Obstfeld Rogoff Inter Temporal

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Chapter 34

THE I NTERTEMP OR L P P R O C H T O THEC U R R E N T C C O U N T

MAURICE OBSTFELD

University of California Berkeley

and

KENNETH ROGOFF

Princeton University

ont en t s

1. Int roduct ion

2. The curren t account : Basic concepts and his tor ical ove rvi ew

3. In te r t empora l approaches to the cur ren t accoun t

3.1. Deterministic models of the current account

3.2, Stochastic models of the current account

4. Empi r i ca l ev idence on the in te r t empo ra l approach

4.1. The relationship between national saving and domestic investment rates

4.2. Tests of intertemporal current-account models5. How useful i s the theory?

R e f e r e n c e s

1732

1733

1742

1743

1764.

1770

1776

17801792

1795

We thank Geun Mee Ahn, Harald Hau, Matthew Jones, Giovanni Olivei, and Clara Wang forexcellent research assistance and the National Science Foundation, the German Marshall Fund ofthe United States, and the Ford Foundation for financial support. Helpful suggestions were madeby David Backus, Richard Clarida, Jon Faust, Kiminori Matsuyama, Cedric Tille, and participantsin the March 1994 conference for the Handbook at Princeton University.

Handbook of International Economics vol. IIl Edited by G. Grossman and K. Rogoff© Elsevier Science B.V. 1995

1731



1 I n t r o d u c t i o n

T h e i n t e r t e m p o r a l a p p r o a c h v i e w s t h e c u r r e n t - a c c o u n t b a l a n c e a s t h e o u t c o m eo f f o r w a r d - l o o k i n g d y n a m i c s a v i n g a n d i n v e s t m e n t d e c i s i o n s . I n t e r t e m p o r a l

a na l y s e s o f t he c u r r e n t a c c oun t be c a me c ommon i n t he e a r l y 1980s a s a r e -

su l t o f papers by Bui te r (1981) , Obs t fe ld (1982) , Sachs (1981) , Svensson and

R a z i n ( 1983) , a nd m a ny o t he r s , a l t hough t he a pp r oa c h ha d e xp l i c i t p r e c u r s o r s

i n w o r k o n t r a d e a n d g r o w t h b y B a r d h a n ( 19 6 7) , B r u n o ( 1 97 0 ), an d H a m a d a

( 1969). 1 A s u s ua l, t h i s ne w f oc us in o pe n - e c o no my m a c r o e c on om i c s r e s u l t e d

b o t h f r o m t h e o r e t i c a l ad v a n c e s in o t h e r p a r ts o f e c o n o m i c s a n d f r o m e c o -

n o m i c e v e n t s t h a t e x i s ti n g o p e n - e c o n o m y m o d e l s s e e m e d i ll e q u i p p e d t o e x -

a mi ne .

L uc a s ' s ( 1976) in f l ue n t i a l c r i t ique o f e c on om e t r i c po l i c y e va l ua t i on w a s on ei m p o r t a n t t h e o r e t ic a l m o t i v a t i o n f o r a n i n t e r t e m p o r a l a p p r o a c h . H i s i n si s te n c e

on g r ound i ng po l i c y a na l y s i s i n t he a c t ua l f o r w a r d - l ook i ng de c i s i on r u l e s o f

e c o n o m i c a g en t s s u g g e s t ed t h a t o p e n - e c o n o m y m o d e l s m i g h t y i el d m o r e r e l i-

a b l e po l i c y c onc l us i ons i f de m a nd a nd s upp l y f unc t i ons w e r e de r i ve d f r om t he

op t i mi z a t i on p r ob l e ms o f hous e ho l ds a nd f i r ms r a t he r t ha n s pe c i f i e d t o ma t c h

r e d u c e d - f o r m e s t i m a t e s b a s e d o n a d h o c e c o n o m e t r i c s p ec if ic a ti o ns .

F u r t h e r i m p e t u s t o d e v e l o p a n i n t e r t e m p o r a l a p p r o a c h c a m e f r o m e v e n t s i n

t he w or l d c a p i t a l ma r ke t , e s pe c i a ll y t he s ubs t a n ti a l c u r r e n t - a c c o un t i m ba l a nc e s

t ha t f o l l ow e d t he s ha r p w or l d o i l - p r i c e i nc r e a s e s o f 1973- 74 a nd 1979- 80 . T he

d i v e r g e n t p a t t e r n s o f c u r r e n t -a c c o u n t a d j u s t m e n t b y i n d u s tr i a li z e d a n d d e v e l -

o p i n g c o u n t r i es r a i s e d t h e i n h e r e n t l y i n t e r t e m p o r a l p r o b l e m o f c h a ra c t e r iz i n g

t he op t i ma l dyna mi c r e s pons e t o e x t e r na l s hoc ks . N e i t he r t he c l as si ca l m on e t a r y

m o d e l s n o r t h e K e y n e s i a n m o d e l s i n v o g u e a t t h e t i m e o f f e r e d r e l i ab l e g u i d a n c e

on t h i s que s t i on . S i mi l a rl y , t he e xp l o s i on in r e c yc l e d ba n k l e nd i ng t o de ve l op i ng

c oun t r i e s a f t e r the f i rs t o i l s hoc k s pa r ke d f e a r s t ha t bo r r o w e r s ' e x t e r na l de b t l e v -

e ls m i g h t b e c o m e u n s u s ta i n a b le . T h e n e e d t o e v a l u a t e d e v e l o p i n g - c o u n t r y d e b t

l e ve l s a g a in l e d n a t u r a l l y t o t h e n o t i o n o f a n i n t e r t e m p o r a l l y o p t i m a l c u r r e n t -

account de f i c i t .

T h i s c h a p t e r s u r v e y s t h e t h e o r y a n d e m p i r i c a l w o r k o n t h e i n t e r t e m p o r a l

a pp r oa c h t o t he c u r r e n t a c c oun t a s i t ha s de ve l o pe d s inc e t he e a r l y 1980s . 2 R e -

c e n t l y , s ome r e s e a r c he r s ha ve s t ud i e d dyna mi c s t oc ha s t i c i n t e r na t i ona l mode l s

w i th c o m p l e t e A r r o w - D e b r e u f o r w a rd m a r k e t s f o r un c e r ta i n c o n s u m p ti o n . T h i s

p a r t i c u l ar o f f s h o o t o f t h e i n t e r t e m p o r a l a p p r o a c h i s t h e c o m p l e t e - m a r k e t s

1A num ber of studies published in the early 1980s based exchange-rate or baLance-of-paymentsmodels on intertemporal foundations. These contributions are surveyed in the chapter by MauriceObstfeld and Alan C. Stockman in volume 2 of this Handbook (Obsffeld and Stockman 1985).

2For a complementary survey, see Razin (t995).

1732



Ch 34: The Intertemporal Approach to the Current Account 1733

m o d e l . B e c a u s e c o m p l e t e - m a r k e t s m o d e l s f i t m o r e n a t u r a ll y i nt o M a r i a n n e

B a x t e r ' s c h a p t e r in th i s H a n d b o o k , t h e y a re s u m m a r i z e d o n l y b ri e fl y h e r e . W e

r e s e r v e t h e t e r m i n t e r t e m p o r a l a p p r o a c h - a s w e l l a s t h e b u lk o f o u r d is cu s -s i on - f o r m o d e l s w i th i n t e r n a t i o n a l b o r r o w i n g a n d l e n d i n g b u t n o t n e c e s s a r i ly

w i t h c o m p l e t e i n t e r n a t i o n a l m a r k e t s i n s t a t e - c o n t i n g e n t c l a i m s .

T h e c h a p t e r b e g i n s w i t h a n i n t r o d u c t o r y s e c t io n , S e c t i o n 2, th a t e x p l o r e s t h e

c o n c e p t o f t h e c u r r e n t a c c o u n t , it s b e h a v i o r in r e c e n t h i s to r y , a n d t h e c o n c e p -

t u al a d e q u a c y o f m e a s u r e s o f t h e c u rr e n t a c c o u n t a s r e p o r t e d b y g o v e r n m c m

a g e n c i e s .

S e c t i o n 3 l a y s o u t b a s i c i n t e r t e m p o r a l m o d e l s o f t h e c u r r e n t a c c o u n t , s ta r1

i n g w i t h t h e d e t e r m i n i s t i c c a s e a n d t h e n e x p l o r i n g s t o c h a s t ic m o d e l s . S e c t i o n 4

s h o w s h o w s t o c h a s ti c m o d e l s c a n b e u s e d t o d e v is e te s ts o f t h e i n t e r t e m p o r a i

a p p r o a c h , a n d g o e s o n t o e v a l u a t e t h e r e su l t in g e v i d e n c e .

M u c h o f t h e d i sc u s s io n t h r o u g h S e c t i o n 4 o f th i s c h a p t e r f o c u s e s o n posizi v~ ~

p r e d i c t i o n s o f t h e i n t e r t e m p o r a l a p p r o a ch . A m a j o r a d v a n t a g e o f t h e a p p r o a c h ,

h o w e v e r , i s i t s r e l e v a n c e t o n o r m a t i v e q u e s t i o n s . S e c t i o n 5 t h e r e f o r e t a k e s u I,

t h e r e a s o n s w h y a n i n t e r t e r m p o r a l a p p r o a c h t o t h e c u r r e n t a c c o u n t i s e s s e n t i a l

f o r s o u n d p o l i c y f o r m u l a t i o n .

F i n a ll y , w e n o t e t h a t , g i v e n t h e e x t e n s i v e r e c e n t l i t e r a t u r e t h is c h a p t e r a s p i r e s

t o e n c o m p a s s , t h e r e a r e s e v e r a l i n s ta n c e s w h e r e s p a c e p e r m i t s u s o n l y to s k e t c h

a l g e b r a i c d e r i v a t i o n s . W e t r y t o a l e r t t h e r e a d e r w h e n e v e r i n t e r m e d i a t e a l g e b r a

h a s b e e n p r u n e d e s p e c i a l ly s e v e re l y , s o t h a t h e o r s h e w il l n o t b e c o m e b o g g e dd o w n d u r i n g a f i r s t r e a d i n g . S p a c e l i m i t s l i k e w i s e a l l o w u s t o p r o v i d e o n l y a n

i l lu s t r a ti v e r a t h e r t h a n a n e x h a u s t i v e s e t o f r e f e r e n c e s .

2 T h e c u r r e n t a c c o u n t : B a s i c c o n c e p t s a n d h i s to r i c a l o v e r v i e w

A c o u n t r y ' s c u r r e n t - a c c o u n t b a l a n c e o v e r a n y t i m e p e r i o d is t h e i n c r e a s e i n

r e s i d e n t s ' c l a i m s o n f o r e i g n in c o m e s o r o u t p u t s , l e s s t h e i n c r e a s e i n si m i l a r

f o r e i g n - o w n e d c la i m s o n h o m e i n c o m e o r o u t p u t . T h u s , i n th e o r y , t h e c u r r e n t

a c c o u n t i n c lu d e s n o t o n l y e x p o r t s le ss i m p o r t s ( b r o a d l y d e f i n e d t o i n c lu d e a llt h e i n c o m e o n a n d p a y o u t s o n c r o s s - b o r d e r a s se ts : d i v id e n d s , i n te r e s t p a y m e n t s ,

i n s u r a n c e p r e m i a a n d p a y m e n t s , e t c . ) , b u t a l s o n e t c a p i t a l g a i n s o n e x i s t i n g

f o r e i g n a s se t s. F r o m t h e c l o s e o f W o r l d W a r I u n t il r e l a t i v e l y r e c e n t ly , m o s t

c o u n t r i e s ' h o l d in g s o f f o r e i g n a ss e ts h a d b e e n l i m i te d b o t h i n q u a n t i t y a n d s c o p e ,

s o th e l a t t e r c o n s i d e r a t i o n w a s s e c o n d a ry . A f o c u s o n t h e c u r r e n t a c c o u n t a s th e

n e t e x p o r t b a l a n c e l e d s o m e e c o n o m i c t h i n k e r s t o v ie w r e l a t iv e in t e r n a t i o n a l

p r i c es as i ts c e n t r a l d e t e r m i n a n t . T h u s w a s b o r n t h e e l a s ti c it ie s a p p r o a c h t o

t h e c u r r e n t a c c o u n t , u n d e r w h i c h t h e d e t e r m i n a n t s o f i n t e r n a t i o n a l e x p e n d i t u r e

l e v e l s a n d i n c o m e s a r e h e l d f ix e d i n th e b a c k g r o u n d w h i l e s t a ti c p r i c e e l a st i c it i e s

o f d e m a n d a n d s u p p l y d e t e r m i n e t h e n e t i n t e r n a t i o n a l f l o w o f c a p it a l.



734 M Obstfeld and K Rogoff

As undergraduate macroeconomics texts demonstrate, however, the current

account also is national saving less domestic investment. If saving falls short of

desired investment, for example, foreigners must take up the balance, acquiringas a result claims on domestic income or output. This alternative viewpoint,

which led to the absorption approach, stresses how macroeconomic factors must

ultimately determine international borrowing or lending patterns [Alexander

(1952)].

The intertemporal approach to current-account analysis extends the absorp-

tion approach through its recognition that private saving and investment deci-

sions, and sometimes even government decisions, result from forward-looking

calculations based on expectations of future productivity growth, government

spending demands, real interest rates, and so on. The intertemporal approach

achieves a synthesis of the absorption and elasticities view, however, by account-

ing for the macroeconomic determinants of relative prices and by analyzing the

impact of current and future prices on saving and investment.

Internat ional capital flows, in the form of trade credits and commercial traffic

in such assets as jewels and precious metals, were already common by biblical

times. By the early fourteenth century, Italian banks spanning western Europe

and the Levant had become large-scale lenders to sovereigns such as King Ed-

ward III of England, whose invasion of France in 1340, aided by foreign finance,

initiated the Hundred Years War. The two most powerful Florentine banking

houses, those of the Bardi and the Peruzzi, were bankrupted along with manylesser banks in 1343 when Edward proved unable to meet his obligations. But

as Europe recovered from this early banking crisis and from the subsequent

Black Death (1348), international financial linkages grew strong once again.

The Catholic church, through its usury doctrine, unwittingly promoted the in-

ternationalization of banking in this period. While domestic loans for interest

were prohibited, there was no definitive ban on exchanges of bills payable in

different countries and currencies, even when the terms negotia ted included im-

plicit interest charges [de Roover (1966)]. Theological constraints thus led the

largest banks to mainta in extensive systems of foreign branches.

The expulsion of the Jews from the Iberian peninsula at the end of the fif-teen th century, followed by widespread and continuing persecutions of Protes-

tants after the Reformation, created networks of refugee communities with

both the motivation and connections to move capital between countries. Dur-

ing European wars of the seventeenth and eighteenth centuries, international

capital markets developed further as some governments turned to large-scale

debt sales to foreigners. [See Neal (1990).] By the early nineteenth century at

the latest, the outlines of modern international capital markets are visible in

investors search for profit opportunities on distant shores.

The era of the classical international gold standard, spanning the late nine-

teenth and early twentieth centuries, is often held up as a benchmark case



Ch 34: The Intertemporat Approach to the Current Account 1735

o f u n f e t t e r e d c a p i ta l m o b i l i t y b e t w e e n n a t io n s . F i g u r e 2.1 s h o w s d a t a o n s av -

i ng , i n v e s t m e n t , a n d t h e i r d if f e r e n c e , t h e c u r r e n t a c c o u n t , f o r a d o z e n c o u n -

t r i e s o v e r 1 8 8 5 - 1 9 1 3 . ( A l l d a t a a r e n o m i n a l f l o w s d i v i d e d b y a n o m i n a l i n -c o m e o r o u t p u t m e a s u r e . ) 3 T h e g r a p h s i n d e e d s h o w s e v e r a l e x a m p l e s o f la r g e

a n d p r o t r a c t e d c u r r e n t - a c c o u n t i m b a l a n c e s , i n d i c a to r s o f e x t e n s iv e t r a d e a c r o ss

t im e . C a n a d a r a n p e r s i s te n t d e fi ci ts w h i ch , b y t h e e v e o f W o r l d W a r I, e x-

c e e d e d 1 5 p e r c e n t o f g ro s s n a t i o n a l p r o d u c t ( G N P ) . T h e s e l a r g e flo w s w e r e

u n d o u b t e d l y p r o m o t e d b y C a n a d a s c l os e p o li ti c a l a n d c u l t u ra l l in k s w i th t h e

U n i t e d K i n g d o m , t h e l a r g e s t l e n d e r . B u t e v e n c o u n t r i e s w i t h o u t s u c h c l o s e

t ie s to p o t e n t i a l l e n d e r s w e r e a b l e t o d r a w e x t e n s i v e l y o n i n t e r n a t i o n a l c a p -

i ta l m a r k e t s . J a p a n r a n a n e x t e r n a l d e f ic it o f 1 0 p e r c e n t o f n a t io n a l e x p e n -

d i t u r e i n f i n a n c i n g i t s 1 9 0 4 - 1 9 0 5 w a r w i t h R u s s i a . D u r i n g W o r l d W a r I , t h e

c o u n t r y r a n a c o m p a r a b l e s u r p lu s t o h e l p f in a n c e it s fi n a n ci a ll y b e l e a g u r e d

a l l i es . 4

D a t a f r o m t h e i n t e r w a r p e r i o d , s h o w n in F i g u r e 2 .2 , r e v e a l a p a r ti a l r e s u r g e n c e

o f n e t i n t e r n a t i o n a l b o r r o w i n g a n d l e n d i n g a s p o s t w a r r e c o n s t r u c t i o n p r o g r e s s e s,

b u t t h is p r o c e s s c o m e s t o a s u d d e n h a l t as r e s t ri c ti o n s o n i n t e r n a t i o n a l p a y m e n t s

p r o l i f e r a t e a f t e r t h e o n s e t o f t h e G r e a t D e p r e s s i o n . s P o st - 1 9 4 5 d a t a d i sc l o se a

r e v e r s e e v o l u t i o n . I n it ia l ly , c u r r e n t - a c c o u n t i m b a l a n c e s w e r e s li gh t b e c a u s e o r

o f f ic i a l r e s t r i c t i o n s o n i n t e r n a t i o n a l c a p i t a l m o v e m e n t s , w i t h m o s t i n d u s t r ia l -

c o u n t r y c u r r e n c i e s b e i n g i n c o n v e r t i b l e t h r o u g h 1 95 9. A f t e r t h e e a r l y 19 7 0s ( s e e

F i g u r e 2 . 3 ), n e t i n t e r n a t i o n a l c a p i ta l flo w s e x p a n d e d a s a r e s u lt o f p e t r o d o l l a rr e c y c li n g , t h e r e m o v a l o f m a n y i n d u s t r ia l - c o u n t r y r e s tr i c ti o n s o n i n t e r n a t io n a l

p a y m e n t s f o l lo w i n g t h e a d o p t i o n o f f lo a t in g e x c h a n g e r a te s , a n d t e c h n o l o g i c a l

e v o l u t i o n i n t h e f i n a n c i a l i n d u s tr y . B y t h e 1 9 8 0s , t h e l a r g e s t i n d u s t r i a l c o u n t r i e s ,

G e r m a n y , J a p a n , a n d t h e U n i t e d S t a te s , w e r e s h o w i n g s u b s t a n ti a l e x t e r n a l i m -

b a l a n c e s . A t t h e s a m e t i m e m a n y d e v e l o p i n g c o u n t r i e s, c a u g h t i n a d e b t c ri sis

b r o u g h t o n i n p a r t b y v i g o r o u s b o r r o w i n g i n th e 1 9 70 s, f o u n d t h e m s e l v e s d e -

n i e d a c c e s s t o r e s o u r c e i n fl o w s . O n l y i n th e e a r l y 1 9 9 0 s d i d t h i s s t a r k b o r r o w i n g

c o n s t r a i n t b e g i n t o e a s e .

U n f o r t u n a t e l y , t h e s a v i n g a n d i n v e s t m e n t f lo w s r e p o r t e d i n n a t i o n a l i n c o m e

a n d p r o d u c t a c c o u n t s ( N I P A ) a n d s h o w n i n F i g u r e s 2.1 t h r o u g h 2 .3 d o n t a l w a y sc o n f o r m c l o s e ly t o t h e o r e t i c a l l y c o r r e c t c o n c e p t s o f s a v in g a n d i n v e s t m e n t , p a r -

t i c u l a r ly w h e n i n t e r n a t i o n a l c a p i t a l m o b i l i t y is e x t e n s i v e . O n e e s p e c i a l l y s e r i o u s

d e f e c t is t h e f a i l u r e o f N I P A n a t i o n a l i n c o m e m e a s u r e s f u l ly t o r e f l ec t c ap i ta l

g a i n s a n d l o s se s o n n e t f o r e i g n as se ts . D u r i n g 1 9 91 , f o r e x a m p l e , t h e N I P A m e a -

3These data, as w ell as th ose shown in F igure 2.2 below , are from Jones and Obstfeld (1994).Finland was actually a possession of R ussia during the 1885-1913 period, b ut it was afforded a fairam ount of ad ministrative autonomy.

4Fo r a discussion of wars and the Japanese current accou nt during the first part o f the tw entiethcentury, see Ob stfeld and Ro goff (1996), ch. 1.

5See Eiche ngreen (1990) for further discussion.



1736

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Sweden

0.3o.¢3(~ 0.2

= 0.10

-0.2 +-/- /--I I I I I ', ', ', ', ; ', ', ; ; ; ; I I t I t I I 111913

1888 1892 1899 1906

0.4

Norway

0.3O.Z(9 0.26

c 0.10.

9U'.o. 1

-0 8 i 1892 1899 1906 191

0.4

Denmark

0.3

El'6~ 0.2

¢ 0.1o

0 ,>.

-0.1 .............................................................................................................................

• 0.2 ' , ' , ' , : ' , ', ', ', L ~ I i I I I I t I I ~ I I ++ -~ -~ -I -~ -~

1885 1892 1899 1906 1913

0.4

Italy

0 . 3

~0 2c 0.1

2 ~ l l : : ~ l ; : l ; ; ; ; l l l t l E I I l i t i l l

~'1 885 1892 1899 1908 1913

- I n v e s t m e n t - S a v i n g - - C u r r e n t A c c o u n t

Figure 2.1. Saving, investment, and the current account: Classical gold standard, 1885-1913.



Ch. 34: The lnter temporal App roa ch to the Current Acco unt1 7 3 7

United States0 4

~ . 0 . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Z

0 . 2 ...................................................................

c 0.1 . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . .o

u. - 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1885 1892 1899 1906 1913

United Kingdom0 . 4 . . . .

O . 0 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

t : 3

(=9 0 . 2

= 9 1

~ 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .

u 0.1 ......................................

1885 1892 1899 1906 1913

0.4

anada

zm 0 . 3

0 0 , 2

c 0.1 .................................................................................9

0

- 0 . 1 . .. .. .. .. .. . ~-~ . . . . . . . . . . . . . . . . . . . . . ~

\ /

1885 1892 1899 1906 1913

France0 , 4

O ~ 0 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C~

0 0 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., o

0 ~ ~ ~ ~- ~ ~. •

_0 , 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0 ,2 ¢ i i i i t=-i r i i i i i [ f--. +-; ; 'r ; : ; ; ; I I I

1885 1892 1899 1906 1913

0.4

Germany

0 . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .z

z 0,2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e 0 1

0

0 2 ~ ~ ~ ~ ' ~ - ~ ' 2 Z > ~ ' ~ : ~ . ~ - ~ ' . ~ - ' ~

u . . 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• .2 I ~ I ~ ~ : I ; : : , : ; i i { ~ i i I-~F =t= ~- i i i i L

1885 1892 1899 1906 1913

Japan

0 4

0 , 3ILl

Z

O 0,2

c 0.1,o

u . -0 .1. . . . . . . . . . . . " - ~ . .. .. .. .. .. .. .. .. . ~ , . .. .. .. .. .. .. .. .. .. .. ..

-0 .2 ~-~ -i f , : , : ; ; ; ; ; ; ; ; i i r ~ i i ~ [ J i

1885 1892 1899 1906 1913

- - I nves t ment - - Sav ing

Fig u r e 2 , 1 , continued.

C ur r en t Accoun t



1 7 3 8

0 . 4

ust ra l i a

0 . 3o

= 0 . 10

0 . .. . . . . . . .. . . . . . . . . . . . . . . . . . . , - ' ~ ~ - , • , ; ~ . ~ . .. .. .. .

u . . 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . > ,~ . . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. .

- 0 . 2 i r i ~ L i i i i i ~ i i i ~ i i

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

0 4

M . O b s t f e l d a n d K . R o g o f f

Fin land

0 . 3

o 2

c 0 . 1

9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -

- 0 . 1

- 0 2 l l q ~ l l l l l ~ l l l l l i l l

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

Swed e n

0 . 4

e . 0 . 3 . . . . . . . . . . . . . . . . . . . . . . . . .

oO 0 . 2

= 0 . 1 ............................................................................... o

a. 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 0 . 2 i i i i i i i i i i i i i r i i i - i - -

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

No rwa y

0 . 4

0 . 3

0 . 2

c 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .o

u. 0.1 .................................................................................

- 0 . 2 - - ~ - - - - - - - ÷ - - ~ t - . f - - f - - ~ - - f - = . f - - t ~ f - - - i i i i

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

Denma r k

0 . 4

0 . 3o .c 3

O 0 , 2 . . . . . . . . . . . . . . . . . . . . . . .

6= 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. o

- 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 0 . 2 i + ~ ~ ~ ~ , , ~ , ~ - ~ - - + - + - - ~ + ,1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

0 . 4

I ta ly

0 . 3 . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .a .

z

= 0 1._o

u . - 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 0 . 2 I I I I I I I I I I I I I I l I I I I

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

- - I n v e s t m e n t - - S a v i n g C u r r e n t A c c o u n t

F i g u r e 2 . 2 . S a v i n g , i n v e s t m e n t , a n d t h e c u r r e n t a c c o u n t : I n t e r - w a r e r a , 1 9 2 1 - 1 9 3 9 .



Ch 34: The lntertemporal Approach to the Current AccountI 7 3 9

0.4United States

0 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

z

° 0 2

c 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0

' -0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 0 ' 2 1 9 L I 2 + ~ - ~- * ~ E i b i ~ - ~ ~1 9 2 7 1 9 3 3 1 9 3 9

0 . 4

0.3Q.E3

(3 0 .2

`6.~ o.1

a . 4 . 1

- 0 . 21 9 2 1

United Kingdom1

J

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IJ

1 9 2 7 1 9 3 3 9 3 9

anada

0,4

0.3 ..........................................................................................o.

zL~ 0.2

c 0 .1.9

-0 ,1 ..................................................................................................................

-0 ,2 ~- I p i i ]=l I I I I P q I I I I I I

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

Germany0 4

0 . 3el.zZ 0 2

`6

e o .1o

u. -17.1

- 0 ' 2 1 9 ~ 1 1 9 2 7 1 9 3 3 1 9 3 9

0.4

Japan

z.u 0. 3 ....................

Z( 3 0 . 2

= 0.1 . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . .

0

o

u. -0 .1

-0 2 ', ', = ; , ; i i i r P i i ] I I l [ E

1 9 2 1 1 9 2 7 1 9 3 3 1 9 3 9

- Inv e s tme nt -Sa v ing

F i g u r e 2 2 continued

- Cur re nt Ac c ount



1 7 4 0

A u s t r a l i a

0 . 4

0 0.20 3 .....................................................................~

c 0 .1 ...............................................................................

0 .~-- -.-.-~ ...........................................................

u . 0 . 1 . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . .

