THE US CURRENT ACCOUNT DEFICIT: A RE-EXAMINATION OF THE ROLE OF PRIVATE SAVING

Transcription

1 THE US UENT AOUNT DEFIIT: A E-EXAMINATION OF THE OLE OF IATE SAING harles Engel esearch Discussion aper 5-9 November 5 eserve Bank of Ausralia Deparmens of Economics and Finance, Universiy of isconsin, 8 Observaory Drive, Madison, I , USA. cengel@ssc.wisc.edu. This paper represens preliminary work on a sudy ha is co-auhored wih John H ogers, Board of Governors of he Federal eserve, o be presened a he arnegie-ocheser onference Series on ublic olicy, on he opic of Inernaional Trade and Globalizaion, 8 9 November 5. ogers has direcly conribued mos of he daa work in his paper, and he overall discussion has evolved hrough our discussions. e have grealy benefied a his sage from many discussions wih David Backus, Menzie hinn, and he saff a he eserve Bank of Ausralia. The views expressed in his paper do no necessarily represen hose of he Board of Governors of he Federal eserve or he eserve Bank of Ausralia.

2 Absrac The large recen US curren accoun deficis have been he subjec of an enormous amoun of sudy in academia, among governmen and cenral bank economiss, in business economic repors, and in he press. Many differen explanaions of he cause of he defici have been offered, and o varying degrees we believe ha all may have played a role: low privae saving in he US; large public-secor budge deficis; a glu of savings in he res of world; and, perhaps even a misalignmen of nominal exchange raes. In his paper we explore he role of one oher facor ha also has been menioned prominenly: privae saving in he US is low because income growh is expeced o be srong. e rework he sandard neoclassical wo-counry model o show how a counry will be a ne borrower when is fuure share of world GD is expeced o increase above is curren share. Our research ulimaely is moivaed by he quesion of wheher he US curren accoun is susainable. The way we approach he quesion is o see wheher he high level of US spending currenly is compaible wih an opimal pah of borrowing. In paricular, wha assumpions abou expeced fuure growh of he US s share of world oupu could jusify is curren accoun defici? e show ha if he defici can be explained by higher fuure income shares, hen he size of he real depreciaion, ha may oherwise be required o reduce he defici, may be quie small. JEL lassificaion Numbers: F, F3, F4 Keywords: curren accoun adjusmen, saving i

3 Table of onens. Inroducion. The Model 9. Equal Discoun Facors, Logarihmic Uiliy. Differen Discoun Facors, Logarihmic Uiliy 4.3 Same Discoun Facors, Non-logarihmic Uiliy 7 3. eal Exchange ae Model 9 4. Model Simulaions 5 4. urren Accoun 5 4. eal Exchange ae 7 5. onclusions 8 eferences 9 ii

4 THE US UENT AOUNT DEFIIT: A E-EXAMINATION OF THE OLE OF IATE SAING. Inroducion harles Engel The large Unied Saes (US curren accoun deficis of recen years have been he subjec of an enormous amoun of sudy in academia, among governmen and cenral bank economiss, in business economics repors, and in he press. Many differen explanaions of he cause of he defici have been offered, and o varying degrees we believe ha all may have played a role in he evoluion of he defici: low privae saving in he US generaed by financial innovaions or asse price inflaion; large public-secor budge deficis; a glu of savings in he res of he world driven by demographic facors in he rich counries and capial marke imperfecions in he emerging markes; and, perhaps even misalignmen of he nominal exchange rae leading o excessively cheap impor prices for he US in he shor run. In his paper we explore he role of one oher facor ha also has been menioned prominenly: privae saving in he US is low because income growh is expeced o be srong in he US. e will discuss briefly some of he oher facors ha deserve consideraion, bu here our focus is on he quesion of how much of he curren accoun defici can be undersood in he conex of a model of opimal saving. e rework he sandard neoclassical wo-counry model o show how a counry will be a ne borrower when is fuure share of world GD (ne of invesmen and governmen spending is expeced o increase above is curren share. Figure is he saring poin of our analysis. I shows wha is perhaps one of he mos sriking economic developmens of he las 5 years: he dramaic increase in See, for example, Backus e al (5, Bernanke (5, Blanchard, Giavazzi and Sa (5, hinn (5, larida, Gorei and Taylor (5, Edwards (5, Gourinchas and ey (5, Kouparisas (5, Kraay and enura (5, Obsfeld and ogoff (, 4, 5, and Truman (5. The US curren accoun defici sood a almos 6 per cen of GD in 4, he larges defici on record over he las 4 years.

