How much depreciaion of he US dollar for susainabiliy of he curren accouns? Eiji Ogawa and Taeshi Kudo Firs version: May 27, 2004 This version: June 6, 2004 This paper is prepared for a conference of he Research Insiue of Economy, Trade, and Indusry (RIETI) on 17-18 June 2004. The auhors appreciae Masaru Yoshiomi and Yoshiai Tojo for heir useful commens. Graduae School of Commerce and Managemen of Hiosubashi Universiy, e-mail: ogawa.eiji@srv.cc.hi-u.ac.jp Graduae School of Economics of Hiosubashi Universiy, e-mail: ged2403@srv.cc.hi-u.ac.jp
1. Inroducion The Unied Saes have been faced wih he increasing curren accoun deficis in he recen years. Is curren accoun deficis were recorded over 5 percen of GDP in 2002. We remember ha he curren accoun deficis were over 3 percen of GDP in he mid of 1980s when he US dollar made a large depreciaion afer he Plaza Accord in Sepember 1985. I is regarded ha he recen curren accoun deficis are going beyond a dangerous level by comparing he recen siuaion wih ha in he mid of 1980s. Though he US dollar began o depreciae several monhs before he Plaza Accord, he depreciaion of he US dollar gained momenum by he Plaza Accord. The real effecive exchange rae of he US dollar depreciaed nearly 40% from he pea in he early 1985 o he early 1988. Following he depreciaion, he curren accoun defici was reduced from 3.4% in he las quarer of 1986 o 1.4% in he second quarer of 1990 (see Figure 1). Some researchers doub ha such he curren accoun deficis of he Unied Saes are susainable in he curren level of he exchange raes because he curren accoun deficis began o increase again and have reached o 5% of GDP. This paper invesigaes how much he US dollar should be depreciaed for reducing he curren accoun deficis in he Unied Saes. This paper quoes our empirical analyical resuls from Kudo and Ogawa (2003) o explain unsusainable curren accoun deficis in he Unied Saes in he nex secion. In Secion 3, we conduc a simulaion analysis o invesigae how much depreciaion of he US dollar is needed o reduce he curren accoun deficis in he near fuure. We use some VAR models o esimae relaionships beween he exchange rae of he US dollar and he curren accouns in he Unied Saes. Then we use he esimaed VAR models o conduc he simulaion analysis abou impacs of hypoheical exchange rae movemens on he curren accoun deficis. We suppose five scenarios of exchange rae movemens; 10%, 30%, and 50% of depreciaion of he US dollar in he second quarer in 2004 and depreciaions of he US dollar in he same ways as he pos Plaza Accord and he Indonesian currency crisis from 1997 o 1998. 1
2. Unsusainable Curren Accoun Deficis in he Unied Saes In his secion, our empirical analyical resuls in Kudo and Ogawa (2003) are explained as for susainabiliy of he curren accoun deficis in he Unied Saes. We used he mehod of Bohn (1995) and Ahmed and Rogers (1995) in order o derive he necessary and sufficien condiions. The susainabiliy of he curren accoun deficis was empirically analyzed from a perspecive based on inernaional capial flows in addiion o perspecives of domesic invesmen-saving relaionship and inernaional rade flows according o Mann (2002). We invesigaed wheher he curren accoun is susainable in he sense of he exernal deb solvency. 2.1. Mehodology and Daa Kudo and Ogawa (2003) conduced empirical analyzes on he susainabiliy of he curren accoun deficis from perspecives of he domesic invesmen-saving relaionship, he inernaional rade flows, and he inernaional capial flows according o Mann (2002). Their heoreical bacgrounds are explained in he Appendix. In our empirical analysis based on invesmen-saving balance, we represen he repaymen for he exernal debs r as RD, he privae savings S as PS, he D 1 privae invesmens I as PI. We use daa on he privae gross savings and invesmens as PS and PI, respecively. We replace he governmen expendiure G by he governmen gross invesmen GE and he ax revenue T by he governmen gross saving GS. In addiion, we mae daa series of he naional gross saving NS and he naional gross invesmen NI. We also mae daa series of he invesmen-saving balances of he privae secor PIS and he public secor GIS as well as he naional invesmen-saving balance NIS. In our empirical analysis based on inernaional rade flows, we represen he expors of goods and services X as EX and he impors of good and services M as IM. In addiion, we mae daa series of a sum he repaymen for exernal deb r D 1 and 2
