A couny epeenave agen eceve a ochac endowmen a each peod. The agen wll ue all he fnancal numen a he dpoal o maxmze he expeced neempoal uly. Thee fnancal numen nclude an abay numbe of ky ae (boh foegn and domec), whch fom an ncomplee make, a well a a kfee bond. A cloed-fom oluon fo he cuen accoun hen deved fom he opmal nclude demogaphc change, change n k n foegn econome, and change n k aveon. 4 Some of hee ude nclude Ghoh (995), Sheffn and Woo (990), Oo (992), Ghoh and Oy (995), Oy (997), and Cahn and McDemo (998), Agéno and ohe (999), Callen and Cahn (999), Adedej (200), and Mlo (200).

6 - 5 - pofolo and conumpon/avng choce of he agen 5. The famewok ued fo he model wa developed n a dffeen conex by Dav and Wllen (2000) and Dav, Nalewak, and Wllen (2000). 6 Thee a ngle conumpon good, whch eve a a numéae. All vaable ae expeed n un of h conumpon good. Wng C a he veco of conumpon level and δ a he dcoun faco, he pogam of he agen : Max U( C) = E0 δ u( c ), { c; ω0, ; ω} = 0 = 0 unde he budge conan BC : c + ω + ω = NI + Rω + R ω 0, j, 0 0, j, j, j= j= () (and we have he nal condon: ω 0, = ω j =, 0) A uffcen condon of anvealy : 7 lm E ω0, + ωj, (2) + j= Le u befly defne he vaable ued above (Appendx II ummaze he noaon): NI ( ne ncome ) a ochac endowmen eceved n each peod by he epeenave agen. Th all he ncome he eceve n peod, wh he excepon of he evenue fom he pa fnancal nvemen. R j, he go ae of eun of ae j a me. Thee ae ock avalable on he wold ock make. They ae exogenouly gven, and hey fom an ncomplee make 8. They can be ehe domec o foegn ock. Each ky ae j=,, pay a 5 The famewok of he Sach model he ame, excep ha he model feaued a unque fnancal numen: a k-fee bond. 6 The focu of hee pape he emaon of k-hang benef povded by fnancal ae n he cae of labo ncome and nenaonal ade. 7 A dcuon of a no Ponz game condon peened n Appendx I. 8 In he model, o have ncomplee make mply mean ha he agen endowmen eam canno be duplcaed, and hu canno be pefecly hedged, wh any combnaon of he avalable ae.

7 - 6 - ochac dvdend d j, a me, and ha a make pce P j,. R j, hu fomally defned by: d j, + Pj, R =. j, Pj, ω j, he holdng of ky ae j a me (lke all ohe vaable, expeed n un of he numéae good). R0 = + he conan nenaonal k-fee ae, a whch all agen can lend o boow. Th nenaonal nee ae aumed o be conan ove me and exogenouly gven 9. ω 0, he holdng of k-fee ae a me. In ode o faclae he devaon of he eul, I need o make a few aumpon: The agen ha an exponenal uly funcon: uc () = exp( Ac), whee A A he coeffcen of abolue k aveon. 0 Ne ncome NI and he go eun have a jon nomal dbuon ( momen can be me vayng).,2 9 Conequenly, I aume a pefecly elac upply (o demand) fom foegne fo bond. The k-fee ae can be made me-vayng a he co of addonal noaonal complexy. 0 Smla eul can be deved wh a quadac uly funcon. Wh a quadac uly funcon, hough, one could no have a cloed-fom oluon fo he pofolo ω. The man nuon would no be aleed by alenave fom of uly funcon. Wha would be dffeen he peence of a wealh effec. Wh an exponenal uly funcon, pofolo holdng do no depend on wealh, whch no ealc. So he man mplcaon of h exponenal uly famewok he abence of h wealh effec. A ealc model hould nclude wealh effec n he analy. The advanage of ung an exponenal uly funcon ha one able o deve cloed-fom oluon fo all he vaable n he model, whch one could no do wh adonal uly funcon. The nomaly aumpon make he model much eae o olve wh he exponenal uly funcon. I can nevehele be elaxed, bu a a vey hgh echncal co n he cae of exponenal uly (ee Gon, ogenon, and Polon, 2000). Th nomaly aumpon no needed wh a quadac uly funcon. 2 The model hu a paal equlbum one, n whch economc developmen n ohe coune do no explcly affec he cuen accoun. In anohe pape (Meceeau, 2002), I develop a geneal-equlbum veon of he model, n whch ky ae pce ae deemned endogenouly.

8 - 7 - B. Expeon of Cuen Accoun The full oluon of he model, a well a he poof, ae gven n Appendx II. I ue h oluon o deve a cloed-fom oluon fo he cuen accoun. In ode o do h, I f ecall ha, by defnon, he cuen accoun he change n he ne foegn poon of a couny 3. I hen ue he expeon found fo he opmal pofolo of he epeenave agen. Th gve u he followng expeon fo he cuen accoun (I call h oluon he global cuen accoun (GCA) fo eaon ha wll become clea momenaly): Popoon 4. Sock-make-augmened fundamenal equaon of he cuen accoun. * ( ) * ' ' ( ( NI )) + ω ( X ) GCA = NI E X E ω () endowmen ncome effec (2) ock make effec A vac + - ( e - e ), (5) ae ock change (3) conumpon lng (4) pecauonay avng + Ln ( ) A δ = ( +) (3) whee X he x veco of exce eun: X = Rj, R 0 =. j me -. ω ( ωj, ) = he x pofolo of ky ae of he epeenave agen a j= e he oal pe capa valuaon of all fnancal ae locaed n he home couny of he epeenave agen (noe ha h ndependen fom he czenhp of he haeholde: an ae locaed n a gven couny can be enely owned by foegne). Rky ae ae ndeed n pove upply. Thee ae φ j hae of ae j. The oal make valuaon of ae j Sj, = Pj, φ j. The oal pe capa valuaon of all fnancal ae locaed n he home couny of he epeenave agen hen defned by: e = S. j home couny' { ock } Fo any vaable Z, Z * he (fuue) pemanen level of he vaable, whch defned o a o afy he followng equaon: * Z = + Z = 0 + = 0 + ( ) ( ) j, 3 An equvalen way o defne he cuen accoun a he um of he ade balance plu all eun on ne foegn ae (nee paymen, capal gan, and dvdend). 4 The poof gven n Appendx I.