5 US oupu relaive o he res of he high-income world. Specifically, he figure plos US GD less governmen spending and invesmen as a share of he sum of G7 GD less governmen spending and invesmen. e ne ou governmen spending and invesmen because our heory suggess ha consumpion spending ulimaely depends on income ha is available for household consumpion, bu a plo of unadjused GD shares looks very similar. The figure also eliminaes he influence of exchange rae swings by comparing real GD growh relaive o GD shares in 99, in a way ha will be explained in greaer deail laer. Share.45 Figure : US Share of Adjused G7 GD Share Source: auhor s calculaions The sriking hing abou his figure is ha since some ime in he 98s, he US share appears as if i is on an upward linear rend. Is share has increased from a rough in 98 of around 39.5 per cen o is level in 4 of approximaely 45.3 per cen. rior o 98, i appears ha he US share flucuaed around a level of roughly 4.5 per cen. GD shares capure wo facors ha are ypically considered separaely in he neoclassical approach o he curren accoun. Firs, if he counry s income is expeced o rise, i may borrow now and run a curren accoun defici. Second, if he world ineres rae is low, he counry s incenive may be o borrow more now.

6 3 One facor ha may lead o lower ineres raes is high saving in he res of he world, which migh in urn be generaed by poor growh prospecs in hose counries. Typically, he wo-counry model (in which he world ineres rae is deermined endogenously has been used when sudying a large counry, such as he US. Our models recas he neoclassical model o show how we can (under cerain assumpions express he opimal consumpion pah as a funcion of he curren and expeced fuure discouned sum of he counry s share of world oupu (adjused for governmen spending and invesmen. This represenaion is useful because i expresses he economic forces in a ransparen and inuiive way; i also gives us a way of esing he model ha does no require modelling of world real ineres raes. The effecs of real ineres raes are implicily capured by he shares model. For example, if he res of he world s income growh is expeced o be slow, in he sandard represenaion, heir high saving will lower ineres raes and hese low raes will simulae consumpion a home. In he shares approach, we see direcly ha home borrowing is encouraged by low growh in he res of he world, because ha low growh will lead o higher fuure oupu shares for he home counry. Anoher nice feaure abou he shares represenaion of he wo-counry model is ha i applies for counries of any size. There is no difference in he represenaion for counries ha are oo small o affec world real ineres raes, and large counries ha can. Our research ulimaely is moivaed by he quesion of wheher he US curren accoun is susainable. The definiion of susainabiliy is a bi slippery and differs from sudy o sudy, and we do no offer a definiion here. e begin from he observaion ha while he US is building up deb obligaions which may imply high deb service obligaions in he fuure, i will almos cerainly also be he case ha US GD will be much higher in he fuure. e need some yardsick o measure how burdensome hose deb service obligaions will be in he fuure. ill he US be worse off from is high curren spending a he expense of having o devoe some of fuure oupu o servicing is exernal deb?

7 4 I seems like he naural way o answer his quesion is in he conex of an opimising model. This allows us o compare he rade-off beween curren and fuure consumpion. The way we approach he quesion is o see wheher he high level of US spending currenly is compaible wih an opimal pah of borrowing. In paricular, wha assumpions abou expeced fuure growh of he US s share of world oupu could possibly jusify is curren accoun defici? I is obvious ha he US canno run primary deficis forever alhough even here, a cavea is necessary. Figure plos he decline in he US exernal ne asse posiion since 98. Alhough here are serious and well-known measuremen issues, he char reproduces he convenional wisdom ha he US has emerged as a large debor. Bu Figure 3 shows he US ne invesmen income as a share of GD. Tha also has declined since 98, which is consonan wih he decline in he US asse posiion. Bu he decline in invesmen income has no been nearly as sharp as he decline in he ne asse posiion, and he char shows ha US ne invesmen income in 4 was sill posiive. Figure : US Ne Inernaional Invesmen osiion er cen of nominal GD % % Source: Bureau of Economic Analysis (BEA, Inernaional Economic Accouns

8 5 Figure 3: US Ne Invesmen Income er cen of nominal GD % %. Toal Direc invesmen orfolio invesmen Source: auhor s calculaions The usual explanaion for his disconnec ha he US is a ne debor, bu is ne invesmen income is posiive is ha he US earns more from is foreign invesmens han foreigners earn from heir invesmens in he US. This in urn is explained by he claim ha he US exernal porfolio is dominaed by direc invesmen and equiies, while foreigners porfolio of US asses is dominaed by holdings of Treasury securiies. haever he reason, if he US can always earn more on is foreign invesmens han foreigners earn on heir invesmens in he US, hen indeed even a primary curren accoun defici could be susained forever. The US could mainain a posiion of zero ne invesmen income in his siuaion if he raio of foreign asses ha i acquires o US asses acquired by foreigners were o equal he rae of reurn on hese US asses relaive o he rae of reurn on foreign asses acquired by he US. If he laer raio is less han one, hen he former raio can also be less han one, which implies a primary curren accoun defici. e will absrac from his possibiliy in our discussions. rimarily we will ake an approach ha ses he curren US ne invesmen income o zero, and assumes ha on fuure ransacions he reurns on US borrowing and lending are equal. e acknowledge ha in some circumsances his may underesimae he fuure deb service obligaions of he US if markes have properly priced long-erm asse