he impors M, which is represened as MM. We also use he rade balance TB. We also es direcly wheher he curren accoun defici CAD is saionary. In our empirical analysis based on inernaional capial flows, we represen he change in foreign reserve as RES, he capial inflows Fin as FIN, and he capial R ouflows Fou as FOUT. In he analysis on he iems in financial accoun, we use he direc invesmen inflow DIIN, he porfolio invesmen inflow PIIN, and he oher invesmen inflow OIIN, and he direc invesmen ouflow DIOUT, he porfolio invesmen ouflow PIOUT, and he oher invesmen ouflow OIOUT. In addiion, we mae daa series on he direc invesmen balance DIB, he porfolio invesmen balance PIB, and he oher invesmen balance OIB. We used he Johansen s mehod o invesigae wheher he relevan variables are coinegraed. 1 We used he uni-roo ess on he relevan variables in he sysems o invesigae wheher all he variables are he elemens of he coinegraion in advance. If he variables are relevan o he coinegraion sysem, hey are expeced o follow he same order inegraion processes. As he resul, we can find ha he sysem is coinegraed. We es wheher he condiions of he coinegraion vecor are saisfied, for he sysems in which all variables are coinegraed. 2 If he sysem passes all of he ess, we can conclude ha he condiion of he curren accoun susainabiliy is saisfied. Based on he analysis in he preceding secion, we analyze he susainabiliy of he curren accoun. The original variables and he sandardized variables by GDP are prepared for all of he daa. Mos of he daa in he analysis based on he domesic invesmen-saving balance are aen from he Naional Income and Producion Accoun Tables by he Bureau of Economic Analysis. The balance of paymens daa are aen from he Inernaional Transacions Accouns. All of he daa were seasonally adjused. The 1 We use he able 1 in Oserwald-Lenum (1992) as he criical value here. 2 Noicing ha he linear resricion which is described in previous secion is imposed on he coinegraion vecor, Miyao (2001) ess he coinegraion by using he framewor of he Engle-Granger es. Though he carries ou uni-roo es on he series of RDIM-EX, his is similar o carry ou he Engle-Granger es on he sysem of RD, IM, EX by imposing he resricion (1,1,-1) on he coinegraion vecor. 3
sample period of he daa covers from he firs quarer of 1960 o he fourh quarer of 2002. The number of observaions is 172. 2.2. Empirical Resuls from he Perspecive on he Domesic Invesmen-Saving Balance In his subsecion, we invesigae he curren accoun susainabiliy from he perspecive based on he domesic invesmen-saving balance. We consider he following paern as (1) RDPIGE-PS-GS, (2) RDNI-NS, (3) RDPISGIS, (4) RDNIS. Equaion (1) is he same as he sysem in equaion (A7) in Appendix. In equaion (2), we define he naional invesmens NI as a sum of privae invesmens PI plus governmen invesmens GE and he naional savings NS as a sum of privae savings PS plus governmen savings GS. This means we analyze he whole economy s invesmen-saving relaionship. In equaion (3), we use invesmen-saving balance of boh he privae and public secors. We analyze he naional invesmen-saving balance in equaion (4). In he case of using he non-sandardized daa, he ADF es rejeced a uni-roo for he governmen savings GS in equaion (1) (Table 1.1). In he case of using he daa sandardized by GDP, a uni-roo is rejeced in he privae invesmens PI and he governmen savings GS in equaion (1). In he case of using he non-sandardized daa, he ADF es did no rejec any uni-roo for all variables in equaion (2) (Tables 1.1 and 1.2). The coinegraion es showed ha his sysem has full ran in he coinegraion relaionship bu ha his is conradicion o he assumpion of his es (Table 1.3). In he case of using he sandardized daa, a uni-roo is rejeced for he naional savings NS in equaion (2). In he case of using he non-sandardized daa, he ADF es rejeced a uni-roo for he privae and public secors invesmen-saving balances, PIS and GIS in 4
