The U.S. Current Account Deficit. and the Expected Share of World Output

Transcription

1 The U.S. Curren Accoun Defici and he Expeced Share of World Oupu Charles Engel Universiy of Wisconsin and NBER John H. Rogers Board of Governors of he Federal Reserve Sysem * Deparmens of Economics and Finance, Universiy of Wisconsin, 1180 Observaory Drive, Madison, WI , USA. cengel@ssc.wisc.edu, and Board of Governors of he Federal Reserve Sysem, Washingon, DC john.h.rogers@frb.gov. This paper was prepared for he Carnegie-Rocheser Conference Series on Public Policy, on he opic of Inernaional Trade and Globalizaion, November 18-19, 005. We have grealy benefied from many discussions wih David Backus, Menzie Chinn, Jaime Marquez and he saff a he Reserve Bank of Ausralia. We especially hank Joong-Shik Kang and Jeffrey Traczynski for excellen research assisance. The views expressed in his paper do no necessarily represen hose of he Board of Governors of he Federal Reserve, or he Federal Reserve Sysem. 1

2 The U.S. Curren Accoun Defici and he Expeced Share of World Oupu Charles Engel and John H. Rogers Absrac We invesigae he possibiliy ha he large curren accoun deficis of he U.S. are he oucome of opimizing behavior. We develop a simple long-run world equilibrium model in which he curren accoun is deermined by he expeced discouned presen value (discouning by he uiliy discoun facor) of is fuure share of world GDP (ne of invesmen and governmen spending) relaive o is curren share of world ne GDP. The model suggess ha under some reasonable assumpions abou fuure U.S. GDP growh relaive o he res of he advanced counries more modes han he growh over he pas 0 years he curren accoun defici is near opimal levels. We hen explore he implicaions for he real exchange rae. Under some plausible assumpions, he model implies lile change in he real exchange rae over he adjusmen pah, hough he conclusion is sensiive o assumpions abou ases and echnology. Then we urn o empirical evidence. A es of curren accoun susainabiliy along he lines of Bohn (005) suggess ha he U.S. is no keeping on a long-run susainable pah. A direc es of our model finds ha he dynamics of he U.S. curren accoun he increasing deficis over he pas decade are difficul o explain under a paricular saisical model (Markov-swiching) of expecaions of fuure U.S. growh. Bu, if we use survey daa on forecased GDP growh in he G7, our very simple model of he curren accoun appears o explain he evoluion of he U.S. curren accoun remarkably well. We conclude ha expecaions of robus performance of he U.S. economy relaive o he res of he advanced counries is a conender hough no he only legiimae conender for explaining he U.S. curren accoun defici. JEL codes: F3, F41

3 Conens 1. Inroducion. The Shares Model of he Curren Accoun.a..b..c..d. Equal Discoun Facors, Log Uiliy Heroic Assumpions Model Simulaions for he U.S. Curren Accoun Power Uiliy or Differen Discoun Facors 3. Real Exchange Rae Model 3.a. 3.b. Model wih Non-Traded Goods and Home Bias Model Simulaions for he U.S. Real Exchange Rae 4. Direc Tes of Curren Accoun Susainabiliy 5. Markov-Swiching Model for Ne GDP Shares 6. Consensus Forecass 7. Conclusion 3

4 1. Inroducion The large U.S. curren accoun deficis in recen 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. 1 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 U.S. 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 U.S. in he shor run. Many sudies pose he quesion of wheher he curren accoun defici is susainable. However, an exac definiion of susainable is elusive. For example, ake he simples smallcounry model of he curren accoun based on ineremporal opimizaion. Assume he counry is growing over ime because of produciviy growh in he radable secor, and ha i faces a consan world ineres rae. The counry will be on a susainable pah meaning i is no violaing is budge consrain and following an opimal pah even hough i runs a curren accoun defici in all periods, is curren accoun defici grows forever, is curren accoun/gdp raio is consan, and is deb/gdp raio rises forever (hough asympoes). This suggess ha here is no obvious shor-cu o deermining wheher a counry s curren accoun defici is leading i ino rouble, or wheher is curren accoun defici is he oucome of opimal decisions. 1 See, for example, Backus e. al. (005), Bernanke (005), Blanchard e. al. (004), Caballero, e. al. (005), Chinn (005), Clarida e. al. (005), Edwards (005), Faruqee, e. al. (005), Gourinchas and Rey (005), Kouparisas (005), Kraay and Venura (005), Obsfeld and Rogoff (000, 004, 005), and Truman (005). These resuls can be derived easily in a small-counry model wih log uiliy of expendiures, and a Cobb-Douglas uiliy over consumpion of raded and non-raded goods, and wih no facor mobiliy. 1

5 Insead of rying o define susainable, we ask wheher here are plausible assumpions under which he U.S. curren accoun defici is consisen wih ineremporal opimizing behavior. This ype of model is probably less useful for examining higher frequency movemens in rade balances, bu we believe i is appropriae for examining he U.S. imbalance since adjusmen is likely o ake place over a long period of ime. Specifically, we underake an exended back-of-he-envelope exercise ha begins by assuming ha households in he U.S. have a relaively high ineremporal elasiciy of subsiuion (uniy). We hen embed he U.S. in a general equilibrium model of he world economy. We derive he simple and inuiive insigh ha he U.S. or any counry opimally will run a curren accoun defici if he sum of is curren and expeced fuure shares of world GDP (ne of invesmen and governmen spending) discouned by households discoun facor in uiliy exceeds is curren share of world ne GDP. Figure 1 plos he evoluion of he U.S. curren accoun over he pas 30 years, as a fracion of GDP and GDP ne of invesmen and governmen spending. We underake a series of calibraion and empirical exercises o assess wheher he U.S. defici (which was abou 7% of ne GDP in 004) can be explained plausibly by opimisic forecass of growh in he U.S. s fuure share of world ne GDP. 3 Figure is he saring poin of our analysis. I shows one of he mos sriking economic developmens of he las 5 years: he dramaic increase in U.S. oupu relaive o he res of he high-income world. Specifically, he char plos U.S. ne GDP as a share of advanced-counry ne GDP. 4 We 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 GDP shares would look very similar. The char also 3 Backus e. al. (005), Caballero e. al. (005), and Faruqee e. al. (005) underake exercises ha have a similar flavor. 4 Advanced counries include he G7 plus Swizerland, Sweden, and Norway.