9 6 posiions. Bu under he convenional wisdom, his assumpion acually is conservaive. Tha is, we ry o uncover wha assumpions abou US growh relaive o he res of he world would jusify he high US curren accoun defici. High US growh combined wih low growh in he res of he world is required. The mos likely deviaion from his siuaion is one in which oal world GD growh urns ou o be lower han he markes currenly expec. Bu if ha were o happen, fuure shor-erm ineres raes would be lower han hose implied by our model. The way in which he US could ge ino rouble wih is curren deb obligaions (which we are, in essence, ignoring on he grounds ha is curren ne invesmen reurns are no negaive is if ineres raes are higher when he curren deb is rolled over a mauriy. Bu ha would require fuure ineres raes o be higher han he raes ha are implici in our model, no lower. eurning o Figure, i is obvious ha i is difficul o forecas he US s fuure share of adjused G7 GD. As we have noed, i appears ha he US share has been on an upward linear rend since some ime in he 98s. Bu mahemaically i is impossible for he share o coninue upward on a linear rend. If nohing else, he rend mus sop when he US share reaches one, bu obviously i will sop long before hen. Bu i is hard o read he ea leaves from Figure. ill he US share coninue o rise, and hen level ou a a higher share? If so, wha will ha share be? Or will he rend reverse, and he US share reurn o somewhere around 4.5 per cen? e consider differen scenarios based on alernaive economeric approaches, bu ulimaely here is no answer in which we can be very confiden. Indeed, ha is he core conclusion we reach: here is a grea deal of uncerainy abou he fuure pah of he US share of world oupu. There are cerainly plausible scenarios in which modes coninued growh in he US share could jusify high US exernal borrowing oday. Our sudy is an exercise in generaing inuiion abou he magniude of he effec of growh in fuure oupu shares, raher han a definiive sudy of he US curren accoun. As we noed from he sar, here are many facors ha conribue o he defici, and we consider only one of hem. e perform a delicae balancing ac in ignoring many of hese facors. One of he firs quesions ha migh be raised is why Figure considers he US share of adjused G7 GD? If we included hina, India, and he eas Asian igers,

10 7 for example, would no he figure show a falling share? erainly, he increase in he US share would no appear as dramaic if i were o include hese counries, bu we leave hem ou for good reason. If we were o rea hese counries symmerically wih he US, he model implies ha hey should be running large curren accoun deficis. Indeed, i is a puzzle ha his se of counries, which mus be expecing high fuure income growh, have curren accoun surpluses in a world of low real ineres raes. Bernanke (5 offers he saving glu explanaion for heir behaviour. He argues ha his se of counries saves a lo now because hey do no have full access o world capial markes. The afermah of he 997 crisis has led ouside lenders o be cauious, and required he emerging-marke counries as a whole o finance invesmen inernally. In addiion, some counries (such as hina may have been building up a war ches as proecion agains he even of a fuure crisis, even if privae capial markes have been willing o lend. And, Bernanke noes, he oil-producing counries have had high saving raes recenly ha have been associaed wih he recen increase in he price of oil. From he perspecive of he US, he relevan poin is ha hese counries are no borrowers on inernaional capial markes. Since hey are running curren accoun surpluses, hey are conribuing o he pool of world saving. This increases he incenive for any oher counry o borrow oday. I is a conservaive assumpion on our par o ignore his pool of saving in assessing wha sor of income growh in he US could jusify is curren low level of saving. Of course our neoclassical model could direcly incorporae an explanaion for he glu of saving in he emerging markes, and he exended model could be esed. e do no ake his approach for hree reasons. Firs, we do no believe he exercise of deermining opimal behaviour for he US necessarily depends on he explanaion for he saving glu. haever he reason, i will lead o lower ineres raes han hose implied by our model, and imply an even greaer incenive for he US o borrow. Second, we are inen on examining a simple and inuiive version of he model. Third, here is a sense in which he shares model can incorporae a high desired saving level in he res of he world in a sraighforward way. e can simply make he ad hoc assumpion ha he res of he world pus a higher weigh on fuure uiliy of consumpion han does he US. e show ha in his conex, he opimal defici for he US is sill a weighed average of curren and fuure expeced oupu shares. Bu he model implies, naurally, ha he US consumpion

11 8 level will be higher he higher he discoun facor (he lower he discoun rae in he res of he world. e also do no direcly consider demographic explanaions for differen saving raes around he world. There is a sense, however, in which our model does capure hese effecs. e model behaviour in each counry as deermined by an infinielylived represenaive household. e do no even consider changes in he number of people in each household. Mainaining his ficion, one migh suppose ha in some households, fuure producion will fall (or grow more slowly as members of he household reire and leave he workforce. In oher households, income will grow as he fracion of working members of he households increases and heir oupu rises. In he young counries, oupu is expeced o increase more rapidly han in he old counries. From his vanage, demographics can be seen as an underlying deerminan of income growh, and herefore a driving variable in he deerminaion of fuure oupu shares. For example, he OED recenly has prediced very low GD growh in he eurozone economies in he decade of he s. The primary reason for his low growh projecion is demographic he OED forecass a shrinking workforce in hese economies. One of he mos conroversial issues ha we are sidesepping is he role of he US governmen budge deficis in conribuing o he curren accoun defici. Figure nes ou governmen spending. To he exen ha budge deficis are caused by increased public expendiure, we have already facored hem ino our analysis. Tha is, higher public expendiure implies a lower share of GD lef over for privae consumpion. So we are only rying o explain ha par of he US curren accoun defici ha canno be explained by higher governmen spending. On he oher hand, our model is based on an infiniely-lived represenaive household, and so he iming of axes does no maer for consumpion decisions. Tha is, icardian equivalence holds. In pracice, however, i may be ha a reducion in axes does no lead o a dollar for dollar increase in privae saving. The empirical evidence is ambiguous on his poin, bu our feeling is ha icardian equivalence does no hold. So when we ask wheher he saving behaviour of he US could be consisen wih an opimising framework, we are o some exen assuming ha he governmen is using is axing powers o deermine opimal See, for example, Marins e al (5.