equaion (3) (Table 1.1). In he case of using he daa sandardized by GDP, a uni-roo is rejeced for he privae and public secors invesmen-saving balances, PIS and GIS in equaion (3) (Table 1.1). In he case of using he non-sandardized daa, every variable follows a firs-order inegraed process in equaion (4) (Tables 1.1 and 1.2). We conduced he coinegraion es for he sysem of equaion (4). The coinegraion es canno rejec ha he sysem has no coinegraion vecor in erms of boh he non-sandardized daa. In he case of using he sandardized daa, a uni-roo is rejeced for he naional invesmen-saving balance NIS. Therefore, each of he sysems of equaion (1), (2), and (3) is no coinegraed in erms of boh he non-sandardized and sandardized daa. On one hand, he sysem of equaion (4) is no coinegraed in erms of he sandardized daa. 2.3 Empirical Resuls from he Perspecive on he Inernaional Trade Flows We invesigae he curren accoun susainabiliy from he perspecive based on he inernaional rade flows. For he coinegraion relaionship in equaion (A10), we consider he following paern as (5) RDIM-EX, (6) MM-EX, (7) RD-TB, (8) CAD. Equaion (5) follows direcly he definiion in equaion (A10) in Appendix. Nex, we use MM raher han RD and IM in equaion (6). In equaion (7), we use he rade balance TB raher han he impors and he expors. In addiion, we conduc a uni-roo es for he curren accoun defici CAD iself in equaion (8). In he case of using he non-sandardized daa, he ADF ess show ha a uni-roo is rejeced for he impors IM in equaion (5) (Table 2.1). Therefore, his sysem has no coinegraion relaionship in erms of he non-sandardized daa. In he case of using he sandardized daa, we canno rejec he repaymen for he exernal 5
deb RD and impors IM following an I(2) process while he expors EX follows a firs-order inegraed process (Tables 2.1 and 2.2). We regard ha he power of he ADF es is very wea and conduc he coinegraion es for his sysem.. In he case of using he non-sandardized daa, we can find ha he sum of he impors and repaymen for he exernal debs MM follows a firs-order inegraed process and ha he expors EX follows a second-order inegraed process in equaion (6). Since he power of he ADF es is wea, we conduc he coinegraion es for he sysem of equaion (6). We obain a resul ha he sysem has a coinegraion vecor. We also es wheher a linear resricion on he coinegraion vecor is saisfied. As a resul, he es rejeced he null hypohesis of a linear resricion on he coinegraion vecor. One hand, in he case of using he sandardized daa, a uni-roo is rejeced for he expors EX. In he case of using he non-sandardized daa, all variables in his sysem follow firs-order inegraed processes in equaion (7) (Tables 2.1 and 2.2). The coinegraion es found ha his sysem has no coinegraion vecor (Table 2.3). In he case of using he sandardized daa, a uni-roo is rejeced for he rade balance TB. In equaion (8), he saionariy of he curren accoun defici CAD is he condiion of he curren accoun susainabiliy. We invesigae wheher his condiion is saisfied. Table 3.1 shows ha we canno rejec any uni-roo for he curren accoun defici. Therefore, each of he sysems of equaions (5), (6), and (7) are no coinegraed. On one hand, he sysem of equaion (8) has a uni roo for he curren accoun defici. Thus, hese resuls show ha he U.S. curren accoun defici is unsusainable from he perspecive based on he inernaional rade flows. 2.4. An Analysis on he Finance for Curren Accoun Deficis We invesigaed he U.S. curren accoun susainabiliy from he perspecives based on he domesic invesmen-saving relaionships and on he inernaional rade flows. These analyical resuls show ha he U.S. curren accoun defici is no 6
susainable. Nex, we invesigae which iems in he inernaional capial inflows finance he curren accoun defici in he long run. Firs, we analyze he coinegraion relaionship among he curren accoun defici, he inernaional capial flows, and he change in he foreign reserves. We conduc uni-roo ess for relevan variables in advance. The resuls are shown in Table 3.1. The resuls is ha he uni-roo is rejeced for he change in he foreign reserves R. The empirical resuls in he previous secion showed ha he curren accoun defici CAD is non-saionary. Therefore, he curren accoun defici CAD and he inernaional capial flows FB should be coinegraed in equaion (A11) in Appendix in order o be consisen wih he fac ha he change in he foreign reserves saionary. R is The resuls of uni-roo and coinegraion ess on he curren accoun defici and he inernaional capial flows are shown in Tables 3.1, 3.2, and 3.3. The resuls of uni-roo ess in he case of using he non-sandardized daa is ha a second-order inegraion is no rejeced for he financial balance FB while he curren accoun defici CAD follows a firs-order inegraion process. In he case of using he sandardized daa, he financial balance FB and he curren accoun defici CAD follow a firs-order inegraion process. We also conduc coinegraion ess beween he curren accoun defici and he financial balance. 