6 eliminaes he influence of exchange rae swings by comparing real GDP growh relaive o GDP shares in 1990, in a way ha will be explained in greaer deail laer. The sriking hing abou his graph is ha since some ime in he 1980s, he U.S. share appears as if i is on an upward linear rend. Is share has increased from a rough in 198 of around 38% o is level in 004 of approximaely 44%. Prior o 198, i appears ha he U.S. share flucuaes around a level of roughly 38.5%. GDP 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. 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. Our model reworks 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 ne oupu. This represenaion is useful because i expresses he economic forces in a ransparen and inuiive way; and i gives us a way of esing he model ha does no require a measure of equilibrium long-run 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 reduce world ineres raes and hese low raes will discourage saving in he U.S.. In he shares approach, we see direcly ha U.S. 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 U.S.. Anoher nice feaure abou he shares model is ha i applies 3

7 o 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. In assessing wheher he U.S. curren accoun defici is compaible wih a plausible projecion of he U.S. s fuure share of world GDP, we have made a number of heroic assumpions o deermine wha se of counries consiue he res of he world, wha is he appropriae measure of he equilibrium real exchange rae used o calculae GDP shares, ec. We discuss hese assumpions below in deail. We find under a baseline calculaion ha if he U.S. share is expeced o grow anoher 7% (percen, no percenage poins) over he nex 5 years, hen our model implies i is opimal o run a curren accoun defici ha is 7% of ne GDP. In oher words, Figure pus he U.S. share a slighly under 44% a he end of 004. The U.S. defici is hen explained if households expec an increase in he U.S. share o 47% by he end of 09. The implicaion of he U.S. defici for adjusmen of he real exchange rae has drawn a lo of aenion. We examine his by adoping a special case of our shares model. In i, each counry produces a non-raded good and specializes in producion of a raded good. Households consume he raded good produced by he U.S. and he res of he world, bu show a home bias in consumpion. Tha is, U.S. households pu a higher weigh on consumpion of raded goods produced in he U.S. (and symmerically in he res of he world.) The se-up is essenially idenical o ha of Obsfeld and Rogoff (004), wih wo significan deviaions. Firs, hey ask wha are he effecs on he real exchange rae from an exogenous change in spending (or exogenous increase in oupu) ha is sufficien o reduce he U.S. curren accoun defici. In conras, we examine he adjusmen of he real exchange rae along an opimal consumpion pah. Second, hey assume in essence ha facors are immobile beween secors wihin a 4

8 counry. We consider a longer-run framework ha allows for iner-secoral facor mobiliy wihin counries. Our findings are reminiscen of he model of Benigno and Thoenissen (003). If U.S. growh is driven in par by produciviy growh in he raded secor, here will be a endency for he price of U.S. raded goods o fall relaive o he price of foreign-produced raded goods. This is simply a supply effec. Bu his works oward a decline in he U.S. consumer price level relaive o he res of he world (a real depreciaion) because of he home bias in consumpion of radable goods. On he oher hand, as long as radable/non-radable produciviy growh is greaer in he U.S. han in he res of he world, here will be an increase in he relaive price of non-raded goods. This works simply hrough he classical Balassa-Samuelson effec. Pracically speaking, he overall effec on he long-run real exchange rae may be very small, because he Balassa-Samuelson effec and he home-bias effec work in opposie direcions. U.S. growh in recen years has been led by produciviy gains in boh raded and non-raded indusries. In our baseline calculaion, if raded/non-raded produciviy rises by a cumulaive 8% greaer amoun in he U.S. han in he res of he world over he nex 5 years, hen under he scenario in which he U.S. ne GDP share rises by 7%, here will be no change in he U.S. real exchange rae. How plausible are hese simulaions? While Figure is a saring poin, i is almos a sopping poin as well. The problem is comes in choosing a model for he fuure U.S. shares. I looks like he U.S. share is rising along a linear rend in Figure, bu of course ha canno lierally be rue. Given ha he upward rend mus hal, Figure gives no clue a all when i will come o an end, and how. 5

9 We ake a few sabs a empirically assessing he susainabiliy of he U.S. curren accoun defici. One approach is similar o he one Bohn (005) akes o address he susainabiliy of he U.S. governmen budge defici. We ask, in essence, wheher here is evidence ha ne expors rise as he deb/gdp rises. Figure 3 shows ha he answer o his quesion is surely no. This Figure plos he raio of ne exernal deb o GDP and ne expors for he U.S., annually, Afer1930, i is clear ha our deb/gdp raio is rising coninuously. There seems o be no hin, on he oher hand, of an improvemen in ne expors. While he shares model may be able o explain he large curren accoun defici/gdp raio of he U.S. in 004, explaining he dynamics of he U.S. curren accoun defici is much more difficul. The problem is in explaining he increasing defici. The model says ha if a counry expecs is world share of GDP o rise, i will run a large defici iniially, bu is primary rade defici will shrink over ime (as is deb/gdp raio rises.) Tha is no consisen wih Figure 3. A second empirical approach we ake is o esimae he shares model on he U.S. daa in Figure. We model he shares as following a Markov-swiching process beween wo AR(1) regimes. We canno le he daa deermine he mean in he second regime. Fiing an AR(1) o pos-198 daa, we find an auoregressive coefficien greaer han one. The implicaion is he share is explosive. Insead, we impose a mean. We ry various values ha are greaer han he maximum value observed in he daa. The idea is ha maybe Figure is rying o ell us ha he U.S. share is converging pos-198, very slowly, o some high value such as 47%. This model is also no successful in explaining he dynamics of he U.S. curren accoun. The problem is no ha i canno accoun for he level of he defici in 004. The problem is ha he assumpions on fuure growh in U.S. shares ha can explain he level in 004 would imply ha he U.S. defici should have been even larger in earlier years. Even wih Bayesian updaing 6

