Journal of Internatonal Economcs 79 (009) 31 41 Contents lsts avalable at ScenceDrect Journal of Internatonal Economcs journal homepage: www.elsever.com/locate/je Composton and growth effects of the current account: A syntheszed portfolo vew Ka Guo 1, Keyu Jn Department of Economcs, Harvard Unversty, Unted States artcle nfo abstract Artcle hstory: Receved 1 September 007 Receved n revsed form 5 February 009 Accepted 5 March 009 Keywords: Current account Portfolo vew Valuaton effects Composton effects Growth effects hs paper analyzes a useful accountng framework that breaks down the current account to two components: a composton effect and a growth effect. We show that past emprcal evdence, whch strongly supports the growth effect as the man drver of current account dynamcs, s msconceved. he remarkable emprcal success of the growth effect s drven by the domnance of the cross-sectonal varaton, whch, under condtons met by the data, s generated by an accountng approxmaton. In contrast to prevous fndngs that the portfolo share of net foregn assets to total assets s constant n a country, both our theoretcal and emprcal results support a hghly persstent process or a unt-root process, wth some countres dsplayng a trend. Fnally, we reestablsh the composton effect as the quanttatvely domnant drvng force of current account dynamcs n the past data. 009 Elsever B.V. All rghts reserved. JEL classfcaton: F1 F3 F41 1. Introducton he U.S.'s wdenng current account defct over the past decade and the growng current account mbalances have become a subject of vast nterest. Alongsde these recent experences of global mbalances s an exploson of nternatonal fnancal asset trade among an expandng group of economes. 3 Wth the ncreasng leverage n natonal portfolos and the potentally huge wealth transfers assocated wth alteratons of the portfolo allocaton, concepts of external We thank Kenneth Rogoff for hs gudance and encouragement over the entre process of ths research. We are grateful to Robert Barro, Rchard Cooper, Graham Ellott, L Han, Elhanan Helpman, Rustam Ibragmov, Dale Jorgenson, Konstantn Styrn, Aleh syvnsk, Erc van Wncoop, and Harvard Internatonal Economcs Workshop, Macroeconomcs, and Econometrcs Workshop partcpants for helpful comments. We thank Florent Ségonne for certan techncal support. Any remanng errors are the responsblty of the authors. Correspondng author. el.: +1 617 817 8903. E-mal addresses: kaguo@post.harvard.edu (K. Guo), kjn@fas.harvard.edu (K. Jn). 1 el.: +1 0 80 3676. he share of U.S. current account defcts n GDP reached an unprecedented hgh of 6.4% n the year of 005 and remans at a hgh level. 3 For ndustral countres, the sum of the stock of foregn assets and foregn labltes relatve to GDP has ncreased by a factor of 7, from 45% to 300% over the perod of 1970 004. For developng countres, t has ncreased from around 40% to 150% over the same perod (Lane and Mles-Ferret, 007). adjustment and external mbalances are no longer adequate wthout reference to the structure of natonal portfolos, accordng to Obstfeld (004), among many others. he recent surge n the lterature on portfolo models of the current account reflects these new trends n global fnance. One of the frst that marked the recent emergence n portfolo models s the partal-equlbrum approach of Kraay and Ventura (000, 003). Accordng to ther theory, nternatonal captal flows, or the current account, s caused by portfolo growth through changes n wealth. Countres nvest the margnal unt of wealth as the average unt, or n other words, portfolo shares (net foregn assets to total assets) are constant, and the current account s smply equal to the changes n wealth tmes the portfolo share. Most recently, the works of Devereux and Sutherland (006a,b,c) and lle and Van Wncoop (008) explctly model portfolo choce for both gross and net nternatonal captal flows, takng nto account the general equlbrum effects of portfolo choce on external adjustment. Whle ther emphass s methodologcal 4, they make the mportant pont that nternatonal captal flows n ther framework can be broken down nto a component assocated wth portfolo 4 hey develop a method for solvng dynamc stochastc general equlbrum openeconomy models wth portfolo choce that can be mplemented both n a complete market settng and an ncomplete market settng. 00-1996/$ see front matter 009 Elsever B.V. All rghts reserved. do:10.1016/j.jnteco.009.03.003
3 K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 growth through savngs and a component assocated wth the optmal reallocaton of portfolo as a result of changes n expected rsk and returns of varous assets. her models also ncorporate valuaton effects, whch have been at the heart of emprcal research on external adjustments, notably Lane and Mles-Ferrett (006), Gournchas and Rey (007), and lle (008). In ths paper, the frst objectve s to show that most of the recent lterature on the current account can be nested nto a non-structural, accountng framework. he accountng framework decomposes the current account nto two factors that are synonymous to the portfolo growth and portfolo reallocaton breakdown emphaszed n the general equlbrum model of lle and Van Wncoop (008). We call these two effects a composton effect and a growth effect. he composton effect s lke a substtuton effect, and refers to the reallocaton of the portfolo towards or away from foregn assets. It s manfested n changes to the portfolo share (share of net foregn assets n total assets). he growth effect s smlar to an ncome effect, and refers to changes n the budget set, or total wealth, that leads to correspondng proportonal changes n both assets and labltes. he framework can also ncorporate valuaton effects and captal gans and losses and ther mpact on the current account. hs non-structural, syntheszed framework, despte ts smplcty, can be very useful as a framework n nestng, and emprcally assessng, varous theores of the current account wthout needng to mpose more structure on the model. hs framework, along wth the general equlbrum models, demonstrates the theoretcal mportance of both the composton effect and the growth effect n accountng for external adjustments. Yet, the Kraay and Ventura (000) theory put forth the growth effect as the source of long-run current account movements. Other theores of the current account, albet not based on portfolo choce models, such as Blanchard et al. (005), Caballero et al. (008), essentally post that the composton effect s the man drver of current account movements. hese three dfferent vews of the current account naturally call for an emprcal nvestgaton on whch factor, f not both, s more quanttatvely relevant. Whle there s stll a dearth n the emprcal assessment of these portfolo choce models, the closest related emprcal work s that of Kraay and Ventura (000, 003). Based on ther vew that portfolo shares are fxed n the long run and current account changes are brought about by changes n wealth, they run a fxed-portfolo regresson to test the theory, and fnd overwhelmng support for the growth-effect theory. 