12 9 saving. Tha is, i lowers axes in hose cases in which i believes ha he oucome of decisions by privae households and businesses leads o oo much saving. u anoher way, he quesion is wheher he ax policy decisions of he governmen are irresponsible, or wheher hey could be consisen wih a responsible governmen ha has higher expecaions of growh, or possibly a lower discoun facor (higher discoun rae, han he public. In paricular, we wan o judge wheher he expeced growh or he discoun facor ha is needed o reconcile he US curren accoun wih plausible esimaes of is fuure income share is responsible or irresponsible. e examine he curren accoun quesion enirely from he perspecive of a neoclassical model. e ake his approach because we view he curren accoun deficis of he US, and he evenual adjusmen of is primary defici, as a long-run phenomenon. This does no mean ha shor-run consideraions are unimporan. They cerainly migh maer for he shor run, and Keynesians believe ha shor-run consideraions maer for policy. e do no believe, however, ha shorrun flucuaions in exchange raes or income will accoun for much of he long-run adjusmen process, so we ignore such facors in order o simplify he analysis. In Secion below, we lay ou he basic shares model and consider a couple of simple generalisaions. Secion 3 akes up a relaed issue does he adjusmen of he US curren accoun require a large real depreciaion? e show ha if indeed he defici can be explained by higher fuure income shares, hen he size of he required real depreciaion may be quie small indeed. Secion 4 hen provides some simple numerical exercises wih he model o assess he impac of he role of growh in fuure oupu shares on he curren accoun. eaders no ineresed in he echnical deails may wan o skip Secions and 3, and head sraigh for he boom line in Secion 4. onclusions are drawn in Secion 5.. The Model e build a wo-counry general equilibrium model in which households choose consumpion opimally over an infinie horizon. e begin wih he case in which households in each counry discoun fuure uiliy by he same facor, (where <, and uiliy of aggregae consumpion is logarihmic (implying a uniary

13 ineremporal elasiciy of subsiuion. e examine he model under he assumpion of perfec foresigh.. Equal Discoun Facors, Logarihmic Uiliy In general, if preferences are homoheic, we can wrie a household s oal nominal expendiure on consumpion as i, where is he exac consumer price index, and i is he real consumpion bundle for household i. If we assume ha here are N idenical households in he home counry, hen he oal naional nominal expendiure is, where is he exac consumer price index, and N is he aggregae real consumpion index. e can also use he noaion o be he oal nominal value of oupu in he home counry, ne of invesmen and governmen spending. (e use as he superscrip o denoe value. The corresponding variables for he foreign counry are labelled wih a. The model we examine is one in which only real values are deermined. I is helpful o mainain he noion ha prices are expressed in erms of a currency, because hen he symmery beween he home and foreign counries will be clearer. Bu we should inerpre all nominal prices as being expressed in a common currency, as if hese wo counries were in a currency union. To reierae, his is merely noaional convenience, and has no implicaions for he resuls in he model. e have no assumed ha preferences are idenical beween he home and foreign counry. A household could, for example, have a home bias in consumpion, whereby i gives greaer weigh in preferences o goods produced in is own counry. There could be non-raded goods, so ha only home-counry households consume home-counry non-raded goods, and likewise for foreign households. All ha we require is ha preferences be homoheic, so ha we can define consumpion aggregaes for each household and heir exac price index. e can aggregae across he budge consrain for each household in he home counry o wrie: i K B K. (

14 Here, is he gross nominal ineres rae for period. B is he home counry s nominal claims on he foreign counry a ime (so ha if he home counry is a debor, B is negaive. The Euler equaion for consumpion is given by:. ( Using his equaion and is foreign counerpar, we ge: (3. ( ( In his derivaion we have used he equilibrium condiion ha he oal value of world consumpion is equal o he oal value of world oupu (ne of invesmen and governmen spending in each period. e use he noaion o denoe he value of world oupu a ime. From Equaion (3 i follows ha:. (4 Subsiuing Equaions ( and (4 ino (, we ge: ( K B. (5 Here, is he home counry s share of world ne GD a ime. e can rewrie his equaion slighly, and express nominal consumpion a ime as: [ K ( ( B ]. (6 This is he key equaion of our model. I says ha he consumpion/oupu raio for a counry will depend on he discouned sum of is curren and fuure share of