10 abou he probabiliy ha we have moved from he sae ha prevailed in (in which he mean U.S. share was abou 39%) o he new sae wih he high long-run share ha we impose for he pos-198 daa, our model implies ha he U.S. should have relaively quickly digesed he good news abou fuure U.S. ne GDP shares. The U.S. should have been running big deficis even earlier. Tha finding reflecs he fac ha consumpion is fron-loaded in he neoclassical model. If here is good news abou fuure oupu, he model implies an immediae rise in consumpion. So from he perspecive of he shares model, he puzzle is no so much why he U.S. defici is so large as why has i been rising? We sugges possible reasons for slow adjusmen, and explore one of hose possibiliies ha markes sysemaically underesimaed he poenial for U.S. growh relaive o he res of he world. Here, we use evidence from surveys of economic forecasers. For he period , we can consruc measures of expeced fuure shares of G7 oupu for he U.S. Using hese measures for expecaions, we find ha he shares model does a remarkably good job of explaining he evoluion of he U.S. curren accoun. Of course, i is possible ha somehing else has driven he recen rise in he U.S. curren accoun defici. The obvious alernaive ha has been emphasized in many sudies is he effec of ax cus in he U.S. Our model incorporaes Ricardian equivalence. In our model, ax cus do no reduce naional saving. Bu, indeed, ax cus migh be he explanaion for he pah of he U.S. curren-accoun defici afer 000. Our conclusions secion noes his, and some oher possible facors ha could influence he curren accoun ha are no incorporaed in our model. The ouline of he remainder of he paper is: Secion lays ou he shares model. We explain he assumpions behind our calculaions, and hen simulae he model. Secion 3 7

11 invesigaes he special case of he model described above, wih non-raded and raded secors. We simulae he model o assess possible pahs for he real exchange rae. Secion 4 presens he esimaes of wheher he U.S. is violaing is long-run budge consrain, in he spiri of Bohn (005). In secion 5, we explore he Markov-swiching model for U.S. ne GDP shares. We hen, in secion 6, examine survey daa o ask wheher markes have underesimaed growh in he U.S. share. Finally, secion 7 concludes wih a lis of caveas and mea culpas.. The Shares Model of he Curren Accoun We build a wo-counry general equilibrium model in which households choose consumpion opimally over an infinie horizon. We begin wih he case in which households in each counry discoun fuure uiliy by he same facor, β, and uiliy of aggregae consumpion is logarihmic (implying a uniary ineremporal elasiciy of subsiuion.) We examine he model under he assumpion of perfec foresigh..a Equal Discoun Facors, Log Uiliy We normalize he number of households in each counry o equal one, bu we allow he number of individuals in each household o be differen in he home and foreign counry. If preferences are homoheic, we can wrie a household s oal nominal expendiure on consumpion as PC, where P is he exac consumer price index, and C is he real consumpion bundle for he represenaive household. We have C =, where is per person Nc c V consumpion, and he number of people per household in he home counry. is he oal N nominal value of oupu in he home counry, ne of invesmen and governmen spending. (The superscrip V denoes value.) The corresponding variables for he foreign counry are labeled wih a *. Y 8

12 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 counry 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. We have no assumed ha preferences are idenical beween he home and foreign counry. A household could, for example, have a home bias in consumpion, in which i gives greaer weigh in preferences o goods produced in is own counry. There could be nonraded goods, so ha only home-counry households consume home-counry nonraded 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. We can wrie he budge consrain for each household in he home counry as: PC PC Y Y = V V 1 1 V 1 (1) PC 0 0 R0B0 Y0 R1 RR 1 R1 RR 1 Here, R is he nominal gross 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: P c Pc G = β R. + 1 N+ 1 G is he gross populaion growh rae, G, which we assume is consan. We can hen N wrie he Euler equaion in erms of aggregae consumpion: 9

13 P+ 1C+ 1 () = β R + 1. PC Noe ha equaion () does no depend on he growh rae of populaion. An analogous equaion holds for he foreign counry, even if is populaion growh rae is differen from home s. In oher words, our model allows for differenial populaion growh raes. From equaion () and is foreign counerpar, we ge: (3) W V * V * * * * * ( ) ( V V W Y = Y + Y = P C + P C = βr PC + P C = βr Y + Y ) = βr Y 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.) We use he noaion W Y o denoe he value of world ne oupu a ime. I follows ha (4) R Y =. β W W Y 1 Subsiuing equaions () and (4) ino (1), we ge: 1 1 β W (5) PC 0 0 = R0B0 + Y0 ( γ0 + βγ1+ β γ + ) V Y Here, γ is he home counry s share of world ne GDP a ime. We can slighly rewrie W Y. his equaion, and express nominal consumpion a ime as: (6) Y PC = V (1 β) RB (1 β) γ βγ+ 1 β γ+ γ This equaion says ha he consumpion oupu raio for a counry will depend on he discouned sum of is curren and fuure share of world ne GDP, relaive o is curren share. Tha is, define he presen value relaionship: 10

14 (7) Γ (1 β) γ + βγ+ 1+ β γ + + Then wrie (6) as: PC RB Γ (8) = (1 β ) +. V V Y Y γ Equaion (8) indicaes ha he home counry will have a high raio of curren consumpion o oupu when is expeced discouned curren and fuure share of world ne GDP, Γ, is high relaive o is curren share of world ne GDP, γ. The ineres rae does no appear in equaion (8), because i has been solved ou. The ineres rae a any ime depends on he growh rae of world ne oupu, 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 fuure share of world oupu is compared o is curren share, he greaer is consumpion/oupu raio will be. 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. We derive a curren accoun equaion by using he naional income accouning ideniy, Y PC NX, where NX is he home counry s ne expor of goods and services (no V = + including ineres paymen on is deb.) We can rewrie equaion (6) above as: (9) Y Y NX = RB V V (1 β) (1 β) γ βγ+ 1 β γ+ γ The curren accoun is given by CA = NX + ( R 1) B. We propose he following approximaion: CA (1 ) ( W NX + β RB = NX + R ϒ ) B, where Y ϒ. Tha is, our W W W Y 1 11