5 Consequentally, t appears that the growth effect s suffcent for descrbng the real-world dynamcs of external adjustment, leavng the composton effect hghlghted by general equlbrum models only as a theoretcal plausblty. he need for more concrete emprcal assessment of these theores leads to the paper's second objectve, whch s to use hstorcal OECD data to emprcally assess the relatve mportance of the composton effect and the growth effect. wo results emerge: frst, we overturn the Kraay Ventura concluson that changes to the current account are explaned by the growth effect, by theoretcally showng that the surprsng result of ther fxed-portfolo cross-country regresson s the outcome of a concdence, whereby an omtted varable bas s concealed by the case of a short tme seres. Furthermore, because the ntal values of net foregn assets are small relatve to the subsequent flows n the data sample, the cross-sectonal varaton s generated only by an accountng approxmaton and therefore contans lmted nformatonal content. Second, we fnd that the portfolo share s consstent wth followng a hghly persstent process, wth some countres dsplayng a determnstc trend, drectly n opposton to the earler clams that the portfolo share s constant. hese fndngs suggest that the exstng emprcal work can be very msleadng n ascrbng the growth effect as the man explanaton for 5 Kraay and Ventura (003) show emprcally that the rule that portfolo shares are constant does not hold well n the short run, but s rather a good descrpton of the data n the long run. nternatonal captal flows. By overturnng the Kraay Ventura result, together wth a varance decomposton of the current account, we are able to establsh the composton effect as the man drver of external adjustment dynamcs, and that the growth effect, whle theoretcally plausble, s quanttatvely nsgnfcant. he paper s organzed as follows. In Secton we derve an accountng framework that exposts dfferent possble channels through whch current account adjustments can occur, and nest the recent current account lterature nto ths framework. Secton 3 gves a theoretcal exposton of the problem of the fxed-portfolo crosscountry regresson results, and Secton 4 undertakes the emprcal analyses. Secton 5 concludes the paper.. he framework.1. heoretcal dervaton In ths secton, we derve an accountng framework of the current account that can nest the myrad of dfferent vews on external mbalances recently put forth n the lterature. hs framework, although non-structural, can emprcally evaluate structural models of the current account such as Kraay and Ventura (000, 003), Blanchard et al. (005), and Caballero et al. (008), and nonstructural models such as Gournchas and Rey (007), at the same tme gvng certan theoretcal predctons related to the current account. In dervng the framework, we frst begn wth an accountng dentty. Defne wealth, W=K+NFA, where W s total wealth, K s the domestc captal stock and NFA s the net foregn asset poston. Defne x as the share of net foregn assets n total wealth. herefore, NFA = x W: akng a total dfferentaton of ths equaton yelds the followng: ΔNFA = Δx W + x ΔW: Here, ΔNFA s the change n net foregn assets, Δx s the change n the portfolo share of net foregn assets, and ΔW s the change n the total wealth, whch we call savngs (explaned below). By defnton, the change n net foregn assets ΔNFA s just the current account CA. hs gves us the followng equaton: CA = Δx W + x S: Eq. (3) leads to an accountng framework that attrbutes the current account balance to the sum of two effects: the effect of a change n the portfolo share, x, what we call the composton effect, and the effect of a change n wealth, whch s n our termnology the growth effect. 6 On one sde of the current account lterature, Blanchard et al. (005), Caballero et al. (008) and part of Cooper (005) argue that current account changes reflect changes n x, the composton effect. 7 Accordng to Eq. (3), ths means that CA=Δx W. On another sde, 6 hese two effects are tantamount to the portfolo growth effect and portfolo reallocaton effect n the general equlbrum model of lle and Van Wncoop (008). 7 Blanchard et al. (005) attrbute the large U.S. current account defct to exogenous shocks to asset preferences, n partcular, a permanent ncrease n demand for U.S. assets. Caballero et al. (008) explan the rse n the share of U.S. assets n the global portfolo and the subsequent large current account defcts by the slow growth condton n Europe relatve to the U.S. and the nablty of Asan fnancal markets to generate suffcent fnancal assets to cope wth ther good growth condtons. Cooper (005) argues that the margnal foregn nvestment n the U.S. exceeds ts average foregn nvestment, and that the U.S. has nvestment opportuntes that produce hgher returns than n Japan and Europe. In essence, all of these papers argue that changes n portfolo composton are the man source of large current account movements, albet for dfferent underlyng reasons. ð1þ ðþ ð3þ
K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 33 Kraay and Ventura (000, 003), among others, argue that the U.S. current account defct s due to a growth effect. 8 Countres mantan a constant portfolo composton as the portfolo enlarges, as t s customary that countres nvest the margnal unt of wealth n the same way as the average unt. 9 Based on the Kraay Ventura clam, a smple rule predcts the current account response to changes n wealth: t s equal to ths constant share of net foregn assets multpled by the addtonal wealth. 