9 - 8 - ( follow ha * Z = Z + + ). + = 0 ( ) Pmed vaable denoe he anpoe of he coepondng veco (e.g., Z he anpoe of veco Z). E (Z) denoe he expeced value of vaable Z a of me. The above popoon ee he hee componen of he cuen accoun. Tem () and (2) conue he conumpon-moohng componen of he cuen accoun. Tem (3) he conumpon-lng componen; em (4) he pecauonay avng one; and em (5) epeen he change n he ock of ae. The adonal (.e., ock-make-fee) fundamenal equaon of he cuen accoun f deved by Sach (982) dd no nclude em (2) and (5). The fundamenal equaon of he cuen accoun ha been vey popula (fo a uvey of he leaue on he opc, ee Obfeld and Rogoff (995) o Obfeld and Rogoff (997, Chap. 2)). I analy, boh heoecal and empcal, ha focued manly on he man cuen accoun componen, he conumpon-moohng one. Whle em (3) and (4) ae alo neeng by hemelve, I wll alo follow h leaue and focu on he conumponmoohng componen of he cuen accoun. Fo accounng eaon, he change n he domec ock make valuaon em mu alo be ncluded n he analy. Th em alo neceay fo a compehenve udy of he ole of ock make. Bu befoe dong o, bef menon mu be made of he ohe wo componen. Tem (3) eflec he conumpon lng componen of conumpon. Cee pabu, he moe paen people end o ave moe (and, heefoe, conume le). Tem (4) a pecauonay avng em. I eflec he fac ha he agen wan o poec agan fuue conumpon vaably, 5 hu avng moe n ode o each h goal. 6 5 Fomally, h come fom he fac ha u >0. Conequenly, no pecauonay avng em appea when one ue he quadac uly funcon nead of he exponenal one (wh a quadac uly funcon u =0). 6 A moe complee analy of h em a follow. Tem (4) due o adonal pecauonay avng behavo. The agen cae no only abou expeced uly, bu alo abou he vaably of conumpon: geae vaably of he agen conumpon nduce a lo of uly. Th mean ha he agen wll ave n ode o poec agan he vaably of fuue ncome (pecauonay avng). The pecauonay avng move and hence em (4) would ex n any ochac model wh u >0, whehe nclude ock make o no. Sock make have an mpac on em (4), hough he vaably of fuue genealzed wealh (and heefoe conumpon) depend on how well one can hedge labo ncome k ung he ock make, a well a on he exploaon of he k pemum. Wllen (997) focue on he mpac of fnancal ophcaon on he ade balance a channeled hough pecauonay avng n a mple famewok. (connued )

10 - 9 - Now, le u un o he conumpon-moohng and change-n-domec-ock-makevaluaon componen of he cuen accoun. They wll be wen a CA. In he emande of he pape, cuen accoun wll efe o hee wo componen of he cuen accoun: * ' ' * CA = ( ) + ( ) ( ). NI E NI Xω E X ω e e (4) (3) ae ock change () endowmen ncome effec (2) ock make effec C. Inepeaon Sach adonal fundamenal equaon of he cuen accoun con moly of em (). I nepeaon a follow: when he conume endowmen ncome hghe han expeced fuue pemanen level, he epeenave agen wll ave moe n ode o mooh he conumpon. Cee pabu, he couny ne ock of foegn ae wll, heefoe, nceae, and he couny wll un a cuen accoun uplu. Followng h lne of eaonng, a cuen accoun defc nohng o be concened abou a long a eflec expecaon of fuue e n he couny ne oupu. Bu em (2) ugge ha a polcymake ung uch eaonng could well m he pon and each nappopae concluon abou he opmaly of he cuen accoun level. Indeed, one alo ha o ake no accoun he ole of fuue ock make pefomance. The nuon behnd h econd effec faly mple: f he agen expec he ock make o do bee n he fuue han doe oday, hey wll boow money n ode o mooh conumpon --and he couny wll un a cuen accoun defc. In ohe (moe pece) em, f oday exce fnancal gan ae malle han he expeced fuue pemanen level, conumpon moohng wll lead he couny o un a cuen accoun defc. Noe ha wha mae no he oal amoun of fnancal gan bu only he hae of n exce of wha he ame nvemen made n a k-fee bond would have yelded. The eaon fo h ha all he welfae gan one can ealze by ung a k-fee bond o mooh neempoal conumpon ae aleady ncopoaed n em (). The exa welfae gan acheved hough he ock make hould, heefoe, nclude only he gan one could no have acheved ung a kfee bond. Th wha expeed by em (2). I neeng o undeand why h pecauonay avng behavo nduce a pove change n he cuen accoun. Indeed, he cuen accoun he ne change n foegn ae holdng. If he domec ock make valuaon doe no change, hen he cuen accoun equal o he change n all ae held by he epeenave agen. So he queon o know why hould an agen hold moe ae a dae han a dae - f he ndvdual expec he ame degee of ncome vaably n he fuue. The anwe ha becaue of he agen pa pecauonay avng, he agen wealh gow ove me, hu ceang exa wealh n he nex peod. The agen oal ae holdng wll gow, and, all hng beng equal, h wll anlae no an nceae n he couny ne ae holdng (.e., he couny un a cuen accoun uplu).