- 0 2 I i ~ i l - + - - - : - ~ t t - - ~ + - - ~ + - F - +1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

M . O b s t f e l d a n d K . R o g o ¢ ]

F i n l a n d

0 . 4

OL 0 .3

0 0 . 2

= 0 .1 . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . .. o

O . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . .

u . d ) . l ~ / ~

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

S w e d e n

0 . 4

0 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .n

0 0 2 •

6= 0 . 1 ................................................................................

O -- . w ~ , < - ~ - ~ . ~ . - .g ~ 2 2 2 2 , - ; ' ~ - ' ~ . . . . . ~ ~ ; ~

t u - 0 . 1 . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

- 0 2 t I - F - - I I I I I I I I ) J r - - ~ - - ~

9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

0 . 4

N o r w a y

0 . 3L

¢ 3

0 0 2

6= 0 .1o

u . - 0 .1

- 0 . 2 ~ -

1 9 7 3

~ . . / /

......... ,- . ~:.~;/ ............................................................

i P I I I ~ i I I ~ i I I I I I I

1 9 7 9 1 9 8 5 1 9 9 1

D e n m a r k

0 . 4

0 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E L

? 0.2= 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

= O

u . 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 0 , 2 + I I + - - ~ I I 1 i - -f - -4 ~ t - -+ - - k -- u ~ I I

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

0 . 4

I t a l y

c~L 0.3 i

O 0 . 2

= 0 . 1 ............................................................................2

0 ~ . . ~ 2 ~ - ~ - ~ . ~ g ; : ~ . z ~ - ~ - ~ - ~ - ~ - , - ~ ; .-

- 0 . 1 .......................................................................................

- 0 . 2 - t I I I . t - ~ ; i ; ; , l ; ; ; - I I t I I

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

- - I n v e s t m e n t - S a v i n g C u r r e n t A c c o u n t

F i g u r e 2 .3 . S a v i n g , i n v e s t m e n t , a n d t h e c u r r e n t a c c o u n t : P o s t - B r e t t o n W o o d s e r a , 1 9 7 3 - 1 9 9 1 .



C h 3 4 : T h e I n t e r t e m p o r a l A p p r o a c h t o t h e C u r re n t A c c o u n t 1741

U ni t e d S t a t e s

0 . 4 0 . 4

0 3

~ 0 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .

,- 0 .1 ................................. ............................................ ............................

. 2

~ -0 .1 ................... ................................ ................................. ..............................

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

0 . 313,

(9 0 . 2

c 0.1o_

u. 0A

U n i t e d K i n g d o m

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

1 9 7 3 1 9 7 9 1 9 8 5 i ~ 9 ~

a n a d an 4

0 . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 . 2

6, - 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .o

÷ - + -

u . - 0. 1 ...............................................................................................

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

r a n c e

0 . 4

o . 0 . 3 . . . . . . . . . . . . . . . . .

( 9 0 , 2 . . . . . . . . . . . . . . . . . . - , . P ~

, - 0 . 1 . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. .

. 2

m 0 .1 .............................................................................................

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

0 . 4

G e r m a n y

0 , 3 ...............................................................................................................0 .

0 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6¢ 0 .1 ................................................................................................................O

u . 4 ). 1 ............................................................................................................

1 9 7 3 1 9 7 9 1 9 8 5 1 9 9 1

J a p a n

o.

• 0 . 3

0 2 Z I I 7

= 0 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i0

u 0. 1 .......................................................................... {i

1 9 7 3 1 9 7 9 1 9 8 5 1 g ~ ,~

- i n v e s t m e n t - S a v i n g

Figure 2 . 5 . col~[muea

C u r r e n ~ A c c o ~



1742 M. ObstJeld and K. Ro go ff

s u r e o f s a v i n g l e ss i n v e s t m e n t f o r t h e U n i t e d S t a t e s , t h e c u r r e n t a c c o u n t , w a s

r e p o r t e d b y t h e U .S . D e p a r t m e n t o f C o m m e r c e a s - 3 . 7 b il l io n . T h e D e p a r t -

m e n t o f C o m m e r c e a ls o c a l cu l a te d , h o w e v e r , th a t o n a m a r k e t - v a l u e ba s is , U . S .a s s e t s h e l d a b r o a d a t t h e e n d o f 1 99 0 a p p r e c i a t e d i n d o l l a r v a l u e b y 6 7 .8 b i l li o n

( m o r e t h a n t h e e n t i r e 1 99 1 p u r c h a s e s o f f o r e i g n a s s e t s b y U . S . re s i d e n t s , 6 2 .2

b i ll i o n ). A t t h e s a m e t i m e , t h e d o l l a r v a l u e o f f o r e i g n c l a i m s o n t h e U . S . a t t h e

e n d o f 19 9 0 r o s e b y 1 7 2 .8 b i ll i o n ( m o r e t h a n 2 . 5 t i m e s a s l a r g e a s t h e 1 9 9 1

f o r e i g n p u r c h a s e s o f U . S . a s s e ts , 6 7 .0 b i ll io n ) . 6 I n e c o n o m i c t e r m s , t h e t r u e

d o l l a r U . S . c u r r e n t - a c c o u n t d e fi ci t f o r 19 91 is p r o b a b l y m u c h c l o s e r t o - 3 . 7

b i l l io n + 6 7 .8 b i l l io n - 1 7 2. 8 = - 1 0 8 . 7 b i l l i o n t h a n t o i ts s i m p l e N I P A m e a -

s u r e . A n d e v e n t h is f ig u r e r e f le c t s o n l y p a r t i a l c o v e r a g e o f i n t e r n a t i o n a l a s s e t

h o l d i n g s .

T h e n u m b e r s i n F i g u r e s 2.1 t h r o u g h 2 . 3 a r e m i s l e a d i n g f o r a n o t h e r r e a -

s o n . A s S e c t i o n 3 s h o w s , i t i s c h a n g e s i n r e a l n o t n o m i n a l , a s s e t h o l d i n g s

t h a t m a t t e r f o r a c o u n t r y 's w e l f a re . T h u s , N I P A m e a s u r e s o f t h e c u r r e n t a c -

c o u n t , e v e n i f c o r r e c t e d t o i n c l u d e n o m i n a l c a p i t a l g a i n s a n d l o ss e s , m u s t b e

a d j u s t e d a s w e l l to c o r r e c t f o r t h e i n f l a t io n a r y e r o s i o n o f f o r e i g n a s s e t s ' r e a l

v a l u e s .

T h e s e p r o b l e m s p l a g u e a ll o f t h e e m p i r i c a l l i t e r a t u r e d i s c u ss e d i n S e c t i o n 4 ,

a l t h o u g h i t w o u l d b e p o s s ib l e to r e m e d y t h e m s o m e w h a t f o r a fe w in d u s tr i al

c o u n t r i e s . I n e m p i r i c a l l y e v a l u a t i n g t h e o r i e s i t is o b v i o u s l y c r u c i al t o a c h i e v e t h e

b e s t p o s s i b l e m a t c h b e t w e e n t h e c o n c e p t u a l f r a m e w o r k a n d t h e d a t a b r o u g h tt o b e a r i n t e s t i n g i t .

3 Inter tem pora l approaches to the current accoun t

A r e a li s ti c e c o n o m i c m o d e l i n c o r p o r a t i n g a ll e l e m e n t s r e l e v a n t t o th e t y p ic a l

c o u n t r y ' s c u r r e n t a c c o u n t w o u l d b e h o p e l e s s l y c o m p l e x . I n s t e a d o f a t t e m p t i n g

t o c o n s t r u c t s u c h a c o m p r e h e n s i v e m o d e l , w e t u r n i n t h is s e c ti o n t o a s u c c e s-

s i on o f m o d e l s t h a t i l lu s tr a te w h a t w e b e l i e v e t o b e t h e k e y e l e m e n t s i n fl u e n ci n g

s a v i n g - i n v e s t m e n t b a l a n c e s i n th e w o r l d e c o n o m y . I n fo l l o w i n g th i s s t r at e g y , w el a r g e ly p a r a l le l t h e d e v e l o p m e n t o f th e o r e t i c a l t h in k i n g o n t h e c u r r e n t a c c o u n t

o v e r t h e p a s t f i ft e en y e a r s A n i m p o r t a n t s e t o f in s ig h t s c an b e d e r i v e d e v e n

f r o m d e t e r m i n i s t i c m o d e l s ; t h i s i s o u r f i r s t o r d e r o f b u s i n e s s . W e t h e n i n t r o d u c e

u n c e r t a in t y a b o u t t h e e c o n o m i c e n v i r o n m e n t a n d d e d u c e a n u m b e r o f e s se n -

t ia l m o d i f ic a t i o n s o f t h e p r e c e d i n g n o n s t o c h a s t i c f r a m e w o r k . T h e i n t r o d u c t io n

o f u n c e r t a i n t y i s, o f c o u r s e , a p r e r e q u i s i t e f o r t h e e m p i r i c a l a n a l y s is o f t h e i n -

t e r t e m p o r a l a p p r o a c h t h a t w e d i s c u s s i n S e c t i o n 4 .

6The Un ited States capital-account surplus, eq ua l to 67.0 billion - 62.2 billion = 4.8 billion,

differs from the recorded current-accou nt deficit by a statistical discrepancy of - 1.1 billion.



Ch 34: The Intertempora l Approach to the Current Acc oun t

3 .1 . D e t e r m i n i s t i c m o d e l s o f t h e c u r r e n t a c c o u n t

7 4 3

T h e f ir st b r o a d c l a s s o f m o d e l s t o b e d e s c r i b e d a s s u m e s t h a t i n d i v i d u a l d e c i s i o nm a k e r s h a v e p e r f e c t f o r es i g h t a n d c o m p l e t e in f o r m a t i o n a b o u t t h e ir e c o n o m i c

e n v i r o n m e n t . W h i l e t h e s e m o d e l s l a ck re a l is m a l o n g s o m e d i m e n s i o n s , t h e y

s e r v e a t l e a s t t w o v e r y u s e f u l p u r p o s e s . F i rs t , t h e y e l u c i d a t e a n u m b e r o f qu e:~

t io n s f o r w h i c h u n c e r t a i n t y i s o f s e c o n d a r y i m p o r t a n c e , a n d s e c o n d , t h e y p r o v i d e

a b e n c h m a r k a g a in s t w h i c h t o m e a s u r e t h e p r e d ic t i o n s o f r ic h e r s t o c h a s ti c ro o d

e ls . A s w e s h a l l s e e l at e r , s t o c h a s t i c m o d e l s i n w h i c h r e a l b o n d s a r c t h e o n i v

a s s e ts c o u n t r i e s t r a d e i m p l y r e s p o n s e s t o s h o c k s s im i l a r t o t h e i m p u l s e r e s p o n s e s

o f d e t e r m i n i s t i c m o d e l s .

3 .1 .1 . A on e -go od m od e l w i th r epre sen ta t i ve na t io na l r e s iden t s

C o n s i d e r a s m a ll o p e n e c o n o m y th a t p r o d u c e s a n d c o n s u m e s a s in g le c o m p o s

i te g o o d a n d t r a d e s f r e e l y w i t h t h e r e s t o f t h e w o r l d . F r e e t r a d e i n c l u d e s t h e

i n t e r n a t i o n a l e x c h a n g e o f as s et s. W e a s s u m e t h a t t h e o n l y t r a d e d a s s e t is a

c o n s u m p t i o n - i n d e x e d b o n d w i t h fi x e d f a c e v a l u e t h a t p a y s n e t i n t e r e st a t t h e

r a t e rt b e t w e e n p e r i o d s t - 1 a n d t . I m p o r t a n t ly , l a b o r is i n t e r n a t i o n a l l y i m m o -

b i le . In p e r c a p i t a t e r m s , l e t A t+ l d e n o t e t h e e c o n o m y s s t o c k o f n e t f o r e i g n

c l ai m s a t t h e e n d o f p e r i o d t , Y t n e t d o m e s t i c p r o d u c t o r o u t p u t in p e r i o d r,

C t p r i v a t e c o n s u m p t i o n , G t g o v e r n m e n t c o n s u m p t i o n , a n d It n e t i n v e st m e m = ~

T h e n t h e i d e n t i t y li n k i n g n e t f o r e i g n a s s e t a c c u m u l a t i o n - t h a t is, th c c urlT elli

a c c o u n t , C A t - t o t h e s a v i n g - i n v e s t m e n t b a l a n c e i s:

C A t = A t + l - A t = r t A t + Y t - C t - G t - L t (3 .1)

D e f i n e t h e m a r k e t d i s c o u n t f a c t o r f o r d a t e s c o n s u m p t i o n b y

1

R , . , = r I = , + l 1 + 3 . 2 /

( w h e r e Rt , t = 1 ). F o r w a r d i t e r a t i o n o f e q . (3 .1 ) l e a d s to

o o

(1 + rt) A t = Z Rt,, (C. ,. + Gs + I~ - Ys ) + l im R, ,sAs+lS ~ O O

S t

B e c a u s e f o r e i g n l e n d e r s w i ll n o t a l l o w th e e c o n o m y t o r o l l o v e r a d e b t in de l;o

i n i t e l y t h r o u g h u n l i m i t e d b o r r o w i n g , t h e c o n d i t i o n l im s-~ ooRt,sA s+ l >~ 0 a p p l i c s

a b o v e . T h e r e s u l t i n g i n t e r t e m p o r a l b u d g e t c o n s t r a i n t f o r t h e e c o n o m y i s t hu s :

o o o o

~- ~ R t , s(C , . + Gs + is ) < (1 + r t ) A t + Z R t , s Y s (3 .3)

s=t s=t

I n t h e m o d e l s w e s u r v e y n o r e s o u r c e s a r e w i l li n g l y f o r g o n e , s o ( 3 .3 ) a l w a y s h o l d s

7 W e w i l l a s s u m e f o r s i m p l i c i t y t h a t c a p i t a l d o e s n o t d e p r e c i a t e .



1 7 4 4 M. Obst fe ld and K. Rogof f

w i t h e q u a l i t y . I n t h a t c a s e , (3 .3 ) s t a t e s t h a t t h e p r e s e n t v a l u e o f t h e e c o n o m y s

e x p e n d i t u r e s m u s t e q u a l i ts i n i ti a l n e t f o r e i g n w e a l t h p l u s t h e p r e s e n t v a l u e o f

d o m e s t i c p r o d u c t i o n .T h e i n t e r t e m p o r a l b u d g e t c o n s t r a i n t d e l i m i ts t h e f e a s i b le c h o ic e s o f t h e e c o n -

o m y . T o d e s c r i b e t h e c i r cu m s t a n c e s i n w h i c h c u r r e n t - a c c o u n t i m b a l a n c e s w i l l

a r is e , h o w e v e r , o n e m u s t s p ec i fy h o w t h e c o m p o n e n t s o f e x p e n d i t u r e a n d o u t -

p u t a r e d e t e r m i n e d . W e a s s u m e t h a t t h e re p r e s e n t a t i v e c o n s u m e r m a x i m i z e s t h e

t i m e - s e p a r a b l e f u n c t i o n

ut = Z uI C d I3.4)s t

w h e r e / 3 c ( 0 , 1 ) , u ' ( C) > O , u ( C) < O .T h e s t r o n g i n t e r t e m p o r a l s e p a r a b i l i t y o f u ti l i ty a s s u m e d i n ( 3.4 ) w i ll f o r m t h e

b a c k b o n e o f o u r f o r m a l a n a ly s i s . B e f o r e g o i n g f u r t h e r , i t i s w o r t h w h i l e t o o f f e r

s o m e j u s t i f i c a t i o n f o r t h i s d e c i s io n .

( 1) O n e m i g h t w i s h t o s t ar t w i th a v e r y g e n e r a l i n t e r t e m p o r a l l y n o n s e p a r a -

b l e u t i l it y f u n c t i o n o f t h e f o r m U t = U ( C t , C t+ l , . . .) . B u t t h i s w o u l d y i e l d f e w

c o n c r e t e a n d t e s t a b l e b e h a v i o r a l p r e d i c t i o n s . I n s t e a d w e p r e f e r t o b e g i n w i t h

a t r a c t a b l e b a s i c s e t u p l i k e e q. (3 .4 ) w i t h s t r o n g i m p l i c a t io n s . P r e f e r e n c e s t h e n

c a n b e g e n e r a l i z e d i f t h e b a s ic s e t u p s e e m s t o b e l e a d i n g u s a s t r a y /

(2 ) A g g r e g a t i o n , a c r os s b o t h g o o d s a n d i n d iv i d u a ls , m a y c a u s e i n t e r t e m p o -

r a l d e p e n d e n c i e s a p p r o x i m a t e l y t o c a n c e l o u t a t t h e l e v e l o f t o t a l p e r c a p i t a

c o n s u m p t i o n .

(3 ) A t t h e l e v el s o f t i m e a g g r e g a t i o n c o m m o n i n m a c r o e c o n o m i c m o d e l s , th e

a s s u m p t i o n o f i n t e r t e m p o r a l s e p a r a b i l it y is n o t i m p l a u s i b l e. I n a n y e v e n t , w h i l e

e m p i r i c a l r e s e a r c h o n d a t a a t t h e s e f r e q u e n c i e s h a s r a i s e d i n t e r e s t i n g q u e s t i o n s

a b o u t t h e t i m e - s e p a r a b l e u t i l i t y m o d e l , it d o e s n o t c l e a r l y p o i n t t o a s u p e r i o r

n o n s e p a r a b l e a l t e r n a t i v e .

H a v i n g d e f e n d e d o u r c h o i c e o f i n t e r t e m p o r a l l y a d d i t i v e u ti l it y f u n c ti o n s , w e

n o w b e g i n t o p u r s u e t h e i r i m p l i c a t i o n s . L e t l i t b e t h e r e a l v a l u e o f d o m e s t i c

f i r m s a t th e e n d o f p e r i o d t - 1 ( af t e r p e r i o d t - 1 d i v i d e n d s h a v e b e e n p a i d ) ,B t t h e s t o c k o f i n te r e s t - e a r n i n g c la im s o w n e d b y t h e d o m e s t i c p r i v a t e s e c t o r a t

t h e e n d o f t - 1 , w t t h e r e a l w a g e i n p e r i o d t , L t t h e p e r c a p i t a s u p p l y o f la b o r ,

a n d T t l u m p - s u m t ax e s le v ie d b y th e h o m e g o v e r n m e n t . T h e n t h e i n t e r te m p o r a l

b u d g e t c o n s t r a i n t o f t h e r e p r e s e n t a t i v e c o n s u m e r i s 9

8 p l a u si b l e n o n - t i m e - s e p a r a b l e a l t e r n a t i v e s t o 3 .4 ) c a n b e a n a l y z e d ; [ s ee , f o r e x a m p l e , D e v e r e u x

a n d S h i 1 9 9 1 ), O b s t f e l d 1 9 8 2) , S h i a n d E p s t e i n 1 9 9 3 ), a n d S v e n s s o n a n d R a z i n 1 9 83 ) ].

9 S tr ic t ly s p e a k i n g , t h e w a y t h e n e x t c o n s t r a i n t i s e x p r e s s e d a s s u m e s p e r f e c t f o r e s i g h t b e t w e e n

d a t e s t - 1 a n d t, s o t h a t a r a t e o f r e t u r n o f rt a c t u a l l y i s e a r n e d o n s h a r e s e x p o s t . T h i s a s s u m p t i o n

i s m a d e o n l y t o a v o id c l u t t e ri n g t h e n o t a t i o n , a n d i s n o t i m p o s e d i n w h a t f o ll o w s. A m o r e g e n e r a l

f o r m u l a t i o n s i m p l y w o u l d re p l a c e 1 + rt Vt b y t h e e x p o s t v a l u e i n c l u s iv e o f d i v i d e n d s ) o f s h a r e s

b o u g h t o n d a t e t - 1 .



Ch. 34: The Intertemporal Ap pr oa ch to the Current Ac co un t 1745

O 0 0 < 3

~ R, ,~c~ = (1 + r , ) (v t + Bt ) + ~ Rt ,s (w sLs - tO C3.51

s=t s=t

W h e n ( 3.4 ) is m ax i m i zed s u b j ec t t o (3 .5 ), co n s u m p t i o n n eces s a r i l y fo l l o w s t h e

i n t e r t e m p o r a l E u l e r e q u a t i o n

u ( C t ) = / 3 ( 1 + r t + l ) u ( C t + l ) ~ c . ,

Th i s o p t i ma l i t y co n d i t io n , s t r e s s ed l o n g ag o b y I r v in g F i s h e r ( 1 93 0 ), eq u a t e~

t h e m ar g i n a l r a t e o f s u b s t i t u t i o n o f p r e s en t f o r f u t u r e co n s u m p t i o n , w h M .. ; ,

j u s t / 3 u ( C t + l ) / u ( C t ) , t o t h e p r ic e o f f u t u r e c o n s u m p t i o n in t e r m s o f p r e s e m

c o n s u m p t i o n , 1 / ( 1 + r t + l ) . A n i mp l i ca t i o n i s t h a t , l e av i n g a s i d e d i s c r ep an c i e s

b e t w e e n / 3 a n d 1 / ( l + r t < ) , o p t i m i zed co n s u m p t i o n w ill f o l l o w a s mo o h , c,onst:ap. ,p a t h ( r eca l l t h a t u ( C ) i s s t r i c t l y concave) . A conven ien t c losed- fo rm descr ip l i ,w_

o f t h e cu r r en t a cco u n t i s o b t a i n e d b y s p ec ia l iz i n g f u r t h e r t o t h e ca s e in w h ic ~

u ( C ) t ak es t h e i s o e l a s t i c f o r m

c 1 - 1 / ~ - 1u ( C ) -

1 - 1 / o

wi th o - > 0 t he e l as t i c i t y o f i n t e r t e m po ra l subs t i t u t i on , In t h is case (3.6 9 impiic ,:

t h a t o p t i m a l c o n s u m p t i o n g r o w t h o b e y s

C t + l = / 3 ~ ( 1 + r t < ) ~ C t (3.7)

T h e c o n s u m p t i o n p a t h d e s c r i b e d a b o v e m u s t s a t is fy t h e e c o n o m y ' s in t e rt o m

pora l cons t r a in t ; u s ing (3 .7 ) t o e l imina t e C s ( s > t ) f rom (3.3) show s 1ha l l he

e c o n o m y ' s d a t e t c o n s u m p t i o n w i l l b e :

C t = 1 + r t ) A t E s = t R t , s Y s - G s - Is ) 3 . 8 )oo RE = t , , , ( / 3 ~ - I R , , ~ ) ~

Eq u a t i o n ( 3 .8 ) le ad s t o an i ll u mi n a t in g g en e r a l ch a r a c t e r i za t i o n o f t h e cu r r cm

a c c o u n t. D e f i n e t h e " p e r m a n e n t " l e v el o f v a r i a b l e X o n d a t e t , X , , b y

£ _ Es t R,,,X~.

a n d d e f i n e ( / 3 / R ) ~ as t h e f o l l o w i n g w e i g h t ed av e r ag e o f r a t i o s o f ( s - - 0 - p e r i o d

s u b j ec t i v e an d m ar k e t d i s co u n t f ac t o r s r a i s ed t o t h e p o w er 0.:

x -, oo R { ° s - t / R ho-( / 3 / R ) ~ = z ..,s = t t , s v ~ / t,s 2

~o RE , , = t t ~ s

T h e n , a f t e r m a n y s te p s , eqs . (3 .1 ) and (3 .8 ) show the cu r ren t ac cou n t su rp lus on



1746 M . O b s t f e l d a n d K . R o g o f j :

d a t e t t o b e :

C A t = ( r t - f t ) A t + ( l i t - L ) - ( G t - G t )

- ( / t - ~ ) + [1 1 ] A t + B - - d t - i t ) 3 . 9 )

( A s w e a l l u d e d i n t h e in t r o d u c t i o n , t h e r e a r e s e v e r a l p la c e s w h e r e w e a d v i s e

t h e r e a d e r t o c o n s i d e r h o l d i n g o f f o n r e p r o d u c i n g a r e s u lt u n t il a la t e r r e a d i n g ;

t h i s is t h e l ir s t. ) E q u a t i o n ( 3 .9 ) y i e l d s a n u m b e r o f i m p o r t a n t p r e d i c t i o n s ( e a c h

o f w h i c h r e q u i r e s a c e t e r i s p a r i b u s c l a u s e ): 1°

( 1) I f t h e e c o n o m y is a n e t f o r e i g n c l a im a n t a n d t h e w o r l d i n t e r e s t r a t e i s

a b o v e i ts p e r m a n e n t a v e r a g e , t h e n t h e c u r r e n t a c c o u n t w il l b e i n g r e a t e r s u r p lu s

a s p e o p l e s m o o t h c o n s u m p t i o n i n th e f a c e o f t e m p o r a r i l y h i g h fo r e i g n i n t e re s t

i n c o m e . I f th e e c o n o m y is a n e t f o r e i g n d e b t o r , t e m p o r a r i l y h i g h i n t e r e s t ra t e s

w i l l h a v e a n o p p o s i t e c u r r e n t - a c c o u n t e f f e c t .

( 2) O u t p u t a b o v e i ts p e r m a n e n t l e v e l w i ll c o n t r i b u t e t o a h i g h e r c u r r e n t -

a c c o u n t s u r p lu s , a g a i n d u e t o c o n s u m p t i o n s m o o t h i n g . S i m il ar ly , t h e p r i v a t e

s e c t o r w i ll u s e f o r e i g n b o r r o w i n g t o c u s h i o n i ts c o n s u m p t i o n f r o m a b n o r m a l l y

h i g h g o v e r n m e n t c o n s u m p t i o n a n d i n v e s t m e n t n e e d s.

( 3 ) T h e l a s t t e r m i n ( 3. 9) re f l e ct s c o n s u m p t i o n t i l t i n g d u e t o d i v e r g e n c e s i n t h e

c u r r e n t a n d f u t u r e p e r io d s b e t w e e n w o r l d r e a l i n t e r e s t r a t e s a n d t h e d o m e s t i c

r a t e o f t i m e p r e f e r e n c e , (1 - f l ) / f i . W h e n t h e h o m e c o u n t r y is o n a v e r a g e m o r ei m p a t i e n t t h a n t h e r e s t o f t h e w o r l d , fl is l o w e r t h a n f u t u r e w o r l d i n t e r e s t ra t e s

w i l l t e n d t o b e , r e s u l t i n g i n ( f l / R ) ~ < 1 . T h e r e w i ll t h e n b e a s e c u la r t e n d e n c y

t o w a r d c u r r e n t - a c c o u n t d e f ic it s, a n d t h u s t o w a r d s e c u l a r ly in c r e a s in g f o r e i g n

d e b t a n d d e c l i n i n g c o n s u m p t i o n . W h e n i t is f o r e i g n e r s o n t h e o t h e r h a n d w h o

a r e ( o n a v e r a g e ) m o r e i m p a t i e n t , s o t h a t ( f i / R ) ~ > 1 , c o n s u m p t i o n ' s t i m e p a t h

w i ll h a v e a n u p w a r d ti l t. T h e t il ti n g e ff e c t is p r o p o r t i o n a l t o t h e e c o n o m y ' s

p e r m a n e n t r e s o u r c e s. A l s o , t h e ti lt in g e ff e c t is s t r o n g e r t h e h i g h e r is t h e c a s e

o f i n t e r t e m p o r a l s u b s t i tu t i o n i n c o n s u m p t i o n , m e a s u r e d b y o-.

i°A less general ve rsion of eq. (3.9) is presented by Sachs (1982). To derive the first entry on theright-hand sid e of (3.9), observe that

l r t _ r t + 2 s T _ t + l R t , sr s ~ s ~ t R t , s r s F t.¢X2 R Oa O0

where we have m ade use of the fact that

~ ~ R t , sr s = 1

s - - t l

The rest is straightforward; for details, see Ob stfeld and Ro goff (1996), ch. 2.