10 In our framework: countres mantanng constant portfolo shares over tme amounts to Δx=0. Namely, only the growth effect remans: CA=x S. he thrd vew of the lterature s represented by the general equlbrum portfolo models developed most recently, such as lle and Van Wncoop (008), and Devereux and Sutherland (006a,b,c). hey pont to the theoretcal mportance of takng nto account both the composton effect and the growth effect n explanng current account adjustments. he followng sectons take up the task of emprcally assessng these three dfferent portfolo vews of the current account... Emprcal results n the lterature Although many theores of the current account from a portfolo perspectve have emerged from ths recent wave of nterest, there has been very lttle lucd emprcal analyss on these theores. No exstng emprcal work, to our knowledge, has specfcally amed at explorng the relatve mportance of the two effects n explanng the current account. he most relevant emprcal study to ths end s the work done by Kraay and Ventura (000), whch tests the valdty of the growth-effect theory. o test the theory that CA=x S, the regresson 11 CA t = β 0 + β 1 ðx t S t Þ + η t ð4þ s performed. CA t and S t denote the current account and savngs as a share of GNP n country n year t; x t s the share of net foregn assets n total assets; and η t s the error term. 1 Accordng to the growth-effect theory, β 1 should be 1. Kraay and Ventura (000) run both the pooled regresson that ncludes all country/year observatons of 13 OECD countres over the tme frame of 1973 1995 and the cross-secton regresson that uses countryaverages of all varables,.e. CA t = β 0 + β 1 x t S t + η (upper bar of a varable denotes ts average over tme). hey fnd that the estmated β 1 s 0.955 n the pooled regresson and 0.996 n the cross-secton regresson, and cannot reject the null that β 1 s equal to 1 n ether 8 Bussere et al. (00) emprcally fnd that n a panel of 18 OECD countres, ntal portfolo allocaton affects current account behavor followng temporary shocks, therefore concludng that these results are compatble wth the new rule suggested by Kraay and Ventura (000). Iurrta (004) extends the Kraay Ventura (000) model to a two-country large open-economy model, and examnes the current account responses to transtory-ncome shocks n a two-country world. 9 he other dmenson of Cooper (005)'s argument also encompasses the growth effect feature n stressng that the large U.S. current account defct s only a natural feature of the ncreasngly globalzed world, where a porton of the world's excess savng s nvested n the U.S. 10 hs seemngly smple equaton yelds surprsng mplcatons that are absent n the standard vew of the current account. An ncrease n savngs wll lead to a current account defct n debtor countres but a current account surplus n credtor countres. For ths reason, Kraay and Ventura's explanaton of the huge current account defct n the U.S. s not a reflecton of shfts towards U.S. assets and away from foregn assets by foregn countres, but of the large ncrease n ts wealth and of the fact that U.S. had been a debtor. 11 Kraay and Ventura (000) confrms that the results of ths regresson hold even after controllng for a number of relevant varables and usng an nstrumental varable to estmate the β1 coeffcent. Omtted varable bas and measurement error seem not to affect much of the result, and therefore we follow Kraay and Ventura n usng ths reduced-form equaton as the bass of our analyss. 1 Note that n runnng ths regresson, Kraay and Ventura's measure of the current account CA does not consstently take nto account valuaton effects and captal gans. Later, we re-run the regresson wth our measure of current account CA, whch nclude these effects. able 1 Duplcaton of Kraay and Ventura (000, 003) results. radtonal CA Mark I data Mark II data (Gross Natonal Savngs/GDP) 0.86 0.939 1.0 (Foregn Assets/otal Assets) (0.136) (0.093) (0.070) R 0.689 0.835 0.869 Number of observatons 0 P-value for null hypothess that 0.376 0.5178 0.7990 coeffcent on savng foregn assets=1 hs table reports the results of estmatng CA t = β 0 + β 1 x t S t + η, where CA t and x t S t denote the average current account to GDP rato and average savngs rate multpled by net foregn asset rato n country over the sample perod; and η s the error term. Standard errors are n parentheses and are corrected for heteroskedastcty. case. We re-run the cross-secton regresson usng three dfferent measures of the current account, ncludng measures that account for valuaton effects, and fnd smlar results, reported n able 1. 13 β 1 =1 cannot be rejected when usng any of the three measures, despte the datasets' dssmlarty. Fg. 1 dsplays the emprcal result of the crosssecton regresson. We make two mportant observatons here. Frst, accordng to our accountng framework, β 1 =1 does not necessarly rule out the mportance of the composton effect, nor by tself provde support for the growth effect. If the composton effect s uncorrelated wth the growth effect, whch s not mplausble, we could well have β 1 =1, whle a sgnfcant porton of current account movements can stll be accounted for by the composton effect. However, the fact that the R n the cross-secton regresson above can be as hgh as 0.85 seems to suggest that the majorty of the cross-sectonal varatons of the current account s attrbuted to the growth effect. he composton effect, on the other hand, s at best margnally mportant. he second observaton s that the emprcal support for the growth effect comes from prmarly the cross-sectonal varatons and not n the least bt from the tme-seres varatons. able compares the outcome of the wthn regresson (tme-seres varaton wthn each country) and between regresson (cross-sectonal varaton). Clearly, there s no evdence supportng the new rule at the tmeseres dmenson whle t performs remarkably well at the crosssectonal dmenson. In Kraay and Ventura (003), they nterpret ths dvergence n performance as the dstncton between a short-run and a long-run phenomenon. hey argue that the new rule may not hold well n the short-run possbly as a result of adjustment costs, but that t nevertheless holds very well n the long-run, as s evdent from the cross-secton regresson results. For ths reason, the next sectons focus exclusvely on the cross-sectonal regressons (n whch the evdence les), and show that the cross-sectonal varatons n the current account are manly drven by an accountng approxmaton, so that the only pece of evdence that remans provdes lttle meanngful emprcal support for the new rule. An mportant and equally surprsng result s: when nstead of runnng the shares regresson above, CA t = β 0 + β 1 x t S t + η, where the current account s the share of GNP, and savngs s taken to be the savngs rate, we run a levels regresson, where CA t s taken to be the levels of the current account and S t s taken to be total savngs, the coeffcent s β 1 now actually close to (able 3). Accordng to the 13 Frst, we expand the orgnal K V dataset, usng conventonal measures of the current account, to 0 OECD countres over 1973 003. Because of data avalablty ssues and especally of the mssng IIP data n the IMF's Balance of Payment Statstcs for some countres n early years, t s an unbalanced panel. We subsequently use the change n net foregn assets and IIP taken from the Lane and Mles-Ferret (007), Mark II dataset for OECD countres over 1973 003 to run the same regresson, also reportng the results usng the Lane and Mles-Ferret (001), Mark I dataset coverng a shorter tme perod of 1973 1998 for the same set of countres, where estmates of net foregn assets are based on a dfferent methodology from the subsequent one and are therefore somewhat dfferent.