11 - 0 - The hd em n he equaon he change of ock n domec ky ae (.e., he change n he valuaon of he domec ock make). Th em unelaed o he behavo of he agen. I ae only becaue of he accounng defnon of he cuen accoun. Indeed, em () and (2) decbed he change n deed oal ae holdng by he epeenave agen. Bu he cuen accoun no he change n deed oal ae holdng by he epeenave agen: he cuen accoun, by defnon, he change n ne foegn ae of he couny. To go fom he fome o he lae, one ha o ubac he change n he oal amoun of ae locaed n he couny. 7 An example hould help explan h pon. Le u uppoe ha he epeenave agen fnd opmal o ae he oal holdng of ae by $0 bllon, bu ha a he ame me he valuaon of he ock make nceae by $5 bllon. Le u f aume ha he domec ock make wa enely owned by domec agen befoe he ock make boom. I ue ha he oal holdng of ae of he agen wll e by $0 bllon. Bu he epeenave agen wll nevehele ell $5 bllon woh of hae (he dffeence beween he $5 bllon nceae n he value of he pofolo and he $0 exa bllon he decde o ave). By conucon, hee hae have o be bough by foegne. The ne effec fo he couny wll, heefoe, be a $5 bllon anfe of domec ae o foegne, whch o ay ha he couny wll un a $5 bllon cuen accoun defc. If, alenavely, he ae locaed n he home couny wee enely owned by foegne befoe he boom, hen he $5 bllon e n domec ock make valuaon coepond o a $5 bllon deceae n he ne foegn poon of he home couny. Bu he domec agen alo wan o nceae he holdng of ae by $0 bllon. Th anlae no a change of +$0 bllon n he ne foegn poon of he couny. So fnally, he oal change n he ne foegn poon of he couny (and hu, he cuen accoun) wll be +0-5=-5 bllon dolla. Th example make clea how he nal degee of foegn ownehp of ock affec he CA mpac of ae value change. We can gve anohe full numecal example o fuhe lluae he accounng. Le u uppoe ha a me -, he valuaon of he fnancal ae locaed n couny h e - = $30 bllon. Of hee $30 bllon, $20 bllon ae owned by domec agen, and $0 bllon by foegne. A he ame me, couny h own $5 bllon of foegn ae. We hu h 20 have: ω = 5. A me, he followng happen: 7 Whle he cuen accoun hould, concepually, be defned a he change n he ne foegn poon of a couny, adonal empcal meaue of ll do no uually nclude capal gan and loe. Howeve, he IMF ha aed gaheng daa, whch nclude capal gan and loe (ee IMF Balance of Paymen Manual, 5 h ed.).

12 - - P The domec ock make nceae by 0 pecen: P =.. Domec d dvdend paymen coepond o 5 pecen of capal: P = The go eun on domec ock ae, heefoe, 5 pecen. Moeove, P e = e =.*30 = $33 bllon. P The go eun on foegn ock happen o be 0 pecen. Wh a 5 pecen k-fee ae, h lead o he followng exce fnancal eun veco: 0. X =. Couny h exce fnancal gan a me ae hu: 0.05 ' h 20 X ω = ( ) 5 =2.25. The agen happen o beleve ha he fuue peen dcouned exce ' h fnancal gan wll be zeo: E Xω = 0. The agen alo happen o expec ha an annuy of he peen dcouned NI (o ne ncome) endowmen exacly equal o he cuen NI NI E NI * = 0. endowmen, o ha ( ) In uch a cae, couny h cuen accoun would be: CA = 0 + (2.25 0) (3.3 3) =+ $.95 bllon. To conclude, em (3) undecoe he mpoance of domec ock a a avng numen: when domec ock make e, he oal amoun of domec ae avalable fo avng pupoe alo e. A a conequence, an nceae n he avng ae doe no necealy lead o a cuen accoun uplu. Equaon (4) allow u o adde a lage ange of ue elaed o he ole of ock make n he cuen accoun dynamc. Some of hem ae peened n he nex econ. III. SOME IMPLICATIONS OF MODEL A. Uned Sae Cuen Accoun Defc: Iaonal Exubeance? The model can be ued o hed lgh on he ecen and unpecedened U.S. cuen accoun defc. I omeme ad ha he U.S. cuen accoun defc n he lae 990 wa due o he unuually hgh pefomance of he ock make and o he (pobly aonal) belef

13 - 2 - ha he ock make would connue o nceae a had dung he decade. Can my model help analyze h occuence? 8 I he cae ha expecaon of eve-ng ock make pefomance would caue a cuen accoun defc (f one expec hghe exce fnancal gan n he fuue, one wll educe avng, and he couny wll un a cuen accoun defc). Bu uch connually ng expecaon ae no neceay o ceae a cuen accoun defc. The defc would have appeaed even f people beleved ha he ecen ock make pefomance wee a one me pove hock (expecaon of a connung boom would only eul n a defc of a lage magnude). To lluae h pon, le u conde wha happen o a U.S. agen whoe hae value have en by, ay, $0,000 followng a e n he ock make. If he agen hnk ha hee gan ae a one-me wndfall becaue of he belef ha he ock make wll no pefom a well agan n he fuue, he agen wll conume only an annuy of h $0,000, ay $2,500, and ave he e. In ohe wod, wha wll occu ha he agen wll ell $2,500 n hae n ode o fnance conumpon (o keep all o pa of he hae and boow he e a a k-fee ae). Bu nce he agen a epeenave agen, all Amecan wll do he ame. Theefoe, he only ndvdual who can buy he $2,500 n hae Amecan wan o ell o fnance he exa conumpon ae, by conucon, foegne. Th anacon a anfe of wealh fom home o foegn agen: a cuen accoun defc fo he home couny. Po o h uge n he make, a numbe of foegne owned ome U.S. ae. The capal gan hey made dung he boom alo coepond o a woenng of he U.S. ne foegn poon and, hu o a cuen accoun defc. 9 8 Fo an alenave pofolo-baed analy of he ecen U.S. cuen accoun defc, ee Venua (200). 9 A full numecal example can help fuhe undeand h pon. Le u uppoe ha a me - he ock make valuaon e - = 60,000. Of hee, 50,000 belong o domec agen, and 0,000 o foegne. A me, he go eun on he domec ock make R =.2. Le u aume ha hee wee no dvdend pad a me, o ha he go eun coepond excluvely o capal gan. The new ock make valuaon wll hu be: e = 60,000*.2 = 72,000. Theefoe, 2,000 e =. If he k-fee ae 5 pecen, he exce eun on domec ae wll be X = 20% - 5% = 5%. A a conequence he exce fnancal gan on domec ae held by domec agen ae: 0.5*50,000 = 7,500. Le u fnally aume ha agen expec ha he peen dcouned value of he fuue exce fnancal gan wll be zeo; ha hey expec he cuen endowmen o be equal o an annuy of he dcouned value of he fuue endowmen; and ha hey expec he cuen exce fnancal gan on foegn ae o be equal o an annuy of he peen dcouned value of he fuue fnancal gan on foegn ae. We hen have: CA =0+(7,500-0)- 2,000=-4,500. The couny hu un a cuen accoun defc of $4,500. Of h amoun, $4,500, $2,500 ae due o he uly-maxmzaon behavo decbed above. The emanng $2,000 ae due o capal gan by foegne.