C h . 3 4 : T h e I n t e r t e m p o r a l A p p r o a c h t o t h e C u r r e n t A c c o u n t 1747

Before exp lo r ing t he shor t - run impl i ca t i ons o f eq . (3 .9 ) , i t i s u sefu l t o cons ider

s o m e o f t h e m o d e l s p r e d ic t i o n s f o r s t e a d y - s t a te c u r r e n t - a c c o u n t b e h a v i o r i n a

g r o w i n g e c o n o m y . A s w e s h a ll s e e , a g r o w i ng e c o n o m y c a n r u n a c u r r e n t- a c c o u n tdef ici t indef in i tely .

I n c o r p o r a t in g t h e i n v e s t m e n t e f f e c ts o f g r o w t h f o r c c s o n e t o m o d e l e x p li c-

i tl y t h e l in k a g e b e t w e e n c a p i t al a c c u m u l a t io n a n d p r o d u c t i o n . A s s u m c t h a t t he

p r o d u c t i o n f u n c t i o n f o r a s m a l l e c o n o m y i s C o b b - D o u g l a s :

g , = O t K ~ L 1 -°~

(c~ < 1 ) , w h e r e K t is t h e en d o f p e r i o d t - 1 cap i t a l s t o ck ( av a i l ab l e f o r p r o d u c t i o n

i n p e r i o d t ), L is t h e co n s t an t l ab o r f o r ce ( w h i ch w e w i ll n o r ma l i ze t o 1 f o r

co n v en i en ce ) , an d t h e p r o d u c t i v i t y co e f f i c i en t 0 g r o w s s o t h a t

Or+1 = 1 + g l - c ~ o t

w i t h g > 0 . A s s u me a l s o t h a t t h e cap i t a l s t o ck can ad j u s t i n a p e r i o d , w i t h o u l

i n s t a l la t i o n co s ts . I n t h e ab s en ce o f u n a n t i c i p a t ed s h o ck s , th e m ar g i n a l p r o d u c t

o f cap i t a l , a O t K ~ - 1 , t h u s mu s t eq u a l r , t h e co n s t an t w o r l d i n t e r e s t r a t e ; r > g

b y a s s u m p t i o n . 11 Th e n , i n a s t ead y - s t a t e eq u i l ib r i u m, i n v e s t m en t is e a s i l y s h o w n

t o b e

~ ) 1 / 1 c0 - ~ )

i t = K t + l - K t = g = Y t

O u t p u t a n d i n v e s t m e n t t h e r e f o r e b o t h g r o w a t r a t e g . I f g o v e r n m e n t s p e n d i n g

i s ze r o , t h en o n e can u s e ( 3.9 ) t o s h o w t h a t t h e o p t i ma l c u r r en t a cco u n t i s g i v en

b y

C A t = A , + I - A t = - [ 1 ( l + r )~ / 3 ~ ] A t - l + g - ( l + r ) ~ f i ~ (1 ~ ) Ytr - g

D i v i s i o n b y Y t y i e l d s a d i f f e r en ce eq u a t i o n i n A / Y ,

At+lYt+l = ( ( l + r ) ° ~ ° x j A t l7 / Y t 1 + g - ( 1 +) ~ / 3 ~ - ~ -g T ~ _ - - ~ ( 1 - ~ )

P r o v i d e d ( 1 + r ) ~ ° < 1 + g , t h e s t ea d y s t a t e is s tab l e ; it is t h e n eg a t i v e n u m b e r

1 - ( a g / r ) (3.10)A / Y - - ( r - g )

N o t i c e t h a t , b e c a u s e a g / r = I / Y , t h e l o n g - ru n r a t i o o f f o r e i g n d e b t t o o u t p u t

e q u a l s t h e r a t io t o c u r r e n t o u t p u t o f th e e n t ir e p r e s e n t v a l u e o f f u t u r e o u t p u t

n e t o f i n v e s tm e n t .

11For the world eco nom y as a whole, the assumption that the growth rate do es not exce ed the

intere st rate can be justif ied using the standard Cass-Koopmans gen eral equil ibrium growth model.



748 M O b s t fe l d a n d K R o g o f f

W h a t s iz e d e b t - o u t p u t r a t i o d o e s e q. ( 3 .1 0 ) i m p l y ? S u p p o s e t h e w o r l d r e a l

i n t e r e s t r a t e r i s 8 p e r c e n t p e r y e a r , g is 4 p e r c e n t p e r y e a r , a n d a = 0 .4 . T h e n

A / Y - - - 2 0 , a n d t h e e c o n o m y ' s t r a d e b a l a n c e su r p l u s e ac h p e r i o d m u s t b e- ( r - g ) A / Y = 8 0 p e r c e n t o f G D P

S u c h l a r g e d e b t l e v e l s a n d d e b t b u r d e n s a r e n e v e r o b s e r v e d i n p r a c t i c e :

e c o n o m i e s t h a t m u s t b o r r o w a t m a r k e t i n t e r e s t ra t e s r a r e l y h a v e d e b t s a s g r e a t

a s a s in g le y e a r ' s G D R T h e a n o m a l o u s p r e d i c ti o n p o i n t s t o s o m e s h o r t c o m i n g s

o f t h e m o d e l . W i t h f i n i te li f e ti m e s , i n d i v i d u a l s c u r r e n t l y a l iv e w o u l d n ' t b e a b l e

t o b o r r o w a g a i n s t t h e e n t i r e p r e s e n t v a l u e o f t h e e c o n o m y ' s o u tp u t . T h e r e is n o

a l l o w a n c e i n th e m o d e l f o r s o v e r e i g n ri sk . F i n al l y , w e n o t e t h a t t h e w o r l d i n t e r -

e s t r a t e r i s d e t e r m i n e d b y t h e r e s t o f t h e w o r l d ' s g r o w t h r a t e . I n t h is e x a m p l e ,

h o w e v e r , t h e w o r l d g r o w t h r a t e m u s t e q u a l ( 1 + r )~ /3 ~ [ s ee O b s t f e l d a n d R o g o f f

( 1 9 9 6 ), c h . 2] , w h i c h i s l e ss t h a n 1 + g b y a s s u m p t i o n . B u t i f a s m a l l e c o n o m y

w e r e t o g r o w f a s t e r t h a n t h e w o r l d f o r a s u f fi c i e n tl y l o n g p e r i o d , i t w o u l d c e a s e

b e i n g s m a l l a n d t h e f ix e d i n t e r e s t r a t e a s s u m p t i o n w o u l d b e v i o l a t e d . I f, o n t h e

o t h e r h a n d , t h e c o u n t r y ' s g r o w t h r a t e e v e n t u a l l y c o n v e r g e s t o t h e w o r l d g r o w t h

r a t e , t h e c o u n t r y ' s a b i l it y a n d d e s i r e to b o r r o w f r o m w o r l d c a p it a l m a r k e t s a r e

r e d u c e d .

3 .1 .2 . T h e r o l e o f c o m p a r a t i v e a d v a n t a g e

T h e t h e o r y o f i n t e r n a t i o n a l t r a d e o f f e r s a u s e f u l p e r s p e c t i v e o n t h e s e r e s u l ts .

T h e r e a s o n i s th a t f o r e i g n b o r r o w i n g a n d l e n d i n g c a n b e v i e w e d a s i n t e r t e m p o r a l

trade, t h a t i s, a s t h e e x c h a n g e o f c o n s u m p t i o n a v a i l a b l e o n d i f f e r e n t d a t e s . T h e

p r i n c i p l e o f c o m p a r a t i v e a d v a n t a g e t h u s a p p l i e s .

I m a g i n e t h a t t h e h o m e c o u n t r y fa c es a c o n s t a n t w o r l d i n t e re s t r a te e q u a l t o

l + r = 1 / f l a n d t h a t l i t > Ys f o r s > t . E q u a t i o n ( 3.9 ) p r e d ic t s t h a t ( a b s e n t o t h e r

c u r r e n t - p e r m a n e n t d i f fe r e n c es ) t h e c o u n t r y w i ll h a v e a c u r r e n t - a c c o u n t s u r p lu s .

T h e p r i n c i p le o f c o m p a r a t i v e a d v a n t a g e m a k e s t h e s a m e p r e d i c t io n . I n t h e a b -

s e n c e o f t r a d e , t h e c o u n t r y ' s a u t a r k y i n t e r e s t r a t e s , e q u a l t o u ( Y t ) / ~ ~ - t u ( Y ~ ) ,

l ie b e l o w t h e c o r r e s p o n d i n g w o r l d i n t e r e s t r a t e s , (1 + r) s~t. I t t h e r e f o r e p a y s f o rt h e r e p r e s e n t a t i v e r e s i d e n t t o e x p o r t p r e s e n t c o n s u m p t i o n b y l e n d i n g a b r o a d ,

s in c e p r e s e n t c o n s u m p t i o n i s c o m p a r a t i v e l y c h e a p a t h o m e , a n d t o i m p o r t f u t u r e

c o n s u m p t i o n b y r e c ei v in g r e p a y m e n t f o r t h e l o a n s a t a l a t e r d a te .

S i m i l a rl y , t e m p o r a r i l y h i g h i n v e s t m e n t n e e d s c a n r a i s e a c o u n t r y ' s a u t a r k y i n -

t e r e s t r a te a b o v e t h e w o r l d le v e l, m a k i n g i t a n i m p o r t e r o f p r e s e n t c o n s u m p t i o n ,

t h a t i s , a n e x t e r n a l b o r r o w e r .

T h i s p e r s p e c t i v e m a k e s c l e a r t h a t i t is o n l y t h e c o u n t r y - s p e c i f ic o r i d i o s y n c r a t i c

c o m p o n e n t s o f s ho c k s t h a t r e s u lt in c u r r e n t - a c c o u n t i m b a l a n c es . T h e g l o b a l

c o m p o n e n t s o f s h o c k s , i n c o n t r a s t , a f f e c t a ll c o u n t r i e s s i m i l a r ly a n d t h u s o p e n u p

n o n e w o p p o r t u n i t i e s f o r g a in s t h r o u g h i n t e r t e m p o r a l t r a d e . C o u n t r i e s c a n n o t a l l



Ch. 34: The lntertemporal App roach to the Current Ac cou nt 1749

s m o o t h c o n s u m p t i o n p e r f e c t l y i n th e f a ce o f a sh o c k t h a t t e m p o r a r i l y d e p re s s e s

w o r l d o u t p u t , f o r e x a m p l e . I n s t e a d , t h e w o r l d r e a l i n t e r e s t r a t e i s b i d u p a n d a l l

c o u n t r i e s t il t t h e i r c o n s u m p t i o n p a t h s u p w a r d .

3 .1 .3 . M o d e l i n g o u t p u t f l u c tu a t i o n s a n d i n v e s t m e n t

O u r e a r l i e r in v e s t m e n t e x a m p l e a s s u m e d t h a t a n a t i o n s c a p i t al s t o ck c a n b c

a d j u s t e d w i t h o u t c o s t t o e q u a t e c a p i ta l s m a r g i n a l p r o d u c t t o t h e w o r l d i n t e re s t

r a t e . E m p i r i c a l o b s e r v a t i o n m a k e s t h is a s s u m p t i o n d i f fi c u lt t o s w a l l o w : e v e n a ,

t h e i n d u s t r y l e v el , w e s i m p l y d o n o t o b s e r v e l a r g e d i s c r e te c h a n g e s i n st o c k s o f

c a p i t a l o v e r v e r y s h o r t p e r i o d s . I f t h e r e a r e c o s t s t o i n s t a ll i n g c ap i t a l, h o w e v e r ,

c a p i t a l s to c k s w i l l m o v e m o r e s l u g g i sh l y a n d p r o t r a c t e d d e v i a t i o n s o f c a p it a l >

m a r g i n a l p r o d u c t f r o m r a r e p o ss i b le . A s i m p l e m o d e l i l l u s tr a t e s h o w c o s t l y

i n v e s t m e n t a f f e c ts c u r r e n t - a c c o u n t d y n a m i c s . 12

A s s u m e t h a t f in a l o u t p u t is p r o d u c e d a c c o r d i n g t o th e s t a n d a r d h o m o g e n e o u s

a n d c o n c a v e p r o d u c t i o n f u n c t i o n O t F K t , L t ) , w h e r e , a s b e f o r e , Ot c a p t u r e s s h i f t s

i n t o t a l f a c t o r p r o d u c t i v i t y , a n d w h e r e K t is g i v e n b y p a s t i n v e s t m e n t d e c i s i o n s.

A f ir m m a k i n g d e c i si o n s o n d a t e t m a x i m i z e s th e p r e s e n t d i s c o u n t e d v a l u e o f

i t s p r o f i t s ( w h i c h e q u a l t h e d i v i d e n d s s h a r e h o l d e r s r e c e i v e ) :

[ a I ]~ _ _ ,R , , , O , F K , , L s ) - w , r s - 1 ~ - 5 g ] ,J 3 . 1 1 )

S f

A b o v e , a eI . ; / K t ) i s t h e d e a d w e i g h t o u t p u t c o s t o f i n s t a l l i n g

K ~ + 1 - K , = I t 3 . l 2 ~

u n i t s o f c a p i t a l , w h e r e a > 0 i s a n a d j u s t m e n t - c o s t p a r a m e t e r . A c c o r d i n g t o

( 3.1 1 ), t h e e f f i c ie n c y o f i n v e s t m e n t i n p r o d u c i n g i n s t a l l e d c a p i ta l d e c l i n e s a t a n

i n c r e a s i n g r a t e a s t h e r a t i o o f i n v e s t m e n t t o i n s t a l l e d c a p i t a l r is e s. G i v e n ( 3.1 1 ),

t h e e c o n o m y s n e t o u t p u t o n d a t e t is Y t = O t F K t , L t ) - ~ I 2 / K t ) .

T h e c o n d i t i o n s f o r m a x i m i z i n g p r o f it s ( 3 .1 1 ) s u b j e ct t o ( 3.1 2 ) i n c l u d e

I - q t - 1 g 3 . 1 3 )

a n d t h e i n v e s t m e n t E u l e r e q u a t i o n

a 2O t + I F K K , + I , g t + l ) + ~ l , + l / K t + l ) + q , <

= (3.14)qt 1 + rt+1

12Matsuyama (1987) develops an open-econo my mo del with costly investment. The effects of

residential investm ent are studied in M atsuyam a (1990).



1 7 5 0 M . O b s t f e l d a n d K . R o g o f f

w h e r e q t ( T o b i n s q ) i s t h e L a g r a n g e m u l t i p l i e r o n c o n s t r a i n t ( 3 .1 2 ) a n d h a s t h e

u s u a l i n t e r p r e t a t i o n a s t h e s h a d o w p r i c e o f i n s t a l l e d c a p i t a l.

F o r w a r d i t e r a t i o n o n ( 3 . 1 4 ) s h o w s t h a t

q t = ~ R t, s [ O s F K K s , L s ) + 2 I s~K s)2]s = t + l

(3 .15)

( w e h a v e e x c l u d e d b u b b l e s i n t h e p r ic e o f c a p it a l) . E q u a t i o n ( 3. 15 ) s t a te s t h a t

q t , t h e e x d i v i d e n d s h a d o w p r i c e o f a u n i t o f c a p i t a l a t t h e e n d o f p e r i o d t ,

e q u a l s t h e p r e s e n t v a l u e o f i ts f u t u r e m a r g i n a l p r o d u c t s p l u s t h e p r e s e n t v a l u e

o f i t s f u t u r e c o n t r i b u t i o n s t o l o w e r i n g t h e c o s ts o f i n v e s t m e n t . 13

M u l t i p l y e q . ( 3 .1 4 ) b y K t + l and use eq . (3 .12 ) to expre s s i t a s

a 2O t + I F K ( K t + I , L t + I ) K t + I q - 2 I ; + 1 / K r + I ) q- qt+l Kt+2 - I t+~)

~ l t t + l : 1 + rt+l

B e c a u s e t h e p r o d u c t i o n f u n c t i o n i s h o m o g e n e o u s o f d e g r e e o n e a n d qt+l z

1 + a I t + l / K t + l ) [ r e ca l l e q . (3 .1 3)] , t h e f o r e g o i n g r e l a t i o n s h i p , i t e r a t e d f o r w a r d

s u c c e s s i v e l y t o e l i m i n a t e t e r m s o f f o r m q ~ K s + l , i m p l i e s t h a t

q t K t + l = R t , s O s F K , , L s ) - w s L s - ls - 2 K ss ] ~ V t+ l

s = t + l

3.16)

T h u s , t h e o p t i m i z i n g f i rm s e x d i v i d e n d m a r k e t v a l u e a t th e e n d o f p e r i o d t ,

V t+ I, i s t h e s a m e a s t h e s h a d o w v a l u e o f i ts i n s t a l l e d c a p i t a l : in H a y a s h i s ( 1 9 8 2)

t e r m i n o l o g y , a v e r a g e q e q u a l s m a r g i n a l q .i4

T o s e e s o m e o f t h e m o d e l s p r ed i c t io n s f o r c u r r e n t a c c o u n t a n d i n v e s t m e n t

d y n a m i c s , l e t us s i m p l i f y b y a s s u m i n g t h a t r , 0 , a n d L a r e c o n s t a n t a n d c o n s i d e r

a s i t u a t i o n i n w h i c h t h e c a p i t a l s t o c k K is in i t i a l ly b e l o w i ts s t e a d y s t a t e l e v e l .

T h u s t h e m a r g i n a l p r o d u c t o f c a p it a l, O F K K t , L ) e x c e e d s r , q > 1 , a n d b o t h K

a n d Y a r e e x p e c t e d t o r i se o v e r t i m e . A s t h e c a p i t a l s t o c k r is e s t o w a r d i ts s t e a d y -

s t a t e l e v e l , K , w h e r e O F K f f ; , L ) = r , q f a l l s t o o n e . i s A c c o r d i n g t o ( 3.9 ) t h e

c u r r e n t a c c o u n t ( a b s t r ac t in g f r o m g o v e r n m e n t - s p e n d i n g c h a n g e s, a n d a s s u m i n g

t h e e c o n o m y c o n si st s o f a r e p r e s e n t a ti v e f i rm o w n e d b y a r e p r e s e n t a t i v e a g e n t )

1 3 E q u a t i o n 3 . 1 5) d e f i n e s t h e e x d i v i d e n d s h a d o w p r i c e o n d a t e t b e c a u s e i t d o e s n o t i n c l u d e t h e

p r o f it e a r n e d o n t h a t d a t e a n d p a i d o u t t o s h a r e h o l d e r s a s di v i d en d s .

1 4 A s H a y a s h i s h o w s , t h i s e q u a l it y i s d u e t o t h e h o m o g e n e i t y o f d e g r e e o n e o f t h e p r o d u c t i o n a n d

i n s t a l l a t i o n - c o s t f u n c t i o n s .

l S F o r d i s c u s s io n s o f t h e s e d y n a m i c s , s e e A b e l 1 9 8 2 ) a n d S u m m e r s 1 9 8 1 ) .



Ch. 34: The InterternporalApproach to the C urrentAccount

i s g i v e n b y

1751

{ rF K t , L ) 2 K t ] l + r s= tA t

r ~ 1 ~ s t q s - - 1 K s ]

- a 1 r s = t - - U -

i n c e K is r i s i n g o v e r t i m e , f i n a l o u t p u t i s r i s in g o v e r t i m e a s w e l l . S i n c e

i n v e s t m e n t a l s o is f a ll in g , 16 d a t e t i n s t a l la t i o n c o s t s e x c e e d t h e i r p e r m a n e n t l e v e l.

Thus , l~ t = O F K t , L ) - a :I / K t ) f a l l s s h o r t o f i t s p e r m a n e n t l e v e l , c o n t r i b u t i n g

a n e g a t i v e c o m p o n e n t t o th e c u r r e n t a c c o u n t . T h e f a c t t h a t i n v e s t m e n t a ls o

is a b o v e i ts p e r m a n e n t l e v e l c o n t r i b u t e s a s e c o n d n e g a t i v e c o m p o n e n t t o th e

c u r r e n t a c c o u n t .

S u p p o s e K i n i t ia l l y l ie s b e l o w i t s l o n g - r u n s t e a d y - s t a t e v a l u e b e c a u s e t h e

e c o n o m y h a s j u st e x p e r i e n c e d a n u n a n t i c ip a t e d p e r m a n e n t i n c re a s e in f a c to r

p r o d u c t i v it y , 0 . W e c a n s e e f r o m t h e p r e c e d i n g a n a ly s is t h a t t h e e c o n o m y r u n s

a c u r r e n t - a c c o u n t d e f i c it . A c l as s ic a l e x a m p l e o f t h is d y n a m i c is N o r w a y i n t h e

1 9 7 0s F i g u r e 2 .3 ) , w h i c h b o r r o w e d e x t e n s i v e l y t o b u i l d u p i ts N o r t h S e a o i l

p r o d u c t i o n f o l l o w i n g t h e f ir st o i l - p r ic e s h o c k .

N o t e t h a t a n u n a n t i c i p a t e d p e r m a n e n t r is e i n 0 n o t o n l y le a d s to a c u r r e n t

a c c o u n t d e f ic it b u t c a u s e s a n i m m e d i a t e r is e in o u t p u t a s w e l l. T h e r e f o r e , w i thp r o d u c t i v i t y s h o c k s t h e m o d e l c a n in p r i n c i p le e x p l a i n th e w e l l - d o c u m e n t e d

c o u n t e r c y e l i c a l b e h a v i o r o f t h e c u r r e n t a c c o u n t , t7 O f c o u r s e , t h is r e s u l t r e s t s

o n t h e a s s u m p t i o n t h a t t h e ri s e i n 0 is p e r m a n e n t . I m a g i n e , i n c o n t r a s t , a n

u n e x p e c t e d r is e i n 0 t l a s ti n g o n l y a s in g l e p e r i o d . T h i s c h a n g e w i ll n o t a f f e c t

i n v e s t m e n t p l a n s f o r f u t u r e d a t e s, a n d s o t h e o n l y e f f e c t is a l ev e l o f o u t p u t

t e m p o r a r i l y a b o v e th e p e r m a n e n t le v e l. E q u a t i o n 3 .9 ) s h o w s t h a t a c u r r e n t

a c c o u n t s u r p l u s w i l l a r i se o n d a t e t . P r o d u c t i v i t y s h o c k s w i t h g r e a t e r p e r s i s t e n c e

c a u s e s o m e i n v e s t m e n t a n d h e n c e s m a l l e r i n it ia l c u r r e n t - a c c o u n t s u rp l u se s , a n d ,

i f p e r s i s t e n t e n o u g h , t h e y c a n p r o d u c e a n i n i ti al d e fi ci t, a s in t h e p e r m a n e n t

c a s e .

1 6 I n v e s t m e n t e q u a l s q - ])K/a, b u t w i t h q f a l l i n g w h i l e K i s r i s i n g , i t m a y n o t b e o b v i o u s t h a t 1

f a l ls o v e r t i m e . T h e a s s e r t i o n i n t h e t e x t i s a l w a y s t r u e i n t h e n e i g h b o r h o o d o f t h e s t e a d y s t a t e . T o

s e e w h y , o b s e r v e t h a t

I t+i - I t = Kt [ ~ q t ) + q t . l - a 1) qt-1)]_

t o a f i r s t -o r d e r a p p r o x i m a t i o n .

1 7S e e t h e a r t i cl e b y M o r r i s G o l d s t e i n a n d M o h s i n S . K h a n i n v o l u m e 2 o f t h is H a n d b o o k G o l d -

s t e i n a n d K h a n 1 9 8 5 ) .




T h e r e a d e r s h o u ld n o t e t h a t in t he p r e s e n t o n e - g o o d s m a l l -e c o n o m y m o d e l ,

c h a n g e s i n i n v e s t m e n t c a n a f f e c t c o n s u m p t i o n , b u t i n v e s t m e n t i t s el f is d e t e r -

m i n e d b y e l e m e n t s th a t a r e independent o f c o n s u m p t i o n p r e fe r e n c e s. I n v e s t m e n td e c i si o n s a r e m a d e t o m a x i m i z e t h e p r e s e n t d i s c o u n t e d v a l u e o f th e c o u n t r y s

o u t p u t , e v a l u a t e d a t t h e w o r l d i n t e r e s t r a t e . T h e c o u n t r y s s a v i n g b e h a v i o r is ir--

r e le v a n t . T h i s i n d e p e n d e n c e o f i n v e s t m e n t f ro m c o n s u m p t i o n p r e f e r e n c e s n e e d

n o t h o l d i f t h e e c o n o m y u s e s c a p it a l t o p r o d u c e n o n t r a d e d g o o d s a n d s e r v ic e s

a s w e l l a s t r a d e a b l e s ; it c a n a l s o b r e a k d o w n i f t h e r e i s a n o n t r a d e d i n p u t i n

p r o d u c t i o n , s u c h a s l ab o r. I n t r o d u c i n g n o n t r a d e d g o o d s a n d s e r v ic e s le a d s t o

a n u m b e r o f o t h e r m o d i f i c a ti o n s o f o u r b a s i c o n e - g o o d m o d e l s r e su l ts , a s w e

s h a l l s e e i n t h e n e x t s e c t i o n .

3.1.4. No ntradeables, consum ption, and investment

A n e c o n o m y t h a t c o n su m e s a n d p r o d u c e s n o n t r a d e a b l e s a s w e l l a s t r a d e a b l e s

m a y b e h a v e q u i t e d i f fe r e n t l y f r o m t h e o n e e x a m i n e d s o fa r. W e b e g i n b y s e e i n g

h o w n o n t r a d e a b l e s c a n a f f e c t c o n s u m p t i o n d e c is i on s .

I n t h i s s e c t i o n , i t w i ll b e c o n v e n i e n t to r e i n t e r p r e t C a s a c o m p o s i t e indexo f t h e r e p r e s e n t a t i v e i n di v id u a l s c o n s u m p t i o n o f t r a d e a b l e s a n d n o n t r a d e a b l e s ,

C T a n d C N , b u t r e t a i n t h e a s s u m p t i o n t h a t t h e p e r i o d u t i l i ty f u n c t i o n u ( C ) is

i s o e l a s t ic w i t h i n t e r t e m p o r a l s u b s t i t u t io n e l a s t i c i ty o-. A s s u m e , m o r e o v e r , t h a t

c o m p o s i t e c o n s u m p t i o n C h a s th e C E S f o rm :

C = [c~l / °C ° -1) / ° + (1 - 'a)l/ C(y°-l)/°]°/(°-l) ( 3 . 17 )

H e r e , p i s t h e ( i n t r a t e m p o r a l ) s u b s t i t u ti o n e l a s ti c it y b e t w e e n t r a d e a b l e s a n d

n o n t r a d e a b l e s . T a k e t r a d e a b l e s a s t h e n u m e r a i r e c o m m o d i t y a n d l et p b e t h e

p r i c e o f n o n t r a d e a b l e s i n te r m s o f tr a d e a b l e s . T h e n , a s o n e c a n e a s i l y s ho w , t h e

e x a c t c o n s u m e r - p r i c e i n d e x ( C P I ) i n t ra d e a b l e s , d e f i n e d a s t h e m i n i m a l c o s t i n

t r a d e a b l e s o f a u n i t o f s u b u t i l it y C , is g i v e n b y

P = [a + (1 - cO pl-°] l/(1-°) ( 3 . 18 )

F o r th e s p e c ia l c a s e O = 1 ( C o b b - D o u g l a s p r e f e r e n c e s ) , P = p l 4. T h e s e s a m e

c a l c u l a ti o n s r e v e a l t h a t, g i v e n C , t h e o p t i m a l c o n s u m p t i o n l e v el s f o r t ra d e a b l e s

a n d n o n t r a d e a b l e s a r e :

CT = c~ C , CN = (1 -- c~) C (3. 19 )

G i v e n t h e i n t r a t e m p o r a l a l l o c a t i o n ru l e s in ( 3 .1 9 ), t h e c o n s u m e r s intertempo-ral d e c is io n p r o b l e m c a n b e a n a l y z e d e n t i r e l y in t e r m s o f c o m p o s i t e c o n s u m p t i o n

C a n d t h e p r i c e i n d e x P . T h e c o n s u m e r m a x i m i z e s (3 .4 ) s u b j e ct to t h e b u d g e tc o n s t r a i n t c o r r e s p o n d i n g t o ( 3. 5) b u t w r i t te n i n t e r m s o f e x p e n d i t u r e o n C :



Ch. 34: The lntertemporal App roach to the C urrent Acco unt 1753

O<3 O0

E R t , s P s C s = 1 + r t ) V t + B t ) + Z n , , s w s L s - T s )

s=t s=t( A b o v e , a s s e t s t o c k s , w a g e s , a n d t a x e s st il l a r e e x p r e s s e d i n u n i t s o f t r a d e a b l e @

T h e i n t e r t e m p o r a l E u l e r e q u a t i o n f o r t h e c o n s u m p t i o n i n d e x C is n o w

c , + ~ = / 3 ~ l + r t + ~ ) ~ ~ c ~ . . . .