34 K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 able he K V wthn regresson. Country radtonal CA Obs Mark I data Obs Mark II data Obs AUS 0.59(.349) 31 0.668(.650) 6.547(.964) 31 AU.017(.636) 31 1.115(.883) 6 1.19(1.693) 31 CAN.7(.400) 31 3.196(.966) 6 1.39(.701) 31 CHE 1.406(.641) 1.596(.813) 6 3.454(.5) 31 DEU 1.914(.671) 1.40(.886) 6.530(.884) 31 DNK 0.118(.409) 13 1.800(.748) 6 0.317(1.066) 31 ESP 0.616(.315) 31.97(1.179) 6 1.673(1.170) 31 FIN 0.588(.156) 31 0.506(.898) 6 1.638(.155) 31 FRA 0.4(.517) 9 1.700(1.00) 6.93(1.338) 31 GBR 0.885(.476) 31 3.557(1.38) 6.54(1.067) 31 IRL N.A..045(.580) 6 1.461(.803) 31 ISR 0.31(.658) 15.117(.806) 6.66(1.34) 31 IA 0.513(.80) 31.4(1.171) 6 1.147(1.59) 31 JPN 1.51(.3) 31 1.588(.4) 6.407(.640) 31 KOR 0.700(1.53) 18.78(.355) 6 0.996(.61) 31 MEX N.A. 0.76(1.141) 6.00(.775) 31 NLD 0.357(.9) 8.587(.53) 6 0.660(1.353) 31 NOR.515(.509) 0.38(.599) 6.669(.416) 31 NZL 0.4(.93) 15 1.953(.643) 6.18(.307) 31 PR 0.453(.650) 8 0.40(1.067) 6 0.404(1.094) 31 SWE 0.969(.468) 31 0.054(.971) 6 1.603(1.695) 31 USA 1.784(0.308) 8 1.810(.83) 6 1.600(.711) 31 hs table reports the results of estmatng the K V wthn regresson (tme seres) for each country usng dfferent measures of the current account. Standard errors are n parentheses. he followng accountng dentty follows: x = NFA 0 + CA 1 + CA + N + CA : ð5þ W 0 + S 1 + S + N + S If the ntal net foregn asset poston NFA 0 and assets W 0 are quanttatvely small compared to the ncremental net foregn assets and wealth over subsequent perods, these ntal values can be gnored. As such, the followng equaton wll be approxmately true: Fg. 1. Duplcaton of Kraay and Ventura (000, 003) Results. hs fgure duplcates the cross-country regresson n Kraay and Ventura (000, 003) usng our own datasets. he top panel uses the tradtonal current account, the mddle panel uses the valuatonadjusted current account taken from the Lane et al. Mark I dataset and the bottom panel uses the valuaton-adjusted current account taken from the Lane et al. Mark II dataset. x = NFA 0 + CA 1 + CA + N CA W 0 + S 1 + S + N S P t =1 = CA t = P t =1 S t = = CA t S t : P t =1 CA t P t =1 S t ð6þ growth-effect theory, these two dfferent specfcatons should be dentcal n terms of predctng β 1 =1, wth the levels regresson beng an even more drect way of assessng the growth-effect theory than CA=x S. he theoretcal analyss n the next secton wll llustrate exactly why one could obtan the result that β 1 =, and how t sheds lght on the Kraay Ventura result. 3. he problem of the K V cross-secton regresson 3.1. he shares regresson he end-of-perod portfolo share x s approxmately equal to the sum of all current account balances n each perod dvded by the sum of savngs n each perod. Consequently, x s smply equal to the average current account over the average savngs (upper bar of a varable denotes ts average over tme). Note that ths approxmaton does not requre a very long tme seres,.e. a large.hereasonsthatfnancal globalzaton and economc growth over the past three decades have served to reduce the quanttatve mportance of ntal net foregn asset postons and wealth compared to the subsequent flow varables. From our sample, whch conssts of the perod between 1973 and 003, the ntal assets represent on average 10% of the sum n the denomnator, We theoretcally derve the explct expresson for the β 1 coeffcent of the cross-secton specfcaton for three dfferent data generatng processes of x, for both the shares and the levels regresson. We wll show that we can n fact obtan β 1 =1 for all of the consdered DGP's of x n the shares regresson, but that the possblty of seeng β 1 = n the levels regresson s only consstent wth x followng a hghly persstent or unt-root process wth some countres dsplayng a trend. By defnton, the portfolo share x of country at tme s equal to the ntal net foregn asset poston, NFA 0, plus the sum of subsequent ΔNFA n every perod current account n each perod), dvded by the ntal total asset poston, W 0, plus the sum of savngs n every subsequent perod. able 3 Levels-regresson results of the K V specfcaton. radtonal CA Mark I data Mark II data (Gross Natonal Savngs).175 1.94 1.71 (Foregn Assets/otal Assets) (0.408) (0.167) (0.386) R 0.613 0.8711 0.8183 Number of observatons 0 P-value for null hypothess that 0.673 0.731 0.464 coeffcent on savng foregn assets= hs table reports the results of estmatng CA t = β 0 + β 1 x t S t + η, where CA t and x t S t denote the average current account and average savngs multpled by net foregn asset rato n country over the sample perod; and η s the error term. Standard errors are n parentheses and are corrected for heteroskedastcty.
K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 35 and the ntal net foregn asset poston represents about 5% of the total sum n the numerator. Rearrangng Eq. (6), weget CA t = x S t whch says that the average current account of country over the sample perod s smply equal to the end-of-perod share of net foregn assets tmes the average savngs over the same perod. It should be noted that Eq. (7) s very smlar to the cross-secton regresson CA t = β 0 + β 1 x t S t + η n Kraay and Ventura (000, 003), albet not dentcal. In the rest of ths secton, we wll show that the accountng approxmaton Eq. (7), whch holds regardless of the underlyng process of x t and S t, may undermne the valdty of the crosssecton regresson n Kraay and Ventura (000, 003). Inpartcular,we show that gven the short tme horzon of the perod n consderaton, ths accountng approxmaton may domnate the cross-secton varatons of the current account for a wde range of processes of x t, regardless of whether t's consstent or nconsstent wth the new rule. A caveat s, should we care about the process of S t, or alternatvely the process of W t? In prncple, yes. o see ths, the regresson CA t = β 0 + β 1 x t S t + η can be rewrtten as h CA t = β 0 + β 1 x t S t + cov t ðx t ; S t Þ + η ; where cov t (x t, S t ) s the tme-seres correlaton between x t and S t n country, whch shows that the process of S t and n partcular ts tme-seres correlaton wth x t matters. A look at the data, however suggests that ths term s quanttatvely neglgble: the correlatons between x t St and xt S t are as hgh as 0.986, 0.998 and 0.997, usng the three dfferent measures of the current account. 14 herefore, n ths case, the key evdence supportng the K V new rule s essentally the followng cross-secton regresson CA t = β 0 + β 1 x t S t + η : It s plausble that there s cross-sectonal correlaton between x t and S t. For nstance, countres whch have hgher savngs may also have a hgher share of net foregn assets. But ths would automatcally nvaldate Kraay and Ventura (000, 003) as ther theory suggests that x should be ndependent of S, partcularly n the cross-secton. Allowng for such a correlaton, however, would only strengthen our results (below) at the cost of more ntrcate algebra. For expostonal purposes, we wll assume that there s no cross-sectonal correlaton between x t and S t. A techncal appendx showng that all results derved below carry through when relaxng ths assumpton s avalable upon request. Why does the pont estmate of β 1 =1 of Eq. (8) smply reflect the accountng approxmaton CA t = x St? o see ths ntutvely, compare Eqs. (8) and (6). he only dfference between the accountng approxmaton and the regresson specfcaton s x and x t. But when the tme-seres s not too long (for example =30, where =30 s more than suffcent for Eq. (6) to hold), the end-of-perod portfolo share x and the average portfolo share x t are