14 - 3 - In concluon, no neceay ha people have hgh o aonal expecaon abou fuue ock make pefomance fo a e n he ock make o ceae a cuen accoun defc. Quanave ude would be needed o know whehe he phenomenon enough o explan he magnude of he U.S. cuen accoun defc o whehe ove-opmm equed. 20 B. Cuen Accoun a a Poenal Pedco of Fuue Sock Make Pefomance Anohe ngh affoded by he model ha he cuen accoun may help pedc fuue ock make pefomance and/o fuue endowmen eam. The eaon ha he cuen accoun deved fom he opmal pofolo and conumpon/avng choce of all he agen. A a conequence, he cuen accoun hould boh ncopoae and eflec all he elevan nfomaon agen have abou fuue ock make pefomance and fuue endowmen. Th foecang popey can be fomally expeed by a e of Gange caualy and Gange caual poy popoon (ee below). Le u now un o he fomal popoon. In ode o deve hem, ueful o f ewe he ock make-augmened equaon of he cuen accoun. Bu befoe dong o, le u ewe, fo he ake of noaonal mplcy, f = X '. ω-, he exce fnancal gan a me. Popoon 2.The ock-make-augmened equaon of he cuen accoun can be ewen a CA + e = E( NI+ ) E( f+ ) = + = +. (5) (In h equaon denoe he f-dffeence opeao.) Popoon 3 (Mulvaae Gange caualy). If equaon (5) hold, hen CA Gangecaue a lea one of ( f, NI ), excep n he vey pecal cae whee CA a lnea combnaon of peen and pa NI, f and e. Popoon 3B (mulvaae Gange caualy). If equaon (5) hold, hen (CA + e ) Gange-caue a lea one of ( f, NI ), excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa NI and f. Popoon 4 (Gange Caual Poy). 2 If equaon (5) hold, hen { f, NI } no Gange Caually Po o (CA + e ), excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa NI and f. 20 Of coue, he cuen accoun defc can alo have been ceaed by ohe faco, uch a expecaon of hghe labo ncome (hghe NI). 2 Fo a bef and vey clea peenaon of he concep of Gange Caual Poy and mulvaae Gange caualy, ee Sm (999).

15 - 4 - Popoon 5 (bvaae Gange caualy). If I have equaon (5), hen (CA + e ) Gangecaue (NI + f ), excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa (NI + f ). Fo poof: ee Appendx I. Popoon 3 ugge a new ngh abou he cuen accoun. I mple ha he cuen accoun may help pedc fuue ock make pefomance and/o fuue endowmen eam. 22 Wha he popoon nuvely mean ha he cuen accoun hould help foeca a lea one of he change n ne ncome and n fnancal gan. Th come fom he fac ha he cuen accoun eflec he expecaon of he agen abou fuue change n ne ncome and n fnancal gan. I neeng o noe ha hee expecaon ncopoae all he nfomaon avalable o he agen (ncludng he nfomaon whch economecan do no obeve). Theefoe, he cuen accoun hould eflec h nfomaon. A a conequence, he cuen accoun may help pedc fuue ock-make pefomance. The poenal pedcve powe of fuue endowmen no new. I wa aleady peen n he ave fo a any day agumen of all lfe cycle model. Campbell (987) deved he coepondng Gange popoon on he pedcve powe of conumpon fo fuue ncome. Bu he poenal pedcve powe of he cuen accoun wh epec o fuue ock make pefomance new. Snce fuue ock make pefomance dffcul o pedc, one hould ake h mplcaon of he model wh cauon. A few pon ae n ode o lluae why h mplcaon may be moe eaonable han can eem. 23 F, n any ae-pcng model whee agen ae k-avee, agen have o expec ha ock wll yeld hghe eun han he k-fee ae (.e., exce eun ) n ode o decde o hold ock. If hee no uch k pemum o compenae people fo he k hey ake by holdng ky ecue, agen would neve puchae ky ae. Expecaon of exce fnancal gan, heefoe, a neceay condon fo holdng of ky ae o ex. 24 Th, of coue, no eay o econcle wh a andom walk vew of he ock make. Two pon can nevehele be made on h ubjec. The f one ha he nfomaon ued by conume o make he decon may no be avalable o ade on Wall See (omehng whch eem eaonable). If o, hen would be poble ha he cuen accoun nfomave abou fuue ock make pefomance whou mplyng ha ome abage oppouny ha no been exploed by ade. The econd pon ha whle abage may lead o a andom walk behavo of he ock make n he ho un, hee may nevehele 22 Thee popoon would no be aleed by non-cara uly funcon. A CARA uly funcon mple a wealh-ndependen pofolo holdng. Howeve, I do no ue he pacula pofolo pedced by he CARA uly funcon n h econ analy. 23 Suvey on ock make pedcably can be found n Cochane (999), and Leau e al. (200). 24 Deemnan of hee expeced exce eun ae dcued n he geneal equlbum veon of he model n Meceeau (2002). They nclude demogaphc vaable, vaance and covaance of dvdend pocee, and k aveon, among ohe. Snce hee paamee ae non-ochac bu me-vayng, expeced exce-eun wll flucuae n a pedcable way a lowe fequence.

16 - 5 - be pedcable medum-un o long-un end n he ock make movemen. The model pecely abou hee longe-em end. Fnally, neeng o noce ha h popey of he model ha he cuen accoun may help foeca fuue change n equy pemum gan n he ame p of an agumen ecenly made by Leau and Ludvgon (200). In h pape, hey ague ha he ao of conumpon o wealh hould help foeca ock eun becaue ncopoae people expecaon abou hem. They make he pon n a faly geneal fomal model. They hen how ha empcally he conumpon o wealh ao he be ngle pedco of fuue ock eun. The ngh gven by ou model o of a genealzaon of he agumen o he naonal open economy. The ohe Gange popoon ae n he ame p a he fome, bu ae omewha weake o le neeng. Thee popoon ae eed fomally n Meceeau (2003). To ummaze, he cuen accoun may help foeca he change n ne oupu and/o of exce fnancal gan becaue eflec he agen nfomaon and expecaon abou hee wo vaable fuue level. C. Ohe Implcaon of Model Implcaon of Holdng Foegn Sock: Inenaonal Tanmon of Shock I noewohy ha n h famewok ock make doe no necealy mean domec ock make. The model doe no dffeenae beween domec and foegn hae: an agen fee o ue all he nenaonal ock make. The conequence of h ha expeced pefomance of foegn ock make can alo have a meanngful mpac fo a couny whch ha nveed (o mply plan o nve) aboad. Fo example, a meanngful poon of he fnancal ncome of a couny, whch, lke Canada, nve heavly n U.S. hae, come fom evenue fom U.S. hae. Theefoe, he expecaon abou he fuue pefomance and ucue of he U.S. ock make wll have a meanngful mpac on he Canadan cuen accoun. To gve a mple example, f he Canadan beleve ha he U.S. ock make gong o pefom exceponally well n he fuue, Canada wll end o un a cuen accoun defc oday, ndependenly of he expeced pefomance of he Canadan economy o ock make. 25 Ol poducng coune ae alo good example of coune whch hold lage ock of foegn ae. 25 In an exeme uaon fo a couny wh a zable ock of foegn ae, a couny ne oupu and fnancal gan on domec ock make could heoecally boh be above he epecve expeced fuue pemanen level, and have he couny un a cuen accoun defc, povded ha hey expec hgh enough eun on foegn ae.