T h i s r e l a t i o n s h i p i s a n a l o g o u s t o E u l e r e q . ( 3 .7 ) , e x c e p t t h a t o v e r a l l c o n s u m F , li.<,~

g r o w t h d e p e n d s o n t h e u t i l i ty - b a s e d r e a l i n t e r e s t f a c t o r (1 + r f + l )( P t / P t+ ), a n d

n o t s i m p l y o n t h e r e l a t i v e i n t e r t e m p o r a l p r i c e o f t r a d e a b l e s 1 + rt ~1. [ D o r n b u s c l"

( 1 9 8 3 ) s t re s s e s t h is p o in t . ] C o m b i n i n g e q s . ( 3 .1 9 ) a n d ( 3 . 2 0 ) sh o w s t h a t t h e E u l e r

e q u a t i o n f o r t r a d e a b l e s e x p e n d i t u r e , C T , is

C T t + I = / 3 ¢ 1 + r t + l ) ¢ Pt ~ ¢ 0 CTt (3 .21)Pt l J

E q u a t i o n s ( 3 , 2 0) a n d ( 3. 21 ) s h o w , i n p a r t i c u l a r, th a t c o n s u m p t i o n n e e d n o

l o n g e r b e i n t e r t e m p o r a l l y s m o o t h e d w h e n t h e t i m e - p r e f e r e n c e r a te a n d w o r l d

t r a d e a b l e g o o d s i n t e r e s t r a t e c o i n c id e . F o r e x a m p l e , if t h e C P I , P , is ri si n g o v e r

t i m e , t h e r e a l i n t e r e s t r a t e w i l l b e b e l o w t h e o w n i n t e r e s t r a t e o n t r a d e a b l e s ,

r . S o t o t a l c o n s u m p t i o n e x p e n d i t u r e m e a s u r e d i n t ra d e a b le s , P C , w i l l f a l l o v e r

t i m e i f o - > 1 a n d r i s e o v e r t i m e i f o- < 1 . S i m i l a r ly , w h i l e a r is i n g p a t h o f P

t il ts t h a t o f C d o w n w a r d w i t h a n e l a s t i c i ty or, t h e p r i c e c h a n g e s c a u s e C T t o r i se

r e l a t i ve t o C w i t h e l a s t i c i t y p [ s ee eq . ( 3 . 19 ) ]. I f p > o - an d 13 ( 1 + r ) = 1 , f o r

e x a m p l e , c o n s u m p t i o n o f t r a d e a b l e s w i ll ri s e o v e r t i m e i f P is ri s in g } s

S o m e g e n e r a l - e q u i l i b r i u m i m p l i c at i o n s o f t h e s e p o i n t s c a n b e i l l u s tr a t e d b y a

s i m p l e m o d e l i n w h i c h t h e e c o n o m y ' s o u t p u t o f n o n t r a d e a b l e s , Y N, is e x o g e n o u s .

I f w e a s s u m e ( f o r s im p l i c it y ) t h a t n e i t h e r t h e g o v e r n m e n t n o r t h e d o m e s t i c

i n v e s t m e n t p r o c e s s u s e s u p n o n t r a d e a b l e s , t h e n t h e c o n d i t i o n o f e q u i l i b r i u m

i n t h e n o n t r a d e a b l e s e c t o r is s i m p l y CN = Y N , a n d b y ( 3 .1 9 ) th e e q u i l i b r i u m

r e l a t i v e p r i c e o f n o n t r a d e a b l e s is

- - o l C T ] 1 / p= [ [ 1 ~ - N ]

I n t h e C o b b - D o u g l a s c a s e p - - 1 , a n d i t i s s i m p l e t o w r i t e d o w n t h e e q u i l i b o

r i u m g r o w t h p r o c e s s f o r t r a d e a b le s c o n s u m p t i o n b y c o m b i n i n g t h e p r e c e d in g

e x p r e s s i o n w i t h e q . ( 3 .2 1 ):

1 . ) ~ - 1 )

o- ¢ ( Y N t+l "~ ,~--(~-I)C T ,< = / 3 ~ ( 1 + r t < ) ~ \ Y Y t J C Tt (3 .22)

18For a p anel of 13 d eveloping countries, Ostry and R ein ha rt (1992) present E uler-eqnationestimates of ~r = 1.27 or 1.22 and p = 0.38 or 0.50 (depen ding on the instrumental variables usedin estimation). The se results indicate that the c ase o- > p m ay be relevant.



:1754 M Obstfeld and K R og of f

N o t i c e t h a t e v e n w h e n n o n t r a d e a b l e s o u t p u t i s c o n s t an t , t h e g r o w t h o f t r a d e -

a b l e s c o n s u m p t i o n u s u a ll y re f le c ts t h e p r e s e n c e o f n o n t r a d e a b l e s i n t h e c o n -

s u m p t i o n b a s k e t . T h e r e a s o n : g r o w t h in C T a ff e c ts p a n d t h us t h e d o m e s t i c re a li n t e r e s t r a t e .

A f u n d a m e n t a l i m p l i c a t i o n o f t h e s e r e s u l ts i s t h a t e m p i r i c a l st u d i e s o f th e i n -

t e r t e m p o r a l a p p r o a c h s h o u l d d is ti n g u is h c a r e f u l l y b e t w e e n f l u c tu a t io n s in t r a d e d

a n d n o n t r a d e d o u t p u ts . A s a n e x a m p l e , s u p p o s e t h a t t h e p a th o f t r a d e d o u t p u t

i s f l a t, t h a t /3 (1 + r ) = 1 , an d t ha t Y N t < Y N t + l. A cc or d i ng t o eq . ( 3 . 22 ) , co n -

s u m p t i o n o f t r a d e a b l e s w i l l b e r i s i n g if o- > 1 a n d f a l l i n g i f o- < 1 . B e c a u s e t h e

c u r r e n t a c c o u n t s u rp lu s i s t h e d i ff e r e n c e b e t w e e n t h e e c o n o m y s e n d o w m e n t o f

t r a d e a b l e s a n d i t s a b s o r p t i o n o f t r a d e a b l e s , e v e n t h e s i g n o f t h e c u r r e n t a c c o u n t

b a l a n c e m a y n o t b e r e l a te d i n a s i m p le w a y t o t h e t i m e p a t h o f th e e c o n o m y s

t o t a l r e a l o u t p u t .

O n e c a n a d d a l a b o r- l e is u r e t r a d e o f f t o th e i n t e r t e m p o r a l m o d e l b y v i e w i n g

l e i su r e a s a n o n t r a d e a b l e ( a ss u m i n g t h e r e is n o i n t e r n a t i o n a l m i g r a t io n ) . I n t h is

c o n t e x t t h e r e a l w a g e p l a y s t h e r o l e th a t t h e r e l a t i v e p r i c e o f n o n t r a d e a b l e s p

p l a y e d a b o v e . ~9

A l s o , a s w e s u g g e s t e d a t th e e n d o f t h e p r e c e d i n g s e c ti o n , t h e p r e s e n c e o f

a s e c to r p r o d u c i n g n o n t r a d e a b l e s p e r m i t s d o m e s t i c c o n s u m p t i o n p r e f e r e n c e s t o

a f f e c t t h e e c o n o m y s i n v e s t m e n t b e h a v io r . A s h if t i n p r e f e r e n c e s t o w a r d n o n -

t r a d e a b l e s , f o r i n s ta n c e , w i ll r e d u c e i n v e s t m e n t i f t h e n o n t r a d e a b l e s s e c t o r i s

t h e r e l a t i v e l y l a b o r - i n t e n s i v e o n e . 2°

A l l o w i n g f o r n o n t r a d e a b l e s is a n i m p o r t a n t s t e p t o w a r d s h a v i n g a m o r e r e a l -

i st ic m o d e l o f c u r r e n t a c c o u n t b e h a v i o r . In t h e n e x t s e c t io n w e c o n s i d e r a n o t h e r

i m p o r t a n t m o d i f i c a t i o n .

3 1 5 Con sumer durables and the current account

E i g h t e e n p e r c e n t o f 1 99 3 U n i t e d S t a te s c o n s u m p t i o n s p e n d i n g w a s d e v o t e d t o

d u r a b l e s ( i n c lu d i n g c lo t h i n g a n d s h o e s) . B u t t h e t h e o r y w e h a v e d e v e l o p e d t h u s

f a r d o e s n o t c a p t u r e t h e p o s s i b il it y t h a t c o n s u m e r p u r c h a s e s in o n e p e r i o d m a y

y i e l d u t i li ty o v e r s e v e r a l p e ri o d s . W e n o w i ll u s t ra t e h o w t h e p r e s e n c e o f d u r a b l e sc a n a l t e r c u r r e n t a c c o u n t r e s p o n s e s.

I n t h is s u b s e c t io n , l e t C s t a n d f o r t h e i n d i v i d u a l s c o n s u m p t i o n o f n o n d u r a b l e s

a n d l e t D b e t h e s t o c k o f d u r a b l e s h e o r s h e o w n s ; a ll g o o d s c a n b e t r a d e d . A

s t o c k D o f d u r a b l e s y i e l d s a p r o p o r t i o n a l s e r v i c e fl o w e a c h p e r i o d , i n c l u d i n g

t h e p e r i o d i n w h i c h i t is ac q u i r e d . T h e c o n s u m e r i n a s m a ll c o u n t r y m a x i m i z e s

u , = £ / 3 s -~ [ ~ l o g c , , + 1 - ~ ) l o g D , ]

t

19For an early analysis of the effects of introducing nontr aded labor on curren t account dynamics

see Bea n (1986).2°See, for ex am ple, M urphy (1986) and Eng el and Kletzer (1989).



C h . 34 : T h e l n te r t er n p o r a l A p p r o a c h t o th e C u r r e n t A c c o u n t 755

s u b j e c t t o t h e f i n a n c e c o n s t r a i n t s

A t + l - - A t = r A t + Y t - C t - G t - ( K t+ j - K t ) - p t [ D t - (1 - 6 ) D t - l l

a n d a s o lv e n c y c o n d i t i o n . H e r e , D t is t h e s t o c k o f d u r a b l e s ( in c l u d in g n e w l y

p u r c h a s e d d u r a b l e s ) h e l d o v e r p e r i o d t , P t is th e i r p r i c e i n t e r m s o f n o n -

d u r a b l e s , 6 i s t h e i r d e p r e c i a t i o n r a t e , a n d r , t h e w o r l d i n t e r e s t r a t e , i s c o n s t a n t .

N o t e t h a t A , Y , C , G , a n d K a r e m e a s u r e d i n n o n d u r a b l e s . D u r a b i l i t y i m p l ie s

6 < 1 .

I n a d d i ti o n t o t h e u s u al i n t e r t e m p o r a l E u l e r e q u a t i o n f o r n o n d u r a b l e s c o n

s u m p t i o n , t h e i n d i v i d u a l s fi r s t - o r d e r c o n d i t i o n s i n c l u d e

a D t P t ~ P t < = - ~ t,

w h i c h e q u a t e s t h e m a r g i n a l r a t e o f s u b s t i tu t i o n o f n o n d u r a b l e s f o r th e s e r v ic e s

o f d u r a b l e s t o t h e u s e r c o s t o r r e n t a l p r i c e o f d u r a b l e s .

A s s u m i n g / 3 = 1 / ( 1 + r ) , c o n s u m p t i o n o f n o n d u r a b l e s i s

C t = -~-+-Tr ( l + r ) A t + ( 1 - a ) p t D t _ , + \ ~ + T r / t ( Y ~ - l s - G s )

s = t

w h i l e c o n s u m p t i o n o f d u r a b l e s s e r vi c e s is

0 - - ~ ) r 1 v , t,, - G )D t - - ~ ( l + r ) ( l + r ) A t + ( 1 - 6 ) p t D t = l + l + r ~

S =t

L e t s s u p p o s e f o r s i m p l i c i ty th a t , P t a n d , h e n c e , t h e u s e r c o s t, Lt, a r e c o n s t a n t .

T h e l as t e q u a t i o n s t h e n i m p l y t h a t t h e c o n s u m e r s m o o t h s , n o t t h e p a t h o f e x p e n -

d i t u r e s p [ D t - ( 1 - 6 ) D r _ l ] o n d u r a b l e s , b u t t h e s e r v i c e f lo w f r o m d u r a b l e s , w h i ch

is p r o p o r t i o n a l t o D t . W i t h d u r a b le s , t h e c u r r e n t a c c o u n t i s t h e s a m e a s i m p l i e d

b y ( 3. 9) ( a s su m i n g , a s w e h a v e h e r e , t h a t r = (1 - / 3 ) / ~ ) , b u t w i t h a n a d d i t io n a l

t e r m t h a t d e p e n d s o n n e w d u r a b l e s p u r c h a s e s ( w e o m i t t h e d e r i v a t i o n ) :

= { ( Y t - Y t ) - ( G t - ~ a t) - (I t - J , ) } + (~ - p ) AD , ( 3 . 23 )A t

N o t i n g t h a t t h e p r i c e o f p u r c h a s i n g a d u r a b l e o u t r ig h t , p , m u s t b e g r e a t e r

T h a n t h e o n e - p e r i o d u s e r c o s t ~, w e s e e th a t t h e i n t r o d u c t i o n o f d u r a b l e s n e c e s -

s a r il y i n c r e a se s t h e v o l a t i li t y o f c u r r e n t - a c c o u n t r e s p o n s e s t o u n e x p e c t e d i n c o m e

c h a n g e s .

3 .1 .6 . T h e t e r m s o f t r ad e a n d t h e t r a n s fe r p r o b l e m

O n e o f t h e e a r l ie s t p r o b l e m s m o t i v a t in g t h e i n t e r t e m p o r a l a p p r o a c h w a s t h en e e d t o u n d e r s t a n d h o w c h a n g e s i n t h e t e r m s o f t r a d e - t h e p r i c e o f a c o u n t r y s




e x p o r t s i n t e r m s o f it s i m p o r t s - a f f e c t s a v i n g a n d t h e c u r r e n t a c c o u n t . E a r l y a p -

p l ic a t i o n s o f K e y n e s i a n m o d e l s b y H a r b e r g e r ( 19 5 0) a n d L a u r s e n a n d M e t z l e r

( 1 95 0 ) h a d m o d e l e d a d v e r s e t e r m s - o f - t r a d e s h o c k s as r e a l i n c o m e - r e d u c t i o n st h a t r e d u c e s a v i n g a n d t h e e x t e r n a l s u r p lu s i n p r o p o r t i o n t o K e y n e s s m a r g i n a l

p r o p e n s i t y t o s a v e. I n s t e a d , t h e i n t e r t e m p o r a l a p p r o a c h e m p h a s i z e d t h e re -

s p o n s e o f f o r w a r d - l o o k i n g i n d iv i d u a ls t o t h e c h a n g e s i n li f e ti m e c o n s u m p t i o n

p o s s ib i li ti e s th a t t e r m s - o f - t r a d e m o v e m e n t s c a u se .

T h e s i m p le s t c as e is o f a s p e ci al iz e d e c o n o m y w i th a n e x o g e n o u s e n d o w m e n t

Y o f i ts e x p o r t g o o d , b u t w h i c h a ls o c o n s u m e s i m p o r t s . A s i n t h e m o d e l w i t h

n o n t r a d e a b l e s , w e a g a i n a s s m n e a n i s o e l as t ic p e r i o d u t il i t y f u n c t i o n d e f in e d o v e r

a C E S i n d e x C ; h e r e i t d e p e n d s o n t h e i n d i v i d u a l s c o n s u m p t i o n s C ~t o f i m p o r t s

a n d C x o f e x p o r t s :

L e t p n o w d e n o t e t h e p r i c e o f e x p o r t s i n t e r m s o f i m p o r t s , w h i c h is d e t e r m i n e d

e x o g e n o u s l y in t h e w o r ld m a r k e t . T h e c o n s u m p t i o n - b a s e d p r ic e l e v el in t e r m s

o f i m p o r t s is a g a in d e n o t e d b y P a n d g i v e n b y f o r m u l a ( 3 .1 8 ).

T h e n a t u r a l b e n c h m a r k c a s e, a s su m e d b y S v e n s s o n a n d R a z i n ( 1 98 3 ), s u p -

p o s e s th a t i n t e r t e m p o r a l t r a d e is d o n e t h r o u g h b o n d s i n d e x e d t o t h e c o n s u m p -

t i o n i n d e x , C . I n t h i s c a s e r is t h e o w n r a t e o f i n t e r e s t o n t h e c o n s u m p t i o n

i n d e x , a n d t h e b u d g e t c o n s t r a i n t c o r r e s p o n d i n g t o ( 3 . 3 ) i n t h e p r e s e n t s e t u p

( a b s t r a c t i n g f r o m i n v e s t m e n t a n d g o v e r n m e n t ) i s

t ,sCs = (1 + rt At + Rt,sS : t S = I

T h e E u l e r e q u a t i o n f o r t h e c o n s u m p t i o n i n d e x is a g a i n ( 3 .7 ), im p l y i n g th e c o n -

s u m p t i o n f u n c t i o n c o r r e s p o n d i n g t o (3 . 8 ), w h i c h h a s I = G = 0 a n d p Y / Pi n p l a c e o f Y . T o f o c u s o n t h e t e r m s o f t r a d e , i t is h e l p f u l t o a s s u m e t h a t

r = (1 - ~ ) / / ~ a n d Y a r e c o n s t a n t , in w h i c h c a s e t h e c o n s u m p t i o n f u n c t i o n

r e d u c e s t o :

Ct = r a t + ~ Z \ l~--rr JS=t

A f a ll i n t h e t e r m s o f t r a d e l o w e r s p ( t h e r e l a t i v e p r i c e o f e x p o r t s i n t e r m s o f

i m p o r t s ) r e l a t i v e to P ( t h e o v e r a l l C P I i n t e r m s o f i m p o r t s ) . T h u s , f l u c tu a t i o n s

i n t h e t e r m s o f t r a d e a f f e c t t h e c o n s u m p t i o n i n d e x a n d t h e c u r r e n t a c c o u n t

( w h i c h h e r e is m e a s u r e d i n c o n s u m p t i o n - i n d e x u n i ts ) e x a c t ly li k e fl u c t u a ti o n s

i n G D P a t c o n s t a n t t e r m s o f t r a d e . I n p a r ti c u la r , a t e m p o r a r y t e r m s - o f - t r a d e

s e t b a c k c a u s e s a c u r r e n t - a c c o u n t d ef ic it , w h e r e a s a p e r m a n e n t s e t b a c k c a u s e s

a n i m m e d i a t e s h i ft t o th e n e w , l o w e r c o n s u m p t i o n l e v e l c o n s i s te n t w i t h e x t e r n a l



Ch 34 The Intertemporal Approach to the Current Account

40

C

P 30

20

8P 10

~ 0

610

-20

AUS

U S

• NOR

• J P

NET IT FR

SWE Bm • • • SP BG E R• DEN

& c

B E L

0.15 0.1 0.05 0 0.05 0.1 0.15

C h a n g e i n N e t F or e i g n A s s e t s / G D P

Figure 3.1. Real currency appreciat ion versus the change i l l foreign assets, 1981-1990.

1757

balance. Obstfeld (1982) and Svensson and Razin (1983) illustrate how this latter

result depends on the strong intertemporal separability of utility. 21

This subsection has, thus far, focused on the response of the current account toexogenous terms-of-trade changes. When countries have some monopoly power

in trade, however, shifts in their current accounts may influence terms of trade

by redistributing wealth internationally.

The impact of international wealth transfers on the terms of trade is a classic

problem of international finance. In the 1920s, Keynes and Ohlin disagreed on

the price effects of German reparations; in the 1990s, observers of the protracted

United States external deficits have debated the need for a fall in the relativeprice of American exports. 22

For a cross-section of 15 OECD countries, Figure 3.1 plots the percent change

in the trade-weighted WPI real exchange rate (a terms-of-trade proxy) againstthe change in the ratio of net foreign assets to output. The net foreign asset

series attempt to account not only for measured current account flows, but for

21Ostry (1988) and Edwards (1989) study interact ions between the terms of trade and the relat iveprice of nontradeables. Gavin (1990) considers the terms of trade in a richer dynamic set t ing. For

developing countries, i t may be natural to assume that bonds are indexe d to impo rts (e.g. dollars ).In tha t case the in ter tem pora l budget const ra in t d i ffers f rom the one we have analyzed , so tha t theEule r equ ation for C is formally the same as (3.20). If the world bond rate is constant , expected terms

of t rade mov emen ts therefore h ave consumpt ion-t il t ing effec ts th rough the consum pt ion-based rea linterest rate.

22See, for example, the papers in Bergsten (1991).



1758 M. Obstfeld and K. Rogoff

c a p i t a l g a i n s a n d l o ss e s. 23 T h e c h a n g e s a r e c a l c u l a t e d a s t h e 1 9 8 6 - 1 9 9 0 a v e r a g e

l e s s t h e 1 9 8 1 - 1 9 8 5 a v e r a g e .

T h e f i g u r e s h o w s a d is t in c t p o s i t i v e r e l a t i o n s h i p - a n i n c r e a s e i n a c o u n t r y sn e t f o r e i g n a s se t s a p p e a r s t o b e a s s o c i at e d w i t h a n i m p r o v e m e n t i n it s t e r m s o f

t r a d e . T h e l e a s t - s q u a r e s r e g r e s s i o n l i n e i s

A l o g ( p j ) = 0 . 0 3 9 + 1 . 0 4 2 2 x ( A / Y ) j + u j ; R 2 = 0 . 3 1

( 0 . 027) ( 0 . 433)

i m p l y i n g a s t a ti s ti c a l ly s ig n i f ic a n t r e l a t i o n s h i p . A c c o r d i n g t o t h e r e g r e s s i o n , a n

i n c r e a s e o f 1 p e r c e n t i n t h e r a t i o o f n e t f o r e i g n a s s e t s to o u t p u t i s a s s o c i a t e d

w i t h a 1 p e r c e n t i m p r o v e m e n t i n t h e t e r m s o f t r a d e .

O b v i o u s l y , t h is r e g r e s s i o n p r o v i d e s o n l y a n o n s t r u c t u r a l c o r r e l a t io n . T o a s se ssa c c u r a t e ly t h e c o n s e q u e n c e s o f an e x o g e n o u s w e a l t h t r a n s fe r w o u l d r e q u i r e

a fu l l e c o n o m e t r i c s tr u c t u r a l m o d e l . G i v e n t h e p e r e n n i a l i m p o r t a n c e o f th e

t r a n s f e r e f f e c t i n p o l ic y d is c u ss io n s , t h e d e v e l o p m e n t o f e m p i r i ca l i n t e r t e m p o r a l

m o d e l s t h a t c a n e x p l a i n it s m a g n i t u d e is a r e s e a r c h p r i o ri ty .

T h e o r e t i c a l ly , t h e t r a n s f e r e f f e c t c a n o p e r a t e t h r o u g h s e v e r a l c h a n n e l s i n a

g e n e r a l - e q u i li b r i u m s e tt in g . T w o p o t e n t ia l m e c h a n i s m s a r e h o m e p r e f e r e n c e f o r

d o m e s t i c e x p o r t s [s ee , f o r e x a m p l e , B u i t e r ( 19 8 9) ] a n d t h e p r e s e n c e o f a n o n -

t r a d e a b l e s s e c t o r t h a t c o m p e t e s f o r r e s o u r c e s w i t h t h e e x p o r t a b l e s e c to r . A

s p e c ia l c a se o f t h e l a t te r m e c h a n i s m is d u e t o t h e e f f e c t o f a w e a l t h c h a n g e o n

l a b o r s u p p l y a n d , h e n c e , o n t h e s u p p l y o f e x p o r t a b l e s .A s i m p l e t w o - c o u n t r y m o d e l e x h i b it s t h e l a b o r - s u p p l y c h a n n e l f o r th e t r a n s f e r

e f fe c t . A s s u m e t h a t th e h o m e c o u n t r y sp e c i al iz e s i n p r o d u c i n g g o o d X a n d

t h e f o r e i g n c o u n t r y g o o d M . M o r e o v e r , a s s u m e t h a t i n b o t h c o u n t r i e s p , th e

e l a st i ci ty o f s u b s ti t u ti o n i n d e m a n d b e t w e e n t h e t w o p r o d u c e d g o o d s , e q u a l s

1. L e t t h e p e r i o d u t il it y f u n c t io n , c o m m o n t o t h e h o m e a n d f o r e i g n c o u n t r i e s ,

b e a n i s o e l a s ti c f u n c t i o n o f a n i n d e x t h a t d e p e n d s o n b o t h c o n s u m p t i o n a n d

l e i s u r e ,

H - = - ° H -~ L I - ~

w h e r e 0 < ~ < 1 , H is a n i n d i v i d u a l s e n d o w m e n t o f ti m e , a n d L h i s o r h e r

l a b o r s up p ly . L e t h o m e o u t p u t b e p r o d u c e d a c c o r d in g t o t h e p r o d u c t i o n f u n c t io n

Y = w L a n d f o r e i g n o u t p u t a c c o r d i n g t o Y * = ~ o*L *. L e t P o n c e a g a i n d e n o t e

2 3 R e al e x c h a n g e r a t e d a t a c o m e f r o m I n t e r n a t i o n a l M o n e t a r y F u n d , International Financial Statis

tics. N e t f o r e i g n a s s e t p o s it i o n s c o m e f r o m OECD Economic Outlook 55 ( June 1994 ) , p . A 54 . Thec o u n t r y s a m p l e i s A u s t r a l i a ( f o r w h i c h t h e C P I w a s u s e d ) , B e l g i u m - L u x e m b o u r g , C a n a d a , D e n -m a r k , F i n l a n d , F r a n c e , G e r m a n y , It al y , J a p a n , N e t h e r l a n d s , N o r w a y , S p ai n , S w e d e n , t h e U n i t e dS t a t e s, a n d t h e U n i t e d K i n g d o m . W e a r e s k e p t ic a l t h a t t h e r e a l a p p r e c i a t i o n o f 3 3 p e r c e n t t h a t t h eI M F r e p o r t s f o r N o r w a y i s a c c u r a t e . ( T h e I M F r e p o r t s a s i m i l a r n u m b e r b a s e d o n C P I s . ) O E C D

d a t a p l a c e N o r w a y s r e a l a p p r e c i a t i o n o v e r 1 9 8 1 - 1 9 9 0 c l o s er to 1 5 p e r c e n t . H o w e v e r , t h e o b s e r v a t i o n

on N or w a y i s no t d r iv ing the r e g r e s s ion r e su l t s r e po r t e d be low .