3 The resuls are shown in Table 3.3. In he case of using he non-sandardized daa, he ran of coinegraion is full-ran and i conradics wih he assumpions. In he case of using he sandardized daa, we can find a coinegraion vecor in he sysem ha includes he curren accoun defici CAD and he financial balance FB. Nex, we conduc he analysis by decomposing he financial balance FB ino he direc invesmen balance DIB, he porfolio invesmen balance PIB and he oher invesmen balance OIB. Because he change in foreign reserves R is saionary, some of he oher variables (DIB, PIB, and OIB) in equaion (A12) in Appendix should 3 Though i is no rejeced for FB o follow he second-order inegraed process, we carried ou he coinegraion es on he sysem since i is said ha he power of ADF es is wea. 7
be coinegraed. The uni-roo ess show ha he curren accoun defici and he porfolio invesmen balance follow firs-order inegraed processes. Table 3.3 shows ha he coinegraion ran is 2 among he variables in he case of using he non-sandardized daa. The coinegraion ran is 1 among he variables in he case of using he sandardized daa. Thus, he coinegraion has full-ran and i conradics wih he assumpions of he analysis in he case of using he non-sandardized daa. On one hand, here is a coinegraion vecor in he sysem which includes he curren accoun defici and he porfolio invesmen balance in he case of using he sandardized daa. Accordingly, we can conclude ha he huge curren accoun defici in he Unied Saes has been financed by he porfolio invesmen from oher counries in he long run in erms of he saionary relaionship. 3. Simulaion Analysis on Depreciaion of he US Dollar for Susainable Curren Accoun Deficis In his secion, we invesigae how impac depreciaion of he US dollar would give on he curren accoun deficis in he Unied Saes and how much depreciaion of he US dollar is needed o mae he curren accoun deficis susainable. 3.1. Mehodology and Daa We simulae how much depreciaion he US dollar is needed for is curren accoun susainabiliy by using he esimaed parameers of vecor auoregression (VAR) models. Three VAR models are esimaed in our analysis. The firs model (Model 1) is a 2 variables VAR model which conains he exchange rae and he curren accoun. The second model (Model 2) is a 3 variables VAR model which conains he exchange rae, rade balance and facor income receip from abroad from a viewpoin of inernaional rade flows. The las model (Model 3) is a 3 variables VAR model which conains he exchange rae, saving-invesmen balances for he privae and he public secors from a viewpoin of domesic invesmen saving balance. 8
We suppose some cases of exchange rae movemens in order o simulae heir effecs on he curren accoun deficis. The supposed cases are ha he US dollar will sharply depreciae in he second quarer of 2004. We suppose hree cases where he US dollar will depreciae agains is rading parners currencies in erms of he real effecive exchange raes by 10%, 30%, and 50% in he second quarer of 2004. In addiion, we suppose wo hypoheical movemens of he exchange rae. One is ha he US dollar is supposed o mae similar movemens as he acual movemens afer he Plaza Accord during he hree years afer he Plaza Accord. The oher is ha he US dollar is supposed o mae similar movemens as he acual movemens during he Indonesian currency crisis period from he hird quarer of 1997 o he second quarer of 1998. In addiion o he daa used in he previous secions, we use he real effecive exchange rae of he US dollar as one of he vecor in he hree VAR models. The real effecive exchange rae daa is aen from he IMF s Inernaional Financial Saisics. Before we esimae he hree VAR models, we es he saionariy of relevan variables by using he Augmened Dicey-Fuller (ADF) ess. The resuls are shown in Table 4. The null hypohesis of non-saionariy is no rejeced for all of he variables a 5% significance level. Nex, we es coinegraion for he hree VAR models. The resuls are shown in Table 5. The firs and hird VAR models are no coinegraed while he second VAR model is coinegraed. The esimaed coinegraion vecor of he second VAR model is shown in Table 6. Considering he resuls as saed above, we esimae he differenced variables VARs in addiion o he original daa VARs, and he vecor error correcion model (VECM) for he second VAR model. 3.2. VAR Models We esimae he hree VAR models in his analysis. The firs VAR model (Model 1) is he wo-variable VAR conains he exchange rae and he curren accoun. In he second model (Model 2), we decompose he curren accoun ino he rade balance and he income receip. On he oher hand, from a viewpoin of he domesic invesmen 9