17 - 6 - Impac of Endowmen Income Shock Ou model can alo be ued o dcu he mpac of endowmen hock on he cuen accoun, an ue ha ha dawn aenon n he leaue. Ou model ee ha endowmen and ock make eun hock hould be jonly analyzed. Inuvely, buyng ock wll allow one o mgae he mpac of endowmen hock. In cona wh he e of he leaue, whch deal excluvely wh he wo exeme cae of an economy wh only a k-fee bond o of complee make, fnancal make ae ncomplee n ou famewok. To make he dcuon omewha moe ubanve, le u examne he cae whee endowmen hock ae eally auo-coelaed (le u we Ψ a he peen value mulple of a hock η on NI ). In he Sach bond-only mall open economy, a pove hock η on endowmen ncome ceae a cuen accoun uplu of magnude Ψη. Indeed, f a + hock ha pove peen dcouned value, he epeenave conume wll conume an annuy of ( Ψη ) and ave he e, ceang a cuen accoun uplu. + In a complee make wold, even mple: he couny puchae n he f peod he pofolo whch wll nue full k hang among coune, and wll keep evey ubequen peod. The cuen accoun, whch he change of ne foegn ae, wll, heefoe, only eflec he capal gan on he ne foegn pofolo. Ou model, wh ncomplee fnancal make, an nemedae (and moe ealc) cae beween hee wo exeme. Wha he mplcaon of make ncompleene? Inuvely, he anwe ha nenaonal ock make allow he couny o paally hedge endowmen hock. I wll help hedge agan hock, becaue one of he deemnan of he couny pofolo wa k hedgng. In ou model, he deed ky ae pofolo ndeed gven by: ω = Σ +EX + - Ψ + Σ +β+, A whee k pemum exploaon k hedgng - Σ + he vaance-covaance max of he ae eun, β + he veco of covaance of he ae eun wh NI and Ψ+ he peen value mulple of a hock on NI. The k-hedgng componen eflec he dee of he couny o hold ock whch pefom well when he endowmen ncome pefom pooly. One way o lluae how h (mpefec) k hedgng povded by he fnancal make nfluence he mpac of an endowmen hock on he cuen accoun o conde he expeced hock on he cuen accoun condonal on he ealzaon of an endowmen hock. Popoon 6 below lluae h pon. Popoon 6. The expeced hock on he cuen accoun condonal on a ne ncome hock :

18 - 7 - E CA E e ( / η ) = Ψ η + Ψ β ' ω { η ( ) ( / η ) + va η PDV of hock PDV of expeced hock hedgng Fo poof, ee Appendx I.. (6) We ee ha he effec on he cuen accoun of a negave peen dcouned value hock on endowmen ncome no longe clea. Th hock ndeed hee-ded. I ha a dec negave effec on wealh. Bu alo poble ha ou pofolo of ky ae povde u wh moe han enough hedgng agan endowmen ncome k and ha he coepondng ky ae hock [em (2)] moe han offe h negave hock. Theefoe, he combned mpac uncean, and he mpac of he hock on deed holdng of he agen could go ehe way (h wha he f wo em eflec). 26 Fnally, o ee whch way he cuen accoun wll move, one alo ha o ake no accoun he change n domec ock avalable. Th dcuon lluae ha eenal o ake he ock make no accoun when one wan o ae he mpac of endowmen hock on a couny cuen accoun. I alo how ha he phenomenon moe complex han pevou model have uggeed. IV. CONCLUSION To ummaze, h pape develop a model o udy he mpac of ock make on he cuen accoun. The model nclude an abay numbe of ky ae, whch fom an ncomplee make, a well a a k-fee bond. A cloed-fom oluon fo he cuen accoun deved fom he opmal pofolo and conumpon/avng choce of a epeenave agen. Fomally, he model can be een a a ock make-augmened veon of he fundamenal equaon of he cuen accoun populazed by Sach. The model can help explan he ecen and exceponal U.S. cuen accoun defc. The model ugge ha he cuen accoun may help pedc fuue ock make pefomance and/o fuue endowmen. A geneal-equlbum veon of he model developed n Meceeau (2002). In a companon pape, Meceeau (2003), he model pu o he e ung U.S. daa. The model pefomed bee han he ame model whou ock make. The foecang popey of he cuen accoun a a poenal pedco of fuue ock make pefomance alo eceved pelmnay empcal confmaon. To conclude, h pape developed a model o udy he ole of ock make n he dynamc of he cuen accoun. To fuhe exploe h ue would be a wohy ole fo fuue eeach. 26 Alhough, n pacce, pobably moe ofen he cae ha fnancal nvemen of a couny wll only paally offe he endowmen ncome hock ahe han ovehoong hem.