Ch. 34: The Intertemp oral Approach to the C urrent Account 1759

t h e p ri c e o f t h e i n d e x C i n t e r m s o f h o m e i m p o r t s , a n d a s s u m e b o n d s a r e

i n d e x e d t o C . T h e h o m e c o u n t r y ' s n e t e x t e r n a l a s se ts a r e A , a n d t h e f o r e i g n

c o u n t r y ' s , t h e r e f o r e , a r e - A . U s i n g t h e s t e a d y - s t a t e c o n s u m p t i o n f u n c t i o n s t os o lv e f o r d e m a n d a n d s u p p l y i n e i t h e r o f t h e g o o d s m a r k e t s , o n e c a n s h o w a f t e r

m a n y s t e p s ) t h a t t h e e q u i l ib r i u m t e r m s o f t r a d e s a t i sf y t h e c o n d i t i o n

poea~H (1 - oe)w*H * _ (1 - (:)(1 - f l ) . A

e P ~ 3

F r o m t h is i m p l i c it t e r m s - o f - t r a d e e q u a t i o n o n e c a n e a s i l y s e e t h e e f f e c t . ,

a n e x o g e n o u s s h i ft i n n e t e x t e r n a l a s s e ts f r o m t h e f o r e i g n t o t h e h o m e c ou nt-~ y

( t h a t i s, o f a r i s e in A ) . A n a b s o l u t e r i s e in p , t h e r e l a t i v e p r i c e o f h o m e e x -

p o r t s , r a i s e s p r e l a t i v e t o P , a n d P i t s e l f r i s e s a b s o l u t e l y . I f A r i se s , a r i s e mp t h e r e f o r e m a i n t a i n s e q u i l i b ri u m . T h e i n t u i ti o n w h y a w e a l t h t r a n s f e r to t h e

h o m e c o u n t r y i m p r o v e s i ts te r m s o f tr a d e is s im p l e . If h o m e r e s i d e n ts r e c e i v e a

f in a n c ia l w i n d f a ll , t h e y s p e n d s o m e o f i t o n l e is u r e. O u t p u t o f th e h o m e g o o d

t h u s f a l l s a n d i ts r e l a t i v e p r i c e m u s t r i s e .

3 . 1 . Z D e m o g r a p h i c s tr u c tu r e , f i s ca l p o l ic y , a n d t h e c u r r e n t a c c o u n t

T h e s i n g le r e p r e s e n t a t i v e a g e n t p a r a d i g m f o l l o w e d s o fa r i n t h is c h a p t e r m a y

f u r n i sh m i s l e a d i n g p r e d i c t i o n s a b o u t t h e c u r r e n t a c c o u n t w h e n t h e e c o n o m y c o n -

s is ts i n s t e a d o f h e t e r o g e n e o u s f a m i li e s b o r n o n d i f f e r e n t d a t e s a n d u n c o n n e c t e db y a l t ru i s ti c l in k s . A m o d e l b a s e d o n t h e o v e r l a p p i n g - g e n e r a t i o n s s t r u c t u r e i n

W e i l ( 1 9 8 9 ) i l l u s t ra t e s s o m e p o s s i b l e im p l i c a t io n s o f a l l o w i n g f o r d e m o g r a p h i c

c o m p l e x i t y .24

W e w i ll id e n t i f y th e e c o n o m y ' s t o t a l p o p u l a t i o n w i t h i ts l a b o r s u pp ly , L t ,

w h i c h g r o w s a t r a t e n : Lt+ 1 = (1 + n ) L t , w i t h L 0 n o r m a l i z e d t o 1 . T h i s l a b o r

f o r c e , h o w e v e r , c o n si st s o f i m m o r t a l u n c o n n e c t e d i n d iv i d u a l s ( o r d y n a s t ie s ) b o r n

o n s u c c es s iv e d a te s . A r e p r e s e n t a t i v e f ro m t h e g e n e r a t i o n b o r n o n d a t e v ( th e

g e n e r a t i o n ' s " v i n t a g e " ) m a x i m i z e s U o , t = ~ . ~ t f ls t u C o , , ) s u b j e c t t o

oo

s=t s - t

( w h e r e Bv , t d e n o t e s v i n t a g e v ' s b o n d h o l d i n g s a n d e a c h i n d i v i d u a l s u p p l i e s o n e

u n i t o f l a b o r p e r p e r i o d ) . N o t i c e t h a t c o n s u m p t i o n a n d w e a l t h a r e v i n ta g e -

s p e ci fi c , w h e r e a s a ll p e o p l e f a c e t h e s a m e w a g e , i n t e r e s t r a t e s , a n d ( b y a s s u m p

t i o n ) l u m p - s u m t a x e s . A k e y a s s u m p t i o n is t h a t V v,~ = B y # = 0 : v i n t a g e s a r e

b o r n w i t h n o f i n a n c ia l w e a l t h , o n l y w i th a l if e t im e e n d o w m e n t e q u a l t o t h e

2aFor alternative o pen-econ om y mo dels with overlapp ing generations, see Buiter (1981, 1989),

Blanch ard (1985), Persson (1985), Frenkel and Raz in (1987), and E aton (1988).



1 7 6 0 M . O b s t f e l d a n d K . R o g o f f

p r e s e n t v a l u e o f a f te r - ta x la b o r i n c o m e . ( O n e c a n t h i n k o f t h e m o d e l a s o n e in

w h i c h p r i m o g e n i t u r e g o v e r n s t h e b e q u e s t o f f a m i ly w e a l th . ) I n v e s t m e n t c a n b e

m o d e l e d e x a c t l y as in S e c t i o n 3 .1 .3 . T h e o n l y d i f f e r e n c e is t h a t a g r o w i n g l a b o rf o r c e r e q u i r e s p o s i t i v e s t e a d y - s t a te i n v e s t m e n t .

T o m a k e t h e m a i n p o i n t s i t s u ff ic e s t o w o r k w i t h t h e s p e c ia l c a s e i n w h i c h t h e

i n t e r e s t r a t e is c o n s t a n t a t r a n d t h e p e r i o d u t i l it y f u n c t i o n is u C ) = l o g ( C ) Y I n

t h i s c a se ,

C v, t --- (1 - / 3 ) (1 + r ) V v , t + B y , t ) + Z w s - T s ) ( 3 . 24 )

S = t

i s t h e c o n s u m p t i o n f u n c t i o n .

I n i n v e s t i g a t in g t h e e c o n o m y s a g g r e g a t e b e h a v i o r , i t is h e l p f u l t o w o r k w i t hp e r c a p i t a a g g r e g a t e m e a s u r e s o f m a c r o - v a r i a b l e s su c h as c o n s u m p t i o n a n d

w e a l t h . A s s u m e t h a t th e e c o n o m y s t ar ts o n d a t e 0 . L e t X v , t b e t h e v i n t a g e -

s p e ci fi c v a l u e o f v a r ia b l e X o n d a t e t. O b s e r v e t h a t t h e s iz e o f g e n e r a t i o n

v = 0 is 1, t h a t o f g e n e r a t i o n 1 i s (1 + n ) - 1 = n , t h a t o f g e n e r a t i o n 2 i s

(1 + n ) 2 - (1 + 17) = n ( 1 + n ) , a n d s o o n u p t h r o u g h v i n t a g e t , w h i c h i s o f s i z e

n ( 1 + n ) t a . T h u s t h e p e r c a p i t a a v e r a g e v a l u e o f X o n d a t e t is:

X t = X o , t + n X l , t + n( 1 + n ) X 2 ,t + . . . + n( 1 + n ) t - l X t , t(1 + n ) t ( 3 . 25 )

T o c o m p u t e a g g r e g a t e p e r c a p i ta c o n s u m p t i o n , o b s e r v e t h a t V t, d e f i n e d a s i nt h e l as t e q u a t i o n , is th e a v e r a g e p e r c a p i ta v a l u e o f c la i m s to d o m e s t i c f ir m s

a t t h e e n d o f p e r i o d t - 1 a n d i s s ti ll g i v e n b y ( 3 . 1 1 ) i f t h e q u a n t i t i e s i n t h a t

e q u a t i o n a r e i n t e r p r e t e d a s p e r c a p i ta a g g r e g a t e s. E q u a t i o n s ( 3. 11 ), ( 3. 24 ), a n d

( 3 .2 5 ) t h u s i m p l y 26

C t = ( 1 - / 3 ) (1 + r ) B t + Z Y s - T s - I s ) ( 3 . 26 )

S=t

A b o v e , c o n s u m p t i o n h a s b e e n e x p r e s s e d a s a f u n c t i o n o f t h e ti m e p a t h o f t a x es .

T o u n d e r s t a n d t h e r o l e o f t a x a t io n , h o w e v e r , w e m u s t f o r t h e f ir st ti m e in t h is

c h a p t e r e x p l i c it ly c o n s i d e r e x a c t l y h o w t h e d o m e s t i c g o v e r n m e n t c o o r d i n a t e s

t h e t i m e p a t h s o f p u b l i c e x p e n d i t u r e s a n d t a x e s .

L e t D t n o w d e n o t e t h e g o v e r n m e n t s p e r c a p i ta d e b t a t t h e e n d o f d a t e

t - 1 . T h e n i f G t d e n o t e s p e r c a p it a g o v e r n m e n t c o n s u m p t io n , t h e i n t e r t e m p o r a l

p u b l i c - s e c t o r b u d g e t c o n s t r a in t o n d a t e t is

2 5 T hi s c a s e c o r r e s p o n d s t o i s o e l a s ti e p r e f e r e n c e s w i t h o - = 1 .

2 6 7 0 d e r i v e t h i s e q u a t i o n , w e a s s u m e p e r f e c t f o r e s i g h t b e t w e e n d a t e s t - 1 a n d t , s o t h a t ( 1 + r ) V t =

Y t - w t - I t V t l . T h e n e x t e q u a t i o n h o ld s , h o w e v e r , e v e n w i t h o u t t h e p e r f e c t f o r e s i g h t a s s u m p t i o n , a s

c a n b e s e e n b y m o d i f y i n g c o n s u m e r s i n t e r t e m p o r a l b u d g e t c o n s t r a in t s a s e x p la i n e d i n t h e f o o t n o t e

p r e c e d i n g e q . ( 3 .5 ) a b o v e . I n d e r i v i n g ( 3 .2 6 ), w e h a v e m a d e u s e o f th e f a c t t h a t t h e p r o d u c t i o n

f u n c t io n i s h o m o g e n o u s o f d e g r e e o n e .



C h . 34. T h e I n t e r t e m p o r a l A p p r o a c h t o t he C u r r e n t A c c o u n t 1761

l+r) l+n) tDt+ \ - ~ r ] l+n)SG*= H (1 + n) T ,

S=l ,9=f

T hi s c ons t r a i n t e qua t e s t he p r e s e n t va l ue o f t a x r e ve nue s t o t he p r e s e n t va l ue

o f s pe nd i ng p l us i ni t ia l deb t . I f r < n ne i t he r t he gove r nm e n t ' s r e v e nu e no r

i ts spen ding has a f in i t e pre sen t va lue , so we as su me r > n . Div i s ion of the

p re c e d i ng c ons t r a i n t by (1 + n) renders i t in pe r capi t a t e rms as :

0o ( 1 + n ~ s t £ 1 +n~ ~l + r ) D t + ~ _ ~ \ l + r j G s = \ l + r ] Ts

S=t S=t

T o s e e w ha t t h is c ons t r a i n t i mp l i e s f o r p r i va t e c ons um pt i on , l e a d i t one pe r i od

a n d o b s e r v e t h a t

(1 + r)Dt + Gt - Tt= (3.27)Dt+l 1 + n

Solving eq . (3 .27) for Tt a nd t a k i ng p r e s e n t va l ue s , w e ob t a i n

\ ~--+-rr,i Ts = (1 + r Dt - Z \ H i nDs+ \ H I G,,s = t S = / + l s=t

w hi c h , a f t e r r e a r r a ng i ng , c a n be e xp re s s e d i n t he fo rm:

( 1 ~s -t = ( 1 ~s-' n

£ \ H J T s £ H J Gs+ l + r ) l - r ) D ts = t s = t

_ f 1 , ~ s - , _ ~ )-~ \~ - ~ r J n(Ds+ 1 - D , ) (3 .28)

S=t

E xpre s s i on (3 . 28 ) s how s t ha t i n t he ove r l a pp i ng -ge ne ra t i ons e c onomy, gov -

e r n m e n t d e b t i s n e t w e a l t h t o t h e p r i v a t e s e c t o r a n d h i g h e r f u t u r e g o v e r n m e n t

defic i ts lower t he p r e s e n t va l ue o f t a xe s fo r t hos e c u r r e n t l y a l i ve , ho l d i ng t he

p a t h o f g o v e r n m e n t c o n s u m p t i o n c o n s t an t . W h y i s t h is s o ? E q u a t i o n ( 3.2 7)

shows tha t i f Dt w e re a un i t h i ghe r t he gove rnme n t w ou l d ha ve t o r a i s e t a xe s

i n al l f u t u r e pe r i ods b y on l y r - n t o ke e p t he pe r c a p i t a pub l i c de b t c ons t a n t .

T hus , a n e x t r a un i t o f gov e rn me n t bonds i n t he ha nds o f s om e on e a l i ve a t t he

s ta r t o f da te t ra i ses h i s or he r d i scounted s t ream of t ax l i ab i l i t i e s by only

H ( r - n ) = ( l + r ) 1 - r5 =t

H ow do c u r r e n t a nd fu t u r e gove rnme n t de f i c i t s a l t e r t he t a x b i l l o f c u r r e n t

ge ne ra t i ons ? L e t t he go ve r nm e n t c u t pe r c a p i t a t a xe s by 1 + n un i ts i n pe r i od

t and f inance th i s tax cu t by i s su ing enou gh ad di t ion a l deb t to ma ke Dt+l on e

uni t h igher [ see eq . (3 .27) ] . I f the government i s to main ta in th i s new higher



1762 M . O b s t fe l d a n d K . R o g o f f

p e r c a p i t a d e b t l e v e l, i t m u s t r a i s e ta x e s b y r - n p e r c a p i t a f r o m d a t e t + 1 o n.

T h u s , f o r s o m e o n e a l iv e o n d a t e t , t h e n e t e f f e c t o f a d e f i c it - fi n a n c e d t a x c u t i s

t o l o w e r t h e p r e s e n t v a l u e o f t a x e s b y

1 + n - r n ) = n

s = t + l

D e f i c i t - f i n a n c e d t a x cu t s i n p e r i o d s a f t e r t h a v e a c o r r e s p o n d i n g d i s c o u n t e d

e f f e c t o n t h e t a x l i a b i li t ie s o f t h o s e a l i v e o n d a t e t .

T h e m e c h a n i s m u n d e r l y i n g t h es e r e s ul ts is w e l l k n o w n : t h e m o r e d e b t t h e

g o v e r n m e n t i s s ue s , t h e m o r e t a x e s c an b e s h i f te d o n t o f u t u r e g e n e r a t i o n s y e t

u n b o r n . S e v e r i n g a l t ru i st ic l i n ks b e t w e e n t h o s e a l i v e t o d a y a n d s o m e o f t h o s e

w h o w i ll b e a l i v e t o m o r r o w c r e a t e s a s i t u a t i o n in w h i c h c u r r e n t g e n e r a t i o n sd o n o t f u l l y i n t e r n a l i z e t h e f u t u r e t a x l i a b il it ie s a r is i n g f r o m g o v e r n m e n t d e b t

i ss u e . I f, i n c o n t r a s t , n = 0 , t h e r e a r e n o f u t u r e e n t r a n t s t o t h e e c o n o m y t o

b e t a x e d a n d , a s (3 .2 8 ) s h o w s , th e t i m e p r o f i le o f g o v e r n m e n t d e b t n o l o n g e r

m a t t e r s t o e c o n o m i c a g e n t s . I n t h i s c a s e , g o v e r n m e n t d e b t i s n o t n e t w e a l t h

a n d t h e R i c a r d i a n e q u i v a l e n c e o f d e fi ci t- a n d t a x - f i n a n c e d g o v e r n m e n t e x p e n d i -

t u r e h o ld s . I n t h e r e p r e s e n t a t i v e - a g e n t e c o n o m y c o n s i d e r e d e a rl ie r , g o v e r n m e n t

b o r r o w i n g h a s n o i n f l u e n c e o n t h e c u r r e n t a c c o u n t .

T h i s is n o t t h e c a s e h e re . B e c a u s e t h e e c o n o m y s o v e r a l l n e t f o r e i g n a s s e t s

a r e A t - - B t - D t s u b s t i t u t io n o f (3 .2 8 ) in t o c o n s u m p t i o n f u n c t i o n ( 3. 26 ) s h o w s

t h a t

C, = (1 - f i ) D t + ~ n D s + l - D s )

S = t

+ (1 + r ) A t + \ ] ~ T J Y s - I s - G , . )

S ~ t

I n p e r c a p i t a t e r m s , t h e d a t e - t c u r r e n t a c c o u n t is (1 + n ) A t + l A t = r a t + Y t -

C t - I t - G t , s o , o t h e r t h in g s e q u a l , a h i g h e r c u r r e n t l e v e l o f g o v e r n m e n t d e b t o r

a h i g h e r t r a j e c t o r y f o r f u t u r e g o v e r n m e n t d e fi ci ts w i ll r a i s e c u r r e n t c o n s u m p t i o n

a n d t h e e c o n o m y s f o re i g n b o r ro w i n g .

D e s p i t e s o m e n o t a b l e e p i s o d e s , i t h a s p r o v e n d i ff ic u lt to v e r i f y a s t r o n g s t a t is -

t ic a l c o r r e l a t i o n b e t w e e n b u d g e t a n d c u r r e n t - a c c o u n t d ef ic it s. B e l o w w e p r e s e n t

c r o s s - s e c t i o n r e g r e s s i o n s f o r in d u s t r i a li z e d c o u n t r i e s o v e r f iv e - y e a r s u b s a m p l e s

o f 1 9 7 6 - 1 9 9 0 . 27 E a c h s u b s a m p l e c r o s s - s e c ti o n o b s e r v a t i o n is f o r m e d b y a v e r -

2 7 T h e s a m p l e c o n s i st s o f t h e O E C D c o u n t r i e s a s o f 19 94 , e x c e p t f o r B e l g i u m , L u x e m b o u r g a n d

T u r k e y . T h e d a t a f o r c u r r e n t - a c c o u n t d e f i c i t s a n d c e n t r a l g o v e r n m e n t b u d g e t d e f i c i t s r e l a t i v e t oG D P c o m e f r o m I n t e r n a t io n a l M o n e t a r y F u n d , I n t e r n a t i o n a l F i n a n c i a l S ta t i st i cs . D ue to l ac k o f da t a ,S w i t z e r l a n d i s o m i t t e d f r o m t h e 1 9 8 1 - 1 9 8 5 r e g r e s s i o n a n d C a n a d a , N e w Z e a l a n d , a n d S w i t z e r l a n d

a r e o m i t t e d f r o m t h e 1 9 8 6 - 9 0 r e g r e s s i o n . R e g r e s s i o n s b a s e d o n g e n e r a l g o v e r n m e n t d e f i c i t s y i e l d

s im i la r r e su l ts [ see Ob sf fe ld an d Rog of f 1996) , ch . 3].



Ch. 34: The Intertemp oral App roach to the C urrent Accou nt 1763

a g i n g a c o u n t r y ' s a n n u a l c u r r e n t - a c c o u n t s u r p l u s r a ti o t o G D P a n d i ts c e n t r a l

g o v e r n m e n t d e f i c i t r a t i o t o G D P .

1 9 7 6 - 1 9 8 0

C A / Y ) j = - 0 . 2 0 8 - 0 . 4 06 d i D / Y ) j + u j; R 2 = 0 .23

(0 .907 ) (0 .171 )

1 9 8 1 - 1 9 8 5

C A / Y ) I = 0 .995 - 0 . 506 A D / Y ) j + u j; R 2 = 0 .32

(1 .206 ) (0 .173 )

1 9 8 6 - 1 9 9 0

C A / Y ) j = - 0 . 8 8 1 - 0 . 0 1 6 A D / Y ) j + u j; R 2 = 0 . 0 0

(0 .707 ) (0 .114 )

O v e r t h e f i r s t t w o s u b s a m p l e s t h e r e i s a s t r o n g n e g a t i v e c o r r e l a t i o n b e t w e e n

b u d g e t d e f ic i ts a n d t h e c u r r e n t - a c c o u n t s u r p l us , a s t h e o v e r l a p p i n g - g e n e r a t i o n s

m o d e l w o u l d s u g ge s t. 2s D u r i n g t h e m o s t r e c e n t s u b s a m p l e , h o w e v e r , t h e c o r r e -

l a t io n e v a p o r a t e s . T h e l as t r e s u lt s u g g es ts t h a t f a c to r s o t h e r t h a n g o v e r n m e n t

b u d g e t s d o m i n a t e d s e v e r a l c o u n t r i e s ' c u r r e n t a c c o u n t s o v e r 1 9 8 6- 1 99 0 . I f o n e

r u n s t h e s a m e r e g r e s s i o n o n a s a m p l e t h a t i n c l u d e s n o n - i n d u s t r i a l i z e d c o u n t r i e s ,

t h e r e s u lt s a r e w e a k e r . B e w a r e : t h e s e s i m p l e c o r r e l a t io n s a r e m e r e l y s u g g e s t i v e

a n d h a v e n o s t r u c t u r a l i n t e r p r e t a t i o n . I n p a r t i c u l ar , t h e y c a n n o t t el l u s t h e e f-

f e c t o f a n e x o g e n o u s i n c r e a s e i n a g o v e r n m e n t ' s b u d g e t d e fi ci t o n t h e c u r r e n t

a c c o u n t . A n o t h e r s e r i o u s i s su e is t o c h o o s e t h e a p p r o p r i a t e m e a s u r e o f t h e in -

t e r g e n e r a t i o n a l i n c i d e n c e o f b u d g e t p o l ic i es . F o r e x a m p l e , e v e n i f t h e s o c ia l

s e c u r i t y a c c o u n t o f t h e b u d g e t i s b a l a n c e d , i t r e p r e s e n t s a h u g e t r a n s f e r f r o m

y o u n g t o o ld . C l e a r ly , a b e t t e r u n d e r s t a n d i n g o f t h e t w i n d e f ic i ts w i ll r e q u i r e

s t r u c t u r a l m o d e l s a n d c a r e f u l a t t e n t i o n t o i n t e r g e n e r a t i o n a l d i s t r i b u t i o n .

M o d e l s i n c o r p o ra t i n g m o r e c o m p l e x d e m o g r a p h i c s h a v e i m p o r t a n t i m p li -

c a t io n s a s i d e f r o m t h e i r p r e d ic t io n s a b o u t g o v e r n m e n t f in a n ci al i m b a l a n c e s.

C o n s i d e r , f o r e x a m p l e , t h e i m p l i c a t io n s o f e x p e c t e d p r o d u c t i v i t y g r ow t h . I n a

r e p r e s e n t a t i v e - a g e n t f r a m e w o r k , h i g h e r p r o d u c t iv i t y g r o w t h w i ll t e n d t o w e a k e n

t h e c u r r e n t a c c o u n t a s p e o p l e b o r r o w t o d a y a g a i n st h i g h e r f u t u re i n c o m e . ( In -

v e s t m e n t e f f e c ts w o u l d s t r e n g t h e n t h is r e s u lt .) I n a l if e - c y cl e s e t ti n g t h e i m p l i -

c a t i o n s o f h i g h e r p r o d u c t i v i t y g r o w t h a r e l e ss c le a r. I f e a c h i n d i v i d u a l b e n e f i t s

i d e n t i c a l l y f r o m t h e c h a n g e r e g a r d l e s s o f h is o r h e r a g e , t h e r e s u l t s a r e m u c h t h e

s a m e a s i n a r e p r e s e n t a t i v e - a g e n t m o d e l . B u t s u p p o s e t h a t p r o d u c t i v i ty g r o w t h

r a is e s th e l a b o r i n c o m e s o f y o u n g w o r k e r s b u t d o e s n o t a f f e c t th e l a b o r i n c o m e s

o f o ld e r w o r k e r s . B e c a u s e y o u n g s a v e rs w il l c o u n t m o r e h e a v i l y in a g g r e g a t e

s a v i n g t h a n o l d d i s s a v e r s , s a v i n g w i ll t e n d t o r is e a n d t h e c u r r e n t a c c o u n t t o

28In a samp le including four industrialized countries and M exico, Bernh eim (1988) finds a similar

correlation betwee n bu dget deficits and current-accoun t deficits over 1976-1985.



1764 M. Obstfeld and K. Ro goff

i m p r o v e . D e a t o n ( 19 9 2) d i s cu s s es h o w l i fe - c y c le t h e o r i e s m i g h t e x p l a i n t h c o b -

s e r v e d t e n d e n c y f o r n a t i o n a l s a v i n g an d g r o w t h r a t e s t o b e p o s i t i v e ly c o r r e l a te d

i n c r o s s s e c t i o n s .A n i m p o r t a n t p r o p e r t y o f o v e r l a p p i n g - g e n e ra t i o n s m o d e l s is th a t t h e y p e r m i t

a s t e a d y - s t a t e w i t h p o s i t iv e c o n s u m p t i o n f o r a s m a l l o p e n e c o n o m y , e v e n i f

i n d i v i d u a l s h a v e f ix e d t i m e - p r e f e r e n c e r a t e s d i f f e r e n t f r o m t h e w o r l d i n t e r e s t

r a t e . In t h e W e i l ( 19 8 9) m o d e l j u s t s k e t c h e d , f o r e x a m p l e , t h e s m a l l e c o n o m y

c a n r e a c h a s t e a d y s t a t e e v e n i f i n d i v i d u a l c o h o r t s c o n s u m p t i o n l e v e l s a r e r is i n g

o r f a l l in g o v e r t i m e ; w h a t i s n e e d e d is t h a t t h e b i r t h r a t e o f n e w i n d i v i d u a ls b e

l a r g e e n o u g h t o o f f s e t t h e d i s c r e p a n c y b e t w e e n / 3 ( 1 + r ) a n d 1 . I f / 3 ( 1 + r ) < 1,

n > 0 g u a r a n t e e s t h i s o u t c o m e ; i f / 3 ( 1 + r ) > 1 , t h e i n e q u a l i t y / 3 ( 1 + r ) < 1 + n i s

n e c e s s a r y .

3 .2 . S t o c h a s t i c m o d e l s o f th e c u rr e n t a c c o u n t

A t h e o r y o f c u r r e n t - a c c o u n t d e t e r m i n a t i o n t h a t m a k e s n o a l l o w a n c e f o r t h e

u n c e r t a i n t y a b o u t t he f u t u re u n d e r l y i n g c o n s u m p t i o n a n d i n v e s t m e n t d e ci s io n s

c a n n o t b e f u l l y s a t is f a c to r y . U n f o r t u n a t e l y , h o w e v e r , t h e i n t r o d u c t i o n o f s to c h a s -

t ic e l e m e n t s c a n r a i s e t h e t e c h n i c a l d if f ic u l ty o f w r i t i n g d o w n s o l u t i o n s t o i n-

d i v id u a ls m a x i m i z a t io n p r o b l e m s b y a n o r d e r o f m a g n i tu d e . B e l o w w e r e v i e w

t h e p r e d i c t i o n s o f s o m e l e a d in g s t o c h as t ic m o d e l s . A k e y t h e m e e m e r g i n g f r o mt h e d i s c u s s io n is t h a t t h e c u r r e n t - a c c o u n t r e s p o n s e t o v a r i o u s sh o c k s d e p e n d s

o n w h e t h e r m a r k e t s e x is t f o r i n su r in g a g a i n s t th e s h o c k s e ff e ct s. T h i s t h e m e

l e a d s u s , a t t h e s e c t i o n s e n d , t o c o n s i d e r a m o d e l i n w h i c h t h e e x t e n t t o w h i c h

s h o c k s a r e i n s u r a b l e i s e n d o g e n o u s .