15 world ne GD, relaive o is curren share. To see his, define he presen value relaionship: Γ ( K. (7 Then we can wrie Equaion (6 as: ( B Γ. (8 (e have used Equaion (4 o subsiue ou for he equilibrium ineres rae. Equaion (8 ells us ha he home counry will end o have a high raio of curren consumpion o oupu when is expeced discouned curren and fuure shares of world ne GD, Γ, is high relaive o is curren share of world ne GD,. The ineres rae does no appear in Equaion (8, since i can be solved for in erms of he growh rae of world oupu (and he discoun facor according o Equaion (4. The relaionship in Equaion (8 could be consisen wih any world growh rae. Tha is, wha maers for he counry s consumpion/oupu raio is is curren and expeced fuure shares of world oupu. The higher is is fuure share of world oupu compared o is curren share, he greaer will be is consumpion/oupu raio. Tha is rue wheher is share of world oupu is rising because is own oupu is rising faser han he res of he world s oupu is rising, or i is falling less quickly han he res of he world s oupu is falling. To see how growh in he share of world income migh maer, consider his simple auoregressive model for he home counry s ne GD share: Then, j j j α ( α. (9 ( α Γ ( α α

16 3 so he discouned sum of he curren and fuure shares, Γ, is a weighed average of he curren share and he long-run seady-sae share,. The more weigh ha individuals pu on he fuure in heir uiliy (larger or he faser he convergence o he seady-sae value (smaller α, hen he greaer he imporance of he longrun oupu share in deermining curren consumpion. To ge o he empirical model ha we will examine in our arnegie-ocheser paper, we use he naional income accouning ideniy, NX, where NX is he home counry s ne expor of goods and services (no including ineres paymens on is deb. e can rewrie Equaion (6 above as: NX B K. ( ( ( The curren accoun is given by A NX ( B. e propose he following approximaion: A NX ( B. Obviously his is no exac, bu how far off is i? Tha is, how close is ( B o ( B? From he soluion for he ineres rae above, we have ha G (, where G is he growh rae of world oupu. Then, G ( B B ( G B. If G, he approximaion would be exac. Bu we believe he difference beween A NX ( B and A NX ( G B is small, so he approximaion is reasonable. ih his approximaion, we can hen rewrie he model as: A K ( ( or z ( K, (3

17 4 where A z. e have derived all of his under perfec foresigh. Now we arbirarily incorporae an expecaions sign in Equaion (3, o ge: [ K] z E. (4 ( If we had derived he model from he beginning under he assumpion of uncerainy, hen Equaion (4 would no hold exacly. So Equaion (4 is no, sricly speaking, derived from he Euler equaion under uncerainy and he res of he model. erhaps fuure work can assess he error involved wih he approximaions used o derive Equaion (4. Equaion (4 implies a relaionship beween a counry s curren accoun relaive o world ne GD ( z and he counry s curren and expeced fuure shares of world ne GD.. Differen Discoun Facors, Logarihmic Uiliy Here we briefly consider how Equaion (4 would look if he discoun facor in each counry were differen. This is a simple way o capure he noion ha some counries which have very good growh prospecs sill end o have high saving raes. Equaions ( and ( sill hold, bu Equaion (3 is replaced by: ( η ( η, ( (5 where η. Then, Equaion (4 is replaced by: ( η ( η. (6

18 5 So we can replace Equaion (6 wih: ( [ ] [ ][ ]. ( ( ( K K η η η η η η η B (7 Bu we can see ha: ( η η η η. (8 Subsiuing ino Equaion (7: ( [ ] [ ]. ( ( ( K K η η η η η B (9 Solving ou for η, we have: K ( ~ ( B, ( where K K ( ( ( ( ( ( ~. Or, for any ime : K ( ~ ( B, ( where K K ( ( ( ( ( ( ~.

19 6 In general, ~ is no consan over ime. I is ineresing, however, o see wha he model implies abou he special case when each counry s share is consan over ime. Then we have: ( ~ ( (. ( ( From Equaion (, i follows in his case (seing ha: ~ ~ B ~ B ( ( (, ( where (. ompared o he case of equal discoun facors (, we can now see ha he home counry s consumpion will be higher if i is less paien (has a lower discoun facor han he res of world. Anoher ineresing case is when he counry s share of world ne GD evolves according o Equaion (9. Alhough he expression for ~ is quie complex, and he closed-form soluion for Equaion ( is no ha inuiive, we can ake a linear approximaion o he soluion around he poin : ~ B ( ( ( ( ( α( ( α ( (, ( ( α ( α (3 where (. To undersand his equaion, begin by noing ha if he share were consan over ime so, hen Equaion (3 would reduce o Equaion (. Also noe ha if he discoun facors were equal, bu he shares were no consan over ime, Equaion (3 would reduce o Equaion (6, wih he soluion for Γ from Equaion ( subsiued in.