saving balance, he hird VAR model (Model 3) conains he exchange rae and he saving-invesmen balances for he privae and he public secors. The resuls of esimaing Model 1 esimaion are shown in Table 7. Almos all of he esimaes in erms of levels are significan a 5% level while all of he esimaes in erms of log difference are no significan. The esimaed parameers of Model 2 are shown in Table 8. Mos of he parameers are significanly esimaed a 5% significance level in he original variables esimaion, while he esimaes in difference variables esimaion are no significan. In he error correcion model esimaion, all variables excep for he income receip equaion are no significan. The resuls of Model 3 are shown in Table 9. In he VAR esimaion using original level variables, almos all of he esimaes are significanly esimaed hough all of he esimaes are no significan in he VARs using he difference variables. 3.3. Resuls of Simulaion Analysis 3.3.1. Impacs of Depreciaion of he US Dollar on he Curren Accoun Deficis In his subsecion, we show resuls of he simulaion analysis based on he hree esimaed VAR models for some scenarios of he US dollar depreciaion. A firs, we suppose hree cases where he US dollar will depreciae agains is rading parners currencies in erms of he real effecive exchange raes by 10%, 30%, and 50% in he second quarer of 2004. In addiion, we suppose wo hypoheical movemens of he exchange rae. One is ha he US dollar is supposed o mae similar movemens as he acual movemens afer he Plaza Accord during he hree years afer he Plaza Accord. The oher is ha he US dollar is supposed o mae similar movemens as he acual movemens during he Indonesian currency crisis period from he hird quarer of 1997 o he second quarer of 1998. A firs, we simulae he curren accoun behavior if he US dollar were sharply depreciaed by 10% in he second quarer of 2004. Figure 2 shows a curren accoun behavior ha is obained by he simulaion analysis based on Model 1. Figure 3 shows a 10
curren accoun behavior based on ha is obained by he simulaion analysis based on Model 2. Figure 4 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 3. The 10% depreciaion would gradually reduce he curren accoun deficis o 2% of GDP by 2018 in he cases of Models 1 and 2. On one hand, i would reduce he curren accoun deficis o 2% of GDP by 2008. Nex, we simulae he curren accoun behavior if he US dollar were sharply depreciaed by 30% in he second quarer of 2004. Figure 5 shows a curren accoun behavior ha is obained by he simulaion analysis based on Model 1. Figure 6 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 2. Figure 7 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 3. The 30% depreciaion would reduce he curren accoun deficis o 2% of GDP by 2011 and hen o 1.6% of GDP in 2018 in he cases of Models 1 and 2. On one hand, i would reduce he curren accoun deficis o 1.3% of GDP in 2008 and hen increase i o 2.5% in 2020 in he case of Model 3. Moreover, we simulae he curren accoun behavior if he US dollar were sharply depreciaed by 50% in he second quarer of 2004. Figure 8 shows a curren accoun behavior ha is obained by he simulaion analysis based on Model 1. Figure 9 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 2. Figure 10 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 3. The 50% depreciaion would reduce he curren accoun deficis o 0.8% of GDP by 2013 in he case of Model 1 and o 1% of GDP by 2015 in he case of Model 2. On one hand, i would reduce he curren accoun deficis o 0.5% of GDP in 2008 and hen increase i o 2.8% in 2020 in he case of Model 3. We suppose wo more scenarios of he US dollar depreciaion. The firs case is ha he exchange rae of he US dollar from he las quarer of 2003 o he hird quarer of 2006 move in he same way as he exchange rae of he US dollar acually moved afer he Plaza Accord. Figure 11 shows a curren accoun behavior ha is obained by he simulaion analysis based on Model 1. Figure 12 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 2. Figure 13 shows a curren accoun behavior based on ha is obained by he simulaion 11