15 W approximaion o he curren accoun is smaller han he rue curren accoun by ( ϒ 1) B. (This erm is zero if he world growh rae is zero.) Wih his approximaion, we can hen wrie V Γ (10) CA = Y 1, γ CA = Γ,where z V Y or, zγ γ. We use his relaionship in our simulaions. I is easy o infer from equaion (10) wha he dynamics of curren accoun adjusmen will look like. Consider a counry whose share of world ne GDP is growing. The share canno Γ Γ grow wihou bound. So, if > 1 a some ime, hen a some poin in he fuure, + j γ γ + j mus decline. A counry ha is expecing growh in is fuure share of world ne GDP will run a curren accoun defici oday, bu is curren accoun defici/gdp will decline in he fuure. If he home counry s growh exceeds he growh in he res of he world, ha increases home consumpion immediaely. The home counry borrows from he foreign counry. Over ime, home and foreign consumpion grow a equal raes equal o he growh rae of ne world GDP. We have derived his under perfec foresigh, bu in he daa we look for a relaionship beween he curren accoun and expeced fuure income shares. We simply ake he shor-cu of puing in an expecaion direcly ino (10): (11) zγ = βγ (1 β) E βγ+ 1+ β γ + +. If we had derived he model from he beginning under he assumpion of uncerainy, hen equaion (11) would no hold exacly. So (11) is no, sricly speaking, derived from he Euler equaion under uncerainy and he res of he model. Perhaps fuure work can assess he error involved wih he approximaions used o derive (11). 1

16 Equaion (11) implies a relaionship beween a counry s curren accoun relaive o world ne GDP ( z γ ) and he counry s curren and expeced fuure shares of world ne GDP. We noe ha i is neiher GDP per capia nor some measure of produciviy ha is relevan for his calculaion. Wha maers is aggregae GDP ne of invesmen and governmen spending. The U.S. s GDP has been rising relaive o he res of he advanced counries in par because is workforce has been increasing. Immigraion, a higher birh rae, and more working hours per year all conribue o he rise in he U.S. s share of advanced-counry oupu..b Heroic Assumpions We use his model o assess wheher he very large U.S. curren accoun deficis could poenially be consisen wih plausible expecaions abou he fuure growh in he U.S. s share of world GDP. In boh our simulaions and empirical work, we use oupu shares as measured in Figure as he basis for our comparisons. We view our model as being a long-run equilibrium model, bu we believe ha here are shor- and medium-run flucuaions in key economic variables ha are no capured in our model. Mos imporanly, our model calls for measuring GDP a world prices. Tha is, he U.S. s share of world GDP should be measured as he value of is GDP divided by he value of world GDP, in nominal erms. Bu here are large swings in real exchange raes ha do no represen long-run equilibrium movemens. How do we calculae equilibrium real exchange raes for purposes of calculaing GDP shares? We considered several ways of smoohing he wide swings in U.S. real exchange raes relaive o oher advanced counries: moving averages over 5-year windows, HP-filering, quadraic derending, ec. Ulimaely, none of hese were enirely saisfacory. Wihou filering he real exchange rae a all, he U.S. share shows an upward rend (as Figure does) bu he 13

17 movemens in he U.S. share are dominaed by movemens coming from real exchange rae swings. Bilaeral real exchange raes have swung by 30-, 40-, or 50-percen over spans of wo or hree years. Because he effecs of he real exchange rae swings can be so large in he shor run, he choice of filer also has a large effec on he shor- and medium-run measuremen of shares. Our decision was simply o measure GDP a consan real exchange raes, hus eliminaing all effecs of real exchange rae movemens. Tha is, we assume ha long-run purchasing power pariy holds among advanced counries. We made ha choice in par because here is o some degree consensus ha long-run PPP does hold among hese counries. For example, Rogoff s (1995) well-known survey saes, a long las, a number of recen sudies have weighed in wih fairly persuasive evidence ha real exchange raes end oward purchasing power pariy in he long run (p. 647.) Also, as we have noed, our model of real exchange raes (se ou below in secion 3) acually implies ha under plausible assumpions he equilibrium real exchange rae will no move very much even if he U.S. s GDP share grows significanly. We use 1990 real exchange raes o measure GDP in each counry for all years. In 1990, he U.S. real exchange rae was approximaely a is mean level over he period of our analysis ( ) relaive o he oher 9 counries in our sudy. We hen measure oupu shares using real oupu for each year, convered ino common unis using he 1990 real exchange rae. Our measure of GDP shares should mach he PPP-correced measures, and in fac i does. We use our own calculaions because we can calculae quarerly measures of GDP shares, bu a he annual frequency our measure is nearly idenical o one calculaed from PPP-adjused GDP repored by he World Developmen Indicaor of he World Bank. 14