20 7.3 Same Discoun Facors, Non-logarihmic Uiliy Le he uiliy funcion each period be given by ( ρ ρ ( (. Then he firsorder condiion becomes: ( ( ρ ρ. (4 In general, we canno derive anyhing excep in he simple case where here is a single homogenous good ha is freely raded and consumed in boh counries. In ha case, we migh as well ake he price as consan. So we can rewrie Equaion (4 as: ( ρ. (5 Adding he equivalen expression for foreign consumpion, and using he world equilibrium condiion, we ge: ρ. (6 The home counry s budge consrain is:. (7 B K K e can use Equaions (5 and (6 o wrie he lef-hand side of Equaion (7 as: K K ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ.

21 8 The discouned sum of GD on he righ-hand side of Equaion (7 can be wrien as: ( ( ( ( K ρ ρ ρ ρ ( ( ( ( ρ ρ ρ ρ K Se iniial deb o zero so ha he expression is easier o look a. Then we can solve Equaion (7 as follows: ρ ρ ρ ( ( ( ρ ρ ρ ( ( ( K K. (8 In his case, iniial consumpion relaive o world income is sill a weighed average of curren and fuure shares of world income. Now he weigh given on our share in period j is given by: j ρ ( j K ρ ρ ρ ( ( ( K. Suppose he growh rae of world income is consan. Then we can rewrie Equaion (8 as simply: ~ ~ ~ ( K. (9 This is idenical o he expression we had in he case of uni ineremporal elasiciy of subsiuion, Equaion (, excep ha he discoun facor,, in Equaion ( is replaced by: ~ ρ G, (3

22 9 ~ where G. Assuming G >, we have < if ρ >. So, if he ineremporal elasiciy of subsiuion is less han one (ha is, ρ >, hen he weigh on fuure shares is lower compared o he model which assumes ha uiliy is logarihmic. hile we are unable o generalise beyond he case of a single homogenous good when he ineremporal rae of subsiuion is no uniy (ha is, uiliy is no logarihmic, we ge he general lesson ha if ρ > and he world growh rae is posiive, hen households effecively discoun fuure shares a a greaer rae han implied simply by he discoun rae in uiliy. 3. eal Exchange ae Model Obsfeld and ogoff (, 4, 5 have argued ha he correcion of he US curren accoun will require a large real depreciaion. I is ineresing o examine wha he evoluion of he real exchange rae would be if he curren accoun defici was opimal, reflecing expecaions of growh in he US s share of world-adjused GD. As in Obsfeld and ogoff, we need o make some specific assumpions abou preferences in order o derive resuls. In each counry, we assume ha preferences are a obb-douglas aggregae over a non-raded consumpion good, and a raded consumpion aggregae: δ δ NT (3 The exac price indices are given by: ( δ ( δ. (3 N T δ N δ δ δ ( δ ( δ T (33 δ δ δ δ ( ( ( δ ( δ N T. (34

23 references over raded goods consumpion are, in urn, a funcion of he consumpion good produced in each counry: ε ε ε ε ε ε ( ε ε T θ H θ F (35 ε ε ε ε ( ε ( ε ε ( ε T θ H θ F. (36 e assume here ha preferences are symmeric, bu ha here is bias oward he consumpion of he good produced locally ( θ > /. rice indices are given by: e have he following demand sysem: ε ε [ θ θ ] ε (37 ( T H F ε ε [ θ θ ] ε ( T H F. (38 H H ε H ( δ θ (39 T N N δ (4 H H ε H ( δ ( θ (4 T N N δ. (4

24 e do no need o wrie down he demand for he foreign-produced raded good. e can ignore ha marke, because by alras s law if he markes for he oher hree goods clear each period and he budge consrains are saisfied, hen he marke for he fourh good will also clear. The equilibrium condiions a ime and in he long run are as follows. e se he price of he foreign-raded good equal o one in each period. e also will consider he simple case in which ne deb a ime is zero. Tha is because, in applying his model o he US o examine how is real exchange rae will evolve, we will use he approximaion ha is curren ne invesmen income is zero: H ε θh δ Γ ε θh θ ε ( Γ θ ( θ H ( ( ε θ H (43 N δ Γ (44 N δ ( Γ. (45 Here we have defined H and N o be he value of he home counry s oupu of raded goods and non-raded goods, respecively, as a share of he value of world oupu. I is helpful o noice from Equaion (44 ha because of he assumpions of uniary ineremporal elasiciy of subsiuion and uniary elasiciy of subsiuion beween non-raded and raded goods, he value of each counry s non-raded oupu as a share of world oupu is consan over ime. e can wrie: N δ Γ, H δ Γ. (46 Now, as in he previous secions, assume a slow increase in he home counry s oupu as a share of world oupu. epeaing Equaions (9 and (: α ( α. (9