3 .2 .1 . C o m p l e t e m a r k e t s

T h e m o s t t r a c t a b l e c a s e o f u n c e r t a i n t y is t h a t in w h i c h i n s u r a n c e m a r k e t s e x i s t

f o r al l f u t u r e c o n t i n g e n c i e s , w i t h o u t c o m e s f u l l y v e r i f i a b l e a n d c o n t r a c t s f u l ly

e n f o r c e a b l e . I n th e c la ss ic A r r o w - D e b r e u w o r l d o f c o m p l e t e m a r k e t s , e q u i li b -r i u m r e s o u r c e a l l o c a t i o n s a r e e f fi c ie n t a n d , f r o m a f o r m a l p o i n t o f v ie w , t h e

e c o n o m y c a n b e a n a l y z e d a s i f p e r f e c t c e r t a i n t y a p p li e d . T h e r e a r e s i m p l y m a n y

m o r e c o m m o d i t i e s , c o m m o d i t i e s n o w b e i n g in d e x e d b y th e s ta t e o f n a t u r e i n

w h i c h t h e y a r e d e m a n d e d a n d s u p p l i ed . 29

29International models with complete m arkets are analyzed by L ucas (1982), Stockman (1988a),Stulz (1988), Co le and Obstfeld (1991), Stockman and Tesar (1995), Backus, Kehoe, and Kydland(1992), and Bax ter and Crucini (1993a), am ong many others. L ucas s (1982) mo del does not actuallyassume complete m arkets, and in fact can contain far more states of nature than assets. How ever,other spec ial assumptions made by Lu cas result in an allocation the same as the one com plete

markets would produce.



Ch 34: The lntertemporal Approach to the Current Account 765

E x c e p t f o r c e r t a i n s p e c ia l c a se s , m a r k e t c o m p l e t e n e s s r e q u i r e s t h a t p e o p l e

b e a b l e t o t r a d e a s m a n y i n d e p e n d e n t a s s e ts a s t h e r e a r e p r o s p e c t i v e s t a te s

o f n a t u r e . E q u i v a l e n t l y , t h e y m u s t b e a b l e t o t r a d e a c o m p l e t e s e t o f A r r o w - -D e b r e u s e c u r it i es , e a c h o f w h i c h p a y s o f f o n l y i n o n e s t a t e . T h e r e s u l t o f t hi s

t r a d e i s t h a t i n d i v i d u a l s e v e r y w h e r e i n t h e w o r l d e q u a l i z e t h e i r m a r g i n a l r a t e s

o f s u b s t i t u ti o n o f p r e s e n t f o r f u t u r e s t a t e - c o n t in g e n t c o n s u m p t i o n t o t h e s a m e

A r r o w - D e b r e u p r i ce s , so t h a t fo r a ll c o u n t r i e s i a n d j , a n d a l l d a t e s t ,

u ( q + l ) JC t + 1 )- 3 . 2 9 ,

u ( C / ) , , ( C / )

g i v e n s h a r e d r a t e s o f t i m e p r e f e r e n c e ( t h a t i s, t h e / % c a n c e l ). C o n d i t i o n ( 3, 29 )

p r e c l u d e s f u r t h e r m u t u a l g a i ns , o n a n y d a t e o r i n a n y s t a te , fr o m i n t e r - c o n s u m e rr i s k p o o l i n g . I n v e s t m e n t d e c i s i o n s a r e m a d e t o m a x i m i z e t h e p r e s e n t v a l u e o ~

p r o f i t s e v a l u a t e d a t s t a t e - c o n t i n g e n t o u t p u t p r i c e s .

W h e n a ll p e o p l e t h r o u g h o u t t h e w o r l d t r a d e p r o s p e c t i v e r i sk s in i n s u r an c e

m a r k e t s , s o m e l o ca l e c o n o m i ~ s h o ck s e f f e c t i v e ly b e c o m e g l o b a l s h o c ks a n d t h e i r

c u r r e n t a c c o u n t e f f e c t s a r e d i m i n i s h e d o r e v e n e l i m i n a t e d . C o n s i d e r , fo r in -

s t an c e , a p u r e e x c h a n g e e c o n o m y t h a t e x p e r i en c e s a t e m p o r a r y i d i o s y n cr a t ic

p o s i ti v e o u t p u t s h o c k . A b s e n t i n s u r a n ce m a r k e t s , t h e c o u n t r y w o u l d r u n a

c u r r e n t - a c c o u n t s u r p l u s , a c c u m u l a t i n g s o m e f o r e i g n a s s e ts s o a s t o s m o o t h t h e

b e n e f it s o f th e s h o c k o v e r a ll f u t u r e p e r io d s . U n d e r c o m p l e t e m a r k e t s , h o w e v e r ,

t h e h o m e e c o n o m y h a s a l r e a d y t r a d e d m u c h o f it s o u t p u t r is k t o f o r ei g n e r s a n d

p u r c h a s e d , i n t u r n , c l a im s o n t h e i r r is k y o u t p u t p r o c e s s e s . T h u s , t h e h o m e e c o n -

o m y ' s p o s i t i v e o u t p u t s h o c k w i l l c a u s e a s m a l l s y n c h r o n i z e d i n c r e a s e i n e v e r y

c o u n t r y ' s c o n s u m p t i o n u n d e r c o m p l e t e m a r k e t s . B u t i t w i l l a l s o ca u s e a s h i ft i n

e v e r y c o u n t r y 's i n o m e a s d i v i d e n d p a y m e n t s f lo w f r o m t h e h o m e c o u n tr y t o

i ts f o r e i g n s h a r e h o l d e r s . W i t h i n t e r n a t i o n a l l y i d e n t i c a l i s o e l a s t ic p r e f e r e n c e s , n o

c u r r e n t - a c c o u n t i m b a l a n c e s r e s u l t . I n d e e d , i n t h a t c a s e , t h e r e a r e n e v e r u n a n -

t i c i p a t e d c u r r e n t a c c o u n t m o v e m e n t s . ( R e g a r d l e s s o f t h e u t i l i t y f u n c t i o n , di f-

f e r e n c e s i n t i m e p r e f e r e n c e c a n g e n e r a t e p r e d i c t a b l e n o n z e r o c u r r e n t a c c o u n t s

u n d e r c o m p l e t e m a r k e ts . )I f p e r i o d u t i l i ty is n o t i s o e l a st i c a n d i d e n t i c a l a cr o s s c o u n t r i e s , w o r l d o u t p u t

s h o c k s w i ll , i n g e n e r a l , c a u s e c u r r e n t - a c c o u n t i m b a l a n c e s . E v e n i n th i s ca s e ,

s h o c k s t h a t a f f e c t t h e d i s t r i b u t i o n o f o u t p u t a c r o s s c o u n t r i e s , b u t l e a v e w o r l d

o u t p u t u n c h a n g e d , h a v e n o c u r r e n t - a c c o u n t i m p l i c a t i o n s .

R e t u r n i n g t o t h e c a s e o f i n t e r n a t i o n a l l y i d e n t i c a l is o e l a s t ic u t i l it y b u t i n-

t r o d u c i n g p r o d u c t i o n , a p o s i t i v e s h o c k to t h e p r o d u c t i v i t y o f d o m e s t i c in v e s t -

m e n t c a u s e s a c u r r e n t - a c c o u n t d e f ic i t, a s in o u r e a r l i e r p e r f e c t - f o r e s i g h t m o d e l s .

B u t t h a t d e f ic i t w i l l r e f l e c t o n l y a n i n f l u x o f s a v in g s f r o m a b r o a d t o s h a r e i n

o w n e r s h i p o f t h e i n c r e m e n t a l i n v e s t m e n t . ( I n d e e d , t h e e x i s t i n g c a p i t a l o f f i r m s

w i ll a l r e a d y h a v e a g l o b a l l y d i s p e r s e d o w n e r s h i p . ) T h e d e f i c it d o e s n o t r e f le c t



1766 M ObstJeld and K Rogoff

c o n s u m p t i o n - s m o o t h i n g e f fe c ts , b e c a u s e a ll c o u n t r i e s i n c o m e p r o fi le s a re r is in g

i n p r o p o r t i o n . D e s p i t e t h e d e f ic it - i n d e e d , b e c a u s e o f i t - t h e i n t e r n a t i o n a l

w e a l t h d i s t r i b u t i o n i s c o n s t a n t .U n d e r l i te r a l ly c o m p l e t e m a r k e t s , r is k s d u e t o c h a n g e s in g o v e r n m e n t c o n -

s u m p t i o n a l so w o u l d b e p e r f e c tl y p o o l e d a m o n g n a t i on s . A n e x o g e n o u s u n -

e x p e c t e d r i s e i n U n i t e d S t a t e s s p e n d i n g o n h i g h w a y r e p a i r s d u e , s a y , t o b a d

w e a t h e r , w o u l d b e f i n a n c e d m o s t l y b y c o n t i n g e n t - c o n t r a c t p a y m e n t s f r o m f o r-

e i g n e r s to t h e U n i t e d S t a te s . T h e o b v i o u s a d v e r s e i n c e n t i v e s i n t r o d u c e d b y s u c h

c o n t r a c t s i l l u s t r a t e w h y , i n p r a c t i c e , a ss e t m a r k e t s a r e h a r d l y c o m p l e t e . I f a c o u n -

t r y s r e s i d e n t s h a v e s o ld m o s t o f d o m e s t i c f ir m s f u t u r e e a r n i n g s o n f o r w a r d m a r -

k e t s, i ts g o v e r n m e n t h a s e v e r y in c e n t i v e to r a i s e c o r p o r a t e t a x e s s h a r p l y a f t e r

t h e f a ct . M o r e g e n e r a ll y , u n d e r a s y m m e t r i c i n f o r m a t i o n , m o r a l h a z a r d s a f f e c t i n g

p r i v a t e a s w e l l as g o v e r n m e n t b e h a v i o r i m p e d e c o m p l e t e r i sk s ha r in g . I n f o r m a l

o b s e r v a t i o n a n d s ta ti st ic a l e v i d e n c e b o t h c o n f i r m t h a t e v e n i n a d o m e s t i c c o n -

t e x t , r is k s a re f a r f r o m b e i n g p o o l e d a s t h e c o m p l e t e - m a r k e t s p a r a d i g m w o u l d

p r e d i c t. I n t h e i n t e r n a t i o n a l c o n t e x t , s o v e r e i g n r is k a n d d i s ta n c e , t o g e t h e r w i t h

c u l t u r a l a n d l e g a l d i f f e r e n c e s , g r e a t l y m a g n i f y t h e d i ff ic u l ti e s. 3°

3 2 2 Bo nd s as the only asset

L e t u s l o o k i n s t e a d a t t h e o p p o s i t e e x t r e m e , t h a t i n w h i c h t h e o n l y a ss e t n a t io n s

t r a d e is a o n e - p e r i o d b o n d i n d e x e d t o t r a d e a b l e c o n s u m p t i o n g o o d s a n d o f f e ri n ga c e r t a in o n e - p e r i o d r e t u r n . T h i s r e s tr i c ti o n o n t h e m e n u o f a s se t s is to o s e v e r e

t o f u r n is h a c o m p l e t e l y re a l is t ic m o d e l , b u t i t d o e s s e r v e t o p r o d u c e a m o d e l

q u i t e c o m p a r a b l e t o t h e d e t e r m i n i s t i c o n e s t u d i e d e a r l ie r . L a t e r o n w e d is c us s

h y b r i d m o d e l s i n w h i c h th e r e a r e m a r k e t s f o r s o m e , b u t n o t a l l, r is k s.

F o r s im p l ic i ty , w e a g a in c h o o s e a s o u r f r a m e w o r k a r e p r e s e n t a t i v e - a g e n t e c o n -

o m y in w h i c h a ll g o o d s a r e t r a d e d . N o w t h e i n d i v i d u a l m a x i m i z e s t h e c o n d i t i o n a l

e x p e c t a t i o n

s u b j e c t to a b u d g e t c o n s t r a i n t l ik e ( 3 .5 ) e q u a t i n g t h e p r e s e n t v a l u e o f c o n s u m p -

t i o n t o i n i t ia l fi n a n c i a l w e a l t h p l u s t h e p r e s e n t v a l u e o f a f t e r - t a x l a b o r i n c o m e .

T h e c o n s u m p t i o n l e v el s i n (3 .3 0) a r e c o n t i n g e n c y p l a n s fo r c o n s u m p t i o n t h a t

d e p e n d o n t h e i n d i v i d u a l s h is t o r y t h r o u g h t h e d a t e t h e p l a n i s i m p l e m e n t e d .

T h e b u d g e t c o n s t r a i n t d e p e n d s o n s t o c h a s ti c f u t u r e e a r n in g s , t a x e s, a n d i n t e r e s t

r a te s . T h e s e q u e n c e o f c o n t in g e n t c o n s u m p t i o n p l a n s t h e c o n s u m e r c h o o s e s o n

3°See Obsffeld (1995) for a survey of evidence . The limited extent of international risk sharing

has pro mp ted S hiller (1993) to pro pose creating international markets in G DP futures.



C h . 3 4 : Th e I n t e r t em p o r a l A p p r o a ch t o t h e C u r r en t A c co u n t 1767

d a t e t m u s t s a t i sfy t h e b u d g e t co n s t r a in t fo r ev e ry p ro s p ec t i v e h i s t o ry o f th e

e c o n o m y .

T h e i n t e r t e m p o r a l E u l e r e q u a t i o n d e r i v e d i n th e c e r t a i n t y c a se n o w h o l d s inex pe c ta t ion [c f . eq . (3.6 )] :

u ( C t ) / 3 ( i + r t + l ) E , 3 . 3 l )

T o o b t a i n c l o s e d - f o r m c o n s u m e r d e ci s io n r u le s , w e a p p r o x i m a t e u C ) by the

q u a d r a t i c f u n c t i o n

h C2u c ) - c -

W ith t h i s ap p ro x im a t io n (3 . 3 1 ) b eco m es

1 1 ( /3(1+rf+ 1)1t C t 1 = / 3 l + r t+ l ) Ct + -~ 1

H e r e w e s e e t h a t t h e r e l a t i o n b e t w e e n / 3 a n d t h e g r o s s w o r l d i n t e r e s t r a t e

i n d u ces a t i l t i n ex p ec t ed co n s u m p t io n g ro wth a s was a l s o t ru e i n Su b s ec t i o n3.131 .

T o s im p l i fy fu r t h e r , a s s u m e t em p o ra r i l y t h a t t h e i n t e r e s t r a t e i s co n s t an t a t r ,

w i th 13 (1 + r ) = 1 ; t h e r e s u l t is t h e r an d o m wa lk p red i c t i o n fo r co n s u m p t io n

der ived by Hal l (1978) :

E t C t l = C t (3.32)

In eq u i l i b r i u m , t h e eco n o m y ' s i n t e r t e m p o r a l b u d g e t co n s t r a in t , eq . (3 .3 ), m u s t

h o l d f o r e v e r y p o ss ib l e s e q u e n c e o f o u t c o m e s w h e n i ts e l e m e n t s a r e r a n d o m .

A p p ly in g t h e d a t e - t ex p ec t a t i o n s o p e ra to r t o b o th s i d es o f (3.3 ) an d u s in g (3 .3 2) ,

w e h a v e t h e c e r t a i n t y - e q u i v a l e n c e c o n s u m p t i o n f u n c t io n :

C, = 1-77r E t (1 + r ) A t + Z \ ] - 7 7 2 Y ~ - G , - l s ) (3.33)S t

E q u a t i o n (3.3 3) y i e ld s p red i c t i o n s fo r cu r ren t a cco u n t s q u a l i t a t i v e ly s im i l a r

t o t h o s e o f t h e d e t e rm in i s t i c co n s u m p t io n fu n c t i o n (3.8 ) d ev e lo p ed ea r l i e r. As a

re s u l t , t h i s eq u a t i o n an d i t s r e l a t i v e s p ro v id e t h e l e ad in g v eh i c l e s fo r em p i r i ca l

s t u d ie s o f c u r r e n t - a c c o u n t d e t e r m i n a t i o n . T h e l i n e a r - q u a d r a t ic f o r m u l a t i o n h as ,

h o wev e r , a t l e a s t t h ree co n cep tu a l d rawb ack s :

31In the p r e c e d ing e qua t ion the r a t i o o f t he g r o s s i n t e r e s t r a t e t o 1 /13 e n t e r s b o th i n t he s lope a ndin t he in t e r c e p t , w i th oppos i t e e f f e c t s on e xp e c t e d da t e @ + 1 ) c onsum pt ion . T he qu a d r a t i c u t i l i tyspe c i f i c a t i on m a ke s s e nse , how e ve r , on ly so l ong a s C < 1 / h , e nsu r ing tha t t he m a r g ina l u t i l i t y

o f c o n s u m p t i o n i s p o s i ti v e . U n d e r t h i s a s su m p t i o n , i t is c l e a r t h a t t h e i n t e r c e p t e f f e c t d o m i n a t e s :

l o w e r i n g / 3 , f o r e x a m p l e , l o w e r s e x p e c t e d d a t e - t + 1 ) c o n s u m p t i o n i n t h e l a s t e q u a t i o n .



1768 M. Obs t fe ld and K. Rogo] f

( 1 ) U n d e r q u a d r a t i c u t i l i t y u ~ (C) ~ - O , s o t h e r e i s n o p r e c a u t i o n a r y s a v i n g .

W h e n , i n s t e a d , u ~ ( C ) > 0 , m a r g i n a l u t i l i t y d ( C ) i s a c o n v e x f u n c t i o n . T h i s

c o n v e x i t y i m p l i e s t h a t a n i n c r e a s e in u n c e r t a i n t y o v e r f u t u r e c o n s u m p t i o n r a is e si ts e x p e c t e d m a r g i n a l u t i l i t y a n d , t h u s , s a v i n g . 32

( 2) I n b o t h e s t im a t i n g a n d s i m u l a ti n g i n t e r t e m p o r a l m o d e l s , it is f r e q u e n t l y

c o n v e n i e n t t o b e a b l e t o l i n e a r i z e o r l o g - l i n e a r i z e f i r s t - o r d e r E u l e r c o n d i t i o n s .

A s s u m i n g q u a d r a t i c p e r i o d u t il it y is r e a ll y j u st a n o t h e r w a y o f l in e a r iz i n g . T h e

b a s i c p r o b l e m w i t h t h is a p p r o a c h is t h a t a l i n e a r iz e d m o d e l w il l b e v e r y i n a c c u -

r a t e f a r a w a y f r o m t h e p o i n t o f a p p r o x i m a t i o n . Y e t i f t h e l i n e a r i z a t i o n im p l i e s,

a s i n ( 3. 32 ), t h a t c o n s u m p t i o n f o l lo w s a r a n d o m w a l k , c o n s u m p t i o n w i ll e v e n t u -

a l ly d r if t a r b i t r a r i l y f a r f r o m a n y i n i ti a l l e v e l . A s O b s t f e l d ( 1 9 82 ) a n d S v e n s s o n

a n d R a z i n ( 1 98 3 ) s h o w e d , o n e w a y to a v o i d a u n i t r o o t i n c o n s u m p t i o n is t o

a s s u m e a n e n d o g e n o u s , r a t h e r t h a n f ix e d , r a t e o f ti m e p r e f e r e n c e . I f t h e r a t e

o f im p a t i e n c e r i se s w i th t h e l e v e l o f c o n s u m p t i o n , a s t a ti o n a r y c o n s u m p t i o n

d i s t r ib u t i o n is p o s s ib l e . U n d e r u n c e r t a in t y , p r e c a u t i o n a r y s a v in g c a n m i m i c t h is

b e h a v i o r ( e v e n w i t h a fi x ed ti m e - p r e f e r e n c e ra t e ) b e c a u s e c o n s u m e r s s a v e le ss a t

h i g h e r w e a l t h l ev e ls . [ ee C a r r o l l ( 1 9 9 2 ) a n d D e a t o n ( 1 9 9 2 ) . ] A n o t h e r s o l u t i o n

is to a s s u m e o v e r l a p p i n g c o h o r t s o f f i n it e -l iv e d a g e n ts w h o l e a v e n o b e q u e s t s .

U n f o r t u n a t e l y , n o a l t e r n a t iv e c a n m a t c h t h e l i n e a r - q u a d r a t i c in f i n it e - li f e ti m e

f r a m e w o r k f o r e a s y e m p i ri c a l im p l e m e n t a t i o n . U l t i m a t e l y t h e ju s t if ic a t io n f o r

u s i n g th e l a t t e r s e t u p m u s t r e s t o n t h e p r e s u m p t i o n t h a t it y i e ld s a r e a s o n a b l e

a p p r o x i m a t i o n t o b e h a v i o r a w a y f i o m b o u n d a r i es . M o r e r e s e a rc h p r o v i n g o rd i s p r o v i n g t h is p r e s u m p t i o n w o u l d b e u s e f u l . 33

( 3) T h e c o n s u m p t i o n f u n c t i o n ( 3. 33 ) d o e s n o t n e c e s s a r i l y c o n s t r a i n c o n s u m p -

t i o n t o b e n o n - n e g a t i v e i n a l l s ta t es o f t h e w o r l d . I f n e g a t iv e l e v e l s o f c o n s u m p -

t i o n a r e r u l e d o u t , c o n s u m p t i o n c a n n o t l i t e ra l ly f o l l o w a r a n d o m w a l k a s in(3 .32 ) .34

W e t u r n n e x t t o i n v e s ti g a ti n g h o w , w h e n b o n d s a r e t h e o n l y i n t e r n a t i o n a l l y

t r a d e d a ss e t, t h e s e p a r a ti o n b e t w e e n d o m e s t i c i n v e s tm e n t a n d c o n s u m p t i o n i m -

p l ie d b y c o m p l e t e m a r k e t s c a n b r e a k d o w n .

I t is n a t u r a l t o a s s u m e a g a i n th a t t h e d o m e s t i c fi rm m a k e s i ts i n v e s t m e n t

d e c i s io n o n d a t e t t o m a x i m i z e th e p r e s e n t d i s c o u n t e d v a l u e o f p r o fi ts . B u t w i t hu n c e r t a i n t y , it is n o l o n g e r o b v i o u s w h a t d i s c o u n t r a t e s h o u l d b e u s e d t o v a l u e

t h e r i s k y s t r e a m o f d i v i d e n d s t h e f i r m i s s u e s t o s h a r e h o l d e r s . W i t h p o p u l a t i o n

n o r m a l i z e d t o 1 , th e f i rm s e x d i v i d e n d v a l u e , V t + l , i s t h e p r i c e o f a p e r c a p i t a

32On precautionary saving behavior, see Leland (1968).33Clarida (1990) develops an ex ac t general-equilibrium m od el of international borrow ing and

lending under endowm ent uncertainty, heterogenous fixed discount rates , and low er l imits on in-dividual assets. H e finds that w hen there is no aggregate output un certainty, there is a stationarydistribution of wealth and consum ption levels n w hich som e households are borrowing-constrained.

34The problem of nonn egativity constraints afflicts the com mo nly us ed consum ption functions

derived in continuo us-time mo dels by stochastic dynam ic programm ing. See Cox and H uan g (1989).



C h . 3 4 : T h e l n t e r t e m p o r a l A p p r o a c h t o t h e C u r r e n t A c c o u n t 1769

s h a r e i n th e f ir m i n d a t e t a s se t tr a d i ng . U s i n g d y n a m i c p r o g r a m m i n g ( t h e d e t a i l s

a r e o m i t t e d h e r e ) , o n e c a n s h o w t h a t V t + l f o l l o w s a s t o c h a s t i c p r o c e s s s u c h t h a t

t h e f o l l o w i n g E u l e r e q u a t i o n h o l d s:

V t + l U ( C t ) = f l E t { [ O t + l V ( K t + l , L t + l ) - W t + l L t + l

- I t + l - a I { + l / Z K t + l + V t + 2 ] u ( C t + l ) }

I t e r a t e d f o r w a r d s u b s t i t u t i o n s f o r V y i e l d a s t o c h a s t i c v e r s i o n o f ( 3 .1 6 ),

O s F ( K s , L s ) - w ~ .L s - I s - 2 -~ sJ (3 .34)

G i v e n t h a t t h e f ir m is o w n e d e n t i r e l y b y d o m e s t i c r e s id e n t s , t h e p r e s e n t v a l u eo f a c l a i m t o i ts f u t u r e d i v i d e n d s i n a n y p a r t i c u la r s t a te o f n a t u r e d e p e n d s o n

d o m e s t i c c o n s u m e r s m a r g i n a l u t i l i t y in t h a t s t a te o f n a t u r e r e l a t i v e t o c u r r e n t

m a r g i n a l u t i l i t y .

W e c a n d e c o m p o s e ( 3. 34 ) f u r t h e r a s 3s

s = t l b l t C t ) E t O s F ( K s , L s ) - w s L s - I s - 2 K ,

+ f i s - t C o v t u ~ -7 ~ t) , O s X ( K s , L s ) - w s L s - Is ,. - 2Ks.---

S=t ]

D e f i n e R L t o b e t h e m a r k e t d i s c o u n t f a c t o r b e t w e e n p e r i o d s t a n d s , t h a t i st,s

t h e p r i c e o f s u r e ( t h a t is , n o n c o n t i n g e n t ) d a t e s c o n s u m p t i o n i n t e r m s o f d a te

t c o n s u m p t i o n . O f c o u r s e , R L i s s i m p l y t h e i n v e r s e o f t h e g r o s s s h o r t r a t e ,t ,t+l1 + rt+ 1.3 6 T h e ( s - t ) - p e r i o d a n a l o g o f e q . ( 3 . 3 1 ) i s

s - t L. ( c , ) = / R t , E t

s o t h e p r e v i o u s e q u a t i o n c a n b e w r i t t e n a s

o~ { a / 2 . ~

V t+ l = ~ R L , . E t O s F ( K ~ , L s ) - w s L s - I s - 2 K ~ J

s~t ]

+ f l , _ t C o v t ( , u ( C s ) O s F ( K s , L s ) - w s C s - I s - 2 K ss : , l I

35The result below uses the fact that if X and X ~ are tw o random variables, E(X X /)E(X )E (X ~) + C o v ( X , X t ) .

36In a deterministic model, R~s = Rt , s as defined in eq. (3.2). Th e equality breaks do wn here

because future short rates are stochastic, whereas R~s is known on date t.



1770 M. Obstjeld and K. Ro go ff

E q u a t i o n ( 3. 35 ) s h o w s t h a t t h e f i rm s v a l u e i s t h e c o n v e n t i o n a l p r e s e n t v a l u e

o f d i v i d e n d s p l u s a r is k p r e m i u m : t h e f i r m is v a l u e d m o r e h i g h l y if i t p a y s o u t

u n e x p e c t e d l y h i g h d iv i d e n d s w h e n t h e m a r g i n a l u t i li t y o f o w n e r s c o n s u m p t i o nis u n e x p e c t e d l y h ig h . T h e p r e s e n c e o f a r is k p r e m i u m i n t r o d u c e s a n a d d i t i o n a l

c h a n n e l t h r o u g h w h i c h s h if ts in c o n s u m p t i o n p r e f e r e n c e s c a n i n f lu e n c e in v e s t-

m e n t b e h a v i o r .