18 If we were calculaing he U.S. share relaive o a larger number of counries, he U.S. share would no have grown as dramaically (or would have fallen), using a PPP-correced measures of GDP. Bu i would be misleading o conclude ha he U.S. share of world GDP is falling. Wha we need according o he model is he U.S. share of GDP calculaed a equilibrium world prices. We have assumed ha equilibrium real exchange raes are consan. Bu ha is differen from assuming ha equilibrium real exchange raes are consan and equal o uniy for all counries which is he assumpion made in calculaing PPP-adjused GDP measures. While ha assumpion is reasonable when we resric ourselves o advanced counries, i is far from rue when we include low-income counries. The U.S. share of advanced counry GDP was approximaely he same in 1990 wheher one measured GDP using acual real exchange raes or PPP-adjused real exchange raes. The same is no rue of U.S. GDP compared o GDP for lowand middle-income counries. For example, in 004, measured a world prices, he combined GDP of Brazil, China, India, Indonesia, Korea, Mexico, Philippines, and Thailand was.43 imes he GDP of he U.S., when one uses PPP-adjused measures of GDP. Bu a world prices, all of hese counries pu ogeher have a GDP ha is smaller han U.S. GDP. Their GDP is only 74.4% percen of U.S. GDP measured a world prices. Tha is, heir weigh relaive o he U.S. is reduced by a facor greaer han hree if GDP is calculaed a world prices raher han PPP prices. So measures of he evoluion of he U.S. share ha use PPP-adjused GDP for all counries give a misleading picure for our purposes. They grealy inflae he size of GDP for low- and middle-income counries. Since many of hose counries have had GDP growh ha exceeds U.S. growh over he pas 5 years, i may appear from hese measures ha he U.S. share is falling or growing very lile. Bu if hose counries receive weighs ha are 15

19 commensurae wih heir size measured a world prices, he growh in he U.S. share would look sronger. Our measure of advanced counry GDP is he sum of GDP for he U.S., he res of he G7, plus Swizerland, Sweden, and Norway. Adding oher advanced counries, such as Ausralia or smaller European counries, would no aler he picure of Figure. Bu why do we no include he larger emerging markes? Why, especially, do we no include China and he emerging economies of Eas Asia ha have experienced rapid growh? Even subjec o he cavea ha he relevan measure of hese counries GDP would be smaller han PPP-adjused measures, including hem would sill make he increase in he U.S. share less dramaic han Figure depics. These rapidly growing counries should really be he big borrowers on world markes, and hey should show curren accoun deficis according o our model. Clearly our model is wrong if we ry o use i o assess Eas Asian curren accouns. Bu given ha i is wrong for Eas Asia, we need o make some adjusmen in applying he model o he U.S. For some reason, here is a saving glu in hese emerging markes. Bernanke (004) advances several hypoheses for his glu including he noion ha hese counries are building up a nes egg o use in he even of anoher financial crisis. They are running curren accoun surpluses, adding o world saving ne of invesmen. We choose o omi hese counries from our analysis. We rea hem as if hey are neiher conribuing o nor drawing from he world pool of ne saving. This assumpion ends o weaken he case ha he U.S. curren accoun defici can be jusified from an ineremporal opimizing sandpoin. If we modeled he conribuion of Eas Asian emerging economies o ne world saving, he effec would be o lower world real ineres raes and increase borrowing in he res of 16

20 he world. The U.S. for one has a greaer incenive o borrow oday because of his glu of saving from he emerging marke counries. One migh argue ha we are ignoring precauionary saving. Even hough hese emerging markes are saving oday, perhaps he U.S. should be more cauious in aking advanage of low world ineres raes. If he glu of saving disappeared if he Eas Asian counries began acing more like our model says hey should hen he U.S. migh be forced o rapidly reduce is borrowing. The adjusmen process could be painful. In ligh of his possibiliy, he U.S. should reduce heir borrowing oday. I is difficul o model his effec, and we do no ry. We will reurn o his poin in our conclusions secion. Our model assumes ha all borrowing and lending akes place a he same ineres rae. In fac, he U.S. apparenly earns a higher reurn on is foreign invesmens han i pays o foreigners who inves in he U.S. Figure 4 plos he decline in he U.S. exernal ne asse posiion since 198. Alhough here are serious and well-known measuremen issues, he char reproduces he convenional wisdom ha he U.S. has emerged as a large debor. Bu Figure 5 shows he U.S. ne invesmen income as a share of GDP. Tha also has declined since 198, which is consonan wih he decline in he U.S. 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 U.S. ne invesmen income in 004 was sill posiive. Gourinchas and Rey (004) and Lane and Milesi-Ferrei (004) offer analyses of his phenomena. There are wo reasons for he discrepancy in reurns. Firs, he U.S. exernal porfolio is more heavily weighed oward direc foreign invesmen and equiies, while foreigners porfolio of U.S. asses is dominaed by holdings of Treasury securiies. Tha is, U.S. invesors buy riskier asses ha have higher average reurns. Even wihin classes of asses, he 17

21 U.S. earns a higher expeced reurn on is foreign invesmens, and Gourinchas and Rey noe ha his acually accouns for more han half he difference in he raes of reurn on he porfolios. Whaever he reason, if he U.S. can always earn more on is foreign invesmens han foreigners earn on heir invesmens in he U.S., hen even a primary defici could be susained forever. We do no consider he effecs of he acual reurn differenial when we assess wheher he U.S. curren accoun is susainable ha is, wheher i could be consisen wih ineremporal opimizing behavior..c Model Simulaions for he U.S. Curren Accoun According o equaion (11), he curren accoun depends on he curren share of world GDP, γ, compared o he expeced discouned sum of curren and fuure share of world GDP, Γ. We consider his simple auoregressive model for he home counry s ne GDP share: j j (1) γ + j = αγ + (1 α) γ Then (13) 1 β β(1 α) Γ = γ + γ, 1 αβ 1 αβ so he discouned sum of he curren and fuure shares is a weighed average of he curren share and he long-run seady-sae share, γ. The more weigh ha individuals pu on he fuure in heir uiliy (larger β ) or he faser he convergence o he seady-sae value (smaller α ), hen he greaer he imporance of he long-run oupu share in deermining curren consumpion. Subsiuing his expression ino equaion (10), we ge (14) CA Y V 1 β β(1 α) γ = αβ 1 αβ γ 18