25 Then we can wrie: ( α Γ. ( α α e can now use hese equaions o solve for H. Define p H. Given assumpions abou and, we can use Equaion ( o derive Γ, and Equaions (9 and (46 o derive H. Equaion (43 can hen be shown o be a quadraic equaion in, whose soluion is: p ε p Aθ B(θ ± 4 θ θ (θ B Dθ ( θ (θ. (47 The parameers A, B,, and D are defined by: H H H H H A ; B Γ ; Γ ; D. δ δ δ δ δ e can hen derive H by using. ε H p Ulimaely, we are ineresed in calculaing he home real depreciaion over some ime horizon from o T, Q T Q, where Q is he I real exchange rae (defined so ha a home real depreciaion is an increase in Q. Using he definiions of he price indices Equaions (33 and (34, we have: δ δ T N Q. (48 N T Since we are seing F, our soluion for H allows us o solve for T and. T Even hough here is home bias in he consumpion of he raded good, his is no a cause of he price of he home-produced raded good, H, changing over ime. As we noe below, in his model oal consumpion expendiure in boh counries rises

26 3 a he same rae, so he home bias does no pu pressure on eiher raded goods price. Bu if he home counry s share of world oupu is growing, hen oupu of he home-raded good is growing faser han he oupu of he foreign-raded good, so is price mus be falling. ha abou he behaviour of he non-raded prices? If here were no home bias in consumpion of he raded good, any change in he real exchange rae would have o come from movemens in he relaive non-raded prices. Indeed, Obsfeld and ogoff (, 4, 5 emphasise he imporance of he non-raded secor. In our model of consumpion, if he ne facor income a ime is zero, from ime ino he fuure we know ha home and foreign nominal consumpion will grow a he same rae: T T T T. (49 (e are saring in period, and T >. This resul is acually quie general in he neoclassical model. Tha is, he resul is based on he assumpion ha preferences are homoheic and ha he ineremporal rae of subsiuion is he same in he wo counries. This is less specific han he log specificaion ha we have been using and does no require ha preferences are he same in he wo counries. Now under our assumpion ha here is a obb-douglas uiliy funcion defined over raded and non-raded goods we can wrie: NT N NT N NT N NT N, (5 where N is he price of he non-raded good, and N is he oupu of he nonraded good. Now we can see how he price of non-raded goods a home changes relaive o he price of non-raded goods in he foreign counry:

27 4 NT N NT N NT N NT N. (5 The change in our non-raded price relaive o he foreign non-raded price depends only on he growh raes of he non-raded goods. I does no depend a all on he shares of non-raded goods in consumpion. hile our opimising model can poenially explain a curren accoun defici if he counry s share of world oupu is expeced o rise over ime, under he obb- Douglas assumpion, none of ha increase can come because he value of nonraded oupu rises as a share of world oupu. e have noed ha N is consan over ime. The assumpion ha our share of world oupu is rising does no require any assumpion on wheher he home counry s non-raded oupu growh is faser or slower han in he res of he world. e consider wo models for ( ( NT N NT N. The firs is simply an endowmen model, as in Obsfeld and ogoff (4. The second model is one in which oupu is produced using labour, and he growh raes of produciviy in he. raded and non-raded secor deermine ( ( In ha model, oupu of he raded secor in he home counry is given by H AH LH, and in he non-raded secor by N AN ( L LH. Here, A H and represen produciviy, which may grow over ime. These equaions A N incorporae labour marke equilibrium, wih he assumpion ha he labour supply is fixed and equal o L. If labour markes are compeiive, hen we have N H AH A N, or N ( AH AN H. Similarly in he foreign counry, we ge A A. N F e hen have: N F N NT N NT N δ δ δ ( A F / AN T Q. (5 ( AH / AN H T

28 5 On he one hand, we have argued ha if he home counry s oupu of he raded good is growing more quickly han he foreign counry s, hen mus be falling. Tha implies ha he ( δ H erm in Equaion (5 mus be rising. In addiion, if here is home bias in consumpion of raded goods, he ( T H T δ erm is also rising. Boh conribue o a real depreciaion for he home counry. Bu working in he oher direcion is he fac ha he relaive growh in he home counry s raded oupu is coming from produciviy growh in he raded secor. Unless home s relaive growh advanage in he non-raded secor is greaer han is relaive growh advanage in he raded secor, ( A / ( / δ F AN AH AN will be falling. This is he sandard Balassa-Samuelson effec. This laer effec migh well ouweigh he firs wo effecs, so in ne erms he home counry could be experiencing a real appreciaion along he adjusmen pah as is curren accoun defici declines. 4. Model Simulaions 4. urren Accoun e ask wha he consequences are if he US consumer is expecing an increase in he US s share of ne world GD. Specifically, we ask wha he effecs are of an expecaion of an increase from is curren share,, o some larger share,. e assume ha he shares will evolve in an auoregressive fashion, wih α deermining he degree of serial correlaion. In paricular, if α is large (close o one, hen he growh in he GD share will be slow. This model of GD shares is given in Equaion (9. e can use he resul of Equaion ( o subsiue ino Equaion ( and ge: A ( α. (53 α α Noe ha he soluion for he curren accoun o GD raio does no depend on he absolue value of he GD shares, bu only he raio of he long-run o he curren