not very dfferent even n the case where x t has a determnstc trend or s nonstatonary, cases whch would be contrary to the new rule. It follows that runnng the cross-secton regresson n Kraay and Ventura (000, 003) can always yeld β 1 =1 as seen n able 1. Whle β 1 =1 s certanly consstent wth the new rule, β 1 =1 s n fact, consstent wth any rule. herefore, t cannot be taken as evdence for, or for that matter aganst, the new rule. 14 hese measures correspond to the Lane et al. Mark I, Mark II, and the tradtonal current account measures. ð7þ ð8þ o be more concrete, consder the followng three possble data generatng processes of x: (a) x s statonary wthout trend,.e. x t =x +ε t, (b) x s nonstatonary wth/wthout trend,.e. x t =α +x t 1 +ε t, t (c) x s a trend-statonary process,.e. x t =x 0 +α t+ j =1 ρ t j ε j, where subscrpts and t represent country and year t, respectvely. Next we attempt to work out the exact value of β 1 for all three cases by pluggng n Eq. (7) nto the regresson. Case (a). he cross-sectonal regresson specfcaton CA t = β 0 + β 1 x t S t + η yelds var x S t β 1 g =1: ð9þ var x S t Proof. See Appendx B. he ntuton s the followng: f x =x +ε, t s roughly the case that x =x t +ε. Namely, the end-of-perod portfolo share x s equal to the average portfolo share plus an error term. he accountng approxmaton CA t = x S t then becomes CA t = x t S t + e S t. Notce that e S t s by assumpton uncorrelated across countres, and denotng t as η, the accountng approxmaton fnally becomes CA t = x t S t + η, precsely the cross-country regresson n Kraay and Ventura (000, 003). So even f ther conjecture that x s roughly constant over tme s correct, these regresson results carry no emprcal content, and consequently do not serve as a valdaton to the growth-effect theory, or the new rule. In fact, ths case mathematcally confrms the pont made n Van Wncoop (003), where he argues that any model that has a steady-state portfolo share can delver β 1 =1 n the K V regresson snce devatons from the steady state would cancel out when takng averages. Gong one step beyond ths argument, n Cases (b) and (c), we wll show that even f there were no steady-state portfolo share x, the cross-secton varatons may stll be domnated by the accountng approxmaton when s not very long, the case of ths partcular data sample. Case (b). he same regresson specfcaton yelds var x 0 S t β 1 = var x 0 S t + A + +1 ð Þ B + C ð10þ 6 A + ð +1Þ 4 B + C; Þ cov x 0 S t ; α S t. + +1 ð +1 Þð +1Þ where A=var(ε t )E(S t ), B=var(α S t), and C = ð +1 Proof. See Appendx B. he frst term of both the numerator and denomnator s dentcal and s a cross-secton varaton nvolvng the ntal net foregn asset share and average savngs rate. Ignorng the other terms, β 1 s just equal to 1, and ths reverts back to Case (a). Other terms n the numerator and denomnator reflect devatons from Case (a). he second terms dffer only by a coeffcent and contan the varance of the random-walk part of x whch we call a whte-nose varaton, and ther rato s close to 1.5 when s very large. he last two terms are related to the trend: the thrd terms represent the trend varaton and ther rato converges to when s very large. he fourth terms, whch we group wth the crosssecton varaton term, are dentcal and ther rato s therefore 1. Consequently, β 1 s a weghted average of 1, 1.5 and, the weghts dependng on the cross-secton varaton (terms 1 and 4), the whtenose varaton (term ), the trend varaton (term 3) and tme.if the cross-secton varaton s large and s not too large, namely, we are not far away from Case (a), more weght s put on 1, and we could see β 1 =1. If, however, the trend varaton s large and/or s very bg, we could see β 1 =. A specal case s f α =0 for all, the case where the portfolo share x has no tme trend, and the last two trend-related terms
36 K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 Fg.. Evoluton of x over tme. hs fgure depcts the evoluton of x over tme for each country, where x represents the share of net foregn assets n total assets. he data s taken from the Mark II dataset and the tme frame s from 1973 to 003. (terms 3 and 4) vanshes, so that β 1 s a weghted average of 1 and 1.5. 15 he key s that wth a relatvely short tme seres of 31 years n ths data sample, t s the case that the cross-secton varaton domnates both the trend varaton and the whte-nose varaton. o llustrate the order or magntude, the sample cross-secton varaton s of order 10 4, the sample whte-nose varaton s of order 10 6,and the sample trend varaton s of order 10 7.Clearly,wth=31, the cross-secton varance (the frst term) domnates the rest of the terms. Snce Case (a) has already shown that the cross-secton varaton s determned by an accountng approxmaton, t s dffcult to see anythng but β 1 equal to 1 because of the relatvely short tme seres. When n the future wll we be able to see β 1 =? he answer s, only after a very long tme, and we would always see β 1 =1 f usng avalable data. Accordng to the above magntudes, wth 50 years of data, the coeffcent wll be only 1.5. Wth 100 years of data, the coeffcent can reach 1.5. And t wll take more than four centures for the coeffcent to reach 1.9! he mportant pont s that even f x follows a nonstatonary process of Case (b), whch s drectly n opposton to the growth-effect's theory of a constant portfolo, β 1 =1 cannot be rejected when the cross-secton varance domnates, precsely the case when the tme seres s relatvely short (b50). Case (c). he same regresson specfcaton as the above yelds var x 0 S t + E 1 ρ ρ + 1 + ρ + 1 A + +1 ð Þ ð1=ρ β 1 = Þ ð1+ρ Þ B + C var x 0 S t + E ð 1 ρ Þ ρ ρ +ρ + 1 +ρ + ρ + A + ð +1Þ ð1 ρ Þð1 ρ Þ 4 B + C ð11þ where A=var(ε t )E(S t ), B=var(α S t ), and C = +1Þ cov x 0 S t ;α S t. 15 β 1 could be close to 1 f the cross-secton varaton s large and s relatvely small, and close to 1.5 f the whte-nose varaton and/or s very large. Proof. See Appendx B. he only change to ths formula from the precedng case (Eq. (10)) s the coeffcents of the second term of both the numerator and denomnator. Both Cases (a) and (b) are encompassed n Case (c) n the lmt. 16 he nterestng case where ρ s between 0 and 1, the rato of the second terms wll be less than 1 and β 1, a weghted average of 1, a value less than 1, and. Agan, f the magntude of the cross-secton varaton s large and the tme seres s short, more weght wll be put on 1 and we can stll obtan β 1 =1. 17 o summarze the theoretcal predctons of β 1 for the crosssectonal regresson specfcaton: Case (a): β 1 =1. Case (b): β 1 s a weghted average of 1, 1.5, and, the weghts dependng on the magntude of the cross-secton varance, the whte-nose varance, the trend varance and. If the cross-secton varance s bg and tme s relatvely small, we can see β 1 =1; f the trend varance and/or s very large, we can see β 1 =. Case (c): when ρ s between 0 and 1, β 1 s a weghted average of 1, a value less than 1, and. If the cross-secton varance s large and s relatvely small, β 1 s equal to 1; f the trend varance s large and/or s very bg, β 1 can be equal to. 16 Note that ρ and α both beng equal to 0 for all brngs us back to the statonary Case (a). ρ =1 brngs us back to the unt root case wthout trend (f α =0 for all ), or the unt root case wth trend (f α s not 0 for all ), as n Case (b). he more nterestng case s when ρ s between 0 and 1. 17 However, t s possble to have β 1 beng below 1 f the magntude of the second terms s larger than the magntude of the thrd terms n a small sample. But when becomes very large, β 1 can gradually converge to as n Case (b).