22 Noe ha he soluion for he curren accoun o GDP raio does no depend on he absolue value of he GDP shares, bu only he raio of he long-run o curren GDP share. So, he calibraion does no depend on any measure of he U.S. 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 U.S. share of adjused GDP could accoun for a curren accoun/ ne GDP raio of -.06 or The raio a he beginning of 004 was approximaely We ge: (15) γ 1 αβ CA = 1 V γ β(1 α) Y. Following usual calibraions, we will assume he annual discoun facor in uiliy is β = If he increase in oupu shares is very gradual, so ha α = 0.95, we find ha in order o have CA Y V γ =.07, we need γ =. Tha is, if he U.S. expecs a gradual 10% (no 10 percenage poin) increase in is share of world GDP, hen a curren accoun o ne GDP raio of -7% can be opimal. Tha seems like a very large increase, bu i is approximaely he size of he increase he U.S. has experienced over he pas 0 years, according o Figure. If he U.S. share is going o gradually rise by his much, wih an auoregressive coefficien of 0.95, hen he growh over he nex 5 years in he share would need o be abou 7.1%. Tha is, he curren accoun/gdp raio of -.07 is consisen wih expecaions ha he share of U.S. ne GDP will grow by 7.1% over he nex 5 years (wih an evenual cumulaive growh of 9.8%). In erms of he shares calculaed in Figure, his ranslaes ino an expeced increase in he U.S. share from is curren level of 44% o around 47% in 5 years. 19

23 If he adjusmen were much slower han in his baseline simulaion, so ha α = 0.98 CA (raher han α = 0.95), hen in order for he shares model o explain =.07, markes would V Y γ have o be expecing a larger evenual increase in he U.S. share: γ =. Bu because his implies slower adjusmen, he implicaion is ha he growh in he U.S. share over he nex 5 years is only 5.6% (i.e., from 44% o 46.5%.) Alernaively, if he adjusmen were much faser α = 0.75 hen in order o explain a curren accoun/ne GDP raio of -.07, he U.S. share would need o grow 7.6% in he long run. Bu essenially all of ha share growh would occur over he nex 5 years, meaning he U.S. share in Figure would rise from 44% o 47.3%. None of hese scenarios seems wildly implausible. Equaion (10) is based on an approximaion ha measures he curren accoun as W CA NX + ( R ϒ ) B, when really CA = NX + ( R 1) B. The discrepancy beween our W measure and he rue measure ( ϒ 1) B. According o he model, ( ϒ 1) B < ( R 1) B. We ignore he discrepancy because Figure 5 indicaes ha he ne facor paymens for he U.S. are nearly zero, bu slighly posiive. Tha is, even hough B < 0, ( R 1) B is slighly posiive W for he U.S. So we are no enirely sure wha he bes way is o rea he erm ( ϒ 1) B which is lef ou of equaion (10). We could rea i as a small posiive number, less han he ne facor paymens of he U.S. Or we can do he calculaion ha is mos unfavorable for he hypohesis ha he curren accoun defici in 004 can be explained by he shares model: From Gourinchas and Rey (005), he deb/gdp raio for he U.S. in 004 was approximaely 6%. Given ha ne GDP/oal GDP in he U.S. in 004 was abou 6%, we have v B / Y Then, aking a 0

24 W world growh rae of %, we conclude ( ϒ 1 ) B Tha is, he curren accoun/ne GDP raio we need o explain is no -0.07, bu raher In ha case, under he baseline parameers ( β = 0.98, α = 0.95), he required value for γ γ is In urn, ha implies ha he U.S. share would need o rise 8.0% over he nex 5 years (from 44% o 47.5%) for he curren accoun defici o be opimal under he shares model. Nex we urn briefly o versions of he model wih consan ineremporal elasiciy of subsiuion (differen from one), and also explore he consequences of differen discoun facors in he home and foreign counry..d Power Uiliy or Differen Discoun Facors The simple model wih log uiliy of aggregae consumpion allows us o derive a simple expression for he curren accoun in erms of curren and expeced fuure shares of ne GDP, while allowing us o assume ha preferences in each counry are general homoheic funcions over all goods (raded or non-raded), and allowing for consan populaion growh ha can be differen in he home and foreign counry. I is ineresing o ge a feel for how he assumpion of log uiliy affecs our calculaions, however. We can derive an equally simple expression for he curren accoun, bu under more resricive assumpions on he srucure of he model. In paricular, we will assume ha here is a single raded good ha is consumed in each counry, and ha he populaion in each counry is consan. 1 C 1 υ Le he uiliy funcion each period be given by ( ) 1 condiion becomes: (16) ( C ) υ β R ( C ) υ =. υ. Then he firs-order 1

25 where R + 1 is he ineres rae in unis of he single good. Wih a lile work, we can derive an expression for he equilibrium world ineres rae: (17) R + 1 υ W 1 Y 1 = β + W, Y where now W Y is world oupu (in real erms, raher han in nominal erms.) Following seps similar o hose in he log-uiliy model, we can derive ha consumpion relaive o world income is a weighed sum of curren and fuure shares of world income: W υ W υ W ( ) + 1( + 1) + ( + ) W 1 υ W 1 υ W 1 υ ( ) + β( + 1) + β ( + ) υ C RB + γ Y + βγ Y + β γ Y = W Y Y Y Y bu he weighs depend on world GDP in each period. +, Suppose he growh rae of world GDP is consan, equal o W ϒ. Then, from (17), he gross world ineres rae is consan, and is given by 1 W υ R = β ( ϒ ). In his case, we can easily derive an expression for he curren accoun analogous o equaion (10): V Γ (18) CA = Y 1. γ Here, Γ is also a discouned sum of curren and fuure shares of world ne GDP 5 : Γ (1 β) γ + βγ+ 1+ β γ + +, bu he discoun facor is modified: W 1 υ. β β( ϒ ) Comparing (18) o (10), we see ha he effec of allowing power uiliy is o aler he weigh on fuure shares of ne world GDP. Log uiliy is he special case of υ = 1. There is no 5 Equaion (18) is derived using he same approximaion as equaion (10). Tha is, we se ( 1 B = 0 ϒ W )