19 - 8 - APPENDIX I APPENDIXES I. Poof of Popoon Soluon of model The pogam of he agen : T Max U( C) = E0 δ u( c ), { c; ω0, ; ω} = 0 = 0 unde he budge conan BC : c + ω + ω = NI + Rω + R ω 0, j, 0 0, j, j, j= j= (and we have he nal condon: ω 0, = ω = j, 0). We can ewe h pogam a: T Max U( C) = E0 δ u( NI R0ω0, Rj, ωj, ω0, ωj, ) + + { ω0, ; ω} = 0 j= j= = 0 Le u we he Eule equaon:. ω ω 0, j, { ( c) δ ( ) u ( c+ )} : E -u' + + ' = 0 { ( c) δ Rj + u ( c+ )} : E -u' + ' = 0, (A) (A2) A a begnnng, le u ewe h yem of equaon. Equaon (A) become: exp( Ac) = δ ( + ) E exp( Ac+ ). Becaue all hock ae nomally dbued by aumpon, he budge conan mple ha conumpon nomally dbued a well. Theefoe, he equaon now ead: 2 A exp( Ac) = δ ( + ) exp AE( c+ ) + va( c+ ), 2 A whch lead o: E( c+ ) = c + va( c+ ) + ln δ ( + ) 2. (A3) On he ohe hand, dffeencng (A) and (A2) lead o:

20 - 9 - APPENDIX I ( + ) '( ) = '( ) E u c+ E Rj, + u c+, whch equvalen o: E( X j, + ) E u' ( c+ ) + cov X j, + ; u' ( c+ ) = 0. Snce he vaable ae nomally dbued, one can ue Sen lemma: cov X j, + ; u' ( c+ ) = E u'' ( c+ ) cov ( X j, + ; c+ ). Ung he fac ha I have an exponenal uly funcon, h can be eaanged n: E X = Acov R ; c (A4) ( ) j, + j, + + We wll now ue (A3) and (A4) o olve he model. The aegy a follow: equaon (A4) wll gve he ky pofolo holdng expeon, whle he ohe equaon wll gve he ohe vaable a funcon of he pofolo holdng. I wll ue a gue and vefy mehod on he pofolo holdng: I wll gue expeon, hen olve fo all ohe vaable a a funcon of pofolo holdng. And fnally, I wll vefy ha equaon (A4) and he expeon found fo he ohe vaable ndeed eul n he gueed ky pofolo allocaon. The gue fo he pofolo of ky ae : ω = + Σ EX - Σ23 β A k pemum exploaon k hedgng whee Σ = cov ( R, ; Rj, ) he x vaance-covaance max of ae eun, and β cov ( NI, Rj, ), j=... = he x max of covaance beween ne ncome and j=,..., ae eun. Boh β and Σ ae exogenou n he model. They can vay ove me, howeve., Le u f fnd he expeon of conumpon. The conumpon found by olvng he budge conan ( BC ) fowad and ung equaon (A3): I ake he um T BC + E BC + and ue he fac ha E [ c ] ( ) = + ++ = E E c Snce I have ( ) aumed ha he f and econd momen of ou exogenou andom vaable ae bounded, ' each elemen of ω wll be bounded, and o wll be X + ω + fo all. va ( c + ) wll alo be bounded. A a conequence, he ee convege when T. T T ' E( X+ ω+ ) and va c+, epecvely, ( ) = = ( ) + +

21 APPENDIX I Solvng fowad he budge conan wll, afe ome aghfowad algeba, lead o: 27 c E ( NI ) + Rω + R' ω + E X ω ( + ) ( + ) ' ( ) + 0 0, + + = 0 = (2) cuen fnancal ncome () labo ncome wealh (3) fuue fnancal exce gan = + A Ln[ δ ( + ) ] - va c A 2 = ( + ) (4) conumpon lng (5) pecauonay avng. Le u now un o he expeon of k-fee ae holdng ω. Pluggng he budge 0, conan a me no equaon (A3) lead o he followng ecuve elaon: ω = ω + z, 0, 0, ( ) ( ) ( + ) ' ( ) ' wh z= NI+ Rω ωj, - E( NI+ ) + R' ω + E X+ ω+ j= = 0 = A + Ln[ δ ( + ) ] + va c A 2 =. I can now vefy ou gue. Ung he expeon I found fo conumpon n equaon (A4) lead o: A E ( X j, + ) = cov Rj, + ; NI+ R, + ω, j,..., + =. + = Th can be ewen n max fom a: [ ω β ] o ω A Σ = EX +, + = + Σ EX - Σ β 23, whch wa ou nal gue A k hedgng k pemum exploaon + 27 We alo aume ha ( ) = 0 + E ( NI ) ex, whch a naual aumpon. If he um + dd no convege, would mean ha he peen dcouned value of he agen labo ncome nfne. She would hen have no neempoal budge conan and he would be fee o conume a much a he whe.

22 - 2 - APPENDIX I Tanvealy condon We alo have o check ha he TVC afed. A uffcen condon fo he TVC o be afed : lm E ω0, + ω j, j = We aw ha becaue he f and econd momen of he exogenou ochac vaable ae bounded ω j, + bounded a well, and, heefoe, lm E ω j, 0 + = j = +. j= We alo have ω0, + = z, + = ( ) ( ) ( + ) ' ( ) ' wh z= NI+ Rω ωj, - E( NI+ ) + R' ω + E X+ ω+ j= = 0 = A + Ln[ δ ( + ) ] + va c. + A 2 = Fom he boundedne of he vaable, whch ha been pevouly dcued, poble o deve ha hee ex a conan K uch ha: ' ' Rω ωj, - R' ω + E( X + ω+ ) j= + = ( + ). A + Ln[ δ ( + ) ] + va c K + A 2 = + ( ) Wng x he vaable beween he abolue value gn above, I hen have: + x =. + = lm E 0 So all I have lef o how n ode o vefy ha he TVC afed ha : + lm E NIk - Ek( NIk ) k= 0 + = 0 ( ) +. nequaly (A5) Le u defne Z NIk. I wll how ha lm EZ 0 + k = 0 =.

23 APPENDIX I I wll do he poof n he ub cae whee + an even numbe. The ohe ub cae whee + odd hen aghfowad. Po + 2n, wh n. 2n n 2n EZ+ = E NIk NIk + + k= 0 k= n. n n n 2n 2n E Z E NI + E NI, whch lead o: + k k + k= 0 + k= n + n n k 2n k + k + k + k= 0 + k= n +. E Z E NI E NI k n By aumpon, ENIk convege. Theefoe, k = 0 + n n k ENI k 0 when n. + k = 0 + k 2n Moeove, E NIk 0 when n + a pa of he edual of a convegng k= n + pove ee. Hence, lm EZ + = 0. Th eul mple ha nequaly (A5) necealy vefed. Indeed, all he ohe em on he LHS ae negave. I, heefoe, have fnally poved ha he TVC vefed. No-Ponz-game condon Wha would be a no-ponz-game condon fo h poblem? One way o hnk abou would be o ay ha he oal amoun of money foegne ae wllng o lend o he domec economy hould no gow fae han he oal ock of ky ae n he economy: lm E ω0, + ω j, + lm E e+ + + j = +. Moe aumpon hould be made on he model o fomally check ha uch a condon vefed, bu hee new condon would be vey weak. Indeed, uffcen o aume, fo example, ha he Ne Income follow an exponenal gowh pah whoe ae below he k-fee ae 28, hen poble o how ha lm E ω0, + ω j, =, o ha + j = he No Ponz game condon afed. 28 Agan, f h ae wee hghe, he peen dcouned value of he couny endowmen ncome would be nfne. The couny epeenave agen would hen be able o conume (connued )