analysis based on Model 3. The exchange rae movemens would reduce he curren accoun deficis o 2% of GDP by 2010 and hen o abou 1% in 2016 in he cases of Models 1 and 2. On one hand, i would reduce he curren accoun deficis o abou 1% of GDP in 2009 and hen increase i o 2.8% of GDP in 2020. The second case is ha he exchange rae of he US dollar depreciaes from he las quarer of 2003 in he same way as he Indonesia rupiah depreciaion in he Asian currency crisis from he second quarer of 1997 o he firs quarer of 1998. Figure 14 shows a curren accoun behavior ha is obained by he simulaion analysis based on Model 1. Figure 15 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 2. Figure 16 shows a curren accoun behavior based on ha is obained by he simulaion analysis based on Model 3. The exchange rae movemens would sharply reduce he curren accoun deficis o 2% of GDP by 2006 in he cases of Models 1 and 2. The curren accouns would be surplus in he case of Model 1 and equilibrium in he case of Model 2 in 2013. Afer hen, he curren accoun deficis would be 1% of GDP in 2020. On one hand, he curren accoun deficis would reduce o 2% of GDP in 2005 and hen urn o surplus by 2007. However, he curren accouns would urn o defici and hen increase o abou 3% in 2017. 3.3.2. Depreciaion of he US Dollar and Susainabiliy of he Curren Accoun We invesigae wheher each series of he simulaed curren accoun deficis is susainable. The Augmened Dicey-Fuller (ADF) es is used o invesigae he susainabiliy of he curren accoun deficis. The analyical resuls can conclude ha he simulaed curren accoun deficis would be susainable if he null hypohesis of uni-roo is rejeced by he ADF es. We conduc he uni-roo es no only for during he full sample period (from he firs quarer of 1976 o he fourh quarer of 2020) bu for he forecased for he sub-sample period (from he fourh quarer of 2003 o he fourh quarer of 2020). While Table 10 shows resuls of he uni-roo ess for he esimaed values during a esimaion period from he firs quarer of 1976 o he hird 12
quarer of 2003, resuls for he esimaed and simulaed values in each of he VAR models during he full sample period and he sub-sample period are shown in Table 11. We find he same endency from he resuls of Model 1 and 2. In hese models, he null hypohesis of uni-roo of he simulaed curren accoun canno be rejeced for he full-sample period while he null hypohesis of uni-roo can be rejeced for he forecased sub-sample period excep for he case of exchange rae movemens in he same way as he pos Plaza Accord (Case 4). From he resuls of he uni-roo ess for he simulaed curren accoun daa based on he hird VAR model (Model 3) conains he exchange rae and he saving-invesmen balances for he privae and he public secors, we find ha he null hypohesis of uni-roo for he series can be rejeced no only for he sub-sample period bu also for he full-sample period. Accordingly, we can regard ha he simulaed curren accoun deficis based on Model 3 are susainable for all of he cases of supposed exchange rae movemens. 4. Conclusion This paper invesigaed how much he US dollar should be depreciaed for reducing he curren accoun deficis in he Unied Saes. We conclude ha some scenarios of he US dollar depreciaion would reduce he curren accoun deficis o a level under 2% of GDP in he nex several years. The resuls are regarded as robus for each of he scenarios hough hey depend on our supposed VAR models. The resuls were derived from he 2 variables VAR model and he 3 variables VAR models by aing ino accoun relaionships beween he curren accouns and he exchange raes wihou exogenously reducing fiscal deficis. I is expeced ha smaller depreciaion of he US dollar should reduce he curren accoun deficis if he US governmen reduced he fiscal deficis a he same ime. In oher words, he US governmen should reduce he fiscal deficis in order ha i should preven a large depreciaion of he US dollar for reducing he curren accoun deficis and mae hem susainable in he near fuure. We can regard ha he simulaed curren accoun deficis based on he hird 13
VAR model (Model 3) conains he exchange rae and he saving-invesmen balances for he privae and he public secors are susainable for all of he cases of supposed exchange rae movemens. I is no so robus o conclude susainabiliy of he simulaed curren accoun deficis because he resul is obained in only Model 3. However, i is possible o obain susainable curren accoun series by aing ino accoun relaionships among he exchange rae, he privae secor s saving-invesmen balance, and fiscal deficis according o Model 3. The resul enables us o speculae ha he fiscal deficis are he mos imporan facors ha would mae he curren accoun deficis in he Unied Saes susainable in he near fuure. Appendix A.1. A Perspecive Based on he Domesic