29 6 GD share. So, he calibraion does no depend on any measure of he US s curren share, bu only on how much is share is expeced o increase. This equaion can be invered o ask wha assumpion abou he long-run increase in he US share of adjused GD could accoun for a curren accoun defici of 6 or 7 per cen of (ne GD. The defici a he beginning of 4 was around 7 per cen. e ge: α A. (54 ( α Following usual calibraion exercises, we will assume he annual discoun facor in uiliy is. 98. If he increase in oupu shares is very gradual, so ha α.95, we find ha in order o have A. 7, we need. 98. Tha is, if he US expecs a gradual per cen (no percenage poins increase in is share of world GD, hen a curren accoun defici of 7 per cen of (ne GD can be opimal. Tha seems like a very large increase in he oupu share, bu i is approximaely he size of he increase he US has experienced over he pas 5 years, according o Figure. If he US share is going o gradually rise by his much, wih an auoregressive coefficien of.95, hen he growh over he nex 5 years in he share would need o be abou 7. per cen. Tha is, if US consumers are expecing he share of US ne GD o grow by 7. per cen over he nex 5 years (wih an evenual cumulaive growh of 9.8 per cen, hen he enire curren accoun defici of he US could be explained by opimal consumpion behaviour, wihou any reference o invesmen spending or governmen spending. Bu Figure only records he US share of adjused G7 GD. I may be less plausible ha he US share would grow as fas if i were compared o world GD. On he oher hand, we have noed ha some of he fases growing counries in he res of he world have high saving raes, so ha heir curren accouns are acually in surplus. If heir saving raes were o remain high, hen he US defici now may be opimal even if he US share of world oupu is no expeced o grow. For example, if we use Equaion ( o assess his possibiliy, hen assuming. 98 bu only a slighly higher level for, he model predics a curren accoun defici

30 7 of 7 per cen of (ne GD. Specifically, we need. 7, which implies a value of.983. If US GD is approximaely per cen of world GD, hen he res of he world s discoun facor would need o equal.986. Tha is, only a small difference beween he US and res of world discoun facor is needed o accoun for a large curren accoun defici. 4. eal Exchange ae Now suppose we ake i as given ha he assumpion ha he long-erm growh in he US share is given by. 98, so ha A. 7 is opimal (wih no difference in discoun facors beween US and foreign households. ha will he evoluion of prices look like in such a model? In addiion o assuming. 98 and α. 95, we need o make assumpions regarding he degree of home bias in consumpion of raded goods, he share of non-raded goods in consumpion, and he elasiciy of subsiuion beween home and foreign goods. e choose hese o be θ. 7, δ. 75 and ε 6, respecively, o mach he assumpions of Obsfeld and ogoff (4. As we have discussed above, he calibraion of he real exchange rae depends on he model ha we use for oupu growh. In he endowmen model, we mus make, he growh rae of he home endowmen an assumpion abou ( ( NT N NT N of he non-raded good compared o he foreign endowmen. Le us suppose ha he horizon for comparison is years we would like o know wha he change in he US real exchange rae will be over he nex years. In an endowmen model, a generous assumpion would be ha he US non-raded share would rise relaive o he foreign non-raded share by per cen in years. Under ha assumpion, he overall real depreciaion for he US in years will be only 5.5 per cen. If insead we ake a model in which facors are mobile beween he secors ha produce raded goods and non-raded goods wihin each counry, hen Equaion (5 deermines he real depreciaion over his period. As we have noed, his model could conclude ha here will be a real appreciaion raher han a real depreciaion for he US. As in he Balassa-Samuelson model, if he US s raded secor is more producive, hen he relaive price of is non-raded goods will rise. orking in he oher direcion are he economic forces ha end o drive he prices

31 8 of US raded goods down relaive o he prices of raded goods in he res of he world. e mus make an assumpion abou he magniude of he change in ( A / A ( A / A : he produciviy of he res of he world s raded secor F N H N relaive o is non-raded secor, compared in urn o he same produciviy raio in he US. e will assume ha he US raded secor shows a per cen improvemen compared o he res of he world over he nex years. Under his assumpion, here is virually no change in he US real exchange rae. The model implies a real appreciaion of.7 per cen over years. So, conrary o he findings of Obsfeld and ogoff (4, if he US curren accoun defici reflecs expecaions of an increase in he US s fuure share of world GD, and if he reducion of he US curren accoun defici occurs as par of an opimal adjusmen pah, hen he required change in he US real exchange rae migh be quie small. 5. onclusions A his sage, our resuls are very preliminary. e have presened a model and provided rough calibraions ha sugges ha here may be some role for an expeced rise in he US share of world GD in explaining he high US curren accoun defici of recen years. e presen plausible scenarios in which modes coninued growh in he US share of world growh could jusify high US exernal borrowing oday. e acknowledge, however, ha here is a grea deal of uncerainy abou he fuure pah of he US share of world oupu. Our forhcoming arnegie-ocheser sudy will examine his model more carefully. I will also esimae a sochasic process for he US share of ne GD, and ask wheher he US curren accoun can be seen as being derived from his opimising model. e will also ake a much longer horizon on he US curren accoun defici and implemen ess much like hose ha Bohn (4 uses o examine he susainabiliy of he US governmen budge deficis.

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