T h e f i r m s i n v e s t m e n t b e h a v i o r c a n b e c h a r a c t e r i z e d b y m a x i m i z i n g t h e s u m

o f c u r r e n t p r o f i t s a n d ( 3 . 34 ) s u b j e c t t o ( 3 .1 2 ). A s i n t h e d e t e r m i n i s t i c c a s e cu r -

r e n t i n v e s t m e n t i s g o v e r n e d b y ( 3 . 1 3 ) , w h e r e q t = V~+I/Kt+I and Vt+ l i s g iven

b y ( 3.3 4 ). T h e r e s u l t is a r i c h e r q m o d e l o f i n v e s t m e n t w i t h c u r r e n t - a c c o u n t

p r e d i c t i o n s s i m i l a r t o t h o s e o f S e c t i o n 3 .1 . 37

3 .2 .3 . Par t ia l ly comp le te marke ts

I n r e a l i t y c o u n t r i e s t r a d e n o t o n l y b o n d s b u t a r i c h m e n u o f as s e ts , in c l u d -

i n g e q u i t y s h ar e s , c u r r e n c y - d e n o m i n a t e d i n s t r u m e n t s , a n d o t h e r s e c u r it ie s w i t h

s t a t e - c o n t i n g e n t p a y o f f s . T h i s t r a d e e n s u r e s t h a t s o m e , i f n o t a ll , c o n s u m p t i o n

r i sk s c a n b e p o o l e d a n d t h a t t h e c u r r e n t - a c c o u n t e f f e c t s a r is i n g i n t h e l a st s e t

o f m o d e l s w i l l b e m u t e d .

E q u a t i o n ( 3.3 1) i m p l i e s t h a t w h e n e v e r t h e r e is f r e e t r a d e i n n o n c o n t i n g e n t

b o n d s b e t w e e n t w o c o u n t r i e s i a n d j, t h e e x p e c t e d g r o w t h r a t e s o f th e i r r es i-

d e n t s m a r g i n a l u t il it ie s f r o m c o n s u m p t i o n a r e eq u a l , a s s u m i n g a c o m m o n r a t eo f t im e p r e f e r e n c e . T h u s ,

} }u c , + 1 ) = E , 3 . 3 6 )E , u ( C [ ) u ( C { )

U n d e r c o m p l e t e m a r k e t s [ s e e e q . ( 3 . 2 9 ) ] , t h i s e q u a t i o n h o l d s e x p o s t , n o t j u s t

i n e x p e c t a t i o n . W h e n o n l y ( 3 .3 6 ) h o ld s , h o w e v e r , d i f f e r e n c e s in m a r g i n a l r a t e s

o f i n t e r t e m p o r a l s u b s t i t u ti o n c a n o c c u r a f t e r t h e f a c t.

W h e n s o m e , b u t n o t a ll, r is k s c a n b e t r a d e d b e t w e e n c o u n t ri e s , c o n s u m p -

t i o n b e h a v i o r w i ll b e i n t e r m e d i a t e b e t w e e n t h e p r e d i c t i o n s o f (3 .2 9 ) a n d ( 3.3 6 ).S p e c if ic a ll y , ( 3.2 9 ) p r e d i c t s t h a t m a r g i n a l r a t e o f i n t e r t e m p o r a l s u b s t i t u t i o n d i f-

f e r e n c e s d o n o t a r i s e , w h i l e ( 3.3 6) p r e d i c t s t h e s e d i f f e r e n c e s c a n a r i s e u n e x p e c t -

e d ly . I n t h e i n t e r m e d i a t e ca s e , t h e e x p o s t d i f f e r e n c e

t

u ( C / ) . ( c j )

w i ll b e c o n d i t i o n a l l y u n c o r r e l a t e d w i t h a n y d a t e - ( t + l ) r a n d o m v a r i a b le o n w h i c h

37See, for exam ple, Baxter an d Crucini (1993b) and Glick and Rog off (1995).




contingent contractual payments can be conditioned. Thus, if Xt+l is a random

variable on which contracts can be written prior to date t + 1,

u c , + 1 ) , x , + l = 0 3 .. 37 )C o v , u ( C / ) u ( C l )

For example, if people in different countries can effectively pool the idiosyn-

cratic consumption risks due to nominal exchange-rate fluctuations through for-

eign exchange marke t deals, then realized exchange rate fluctuations will be sta-

tistically unrelated to international differences in the growth of u/(C).3~ Because

it is only partial, however, such insurance dearly leaves scope for unexpected

current-account movements.

Svensson (1988) develops a two-period model in which period 1 asset tradingserves to pool consumption risks for period 2. Svensson shows that the usual

logic of trade theory can be extended to analyze not only the current account

under uncertainty, but also the asset composition of gross capital flows between

countries. He develops a two-period pure exchange model of international trade

in a possibly incomplete set of risky assets. In that model, a multi-commodity

comparative advantage principle applies [see Dixit and Norman (1980), p. 95]:

the inner product of a country s net asset import vector with the vector of home

m i n u s foreign autarky asset prices is positive.

When countries trade equity shares as well as noncontingent bonds, the sep-

aration between domestic investment and consumption may still obtain even

though asset markets are incomplete. As (3.37) shows, domestic and foreign

residents must attach the same values to the state-contingent profits of a firm

that they trade. A sufficient condition for the separation property to hold is that

investment decisions themselves do not change these common valuations [see

Ekern and Wilson (1974)].

3 2 4 E n d o g e n o u s m a r k e t i n c o m p l e t e n e s s

We have seen that some of the model s predictions concerning current account

behavior depend critically on the structure of asset markets and in particular the

degree to which complete markets prevail. We have argued that the complete

marke ts model is inadequate empirically, but if so it would be helpful to have

a deeper understanding of the frictions that impinge on market completeness,

rather than just assuming market limitations exogenously.

In this section we present an example, drawn from Gertl er and Rogoff (1990),

of how international capital flows behave in the presence of moral hazard de-

riving from asymmetric information at the microeconomic level. A key insight

38For a formal derivation, see Obstfeld (1994).



772 M Obs t fe l d and K Ro go f f

f r o m t h e m o d e l , w h i c h c a r r i e s o v e r t o o t h e r s e t t i n g s , i s t h a t i n t e r n a t i o n a l a s s e t

m a r k e t s c a n b r i n g t h e g l o b a l a l lo c a t i o n o f r e s o u r c e s p a r t o f t h e w a y , b u t o n l y

p a r t o f t h e w a y , t o w a r d t h e f u l l - in f o r m a t i o n o p t i m u m . T h u s , t h e i n t e r t e m p o r a la p p r o a c h , a s s k e t c h e d a b o v e , m a y w e ll g et t h e d i r e c t i o n s o f n e t i n t e r n a t i o n a l

c a p i t a l f l o w s r i g h t w h i l e o v e r s t a t i n g m a g n i t u d e s .

W e n o w a d o p t a t w o - p e r i o d , s in g le g o o d s e t u p i n w h i c h e a c h o f t h e n u m e r o u s

a t o m i s t i c r e s id e n t s o f a s m a l l c o u n t r y m a x i m i z e s

u c l , c 2 ) = G 3 . 3 8 )

g i v e n e x o g e n o u s e n d o w m e n t s E1 o f t h e c o n s u m p t i o n g o o d i n p e r i o d i a n d E 2

i n p e r i o d 2 . T h e u t i l i t y f u n c t i o n ( 3 .3 8 ) i s o b v i o u s l y v e r y s p e c i a l ( c l e a r l y C 1 = 0

i s o p t i m a l ) b u t i t a ll o w s u s t o s i m p l i fy t h e a n a l y s i s w h i l e s t il l m a k i n g o u r m a i np o i n t s . T h e f o c u s , i n s t e a d , i s o n i n v e s t m e n t . E a c h r e s i d e n t h a s t w o w a y s t o

t r a n s f o r m E 1 i n t o f u t u r e c o n s u m p t i o n . H e o r s h e m a y l e n d in t h e w o r l d c a p it a l

m a r k e t a n d e a r n a ri s k le s s n e t r a t e o f r e t u r n r . A l t e r n a t i v e l y , c u r r e n t r e s o u r c e s

c a n b e i n v e s t e d i n a r i s k y d o m e s t i c p r o j e c t . I f a r e s i d e n t i n v e s t s K i n p e r i o d 1 ,

t h e n t h e p r o j e c t s s t o c h a s t i c p a y o f f in p e r i o d 2 is Y , w h e r e

4 > 0 w i t h p r o b a b i l i t y o r ( K )

Y = 0 w i t h p r o b a b i l i t y 1 - ~ r (K )

A b o v e , ~ - (K ) i s in c r e a s in g , s t ri c tl y c o n c a v e , a n d t w i c e c o n t i n u o u s l y d i f f e r e n -

t i ab le , w i th ~ r(0) = 0 , 1 r(oo ) = 1 , an d 1 + r < 4 ~ -~(0 ) < ec . Th es e a s su m pt io ns

e n s u r e t h a t h i g h e r i n v e s t m e n t in c r ea s e s t h e l i k e l i h o o d o f a s uc c es s fu l o u t c o m e

( b u t a t a d i m i n i s h i n g r a t e ) a n d t h a t t h e p r o s p e c t o f su c c e s s w o u l d j u s t i fy n o n z e r o

i n v e s t m e n t u n d e r s y m m e t r i c i n f o r m a t i o n . E v e r y i n d i v i d u a l h a s o n e p o t e n t i a l in -

v e s t m e n t p r o j e c t a n d d i f f e r e n t i n d i v id u a l s i n v e s t m e n t o u t c o m e s a r e s t a ti s ti c al ly

i n d e p e n d e n t .

I n t h is m o d e l , t h e o p t i m a l f u l l - in f o r m a t i o n i n v e s t m e n t l e v el is K * , d e f i n e d b y

~- (K*)4 = 1 + r (3 .39)

A t t h is p o i n t , th e m a r g i n a l r e t u r n t o i n v e s t i n g e q u a l s t h e r e t u r n t h a t c a n b ee a r n e d t h r o u g h l e n d i n g a b r o a d . L e t us a s s u m e t h a t

E z K *E J + l + r <

T h i s i n e q u a l i t y i m p l ie s t h a t e a ch r e s i d e n t n e e d s t o b o r r o w a p o si ti v e a m o u n t

f r o m f o r e i g n e r s t o b e a b l e t o i n v e st o p ti m a l ly . F u r t h e r m o r e , t h e c o n d i t i o n is

e q u i v a l e n t to t h e i n e q u a l i t y E 2 < (1 + r ) K * - E l ) , w h i c h s t a t e s t h a t i t i s i n -

f e a s i b l e f o r l e n d e r s t o f i n a n c e th e i n v e s t m e n t l e v e l K * t h r o u g h a r is k - f r e e l o a n .

I f a n i n v e s t m e n t p r o je c t f a il s, e v e n t h e b o r r o w e r s e n t i r e p e r io d 2 e n d o w m e n t

i s i n s u f f i c i e n t t o r e p a y l e n d e r s ( 1 + r ) K * - E l ) . T h u s , l o a n c o n t r a c t s t a k e t h e



Ch. 34: The ln ter temporal Approach to the Current Account 1773

f o l l o w i n g , s t a t e - c o n t i n g e n t , f o r m : in r e t u r n f o r a l o a n o f si ze L i n p e r i o d 1 , t h c

b o r r o w e r p r o m i s e s t o r e p a y Z g i n p e r i o d 2 in th e e v e n t h i s o r h e r i n v e s t m e n t

i s s u c c e s s f u l a n d Z b < z g i n t h e e v e n t i t f ai ls . L e n d e r s a r e c o m p e t i t i v e a n d d o

n o t o f f e r a l o a n c o n t r a c t u n l e s s i ts e x p e c t e d g r o s s r e t u r n e q u a l s 1 + r :

~ r ( K ) Z g + [1 - ~ r ( K ) ] Z / ' = ( 1 + r ) L ( 3 .4 0 )

T h e p r o v i s i o n s o f l o a n c o n t r a c t s a r e a s s u m e d t o b e f u l ly e n f o r c e a b l e .

T h e m o r a l h a z a r d p r o b l e m u n d e r l y i n g th e m o d e l a r i se s f r o m i t s i n f o r m a t i o n

s t ru c t u re . L e n d e r s o b s e r v e a b o r r o w e r ' s e n d o w m e n t s a n d t h e o u t p u t o f t h e

i n v e s t m e n t p r o j e c t ( t h a t i s, w h e t h e r t h e p r o j e c t i s s u c c e s s f u l o r n o t) ; o f c o u r s e ,

t h e y a l s o k n o w t h e s i ze o f t h e l o an . T h e y c a n n o t , h o w e v e r , v e r i f y th e l e v e l o f

i n v e s t m e n t , K . T h u s , b o r r o w e r s c a n n o t c o m m i t t h e m s e l v e s t o a n y s pe c if ic l e ve l

o f i n v e s t m e n t b y w r i t in g p r o m i s e s a b o u t K i n t o th e l o a n c o n t r a c t . F o r e x a m p l e ,

t h e r e i s n o w a y l e n d e r s c a n p r e v e n t b o r r o w e r s f r o m i n v e s t i n g n o t h i n g a t al l a n d

i n s t e a d s e c r e t l y p l a c i n g a l l o f t h e ir r e s o u r c e s, b o r r o w e d a s w e l l as n o n b o r r o w e d ,

i n f o r e i g n a s se t s ( a n a c t i o n r e m i n i s c e n t o f c a p i t a l f li g h t ) . B u t i f b o r r o w e r s d o

s o, t h e r e i s n o c h a n c e t h e i r p r o j ec t s w il l s u c c e e d . T h e i n f o r m a t i o n a l a s y m m e t r y

a l l o w i n g th is k i n d o f b e h a v i o r l e a d s t o i n e ff i ci e n t i n v e s t m e n t a n d b o r r o w i n g

l e v e l s , a s w e ow s h o w . 3 9

G i v e n t h e a v a i l a b l e l o a n c o n t r a c t , a t y p ic a l b o r r o w e r m a x i m i z e s e x p e c t e d

s e c o n d p e r i o d c o n s u m p t i o n

E { C 2 } = ~ ( K ) ( q 5 - Z ~') - [1 - ~ r ( K ) ] Z b + ( 1 + r ) ( E l + L - K ) + E 2 ( 3 .4 1 )

s u b j e c t t o t h e c o n s t r a i n t

E1 + L _> K (3 .4 2)

C o n s t r a i n t ( 3. 42 ) d o e s n o t b i n d w h e n t h e b o r r o w e r is se c r e t ly i n v e s ti n g re -

s o u r ce s a b r o a d r a t h e r t h a n a t h o m e . T h e n e c e s s a ry K u h n - T u c k e r c o n d i t i o n s

f o r a m a x i m u m a re :

z r / (K)[q5 - ( Z g - Z I ) ] = 1 + r + h (3 .43 )

A > 0 , A ( E 1 + L - K ) = 0 ( 3 .4 4 )

C o n d i t i o n s ( 3 .4 3 ) a n d ( 3 .4 4 ) i m p l y t h a t e v e n a b o r r o w e r w i t h a c c e ss t o a l o a n

L l a r g e e n o u g h t o p e r m i t t h e d e s i r e d i n v e s t m e n t l e v e l ( s o t h a t h = 0 ) p i c k s a

K t h a t s a t i s f i e s

39If borrowers could com mit to invest K*, lenders would break even by lending them L = K* - E l

and setting Z l~ = E2, z g = (1 + r) [K* - E1 - (1 - ~r(K*))E2J/Tr(K *). [Be cau se ~-(K) is strictlyconcave an d ~r(0) = 0, Zg < ~b + E2.] In th is model, there is an implicit assumption that foreigndirect investment cannot substitute perfectly for lending; that is, foreigners cannot circumvent theagency problem by purchasing investm ent opportunities in the borrowing country an d exploitingthem optimally themselves. This assumption could be justified by a threat of nationalization, orsimply by a comparative informational advantage of local residents in finding suppliers, monitoring

workers, greasing the collective palm of local officialdom, etc.



1774 M. O bstfeld and K. R ogoff

~v ( K) [ 4 , - ( Z g - zb ) ] = 1 + r ( 3 . 45 )

a n d , t h u s , i s s t r i c t l y b e l o w t h e f u l l - i n f o r m a t i o n o p t i m u m l e v el d e s c r i b e d b y e q .( 3. 39 ). T h e r e a s o n is t h a t t h e c h a n g e i n p a y o f f t o t h e b o r r o w e r w h e n a p r o j e c t

s u c c e e d s i s

4 , - z ~ - ( - z I , ) = 4 , - ( z ~ - z ~ ) < 4 ,

A l t h o u g h l e n d e r s c a n n o t o b s e r v e K d i re c tl y , t h e y h a v e r a t i o n a l e x p e c t a t i o n s

a n d t h u s c a n f ig u r e o u t t h e l e v e l o f K b o r r o w e r s w i ll c h o o s e f o r a g i v e n l o a n c o n -

t ra c t . T h e y t h e r e f o r e o f f e r a l o a n c o n t r a c t su c h t h a t t h e K t h e b o r r o w e r c h o o s e s ,

g i v e n L , z g , a n d Z b , s a ti sf ie s t h e r e q u i r e d r a t e o f r e t u r n c o n d i t i o n ( 3 .4 0 ). C o m -

p e t i t i o n a m o n g l e n d e r s e n s u r e s t h a t t h i s c o n t r a c t i s o p t i m a l f o r t h e b o r r o w e r ,

s u b j e c t t o t h e c o n s t r a in t s m e n t i o n e d . F o r m a l l y , t h e o p t i m a l i n c e n t i v e - c o m p a t i b l e

c o n t r a c t ( L , zg , Z ~ ) m a x i m i z e s E { C 2 } s u b j e c t t o ( 3 . 4 0 ), ( 3 .4 2 ), ( 3 .4 5 ) , a n d t h e

i n e q u a l i t y Z b < E 2 .

T h e o p t i m a l c o n t r a c t s a t is fi e s Z b = E 2 ( s o a s t o m i n i m i z e t h e g a p ;~ - Z g - Z b

a n d , t h u s , t h e g a p b e t w e e n K a n d K * ) . 4° F u r t h e r m o r e , t h e c o n t r a c t s a ti sf ie s

( 3 .4 2 ) w i t h e q u a l i t y : i n c r e a s i n g L a b o v e K - E 1 w o u l d f o r c e a r is e in z g a n d ,

w i t h i t, a w o r s e n i n g i n i n v e s t m e n t in c e n t iv e s . C o m b i n i n g t h e s e f a c ts w i t h t h e

i n c e n t i v e - c 0 m p a t i b i l i t y c o n s t r a i n t ( 3. 45 ) a n d t h e l e n d e r s z e r o - p r o f i t c o n d i t i o n

( 3 . 4 0 ) , w e s e e t h a t t h e o p t i m a l c o n t r a c t i s t h e s o l u t i o n t o t h e t h r e e - e q u a t i o n

s y s t e m

~ ( K ) ( 4 , - 2 ) = ~ + r

2 = (1 + r) K - E ,, - T T ; r / ~ K )

L = K - E 1 .

T h i s s o l u t i o n h a s a n u m b e r o f im p o r t a n t i m p l i c a ti o n s :

( 1) T h e i n c e n t i v e - c o m p a t i b l e i n v e s t m e n t l e v e l is b e l o w t h e f u l l - i n f o r m a t i o n

o p t i m u m o f ( 3 .3 9 ). A c c o r d i n g l y , p e r i o d 1 c a p i t a l in f l o w s a r e b e l o w t h e l e v e l a

f u l l - i n f o r m a t i o n m o d e l w o u l d p r e d ic t .( 2) A n i n c r e a s e i n th e p r o d u c t i v i t y p a r a m e t e r 4, in c r e a s e s t h e p e r i o d 1 c a p i t a l

i n fl o w a n d i n v e s t m e n t l e v e l, b u t i t al so w i d e n s t h e s p r e a d Z , b e t w e e n t h e g o o d -

a n d b a d - o u t c o m e l o a n p a y m e n t s . T h u s , ( u n d e r m i l d re s t ri c ti o n s o n ~ - (K ) ) th e

r e s u l t i n g c a p i t a l i n fl o w is le s s t h a n i n t h e f u l l - i n f o r m a t i o n c a se .

( 3) T h e e x p e c t e d m a r g i n a l p r o d u c t o f c a p i t a l, ~ r ~( K )4 ,, e x c e e d s t h e w o r l d

( a n d d o m e s t i c ) r i sk l e s s i n t e r e s t r a t e , 1 + r .

( 4) A n i n c r e a s e i n e i t h e r e n d o w m e n t , E 1 o r E 2 , r a is e s i n v e s t m e n t b y l o w e r i n g

Z . I n t h e f ir s t c a s e t h i s e f f e c t is d u e t o a l e s s e r r e l i a n c e o n e x t e r n a l f u n d s , i n

4°See Ge rtler a nd Rog off (1990) for details.




t h e s e c o n d t o t h e p o s s ib i li ty o f a l a r g e r l o a n p a y m e n t i n t h e b a d - o u t c o m e s t a te .

T h e i n v a r i a n c e o f i n v e s t m e n t w i th r e s p e c t to i n t e r t e m p o r a l p r e f e r e n c e s t h a t

c h a r a c t e r i z e d t h e s i n g l e -s e c t o r m o d e l s d e s c r i b e d e a r l i e r n e e d n o t h o l d w h e ni n v e s t m e n t i s s u b j e c t t o m o r a l h a z a r d . 41

I n a tw o - c o u n t r y g e n e r a l e q u i l i b r iu m v e r s i o n o f t h e m o d e l , o n e c a n s h o w t h a t

e n d o g e n o u s d i f f e r e n c e s in c a p i ta l m a r k e t i m p e r f e c t i o n s c a n d r a m a t i c a l l y re d u c e

t h e f lo w o f c a p i t a l f r o m r i c h t o p o o r c o u n t r i e s , a n d e v e n r e v e r s e i t [s ee G e r t l c r

a n d R o g o f f ( 1 9 9 0 ) ] .

T h e p r e c e d i n g m o d e l h a s a b s t r a c te d b o t h f ron ~t t h e c o n s u m p t i o n s m o o t h i n g

m o t i v e b e h i n d t h e c u r r e n t a c c o u n t an d fr o m t h e b o r r o w e r s d e s i re t o e n g a g c

i n a ss e t tr a d e s t h a t r e d u c e t h e u n c e r t a i n t y o f s e c o n d - p e r i o d c o n s u m p t i o n . I t is

s t r a i g h t f o r w a r d t o a d d s e c o n d - p e r i o d r i s k a v e r s i o n t o t h e m o d e l b y a s s u m i n g

t h a t ( 3 .3 8 ) is r e p l a c e d b y

h 2u C 1 , C ~ ) = C 2 - ~ C 2

I n o r d e r t o f o c u s o n t h e n e w i ss u e s t h a t a r is e , i t is c o n v e n i e n t t o s u p p o s e l h a t

E 1 _> K * . I n th i s c as e , d o m e s t i c r e s i d e n t s e n d o w m e n t is l a r g e e n o u g h s o t h a t

t h e y h a v e n o n e e d t o b o r r o w t o fi n a n c e i n v e s t m e n t , a n d t h e i r o n ly m o t i v e f o r

t a p p i n g t h e i n t e r n a t i o n a l c a p i ta l m a r k e t is t o in s u r e p e r i o d 2 c o n s u m p t i o n . H e r e

a g a i n w e h a v e a m o r a l h a z a r d p r o b l e m b e c a u s e n o n v e r i f i a b l e i n v e s t m e n t d e ci -

s io n s a f f e c t t h e p r o b a b i l i t y d i s tr i b u t io n o f s e c o n d - p e r i o d o u t p u t . I t c a n b e s h o w n

t h a t u n d e r t h e o p t i m a l in c e n t i v e - c o m p a t i b l e c o n t r a c t , c o n s u m p t i o n i n s u r a n c e

w i l l b e p a r t i a l a n d K w i l l b e b e l o w K * . 42

T h e g e n e r a l c o n c l u s i o n is t h a t a s y m m e t r i c i n f o r m a t i o n n e e d n o t c a u s e f in a n -

c ia l m a r k e t s t o b r e a k d o w n e n t ir e ly . I n s t ea d , f i n a n c ia l m a r k e t s m a y d o o n l y

p a r t i a l ly t h e j o b t h e y c o u l d d o i n a w o r l d o f fu l l i n f o r m a t i o n . N o t e a ls o t h a t

i n t h i n k i n g a b o u t t h e i n c o m p l e t e n e s s o f m a r k e t s , it m a y b e m i s l e a d i n g t o t h in k

o f ri sk s a s b e i n g e i t h e r in s u r a b l e o r n o n i n s u r a b l e . I n m a n y c a s es , t h r o u g h w h a t

i s b a s i c a l l y a c o i n s u r a n c e m e c h a n i s m , s o m e g a i n s f r o m t r a d e a c r o s s s t a t e s o f

n a t u r e w i ll b e r e a l i z e d e v e n u n d e r m o r a l h a z a r d . 43 T h e s a m e p o i n t a p p l ie s t o

t r a d e a c r o s s t i m e .

W e h a v e f o c u s e d o n c a p i t a l - m a r k e t i m p e r f e c t i o n s a r i s i n g f r o m a s y m m e t r i c

i n f o r m a t i o n a t t h e m i c r o l ev e l. A n o t h e r v e r y i m p o r t a n t c a u se o f in t e r n a ti o n a l

c a p i t a l - m a r k e t i m p e r f e c t i o n is s o v e r e i g n d e f a u l t r is k a t t h e m a c r o l e ve l . S o v c r -

e i g n r is k n e e d n o t b e r e l a t e d t o a s y m m e t r i c i n f o r m a t i o n , b u t c a n h a v e q u a l it a -

41It i s aga in easy to see th a t Zg < q~ + E 2 .

42Se e O b s t f e ld a nd R og of f 1996 ) , c h . 6 .

43The im p l i c a t i ons o f a dve r se s e l e c t i on p r ob le m s c a n be qu i t e d i f f e r e n t , a l t hough w e do no tc o n s i d e r t h e m h e r e . A t k e s o n a n d L u c a s 1 9 9 2 ) s t u d y a d i f f er e n t m o r a l h a z a r d p r o b l e m , o n e mw h i c h p e o p l e o r c o u n t r i es ) w i s h t o in s u r e a g a i n s t p r e f e r e n c e s h o c k s. T h e y f in d t h a t u n d e r o p t i m a l

i n c e n t i v e - c o m p a t i b l e a r r a n g e m e n t s , t h e d e g r e e o f c o n s u m p t i o n i n e q u a l i t y i n t h e w o r l d i n c r e a s e s

cont inua l ly .




t i v e ly s i m i l ar im p l i c a ti o n s . 44 J o n a t h a n E a t o n a n d R a q u e l F e r n a n d e z p r e s e n t a

d e t a i l e d a n a l y s i s o f t h e e f f e c t s o f s o v e r e i g n r i s k in t h e i r c h a p t e r i n th i s H a n d -

b o o k . A c o m m o n t h e m e in s o v e re i g n - ri s k m o d e l s is t h a t t h e c o n s u m p t i o n -s m o o t h i n g a n d r i s k - s h a r i n g r o le s o f i n t e r n a t i o n a l c a p i t a l m a r k e t s s t il l o p e r a t e ,

b u t a r e t e m p e r e d b y d e fa u l t r is k.