26 consensus on he rue measure of υ, and he model of consumpion based on power uiliy and ime-separable preferences is known o be inadequae. Sill, he model is widely applied, and he consensus in applicaion is o se υ > 1. Tha lowers he weigh on fuure ne GDP shares in he calculaion of he discouned sum. Therefore, expeced fuure GDP growh has less influence on he curren accoun. In choosing parameers for a reasonable calibraion, we noe ha he real ineres rae W from (17) is given by R =ϒ / β. In he previous sub-secion, he baseline calibraion chose β = Tha specificaion did no require any assumpions abou he world growh rae of GDP in order o calculae he implied curren accoun. Bu if we had chosen, for example, W ϒ = 1.0, hen under log uiliy, he implied world ineres rae is 4% ( R = 1.04.) W Suppose ha we coninue o assume β = 0.98, and ϒ = 1.0, bu le υ =. The implied real ineres rae is hen a bi high, R = Under his se of parameers, we find β = We use equaion (1) o model he evoluion of oupu shares, and se α = In CA order for he model o accoun for =.07, we now need ha he long-run ne GDP share V Y γ grow by almos 13%, 1.17 γ =. The growh over he nex 5 years in he share would need o be abou 9.%. Wih reference o he shares calculaed in Figure, his implies an expeced increase in he U.S. share from is curren level of 44% o around 48% in 5 years. Larger values for υ would imply ha an even greaer growh rae of GDP shares is required in order o explain a curren accoun/ne GDP raio of However, as we increase υ, he implied value of he world real ineres rae also rises. We can simulaneously increase υ 3

27 and increase β o keep he real ineres rae around 6%, bu hen he implicaions for he W required growh rae of U.S. shares does no change, since R =ϒ / β. As we have noed, Figure records he U.S. share of GDP of a se of 10 advanced counries. I may be less plausible ha he U.S. share would grow as fas if i were compared o world GDP. 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 posiive. If heir saving raes were o remain high, hen he U.S. defici now may be opimal even if he U.S. share of world oupu will no grow. Suppose ha he U.S. share of world GDP is consan over ime, bu he U.S. discoun * facor, β, is differen han he discoun facor in he res of he world, β. Revering o he model wih log uiliy over expendiures, wih a lile algebra we find 6 (19) CA Y v W β β =, W 1 β where W * + (1 ), and γ is he U.S. s (consan) share of world ne GDP. The model β γβ γ β W β β predics a curren accoun o adjused GDP of -.07 when =.07 W 1 β. If β = 0.98, he W implied value of β is If he U.S. GDP is approximaely 0 percen of world GDP, hen he res of he world s discoun facor would need o equal A small difference beween he U.S. and res of world discoun facor can accoun for a large curren accoun defici. 6 See Engel (005) for deails on his and some of he oher derivaions. Equaion (19) makes an approximaion similar o hose in earlier equaions, β R = 1, where 1 (1 )(1 *)/(1 W β β β β ). 4

28 3. Real Exchange Rae Model Obsfeld and Rogoff (000a, 004, 005) have argued ha he correcion of he U.S. 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 U.S. s share of world adjused GDP. As in Obsfeld and Rogoff, we need o make some specific assumpions abou preferences in order o derive resuls. 3.a. Model wih Non-Traded Goods and Home Bias In each counry, we assume preferences are a Cobb-Douglas aggregae over a nonraded consumpion good, and a raded consumpion aggregae: (0) C =, * ( * δ C C ) ( C * ) 1 C C δ 1 N T N T δ =. The exac price indexes are given by: * * δ * = ) P ( P ) ( P ) (1) P P δ P δ ( δ δ (1 δ) δ, N T δ = ( δ (1 δ) N T Preferences over raded goods consumpion, in urn, are a funcion of he consumpion good produced in each counry: δ δ 1 ). () ε 1 ε 1 1 ε 1 ε 1 ε ε ε ε T = θ H + (1 θ) F C C C, ε 1 ε 1 1 ε 1 1 * * * ε ε ε ε ε T = (1 θ) ( H ) + θ ( F ) C C C. We assume here ha preferences are symmeric, bu ha here is bias oward he consumpion of he good produced locally ( θ > 1/). This maches he assumpion in Obsfeld and Rogoff (004, 005), and Benigno and Thoenissen (003). Price indexes are given by: (3) 1 1 ε 1 (1 ) ε 1 T = θ H + θ F ε P P P, 1 * 1 1 (1 ) ε ε 1 T = θ H + θ F ε P P P. We have he following demand sysem: 5

29 (4) PC P H = (1 δθ ) PT 1 ε PC H H = (5) PC N N δ PC (6) (7) PC P H = (1 δ)(1 θ) 1 ε PC * * * * H H * PT PC = δ PC. * * * * N N Using Walras Law, we do no need o wrie down he demand for he foreign-produced raded good. We will assume ne deb service a ime is equal o zero. Tha is because, in applying his model o he U.S. o examine how is real exchange rae will evolve going forward from 004, we will use he approximaion ha is curren deb service is approximaely zero in 004. (In he calculaions below, period is defined as he period in which ne deb service is zero.) In PC ha case, equaion (8) gives us W Y = Γ. Bu hen, combining equaions () and (4), we see ha PC Y P C = +, for all j 0. Tha allow us o conclude ha + j j W W Y+ j P C + j + j W Y+ j =Γ, for all j 0. We se he price of he foreign raded good equal o one in each period ( P + = we derive he equilibrium condiions: F, j 1.) Then (8) γ 1 ε 1 ε θp (1 θ) P = (1 δ) Γ + (1 Γ ). θph, + j+ 1 θ (1 θ) PH, + j+ θ H, + j H, + j H, + j 1 ε 1 ε (9) γ N, + j = δγ. (30) * γn, + j= δ(1 Γ). 6