Invesmen-Saving Balance In his appendix, we explain he economeric mehods ha we use in our analysis and summarize he hree perspecives ha Mann (2002) poined ou. As he firs perspecive, we invesigae he relaionship among he domesic invesmen-saving balance, he curren accoun defici, and he exernal debs. As we described above, we invesigae he invesmen-saving balance for each of he secors (privae and public secors). Firs, he relaionship beween he change in he exernal debs in he end of he period D and he curren accoun defici CAD is represened by (A1) D D = CAD. 1 The curren accoun defici increases he exernal debs as he curren accoun defici is financed he inernaional capial inflows. This can be inerpreed as a budge consrain of he whole economy in period. Nex, we consider boh he domesic invesmen and saving behavior of each of he secors. 4 The budge consrain of he privae secor in period is represened by (A2) A A 1 = r A 1 S I, 4 Masubayashi (2002) analyzes ha each secor s budge consrain is saisfied from he view of he necessary condiion and sufficien condiion. Bu, we will no consider each secor s budge consrain for focusing on he curren accoun susainabiliy. 14
where is he ineres rae, is he asse holdings by he privae secor, which include he claims on he public secors and foreigners, is he savings of he privae secor, and is he invesmens of he privae secor. r A S I The budge consrain of he public secor (governmen) is represened by (A3) T G B r B B = 1 1, where is he governmen debs, is he governmen expendiures, and is he ax revenues. The governmen bonds are held by he privae secor and foreigners. B G T We obain since he governmen bond holdings by he privae secor equal o he liabiliies of he public secor o he privae secor. From equaions (A2) and (A3), we derive he relaionship beween he curren accoun defici and he domesic invesmen-saving balance as D A B = (A4) T S G I D r CAD = 1. We define he sochasic discoun facor of he privae secor as, where is consumpion, )] '( ) / '( [, C u C u Q = β C ) ( u is uiliy funcion and are saisfied, and 0 ) ( ' ' 0, ) ( ' < > u u 1, = Q. The Euler equaion of ineremporal consumpion is (A5). 1 ) (1 0, = = j j r Q E Subsiuing equaion (A4) ino equaion (A1), we obain a difference equaion of. We solve forward he equaion and use equaion (A5) o derive he whole economy s ineremporal budge consrain based on he domesic invesmen-saving balance: D (A6) ). ( lim ) (1 ) ( ) ( ) ( ) (, 1 0, 0, 0, 0, K K K D Q E D r T Q E S Q E G Q E I Q E = = = = = Now, we consider solvency of he exernal debs based on he equaion (A6). We suppose ha he ransversariy condiion 0 ) ( lim, = K K K D Q E o obain ). ( ) (1 0, 1 G I T S Q E D r = = This means ha he exernal debs a he presen ime should be equal o he presen 15
value of he ne savings in he presen and he fuure because he presen value of he exernal debs in he erminal period o converge o zero in order o saisfy he ransversariy condiion. Thus, he curren accoun susainabiliy condiion of he economy is ha he exernal debs a he presen ime have o be repaid by he ne savings in he presen and he fuure. Ahmed and Rogers (1995) derived he necessary and sufficien condiions of he curren accoun susainabiliy by ransforming he equaion (A6) o an applicable economeric mehod. According o hem, we difference he boh sides of equaion (A6) o obain: (A7) E = 0 ( Q, I ) E E = 0 = 0 ( Q ( Q, = lim E ( Q K, T, K G D ) E ) ( r D K 1 = 0 ) lim E K I ( Q 1, G ( Q S S ) 1, K 1 T ) D K 1 ), where is he difference operaor. From his equaion, Ahmed and Rogers (1995) show ha he necessary and sufficien condiions of he curren accoun susainabiliy or he ransversariy condiion is ha r D I, G, S, T 1, are coinegraed and have he coinegraion vecor (1,1,1, 1, 1) under some assumpions. 5 We analyze he coinegraion among hese variables o invesigae wheher he curren accoun susainabiliy condiion is saisfied. A.2. A Perspecive on he Inernaional Trade Flows Nex, we consider he solvency of he exernal debs from he inernaional rade flows as he second perspecive of he curren accoun susainabiliy. By 5 The following condiions should be saisfied. (i) I, G, S, T follow I(1) processes, (ii) he uiliy funcion is separable for ime, he marginal uiliy of consumpion u' ( C ) follows a random-wal process, and he subjecive discoun facor saisfies β (0,1), (iii) all riss are invarian for any ime period i.e. he covariance beween he sochasic discoun facor and each variable is consan, (iv) he series of he exernal deb follows I(1) process, and (v) he expecaion operaor E represens he raional expecaion. Under hese assumpions, Ahmed and Rogers (1995) show ha he saionariy of he righ hand side of equaion (7) is idenical o coinegrae he relevan variables. 16