24 APPENDIX I Poof of popoon (ock make-augmened fundamenal equaon of he cuen accoun). By defnon, he cuen accoun he change n ne foegn ae: ' h, f ' f, h ' h, f ' f, h, GCA = ω + ω ω ω + ω ω, whee ω h f he veco of foegn ( ) 0, 0, f, h ω ae owned by domec ( home ) agen, and by foegn agen. he veco of domec ae owned Ung he fac ha j = ω = e ω + ω ' f, h ' h, f j,, he GCA can be ewen a: GCA = ω + ω ω + ω e e ( ). 0, j, 0, j, j= j= Ung he ecuve elaon found above fo he k-fee ae holdng yeld: ' = ωj, ωj, + + ω ωj, j= j= j= GCA NI R - E ( NI ) + R' ω + E X + ( ) + ( + ) A + Ln[ δ ( + ) ] + A 2 va c e e = + ' ( ω ) = 0 = ( ) Ung he defnon of he fuue pemanen level opeao * ( Z = + Z = 0 + = 0 + ) and eaangng he em gve: ( ) ( ) ( ) +. * ' ( ) + ' ω ( ) X * () labo ncome effec (2) ock make effec A + Ln δ ( ) + A + 2 va c+ - ( e - e-) = ( + ) (3) conumpon lng (4) pecauonay avng GCA = NI E NI X E ω. a much a he wan a each peod, fo he would no face any neempoal budge conan. So he equed condon ae weak ndeed.

25 APPENDIX I Fnally, noe ha va(c) can alo be expeed a a funcon of he exogenou paamee: 2 2 ' - ' - va ( c) = ( Ψ) va ( η) βσ β + EX 2 Σ EX whee η he A undvefable pa of doyncac k nnovaon of ne oupu, - Σ he vaance-covaance max of he ae eun, ae eun wh NI. Poof of popoon 2 pemum exploaon k Ψ he peen value mulple of he nnovaon on ne oupu, β he veco of covaance of he To pove popoon 2, one hould a wh wng down he RHS of he equaon I wan o pove: RHS E( NI+ ) E( f+ ) = + = +. Then all one ha o do o pl each um no wo um (ecall ha boh ee T T E( f ) and + NI + = ( + ) = ( + ) and eaangng hen yeld he ock make-augmened equaon of he cuen accoun. convege when T ). Smplfyng em by em Poof of popoon 3 o 5 (Gange popoon) I wll do he poof fo popoon 3B and 4 (I wll gve wo alenave poof n each cae). The ohe poof ae mla. Le u f ecall he equaon I aed wh: CA + e = E( NI+ ) E( f) = + = + (whee f denoe he equy pemum gan pevouly wen a X ' +. ω+ ). (A6) Le u alo we I he nfomaon e conanng all he peen and pa value of (CA + e ), NI, and f. Then I have he followng popoon: Popoon 3B (mulvaae Gange caualy). If equaon (A6) hold, hen (CA + e ) Gange-caue a lea one of ( f, NI ), excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa NI and f. Poof: In he ene analy, I ea condonal expecaon a equvalen o lnea pojecon on nfomaon.

26 APPENDIX I Le u poceed ad abudum. Le u aume ha (CA + e ) Gange-caue nehe f no NI, and ha (CA + e ) no a lnea combnaon of peen and pa NI and f. Then he fac ha (CA + e ) doe no Gange-caue f mple ha: E( f + / I ) = E( f + / f, f -, f -2., NI, NI -, NI -2 ) fo all. In he ame way, he fac ha (CA + e ) doe no Gange-caue NI mple ha E( NI + / I ) = E( NI + / f, f -, f -2., NI, NI -, NI -2 ) fo all. Ung equaon (), I have: E ( CA + e / I) = E ( NI+ / I) E( f / I) = + = +, and heefoe: E ( CA + e / I) = E ( NI / f, f,..., NI, NI,... ) + = + E( f / f, f,..., NI, NI,... ), = + E CA + e / I an exac lnea combnaon of he peen and pa whch o ay ha ( ) NI and f. Bu (CA + e ) belong o I. Hence, ( / ) E CA + e I = CA + e. Theefoe (CA + e ) an exac lnea combnaon of he peen and pa NI and f, whch conadc ou nal aumpon. Noe: An alenave poof could be done n he pecal of a VAR model. A( L) A2( L) A3( L) NI Le u we I A2 ( L) A22( L) A23( L) f = ε. Sackng h equaon o fom A3( L) A32( L) A33( L) CA + e a f ode yem, hen eay o how ha f A 3 =A 23 =0 hen E( f + / I ) and E( NI + / I ) ae lnea combnaon of peen and pa NI and f (all one ha o do o we he VAR foeca of each of h em). Theefoe, (CA + e ) elf an exac lnea combnaon of he peen and pa NI and f. Popoon 4 (Gange Caual Poy). If equaon (A6) hold, hen { f, NI } no Gange Caually Po o (CA + e ), excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa NI and f. Poof: Th an mmedae conequence of Popoon. Indeed, le uppoe ha { f, NI } Gange Caually Po o (CA + e ). Then, by defnon of Gange-caual poy, (CA + e ) doe no Gange caue { f, NI }. Bu h conadc Popoon (excep n he vey pecal cae whee (CA + e ) a lnea combnaon of peen and pa NI and f ). Noe ha alo aghfowad o do a poof n he VAR cae (n a 3 vaable-yem, { f, NI } Gange Caually Po o (CA + e ) necealy mple A 3 =A 23 =0, whch conadc Popoon ).

27 APPENDIX I Poof of popoon 6 Popoon 6 a mple applcaon of he fac ha f wo vaable x and x 2 have a jon nomal dbuon: x µ Σ Σ2 ~ N ;, hen he dbuon of x condonal on x 2 : x2 µ 2 Σ2 Σ22 ( ) x ( ) / x2 ~ N µ +Σ2Σ22 x2 µ 2 ; Σ Σ2Σ22Σ2. In ou cae x CA and x 2 NI.