K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 37 able 4 Frst-order autocorrelaton of x. Country AUS AU CAN CHE DEU DNK ESP FIN α 1 0.947 0.73 0.968 0.644 0.908 0.930 1.016 0.673 (0.086) (0.117) (0.05) (0.148) (0.081) (0.086) (0.101) (0.139) α 0 0.01 0.01 0.0003 0.081 0.00 0.00 0.004 0.047 (0.011) (0.005) (0.006) (0.033) (0.003) (0.01) (0.006) (0.030) Country FRA GBR IRL ISR IA JPN KOR MEX α 1 0.84 0.875 0.881 0.73 0.869 0.955 0.943 0.644 (0.099) (0.098) (0.087) (0.15) (0.105) (0.08) (0.033) (0.10) α 0 0.000 0.000 0.03 0.041 0.005 0.003 0.003 0.065 (0.00) (0.004) (0.00) (0.019) (0.003) (0.003) (0.006) (0.01) Country NLD NOR NZL PR SWE USA α 1 0.867 1.090 0.888 1.08 0.830 1.036 (0.094) (0.058) (0.075) (0.093) (0.097) (0.053) α 0 0.00 0.010 0.040 0.001 0.010 0.003 (0.006) (0.004) (0.03) (0.010) (0.007) (0.00) hs table reports the results for estmatng x t =α 0 +α 1 x t 1 +ε t for each country n the sample usng the Mark II dataset, where x t denotes the share of foregn assets n total assets n year t; and ε t s the error term. he tme perod s 1973 003. Standard errors are n parentheses. Clearly, the result that β 1 =1 should not be consdered as a verfcaton to the growth-effect theory and the result s consstent wth all three cases of x. However, at ths pont, not much can be sad about the underlyng DGP of x. Wth 31 years of data, we are stuck wth a relatvely short tme-seres that make all of these cases a possblty. 3.. he levels regresson One way to get around ths dffculty and to be able to say somethng about the DGP of x s to do the same exercse for the levels regresson, CA t = β 0 + β 1 x t S t + η, where CA t and S t are now actually levels of the current account and levels of savngs. In the prevous secton, we are confronted wth the puzzlng regresson result that β 1 = n ths levels specfcaton, even though the new rule prescrbes the two specfcatons to be equvalent n predctng β 1 =1. he explct formula of β 1 n ths specfcaton s the same as before except that the levels replace shares for each of the terms. As we know, savng rates dffer lttle across countres relatve to the dfference n the levels of savngs across countres, the szes of economes beng remarkably dfferent. Hence, swtchng to the levels regresson amounts to effectvely puttng more weght on the trend varaton term, thus reducng the short tme-seres problem by effectvely magnfyng the trend varance term and puttng enough weght on so that even wth a relatvely short tme seres, we may stll observe f the true DGP were Case (b) or Case (c). 18 From the data sample, the cross-sectonal varaton s on the order of magntude of 10 19, the sample whte-nose varaton, +1 10 19, and the sample trend varaton, +1 ð Þ 10 18. Wth =31, the number of years n our sample, t s clear that the trend varaton term can domnate, pushng β 1 towards. In ths case, the result that β 1 = n the levels regresson s not consstent wth Case (a), but wth Cases (b) and (c). Recall that n the shares regresson specfcaton β 1 =1 s consstent wth all three cases, so that we can conclude that only Case (b) and Case (c) are the possble true DGP of x. he supportng evdence for the growth-effect theory was n fact msnterpreted. 4. Emprcal analyss Wth the theoretcal analyss n the prevous secton suggestng that the process of x (consstent wth β 1 =) s a nonstatonary process or a hghly persstent process wth trend, we proceed to nvestgate ths drectly. A frst glance at the graphs (Fg. ) of the 18 More specfcally, the levels regresson puts more weght on large economes and large economes, such as the U.S. and Japan, happen to have trends n ther portfolo shares. portfolo share over tme for each of the countres seems to suggest that x s unlkely to be constant, but rather changng over tme, wth some countres seemng to dsplay a secular trend. o be more concrete, we run a few econometrc tests to examne the process of x. Consder the smplest possble case of x followng an AR(1) process, where x t =α 0 +α 1 x t 1 +ε t. 19 Results are reported n able 4.It s clear that α 1 s very close to 1 (wthn standard devatons) or even slghtly greater than 1, for most countres n our sample. hs suggests that x may follow a unt-root process. In ths case, we proceed to conduct augmented Dckey Fuller tests for each ndvdual country. Wth varous specfcatons that nclude and exclude tme trends and dfferent lengths of tme lags, unt roots can be rejected for at most eght countres out of the twenty-two countres n the sample. 0 here are fourteen countres n our sample for whch none of the Dckey Fuller tests can reject unt root at conventonal sgnfcance levels. hese results notwthstandng, t s a well known fact that these untroot tests have very low power for short tme seres, not easly rejectng the null hypothess of a unt root. Gven that there are only 31 observatons (1973 003) for each country, the above results cannot be conclusve. Nevertheless, the results of these smple econometrc tests show that x s lkely to be a hghly persstent AR (1) process or a untroot process, wth some countres dsplayng a tme trend, effectvely gvng support to our theoretcal analyss n the prevous secton. 1 We have shown that results taken to be evdence for the growtheffect theory are overturned, both from our theoretcal and emprcal analyses. he follow-up queston s, to what extent should current account movements be attrbuted to portfolo composton adjustments and to what extent s the growth effect stll quanttatvely mportant, accordng to the syntheszed accountng framework? 19 hs regresson s run for each ndvdual country usng the Mark II data, whch has the longest tme seres. 0 he Dckey Fuller test wthout trend or lags rejects unt root for Mexco. he specfcaton ncludng tme lags rejects unt roots for Swtzerland, Korea and Mexco, and the specfcaton ncludng a tme trend rejects Israel and Japan. Includng both lags and trends rejects unt roots for Austra, Canada, Swtzerland, Japan and New Zealand. 1 An mportant caveat s that x beng a hghly persstent process or unt root process wth trend n the very long run s somewhat nconcevable and dffcult to reconcle wth theores that have a steady-state portfolo share. But avalable data smply cannot reject ths result. hs outcome may reflect the fact that the world s stll on a transtonal path to a new steady state, wth countres ntegratng more deeply nto the global economy wthout havng yet fully reached ts steady state portfolo equlbrum. Our man pont s that so long as the process of x s observatonally equvalent to a unt root process wth trend for ths sample perod, the regresson result β=1 based on ths data sample wll nevtably be the outcome of the domnance of a cross-sectonal varaton generated by an account equaton. On the other hand, even f x s statonary n the very long run, whch may be lkely, β 1 =1 n a cross-secton regresson remans to be drven by accountng, and therefore contnues to confer no nformaton.