absracing he ne receips of labor income and he curren ransfers in he balance of paymens, we can represen he curren accoun defici as (A8) CAD = r D 1 X M, where X is expors of goods and services and M is impors of goods and services. We subsiue equaion (A8) ino equaion (A1) o obain a difference equaion of D. We solve forward he difference equaions and use equaion (A5) o derive he economy s ineremporal budge consrain based on he inernaional rade flows: (A9) E = 0 ( Q, M ) E = 0 ( Q, X ) (1 r ) D 1 = lim E ( Q K, K D K ). The ransversariy condiion in equaion (A9) means ha he iniial exernal debs are repaid by he ne expors in he presen and he fuure. We difference he boh sides of equaion (A9) o obain: (A10) E = 0 ( Q, M ) E = 0 ( Q, = lim E ( Q K X, K ) ( r D D K 1 X ) lim E K M ) 1 ( Q 1, K 1 D K 1 ). According o equaion (A10), he necessary and sufficien condiions of he curren accoun defici susainabiliy should be ha he coinegraion vecor are coinegraed and have. Thus, from he perspecive on he inernaional rade flows, we analyze his coinegraion relaionship o invesigae he curren accoun susainabiliy. (1, 1, 1) r D X, M 1, A.3. A Perspecive on he Inernaional Capial Flows Finally, we consider he condiion of he curren accoun susainabiliy from he perspecive on he inernaional capial flows. The definiion of he balance of paymens ells us ha he relaionship beween he curren accoun defici and he inernaional capial flows should be represened by he following equaion: (A11) CAD = Fin Fou R, where Fin is he capial inflows, Fou is he capial ouflows, and R is he foreign 17
reserves. The definiion of he balance of paymens ells us ha equaion (A11) always holds. Accordingly, we should analyze wheher he privae capial flows finance he curren accoun defici. We analyze he coinegraion relaionship by omiing he change in foreign reserves in equaion (A11). If we find he coinegraion beween he curren accoun defici and he capial flows in equaion (A11), hen we will consider which iems in he financial accoun finance he curren accoun defici. Focusing on each of he inernaional capial flows in equaion (A11), we can rewrie equaion (A11) as (A12) CAD = DIB PIB OIB R, where DIB is direc invesmen in he financial accoun, PIB is porfolio invesmen in he financial accoun, and OIB is oher invesmen in he financial accoun. If variables in he sub-sysem including he curren accoun defici and some of he imes in equaion (A12) are coinegraed, hen he iems would suppor he curren accoun defici in he long run. Thus, we also es he coinegraion relaionship in he sub-sysem of he equaion (A12). References Miyao, R., (2001) Anoher Loo a Origins of he Asian Crisis: Tess of Exernal Borrowing Consrains, presened a he inernaional worshop The Asian Crisis and Afer, Economic and Social Research Insiue, Cabine Office. Ahmed, S. and J. H. Rogers, (1995) Governmen Budge Deficis and Trade Deficis: Are Presen Value Consrains Susained in Long-erm Daa? Journal of Moneary Economics, 36, pp.351-374. Bohn, H., (1995) The Susainabiliy of Budge Deficis in a Sochasic Economy, Journal of Money, Credi and Baning, 27, pp.257-271. Hused, S., (1992) The Emerging U.S. Curren Accoun Defici in he 1980s: A Coinegraion Analysis, Review of Economics and Saisics, 74, pp.159-166. Kudo, T. and E. Ogawa, (2003) The U.S. Curren Accoun Defici is suppored by he 18
Inernaional Capial Inflows? Hiosubashi Universiy, Faculy of Commerce and Managemen, Woring Papers, No. 92. Mann, C. L., (2002) Perspecives on he U.S. Curren Accoun Defici and Susainabiliy, Journal of Economic Perspecives, 16, pp.131-152. McKinnon, R. I., (2001) The Inernaional Dollar Sandard and he Susainabiliy of he U.S. Curren Accoun Defici, Brooings Papers on Economic Aciviy, 2001(1), pp.227-239. Masubayashi, Y., (2002) Are U.S. Curren Accouns Deficis Unsusainable?: Tesing for he Privae and Governmen Ineremporal Budge Consrains, mimeo. Milesi-Ferrei, G. M. and A. Razin, (1996) Curren-Accoun Susainabiliy, Princeon Sudies in Inernaional Finance, 81. Oserwald-Lenum, M., (1992) A Noe wih Quaniles of he Asympoic Disribuion of he Maximum Lielihood Coinegraion Ran Tes Saisics, Oxford Bullein of Economics and Saisics, 54, pp.461-472. 19
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