30 Here we define γ and H, + j, γ N + j o be he value of he home counry s oupu of raded goods, and nonraded goods respecively, as a share of he value of world oupu. I is helpful o noice from (9) ha because of he assumpions of uniary ineremporal elasiciy of subsiuion and uniary elasiciy of subsiuion beween nonraded and raded goods, he value of each counry s nonraded oupu as a share of world oupu is consan over ime. We can wrie γ N = δγ, and γ H, + j γ+ j δ = Γ. The quesion we answer here is, if he U.S. curren accoun is explained by he shares model, hen under he baseline calibraion of secion.c, wha are he implicaions for he evoluion of he U.S. real exchange rae? So, assume he U.S. ne GDP shares evolve as in equaions (1) and (13) above (repeaed here for convenience): j j (1) γ + j = αγ + (1 α) γ, (13) 1 β β(1 α) Γ = γ + γ. 1 αβ 1 αβ We can now use hese equaions o solve for P H, + j. Define p 1 j P ε + H, + j =. Given assumpions abou γ and γ, we can use (13) o derive Then wrie equaion (8) is a quadraic equaion in p + j Γ, and (11) and (9) o derive H, j, whose soluion is: γ +. (31) p + j = 4 Aθ + B(θ 1) ± θ + Cθ (θ 1) + B (θ 1) Dθ(1 θ) The parameers A, B, C, and D are defined by: γ A = 1 1 δ H, + j ; = +Γ H, j B γ + 1 δ 0 1 ; γ γ C = Γ + 1 δ 1 δ H, + j H, + j 0(1 ) 1 ; γ D = 1 δ H, + j ( 1). We can hen derive P H, + j by using P 1 1 H, + j p+ j ε =. 7

31 To summarize his secion so far, we find ha we can infer he behavior of he erms of rade given assumpions abou he evoluion of he home counry s share of world ne GDP. The home counry s erms of rade he price of is expors relaive o is impors is given by P H, + j, since he price of foreign raded goods is he numeraire. The reason ha we can infer he erms of rade only from knowing he pah of shares of GDP can be seen from equaion (8). The righ-hand-side of he equaion shows ha oal world demand for he home raded good as a fracion of oal world oupu depends only on Γ and H, j P +. Demand depends only on hese variables because oal home consumpion spending a ime +j as a fracion of he value of world oupu a ime +j, is consan over ime and deermined by Γ. The preference srucure gives us ha demand for he home raded good in each counry depends only on P H, + j and oal consumpion spending in each counry. The lef-hand-side of equaion (8) is he value of oupu of he home raded goods as a funcion of he value of oal world oupu. Bu we have already seen ha he assumpion of log preferences over oal expendiures, and Cobb-Douglas uiliy over consumpion of non-raded goods and he raded goods aggregae gives us γ H, + j = γ+ j δγ. So, once we make assumpions abou he evoluion of γ + j, we can derive Γ and γ and hen use equaion (8) o solve for H, + j P H, + j. Ulimaely, we are ineresed in calculaing Q + j Q, where Q * P is he C.P.I. real P exchange rae (defined so ha a home real depreciaion is an increase in Q ), over some ime horizon from o +j. Using he definiions of he price indexes in (1), we have (3) Q δ * * N PT P = P P N T 1 δ. 8

32 Since we are seing P = 1, our soluion for F * P allows us o solve for P and P. Bu we sill H T T need o solve for he pahs of prices of non-raded goods in each counry. We consider a model in which oupu is produced using labor, and labor is mobile beween he raded and non-raded secor in each counry. Oupu of he raded secor in he home counry is given by YH = AHLH, and in he nonraded secor by YN = AN ( L LH ). (We are now considering a model wih no populaion growh.) Here, A H and A N represen produciviy, which may grow over ime. These equaions incorporae labor marke equilibrium, wih he assumpion ha he labor supply is fixed and equal o L. If labor markes are compeiive, hen we have P P N H = A A H N AH, or PN = P H. Similarly in he foreign counry, we ge A N P P A = =. * * N * F P * N * F AN We hen have (33) Q * * δ δ * 1 δ F N T ( A / A ) 1 P = ( A / A ) P P H N H T. 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 P H mus be falling. Tha implies ha he erm in equaion (33) mus be rising. In addiion, if here is home bias in consumpion of raded 1 P H δ goods, he P P * T T 1 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 nonraded secor is greaer han is relaive growh advanage in 9

33 δ * * ( AF / A ) N he raded secor, ( AH / AN ) will be falling. This is he sandard Balassa-Samuelson effec. This laer effec migh well ouweigh he firs wo effecs, so on ne home could be experiencing a real appreciaion along he adjusmen pah as is curren accoun defici declines. Before urning o numerical assessmens of he required change in he real exchange rae, i may be helpful o review wha we have done in his secion. Raher han beginning from assumpions on he growh of produciviy in each of four secors (raded and non-raded in each counry), we have aken a slighly differen ack o inferring real exchange rae behavior. We have found ha if we make assumpions on he evoluion of GDP shares, and on relaive produciviy wihin each counry ( A / A and H N A / A ), we can infer he pah of he real * * F N exchange rae. In essence, we make an assumpion on he pah of an endogenous variable ( γ ) * insead of on an exogenous variable ( A A ) o solve for he real exchange rae. H, / F, 3.b Model Simulaions for he U.S. Real Exchange Rae Now suppose we ake as inpu he assumpion ha he long-erm growh in he U.S. share γ CA is given by = 1.098, so ha he 5-year growh in he U.S. share is 7.1%, and =.07 is V γ Y opimal. Wha will he evoluion of prices look like in such a model? In addiion o assuming β = 0.98 and α = 0.95, we need o make assumpions on he degree of home bias in consumpion of raded goods, he share of nonraded goods in consumpion, and he elasiciy of subsiuion beween home and foreign goods. We choose hese o be θ = 0.7, δ = 0.75, and ε = 6, respecively, o mach he assumpions of Obsfeld and Rogoff (000a, 00b, 004), hough we discuss he choice of ε in greaer deail below. 30