38 K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 Fg. 3. A decomposton of the current account. hs fgure depcts a decomposton of the current account for each country. he sold lne represents the composton effect and the dashed lne represents the growth effect, both of whch are n terms of shares of current GDP. he data s taken from the Mark II dataset and the tme frame s 1973 003.
K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 39 Fg. 3 (contnued). o see ths, we decompose the change n net foregn asset postons nto the composton effect and the growth effect usng Eq. (3) and normalze them by current GDP. Fg. 3 plots these two tme seres for Here we use the data taken from the Mark II dataset. each country. wo salent features emerge: Frst, the growth effect s smooth and changes slowly. For example, as the U.S. gradually sld nto a bg debtor n the md 1980's, the growth effect also gradually turned from postve nto negatve. he opposte case s Japan, the growth effect becomes more and more postve as Japan accumulates huge foregn assets. he growth effect does seem to capture some long-run
40 K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 Fg. 3 (contnued). movements n the current account but for reasons that are completely dfferent from the one argued by Kraay and Ventura (000, 003). It smply reflects an accountng fact: a country that contnues to run current account defcts must become a debtor and a debtor country must be runnng current account defcts on average. Second, the composton effect s very volatle and accounts for most varatons of the current account n a country over tme. o be more concrete, we perform a varance decomposton exercse on the accountng equaton, CA=Δx W+x S. he results are reported n able 5. Clearly, the composton effect s much more mportant n explanng the varatons of the current account than the growth effect for most countres n our sample. It s noteworthy that ths emprcal result s also n lne wth results that emerge from a numercal example n lle and Van Wncoop (008), whch decomposes nternatonal captal flows generated by the model nto the growth effect (portfolo growth) and the composton effect (portfolo reallocaton). 3 In ther example t s also true that the growth effect s qute smooth whle the majorty of the varaton n the current account s due to the composton effect. 4 5. Concluson We have analyzed a non-structural framework of the current account that s based upon an mportant accountng dentty that hghlghts two channels of current account adjustment: a composton effect and a growth effect. he framework s general enough to nest the majorty of the lterature on the portfolo vew of the current account, whle allowng for the nterplay between the composton effect and the growth effect also emphaszed n the recent general equlbrum portfolo models. hs framework can be used as a gudelne for more specfc theores, whch wll have to be compatble wth our emprcal fndngs regardng the quanttatve mportance of the two effects. We have shown that partal-equlbrum models, wthout reference to a syntheszed framework may gve rse to msleadng nterpretatons of current account movements. Our basc message s clear: never agan run a K V-type cross-country regresson regardless of the underlyng DGP of the portfolo share; there s smply no nformaton embedded n ths regresson. It s therefore clear that partal-equlbrum portfolo models cannot supplant general equlbrum models n explanng external adjustments despte ther seemngly remarkable emprcal success n the past. hs paper attempts to further the very lttle exstng emprcal work on portfolo models of the current account. Usng the accountng framework as a gudelne, we theoretcally and emprcally overturn the growth effect theory, and reestablsh the composton effect as the quanttatvely sgnfcant drver of current account dynamcs. Usng both drect and ndrect emprcal evdence, we show that the net 3 hey further decompose the composton effect nto parts that come from changes n expected excess returns and that whch come from tme-varyng second moments. See Chart 8 and 9 n lle and Van Wncoop (008). 4 More specfcally, t s due to tme-varyng second moments. foregn asset share s far from beng constant or even statonary, as s requred by a grow-effect theory, but s n fact a hghly persstent process or a unt-root process, wth some countres dsplayng a trend. Along wth general equlbrum models, ths syntheszed framework ponts to the components that matter for the current account, ncludng the components that have not mattered so much n the past but may potentally matter qute substantally n the future. In a world wth explodng gross holdngs of external assets and labltes, t s possble that the growth effect may overtake the composton effect n contrbutng to current account dynamcs, and ts systematc ncluson despte ts small relevance n the past data may become essental. Newly developed general equlbrum models embody precsely ths level of comprehensveness and can therefore serve to be a benchmark for future analyses on portfolo vews of external mbalances. In a fnancal world that s ntegratng ever more profoundly, theoretcal and emprcal works n ths area need to keep up wth global trends furtherng our understandng of the facts and the theory wll be mportant for handlng the massve global captal flows that we wll, n all lkelhood, contnue to wtness. Appendx A. Data descrpton Our dataset conssts of OECD countres. he countres nclude Austra, Australa, Canada, Swtzerland, Germany, Denmark, Span, Fnland, France, Great Brtan, Ireland, Israel, Italy, Japan, Korea, Mexco, Netherlands, Norway, New Zealand, Portugal, Sweden, and the U.S. 5 We select post-1973 data, the years after Bretton Woods collapsed. For measures of the net foregn asset poston and the current account, we use both the tradtonal measure taken from the IIP data n IFS and Mark I and Mark II estmates from Lane and Mles- Ferret (001) and Lane and Mles-Ferret (007), whch consstently account for valuaton effects and captal gans, although the methodologes have slghtly changed from one dataset to another. hey provde an accountng framework whch hghlghts the lnk between the balance and payment flows and the underlyng stocks, as well as the mpact of unrecorded captal flght, exchange rate fluctuatons, debt reducton, and valuaton changes not captured n the conventonal current account defnton. hrough ths lnk, they show that one method of estmatng net foregn assets s cumulatng the current account and adjustng for the captal account balance. We take ther net foregn asset measure, whch s just the adjustedcumulatve current account. For our current account, we take the frst dfference of ther adjusted-cumulatve current account measure wth consstent captal gans and losses and valuaton effects. By dong so, we effectvely capture the valuaton effect and captal gans and losses for both the current account and net foregn assets measure. 5 We omt the followng OECD countres: Belgum, Greece, Hungary, and Luxemburg, Czech Republc, Poland, Slovak Republc, and urkey for the reason that, except for Belgum and Luxembourg, these countres do not have full tme seres of all varables between 1973 and 003. Belgum and Luxembourg are omtted because they are often reported as one n some datasets whle reported separately n others.