28 APPENDIX II II. Summay of Man Noaon Decpon Noaon Dmenon Ne ncome NI = Y I G D x Toal amoun of dvdend dbued D x by domec compane Rk fee nee ae R0 = + x Dvdend pad by company j d j, x Pce of ock j P j, x Go eun R x Go eun of ock j R d j, + Pj, = x Exce eun j, Pj, Exce eun of ock j j, ( j, 0) X x X = R R x Rk fee ae holdng ω 0, x ω = ω x Rky ae holdng by domec agen ( j, ) Toal endowmen of ky ae n he e x domec economy (=ock make valuaon) Exce fnancal gan f = X ' ω x Tade balance TB Y C I G x Rae of me pefeence δ x Coeffcen of abolue k aveon A x Vaance-covaance max of ae Σ= cov ( R ; R ) x eun Covaance beween ne ncome and ae eun j=, j, ( NI R ) j, j, =... β = cov, x j=,...,

29 Refeence Adedej, Olumuywa, 200, The Sze and Suanably of he Ngean Cuen Accoun Defc, IMF Wokng Pape 0/87 (Wahngon: Inenaonal Moneay Fund). Agéno, Pee-Rchad, Claude Bmu, Paul Cahn, and ohn McDemo, 999, Conumpon Smoohng and he Cuen Accoun: Evdence fo Fance, , ounal of Inenaonal Money and Fnance, Vol. 8 (Febuay), pp. 2. Callen, Tm, and Paul Cahn, 999, Aeng Exenal Suanably n Inda, IMF Wokng Pape 99/8 (Wahngon: Inenaonal Moneay Fund). Campbell, ohn, 987, Doe Savng Ancpae Declnng Labo Income? An Alenave Te of he Pemanen Income Hypohe, Economeca, Vol. 55 (Novembe) pp , and Robe Shlle, 987, Conegaon and Te of Peen Value Model, ounal of Polcal Economy, Vol. 95 (Ocobe), pp Cahn, Paul, and ohn McDemo, 998, Ae Auala Cuen Accoun Defc Exceve? Economc Recod, Vol. 74 (Decembe), pp Dav, Seven, eemy Nalewak, and Paul Wllen, 2000, On he Gan o Inenaonal Tade n Rky Fnancal Ae, NBER Wokng Pape No (Cambdge, Ma.: Naonal Bueau of Economc Reeach). Dav, Seven, and Paul Wllen, 2000, Ung Fnancal Ae o Hedge Labo Income Rk: Emang he Benef (unpublhed; Chcago: Unvey of Chcago, Gaduae School of Bune), avalable va he Inene a: hp://gbwww.uchcago.edu/fac/even.dav/eeach/. Ghoh, Ah, 995, Inenaonal Capal Mobly Among he Majo Indualzed Coune: Too Lle o Too Much? Economc ounal, Vol. 05 (anuay), pp , and onahan Oy, 995, The Cuen Accoun n Developng Coune: A Pepecve fom he Conumpon Smoohng Appoach, Wold Bank Economc Revew, Vol. 9 (May), pp Gon, Anne, Deck ogenon, and Nchola Polon, 2000, Rk Unceany: Exenon of Sen Lemma, (unpublhed; Chcago: Unvey of Chcago). Kaay, Aa, and aume Venua, 2000, Cuen Accoun n Debo and Cedo Coune, Quaely ounal of Economc, Vol. 5 (Novembe), pp

30 Leau, Man, and Sydney Ludvgon, 2000, "Foecang Sock Reun: New Ou-of- Sample Evdence." Now avalable a "Conumpon, Aggegae Wealh and Expeced Sock Reun," ounal of Fnance, Vol. 56, No. 3, pp Ludvgon, Sydney and Chale Sedel, 999, How Impoan he Sock Make Effec on Conumpon? Economc Polcy Revew, Fedeal Reeve Bank of New Yok, Vol. 5 (uly), pp Mahall, Davd, and Nayan Paekh, 999, Can Co of Conumpon Adjumen Explan Ae Pcng Puzzle? ounal of Fnance, Vol. 54 (Apl), pp Meceeau, Benoî, 2002, Cuen Accoun and Real Exchange Rae n an Ineempoal Geneal Equlbum Model wh Incomplee Make (Deaon The; New Haven: Yale Unvey, Economc Depamen)., 2003, Role of Sock Make n Cuen Accoun Dynamc: Empcal Evdence fom he Uned Sae, IMF Wokng Pape 03/08 (Wahngon: Inenaonal Moneay Fund). Mlo, Alex, 200, "Capal Mobly and Conumpon-Smoohng n a Two-Seco Model: The Cae of Mexco" (unpublhed; New Haven: Yale Unvey, Economc Depamen). Obfeld, Mauce, and Kenneh Rogoff, 995, The Ineempoal Appoach o he Cuen Accoun, n Handbook of Inenaonal Economc, Vol. 3, ed. by Gene Goman, and Kenneh Rogoff, (Amedam: Eleve Pe), pp , 997, Foundaon of Inenaonal Macoeconomc (Cambdge, Maachue: MIT Pe). Oy, onahan, 997, Cuen Accoun Imbalance n ASEAN Coune: Ae hey a Poblem? IMF Wokng Pape 97/5 (Wahngon: Inenaonal Moneay Fund). Oo, Glen, 992, Teng a Peen Value Model of he Cuen Accoun: Evdence fom U.S. and Canadan Tme See, ounal of Inenaonal Money and Fnance, Vol. (5), pp Sach, effey, 982, The Cuen Accoun n he Macoeconomc Adjumen Poce, Scandnavan ounal of Economc, Vol. 84, pp Sheffn, Seven, and Wng Thye Woo, 990, Peen Value Te of an Ineempoal Model of he Cuen Accoun, ounal of Inenaonal Economc, Vol. 29 (Novembe), pp Sm, Chophe, 999, Gange Caualy, lecue noe, avalable va he Inene a hp://eco b.pnceon.edu/yfp/tmef99/gcp.pdf.

31 Venua, aume, 200, A Pofolo Vew of he US Cuen Accoun Defc, Bookng Pape on Economc Acvy, Vol. (uly), pp Wllen, Paul, 997, The Effec of Fnancal Sophcaon on he Tade Balance, (unpublhed; Chcago: Unvey of Chcago, Gaduae School of Bune), avalable va he Inene a hp://gbwww.uchcago.edu/fac/paul.wllen/eeach/reeach.hm.