K. Guo, K. Jn / Journal of Internatonal Economcs 79 (009) 31 41 41 able 5 Varance decomposton of the current account. Country R Composton effect Growth effect cov AUS 0.980 1.193 0.06 0.51 AU 0.9800 1.140 0.067 0.07 CAN 0.973 1.07 0.058 0.69 CHE 0.9894 0.578 0.100 0.344 DEU 0.9965 1.15 0.044 0.15 DNK 0.9747 1.433 0.096 0.507 ESP 0.9938 0.943 0.035 0.039 FIN 0.8611 1.69 0.177 0.846 FRA 0.9985 1.06 0.013 0.075 GBR 0.995 1.105 0.04 0.147 IRL 0.9666 0.914 0.058 0.08 ISR 0.9771 1.390 0.083 0.443 IA 0.9945 1.041 0.03 0.064 JPN 0.9903 0.745 0.089 0.140 KOR 0.9837 1.01 0.05 0.53 MEX 0.9471 1.94 0.353 0.647 NLD 0.9835 1.7 0.044 0.316 NOR 0.9993 0.683 0.051 0.66 NZL 0.9190.08 0.389 1.417 PR 0.9966 0.97 0.016 0.057 SWE 0.998 1.143 0.00 0.163 USA 0.9919 0.91 0.068 0.011 hs table reports the varaton decomposton of the current account for each country n the sample accordng to Eq. (3). he R s the proporton of the varaton of current account that can be explaned by ths equaton. he formula for the varance decomposton s var(δx W+x S)=var(Δx W)+var(x S)+cov(Δx W, x S).he three terms on the rght correspond to the composton effect, growth effect and cov n the table, respectvely, the sum of whch should be 1. omeasurethedomestccaptalstock,weusetheperpetualnventory method: 6 we cumulate gross domestc nvestment n current U.S. dollars taken from the World Bank's Global Development Indcators, assumng a deprecaton rate of 4% a year, and n each year revalung the prevous year's stock usng the U.S. GDP deflator. We take 1965 as the startng year. he captal stock n 1965 s estmated usng the average captal-output rato over the perod 1960 1965 n Nehru and Dhareshwar (1993), multpled by GDP n 1965. All varables are denoted n current U.S. dollars. Appendx B Case (a). Snce P x t =x +ε t, n partcular, we have x =x +ε and j = 1 x t = x + e j gx, where the second equalty comes from the fact that the average of ndependent shocks s approxmately 0 (a more detaled dervaton wthout takng ths approxmaton s avalable upon request). Eq. (7), CA t = x S t, mples that CA t = ðx + e Þ S t. Pluggng these equatons nto the regresson CA t = β 0 + β 1 x t S t + η, we then have (x t + ε ) S t = β0 + β 1 (x ) S t + η. herefore β 1 = cov ð ðx S t ; ðx + e ÞS t Þ = var ð x S t Þ = 1. For the savngs rate case, varððx S t Þ varðx S t Þ smply replace S t by S t Y t. t Case (b). Snce x t =α +x t 1 +ε t,wehavex t =x 0 +α t+ j =1 ε j.in partcular, x = x 0 + α + Σ j =1 ε j and x t = x 0 + α ð +1Þ + e 1 + ð 1Þe + N e. Agan, Eq. (7) CA t = x S t mples that CA t =(x0 + α + t j =1 ε j ) S t. Pluggng these equatons nto the regresson CA t = β 0 + β 1 x t S t + η, we then have β 1 = cov P x 0 + α + e j = 1 j S t ; x 0 + α ð + 1Þ + e 1 + ð 1Þe + N e var x 0 + α ð + 1Þ + e 1 + ð 1Þe + N e S t Þ Expandng the varances and covarances term by term, we obtan fnally β 1 = var ð x 0S t Þ + + 1 A + ð + 1Þ B + C ; where A=var varðx 0 S t Þ + ð + 1Þð + 1Þ 6 A + ð + 1Þ 4 B + C (ε t )E(S t ), B=var(α S t), and C = ð +1Þ cov x 0 S t ;α S t. S t. Notce that for the case that α =0 for all (non-statonary case wthout trend), we have β 1 = var ð x 0S t Þ + + 1 varðe t ÞEðS t Þ. For the varðx 0 S t Þ + ð + 1Þð + 1Þ varðe 6 t ÞEðS t Þ savngs rate case, smply replace S t by S t t t Case (c). Snce x t =x 0 +α t+ j =1 ρ j ε j, n partcular, we have x = x 0 + α + j =1 ρ j ε j and x t = x 0 + α ð +1Þ + 1 1 ρ P j = 1 1 ρ + 1 j j e j. Agan, Eq. (7), CA t = x S t, mples that CA t = x 0 + α + P j =1 ρ j e j S t. Pluggng these equatons nto the regresson CA t = β 0 + β 1 x t S t + η, we then have β 1 = Y t. 0 0 cov x 0 + α + P B j =1 ρ j B e j S t x 0 + α ð +1Þ @ @ + 0 B var x 0 + α ð +1Þ @ + P 1 1 1 ρ ð1 ρ + 1 j Þe j j =1 C A S t Þ P 1 1 1 1 ρ + 1 j 1 ρ ð Þe j j =1 C C A S t A Expandng the varances and covarances term by term, we obtan fnally var x 0 S t + E 1 ρ ρ + 1 + ρ + 1 A + +1 ð Þ ð1 ρ β 1 = Þ ð1+ρ Þ B + C ; var x 0 S t + E ð 1 ρ Þ ρ ρ +ρ + 1 +ρ + ρ + A + ð +1Þ ð1 ρ Þð1 ρ Þ 4 B + C where A=var(ε t )E(S t ), B=var(α S t), and C = ð +1Þ cov X 0 S t ; α S t. For the savngs rate case, smply replace S t by S t Y. t References Blanchard, O., Gavazz, F., Sa, F., 005. he U.S. current account and the dollar. NBER Workng Papers, vol. 11137. Bussere, M., Chortareas, G., Drver, R., 00. Current accounts, net foregn assets, and the mplcatons of cyclcal factors. Bank of England Workng Paper. Caballero, R., Farh, E., Gournchas, P.-O., 008. An equlbrum model of global mbalances and low nterest rates. 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