4 E m p i r ic a l e v id e n c e o ll t h e i n t e r te m p o r a l a p p r o a c h

T h e i n t e r t e m p o r a l a p p r o a c h t o t h e c u r r e n t a c c o u n t h a s b e e n s u b j e c t e d t o e x t e n -

s iv e f o r m a l t e st in g ; m u c h o f t h e m e t h o d o l o g y u s e d g r o w s o u t o f H a l l s ( 1 97 8)

s e m i n a l w o r k o n t h e i m p l i c at i o n s o f th e r a t i o n a l - e x p e c t a t i o n s a s s u m p t i o n f o r

f o r w a r d l o o k i n g c o n s u m p t i o n t h eo r ie s . A l es s f o r m a l e m p i r ic a l m e t h o d o l o g y ,

p i o n e e r e d b y F e ld s t e i n a n d H o r i o k a ( 19 8 0) , h a s b e e n u s e d to a r g u e t h a t th e

c l o se r e l a t io n s h i p b e t w e e n n a t i o n a l s a v i n g a n d i n v e s t m e n t r a t e s in p o s t - W o r l d

W a r I I d a t a f u r n i s h e s a p r i m a f a ci e c a s e a g a i n s t t h e p r a c t i c a l r e l e v a n c e o f th e

i n t e r t e m p o r a l a p p r o a c h . T h e s e t w o r e s e a r c h a v e n u e s a r e c l o se l y i n t e rt w i n e d , a s

a n y a t t e m p t t o re c o n c i l e t h e F e l d s t e i n - t t o r i o k a f in d in g s w i t h t h e i n t e r t e m p o r a l

a p p r o a c h r e s t s o n t h e v a l i d i t y o f m o d e l s s u c h a s t h o s e s u r v e y e d i n S e c t i o n 3. 45

4 1 T h e r e l a t i o n s h i p b e t w e e n n a t i o n a l s a v i n g a n d d o m e s t i c i n v e s t m e n t r a te s

I n a c l o s e d e c o n o m y , n a t i o n a l s a v i n g e q u a l s d o m e s t i c i n v e s t m e n t a n d t h e c ur -

r e n t a c c o u n t i s a l w a y s z e ro . F u r t h e r m o r e , a n y o b s e r v e d i n c r e a s e i n n a t i o n a l

s a v in g w il l a u t o m a t i c a l l y b e a c c o m p a n i e d b y a n e q u a l r is e in d o m e s t i c i n v e s t-

m e n t . A b a s i c p r e m i s e o f th e i n t e r t e m p o r a l a p p r o a c h is t h a t c a p it a l is t o s o m e

d e g r e e i n t e r n a t i o n a l l y m o b i l e , so th a t c u r r e n t a c c o u n t i m b a l a n c e s a r e a p o s -

s ib il it y. G i v e n t h is p r e m i s e , t h e i n t e r t e m p o r a l a p p r o a c h p r e d ic t s a n u m b e r o f

s i t u a t io n s i n w h i c h d i v e r g e n c e s b e t w e e n s a v i n g a n d i n v e s t m e n t w il l a r is e . A n

e m p i r i c a l f i n d i n g t h a t n a t i o n a l s a v i n g r a t e s a f f e c t d o m e s t i c i n v e s t m e n t r a t e s

w i t h u n i t c o e ff i c ie n t s w o u l d t h e r e f o r e a p p e a r t o b e s tr o n g e v i d e n c e a g a i n s t th ea p p l i c a b i li t y o f t h e i n t e r t e m p o r a l a p p r o a c h .

F e l d s t e i n a n d H o r i o k a ( 1 98 0 ), in t h e f ir st o f a s e ri e s o f r e l a t e d p a p e r s b y

F e l d s t e i n a n d c o a u t h o r s , a r g u e d t h a t c a p i t a l m o b i l i t y i s s u f fi c ie n t ly li m i t e d , a t

44Atkeson (1991) presents an interesting analysis incorporating bo th asym me tric information andsovereign risk.

45We do not survey the methodology of calibrating open-economy models with incomplete m ar-kets so as to match mom ents of actual aggregate data. Interesting recent w ork alon g this line,exem plified by B axter a nd C rucini (1993b) and Kollm ann (1992), is discussed in M arianne B axter schapter in th is Handbook. We also refrain from more than a brief and highly selective account ofthe cop ious literature on m easuring international capital mobility. See Fran kel (199 3) and Ob stfeld

(1995) for recent surveys.



C h. 34 : T h e l n t e r t e m p o r a l A p p r o a c h t o t h e C u r r e n t A c c o u n t

0 3 3

0 3 0

0 27

0 2 4

0 21

0 1 8

0 1 5

0 1 2

0 1 2 0 1 5

J A P

F I N P O R N O R

A U S • •

N Z • A U T

• I R E= • S P A

I C E • I T A

G E R

Q . E c A . F . . N T

D E N • S W E

U S A •

• B E LU K

,

0 1 8 0 2 1 0 2 4 0 2 7 0 3 0 0 3 3

S/Y

F i g u r e 4 . l . S a v i n g a n d i n v e s t m e n t a v e r a g e s , t 9 8 2 - 1 9 9 1 a s a f r a c ti o n o f G D P ) .

1777

least over long horizons, that changes in national saving rates ultimately feed

through fully to domestic investment rates. As evidence, they reported cross-

sectional regressions of gross domestic investment rate averages I / Y ) on gross

national saving rate averages S / Y ) . These ratios of nominal flows, of course,suffer from all the conceptual deficiencies discussed at the end of Section 2. For

a sample of 16 OECD countries over 1960-74, Feldstein and Horioka found

that:

l / Y ) j ~ - 0 . 0 3 5 + O . 8 8 7 S / Y ) j + u j ; R 2 = 0.91

(0.018) (0.074)

Feldstein and Bacche tta (1991) report similar results for a 1974-86 sample of

23 OECD members. Figure 4.1 shows the cross-sectional saving-investment as-

sociation in the OECD sample over the decade 1982-91, with Luxembourg,

which is an outlier, omitted. The estimation result for this sample, leaving outdeveloping Turkey, is:

I / Y ) j = 0.088 + 0 . 6 2 2 S / Y ) y + u y; R 2 -~- 0.69

(0.020) (0.094)

This equation shows a weakening, but still very significant, positive association.

Feldstein and his collaborators argue that if capital indeed were highly mobile

among countries, slope coefficients like the one above should be much smaller

than 1, as a country's savings would then be free to seek out the most produc-

tive investment opportunities worldwide. Although the intertemporal approach

is consistent with a world in which changes in saving behavior impinge on do-



1778 M O b s t f el d a n d K R o g o f f

m e s t i c i n v e s t m e n t , i t c e r ta i n l y d o e s n o t s u p p o r t t h e p o l i c y c o n c lu s i o n , p r e f e r r e d

b y F e l d s t e in , t h a t g o v e r n m e n t m e a s u r e s t o r a is e a c o u n t r y ' s s a v in g r a t e w ill

a u t o m a t i c a l l y c a u s e a l o n g - r u n p a r i p a s s u i n c r e a s e i n i ts i n v e s t m e n t r a t e .I f c a p i ta l is tr u l y im m o b i l e a n d t h e in t e r t e m p o r a l a p p r o a c h i r r e le v a n t , h o w -

e v e r , t h e n t h e t i m e - s e r i e s re l a t i o n s h i p b e t w e e n i n d i v id u a l c o u n t r i e s ' s a v i n g a n d

i n v e s t m e n t r a t e s , l i k e t h e c r o s s - s e c t i o n a l r e l a t i o n s h i p a m o n g l o n g s a v i n g a n d

i n v e s t m e n t a v e r a g e s , a l so s h o u l d b e d o s e . W e c a n t h i n k o f t h e t i m e - s e r ie s re l a-

t io n s h i p a m o n g c o n t e m p o r a n e o u s d e t r e n d e d s a vi ng a n d i n v e s t m e n t r a te s a s ca p -

t u r i n g t h e c o h e r e n c e o f h i g h -f r e q u e n c y c h a n ge s , w h i le t h e F e l d s t e i n - H o r i o k a r e -

g r e s s io n c a p t u r e s t h e a s s o c ia t io n b e t w e e n l o w - f r e q u e n c y o r s u s t a i n e d c h a n g e s .

I n d e e d , i t i s h a r d t o s e e h o w c a p i t a l c o u l d b e t r u l y i m m o b i l e i n t h e l o n g r u n

b u t n o t i n t h e s h o r t r u n , s i n c e t h e l o n g r u n is j u s t a s u c c e s s i o n o f s h o r t r u n s .

A n d e v e n i f i n t e r n a t i o n a l t r a d e i n l o n g - t e r m i n s t r u m e n t s o r l o n g - li v e d a s se ts

w e r e h i g h l y l i m i t e d - a h y p o t h e s i s t h a t t h e d a t a d o n o t s u p p o r t - s h o r t - t e r m

i n s t r u m e n t s c a n b e r o l l e d o v e r .

T h e t i m e - s e r i e s a n d c r o s s - s e c t i o n a s p e c t s o f t h e s a v i n g - i n v e s t m e n t r e l a t i o n -

s h i p a r e q u i t e d i s t i n c t : t h e t i m e - s e r i e s r e l a t i o n s h i p c o u l d b e c l o s e a n d t h e c r o s s -

s e c t i o n r e la t i o n s h i p n o t , o r v ic e v e r sa . A n e x a m p l e is p r o v i d e d b y t h e U n i t e d

K i n g d o m d u r i n g t h e p r e - W o r l d W a r I g o l d s t a n d a r d ( F i g u r e 2 . 1 ) . I t i s a p p a r e n t

t h a t t h e s h o r t - r u n s a v i n g - i n v e s t m e n t c o r r e l a t i o n is v e r y c l o se . 46 N o n e t h e l e s s ,

t h e U . K . r a n c u r r e n t - a c c o u n t s u r p lu s e s a p p r o a c h i n g 1 0 p e r c e n t o f G D P i n t hi s

s a m e p e r i o d .I t is a s t y l i z e d f a c t , s o m e w h a t s e n s it iv e t o t h e d e t r e n d i n g m e t h o d a d o p t e d ,

t h a t t h e t i m e - s e r i e s s a v i n g - i n v e s t m e n t c o r r e l a t i o n is f a i r l y s t r o n g i n r e c e n t d a t a .

( S e e F i g u r e 2 . 3 f o r s o m e i n d u s t r i a l- c o u n t r y d a t a, b u t t h e r e a r e e x c e p t i o n s , t h e

m o s t g l a r i n g o f w h i c h is N o r w a y w i t h i t s h ig h l y n e g a t i v e l y c o r r e l a t e d s a v in g

a n d i n v e s t m e n t r a te s .) F o r th e O E C D c o u n t r i e s in c lu d i n g L u x e m b o u r g b u t e x -

c l u d i n g T u r k e y , t h e a v e r a g e c o r r e l a t i o n b e t w e e n s a v in g a n d i n v e s t m e n t r a t e s is

0 . 4 9 5 o v e r 1 9 7 4 - 9 0 a f t e r l i n e a r t i m e d e t r e n d i n g . T h e c o r r e l a t i o n i s 0 . 5 1 2 w h e n

t h e d a t a a r e f i r s t- d i f fe r e n c e d to r e m o v e t r e n d .

E v e n i n a w o r l d o f c o m p l e t e c a p i ta l m o b i l i ty th o u g h , s u c h c o r r e l a t i o n s a r e n o t

n e c e s s a r i l y s u r p r is i n g a n d c a n e a s i ly b e e x p l a i n e d o n t h e b a si s o f t h e i n t e r t e m -p o r a l a p p r o a c h . F o r e x a m p l e , t h e d i sc u s si o n o f g r a d u a l c a p i t a l - s t o c k a d j u s t m e n t

i n S e c t i o n 3 i m p l i e s t h a t a s h o c k t o t o t a l f a c t o r p r o d u c t i v i t y , if s h o r t - l i v e d b u t n o t

c o m p l e t e l y tr a n s i t o r y , r a i se s s av i n g as w e l l as i n v e s t m e n t . B a x t e r a n d C r u c i n i

( 1 9 9 3 a , b ) a n d M e n d o z a ( 1 99 1 ) ( th e l a t t e r in a s m a l l - c o u n t r y s e tt i n g , t h e f o r -

m e r i n a g l o b a l - e c o n o m y s e tt in g ) h a v e s h o w n t h a t i n t e r t e m p o r a l m o b i l e - c a p i t a l

m o d e l s b a s e d o n i n v e s t m e n t - a d j u s t m e n t co s ts c a n e a si ly p r o d u c e t i m e - s e r ie s

s a v i n g - i n v e s t m e n t c o r r e l a t i o n s a t l e a st as la r g e a s t h o s e i n th e d a t a . P a r t o f

t h e m e c h a n i s m u n d e r l y i n g th e B a x t e r - C r u c i n i f i nd i ng s is a ll o w a n c e f o r g l o b a l

46See Ob stfeld (1986) for a m ore d etailed statistical analysis of the U.K . data.



Ch 34: The Interternporal Approach to the Current Account 1779

e c o n o m i c sh o c k s , w h i c h o b v i o u s l y w il l i n d u c e p o s i t i v e s a v i n g - i n v e s t m e n t c o rr e -

l a t i o n s .

W e h a v e b e e n f o c u s in g o n t im e - s e r ie s e v id e n c e , b u t F e l d s t e i n a n d H o r i o k a sc r o s s - s e c t io n a l f in d i n g s c a n a l s o b e r a t i o n a l i z e d b y th e p r e s e n c e o f c o m m o n

f a c to r s t h a t m i g h t s i m u l t a n e o u s l y i n f lu e n c e c o u n t r i e s s a v i ng a n d i n v e s t m e n t

r a t e s .

I t s e e m s l i k e ly t h a t o f t h e m a n y p o t e n t i a l e x p l a n a t i o n s o f t h e F e l d s t e i n -

H o r i o k a r e s u l t s, n o s i n g l e o n e f u l l y e x p l a i n s t h e b e h a v i o r o f a l l c o u n t r i e s . T a k e n

t o g e t h e r , h o w e v e r , a n d c o m b i n e d w i t h o t h e r e v i d e n c e i n d i c a t i n g s u b s t a n t i a l i n -

t e r n a t i o n a l m o b i l i t y o f c a p it a l, th e a r g u m e n t s b e l o w s u g g e st t h a t t h e F e l d s t e i n -

H o r i o k a f i n d i n g p r o v i d e s n o b a s is a t a l l f o r d i s m i s s i n g t h e b a s i c p r e m i s e s o f t h e

i n t e r t e m p o r a l a p p r o a c h :

( 1) E v e n p o st -1 9 7 3, g o v e r n m e n t s h a v e s o m e t i m e s a d j u s t e d f is ca l o r m o n e t a r y

p o l ic i es t o a v o i d l a rg e a n d p r o t r a c t e d c u r r e n t - a c c o u n t i m b a l a n c e s . T h e e v i d e n c e

o n t h is c u r r e n t - a c c o u n t t a r g e t i n g h y p o t h e s i s is m o s t l y a n e c d o t a l , h o w e v e r , a n d

t h e r e a r e o f c o u r s e p r o m i n e n t i n s t a n c e s ( li k e t h e U n i t e d S t a t e s i n t h e 1 9 80 s) i n

w h i c h m a c r o e c o n o m i c p o l i ci e s h a v e i n s t ig a t e d m a j o r e x t e r n a l i m b a l a n c e s . 47

(2 ) O E C D c o u n t r ie s m a y b e s u f f ic i en t ly w e l l e n d o w e d w i t h c a p it a l to h a v e

r e a c h e d s t o c h a s t i c s t e a d y s t a t e s f o r t h e i r e x t e r n a l d e b t o r a s s e t l e v e l s . I n t h i s

s i t u a t io n t h e i n t e r t e m p o r a l b u d g e t c o n s t r a i n t o f t h e e c o n o m y w o u l d i m p l y t h a t

l o n g a v e r a g e s o f s a v i n g - i n v e s t m e n t d i f fe r e n c e s a r e s m a l l . D e v e l o p i n g c o u n t r ie s ,

w h i c h p r e s u m a b l y c o u l d re a l iz e g r e a te r g a in s fr o m i n t e r t e m p o r a l t r a d e t h r o u g h

b o r r o w i n g f o r i n v e s t m e n t p u r p o s e s , a r e l i k e ly t o b e m o r e d i s t a n t f r o m a s ta -

t i o n a r y d i s t ri b u t i o n o f f o r e i g n d e b t. T h i s i n t e r p r e t a t i o n s e e m s b o r n e o u t b y t h e

c r o s s - s e c t io n a l r e s u l ts f o r d e v e l o p i n g c o u n t r i e s p r i o r t o t h e o n s e t o f t h e i r d e b t

c r is i s i n 19 82 . F o r t h i s s a m p l e , t h e c r o s s - s e c t i o n a l s a v i n g - i n v e s t m e n t a s s o c i a t i o n

is m u c h l o o s e r t h a n f o r t h e O E C D s a m p l e . 48

(3 ) T h e G e r t l e r - R o g o f f i n v e s t m e n t m o d e l d i sc u s s ed in S e c t i o n 3 s h o w s w h y

i n v e s t m e n t m a y r e s p o n d p o s i t iv e l y t o h i g h e r r e t a i n e d e a r n in g s , t h a t is , t o h i g h e r

c o r p o r a t e s a v i n g . T h u s , i t s e e m s p l a u s i b l e t h a t i n c o u n t r i e s w i t h h i g h e r s a v i n g

r a t e s , t h e c o s t o f c a p it a l w i l l b e l o w e r a n d i n v e s t m e n t h i g h e r. A m a i n p r e d i c t i o n

o f t h e m o r a l - h a z a r d m o d e l i s t h a t r i s k - f r e e i n t e r e s t r a t e s a r e e q u a l i z e d a m o n gc o u n t r i e s - a s i n d e e d t h e y m o s t l y a r e i n t h e i n d u s t r i a l i z e d w o r l d ( O b s t f e l d 1 9 9 5)

- w h e r e a s t h e m a r g i n a l p r o d u c t o f c a p it a l is h i g h i n c o u n t r i e s w i t h l o w c o r p o -

r a t e w e a l t h . A l t h o u g h t h e r e i s s o m e e v i d e n c e i n f a v o r o f t h i s h y p o t h e s i s , a n

a c c o u n t o f h o w c o r p o r a t e s a v in g a n d i n v e s t m e n t a r e r e l a t e d n e e d n o t h a v e

s t r o n g i m p l i c a t i o n s f o r t h e r e l a t i o n s h i p b e t w e e n t o t a l s a v i n g a n d i n v e s t m e n t .

F o r e x a m p l e , p r iv a t e d o m e s t i c o w n e r s o f fi rm s m a y p i er c e t h e c o r p o r a t e v e il

47The fragility of the econo m etric evidence is illustrated by Feldstein and Bacch etta s (1991)reinterpretation of the regressions Sum mers (1988) offers as evidence of current-accoun t targeting.

48See Fieleke (1982), Do oley, Frank el, and M athieson (1987), and Sum me rs (1988).



178 M Obs t fe l d and K Ro go f f

and offset corporate saving decisions through their own consumption. To the

extent that the investing firms are owned by foreigners, their decision to retain

earnings increases foreign rather than domestic saving, other things equal.(4) In a Heckscher-Ohlin framework, a nonspecialized economy experiencing

a rise in saving can absorb more capital without a fall in capital's domestic rate

of return. Alternative explanations of the saving-investment association based

on this observation are suggested by Fukao and Hamada (1994) and Obstfeld

(1995).

(5) In the life-cycle theory of consumption, sustained demographic or pro-

ductivity changes that increase a country's long-term investment rate also may

increase its saving rate. Section 3.1.7's discussion of overlapping-generations

models provides a leading example: higher productivity growth that affects most

strongly the incomes of young workers will cause saving as well as investment

to rise. Feldstein and Bacchetta (1991) and Summers (1988) have dismissed

this line of explanation, notwithstanding some supportive evidence offered by

Tesar (1991). In a more recent contribution, however, Taylor (1994) revisits the

Feldstein-Horioka equation, controlling for (a) measures of domestic relative

prices, (b) the age-structure of the population, and (c) the interaction of the age

structure with the growth rate of domestic output. He finds that for a number

of country samples the cross-sectional saving-investment association disappears.

Far from showing the irrelevance of the intertemporal approach, the large

literature spawned by Feldstein and Horioka's (1980) nonstructural explorationsuggests to us that models like those reviewed in Section 3 capture key elements

behind the cross-sectional and time-series regularities governing saving and in-

vestment rates. The further empirical challenge for the intertemporal approach

is to show that structural forward-looking models of the current account are

not grossly incompatible with actual experience. We turn next to tests of such

models.

4 . 2 . T es t s o f i n t e r t e m p o r a l c u r r e n t - a c c o u n t m o d e l s

Most structural time-series studies of the intertemporal approach to the current

account essentially test versions of eq. (3.9), according to which the current

account depends on deviations of interest rates, output, government spending,

and investment from permanent levels. Indeed, most (but not, as we shall

see, all) of these studies focus on the special case of (3.9) with a constant real

interest rate r = (1 -/3)//3

C A t = ( Y t - Y t ) - ( G t - G t ) - ( I t - I t ) (4.46)

Though less general than eq. (3.9), eq. (4.46) embodies many central ele-

ments of the intertemporal approach. It therefore is reasonable to ask whether




t h e r e i s a n y e v i d e n c e i n fa v o r o f 4 .4 6 ) b e f o r e t u r n i n g t o m o r e c o m p l e x m o d e l s .

F o r e x a m p l e , d o t e m p o r a r y r is es in g o v e r n m e n t s p e n d i n g c a u se c u r r e n t- a c c o u n t

d e f ic i ts ? Q u e s t i o n s l ik e th is o n e s e e m s i m p l e e n o u g h , b u t a n u m b e r o f e m p i r i c als u b t l e t i e s a r i s e i n a n s w e r i n g t h e m .

4 .2 . l . M e a s u r i n g p e r m a n e n t v a lu e s : A d i g r e s s i o n

E v e n b e f o r e t u r n i n g t o t h e e c o n o m e t r i c st u d ie s , it is u s e fu l t o a d d r e s s w h a t

is p e r h a p s t h e m o s t p r o b l e m a t i c i ss u e o f a ll , t h e c o n s t r u c t i o n o f t h e e x p e c t e d

p e r m a n e n t v a lu e s Y , G , a n d I .

A f ir s t d i f f i c u l t y i s t h a t i t i s n o t o b v i o u s w h a t r e a l i n t e r e s t r a t e t o u s e t o

d i s c o u n t e x p e c t e d f u t u r e o u t p u t f lo w s. 49 M o s t o f t h e s t u d ie s s u r v e y e d b e l o w

u s e f a i r ly lo w d i s c o u n t r a te s , i n t h e r a n g e o f 2 to 4 p e r c e n t p e r y e a r. T h e s e

n u m b e r s c o r r e s p o n d r o u g h l y to a v e r a g e e x p o st r e a l re t u r n s o n U . S. T r e a s u r y

b i ll s p o s t - W o r l d W a r II . B u t is a n o m i n a l l y ) r is k l e ss r a t e t h e a p p r o p r i a t e o n c

f o r d is c o u n t i n g v e r y ri s k y f u t u r e o u t p u t f l o w s? F o r t h e U n i t e d S t a te s , th e m e a n

r a t e o f r e t u r n o n r i sk y a s se ts h a s h i s to r i ca l ly b e e n m u c h h i g h e r t h a n t h a t o n

b o n d s [ M e h r a a n d P r e s c o t t 1 9 8 5 )] , a t l e a s t s i n c e t h e l a te n i n e t e e n t h c e n t u ry .

T o t h e e x t e n t d a t a a r e a v a i la b l e , a si m i la r r e s u l t se e m s t o h o l d f o r a n u m b e r o f

o t h e r c o u n tr i e s. B e r n a n k e 1 9 85 ) ar g u e s th a t a n a n n u a l r e a l i n t e r e s t r a t e a s h i g h

a s 1 4 p e r c e n t is n e e d e d t o r a t io n a l i z e U .S . c o n s u m p t i o n - i n c o m e r e l a ti o n s h i p s

i n a r e l a t e d c l o s e d - e c o n o m y se tt in g .

A s e c o n d d i f f ic u l t y c o n c e r n s t h e s e n s i t i v i ty o f e m p i r i c a l m e a s u r e s o f Y , G ,

a n d i t o a p p a r e n t l y b e n i g n d i f f e re n c e s in t h e t i m e s e r ie s p ro c e s s g e n e r a t i n g t h e

u n d e r l y i n g v a l u e s o f Y , I , a n d G . T h i s p r o b l e m i n t e r a c ts w i t h t h e p r e v i o u s o n e ,

b e c a u s e t h e s e n s i ti v i ty to t h e d a t a - g e n e r a t i n g p r o c e s s is e s p e c ia l l y a c u t e u n d e r a

l o w i n t e r e s t r a te . 5° C o n s i d e r t h e f o l lo w i n g e x a m p l e , i n w h i c h o u t p u t e x p r e s s e d

a s a d e v i a t i o n f r o m m e a n o u t p u t ) is g e n e r a t e d b y th e p r o c e s s

Y t = P Y t - 1 + v t 4.47)

w i th 0 < p _ 1 , v t a w h i t e - n o i s e e r r o r , a n d t i m e m e a s u r e d i n y e a r s . I f a lo w r e a l

i n t e r e s t r a t e is u s e d t o c o n s t r u c t p e r m a n e n t o u t p u t

r E ¢ Y¢+ I + _ _ + . . 4.48), - -- - - l + r 1+---7- ( l + r ?

d i s t a n t f u t u r e i n c o m e s w i l l h a v e r e l a t i v e l y l a r g e w e i g h t s . W h e n r - - 0 . 0 3, E t Y t+20,

f o r e x a m p l e , t h o u g h d i s c o u n t e d , s ti l l h a s a w e i g h t m o r e t h a n h a l f th a t o f c u r r e n t

o u t p u t , Y r . T h i s m e a n s t h a t w h e n r is lo w , e s t i m a t e s o f Y t m a y b e v e r y s e n si ti v e

t o t h e s e r i a l - c o r r e l a t io n p a r a m e t e r p , e sp e c i a ll y i n th e n e i g h b o r h o o d o f p = 1.

N o t i n g t h a t u n d e r e q . 4 . 47 ) E t Y t+ k = p k Y t , o n e se e s t h a t e q . 4 . 4 8 ) i m p l i e s :

49S om e t im e s th i s i s sue c a n b e f i ne s se d [ se e t he d i s c us s ion o f G l i c k a nd R og of f 1995 ) be low .]

5° Th i s d i s c us s ion d r a w s on G l i c k a nd R ogof f 1995 ) .



1782 M. ObstJeld and K. Rogoff

Yt -- r Yt - txYt (4.49)l + r - p

When p = 1, /~ = 1 and so lTt = Yt, regardless of the value of r. But when

r = 0.03 and p --= 0.97 (a value dif fering from 1 by an amou nt genera lly too

small to detect empirically),/x drops to only 0.5: permanent output is half of

current output. As p becomes small this hypersensitivity abates. In practice,

unfortunately, p tends to be quite close to 1, so that the presence of a unit

root is difficult to reject. It should be clear that estimates of Yt can be similarly

sensitive to est imates of time trends. 51

The present-value calculations are less sensitive to p when the real interest

rate is higher. How high must real interest rates be'? With r = 0.14 (the value

me nt io ne d by Bernan ke) and P -- 0.97 in eq. (4.49), /~ = 0.824. With r - 0.5,/x -- 0.943. Real interest rates high enough to make /x insensitive to p in the

vicinity of a unit root appear implausible.

With these cautions in mind we proceed to look at the literature.

4.2.2. Early tests

Early econometric tests of the intertemporal approach as represented by eq.

(4.46) include Ahmed (1986, 1987), Hercowitz (1986), and Johnson (1986).

Hercowitz, who looks at Israeli data over 1950-1981, presents some support

for an intertemporal model but also finds that the model exaggerates the cur-rent account's response to output fluctuations. Johnson focuses on Canada over

1952-1976. He rejects Ricardian equivalence, but concludes that Canada's pri-

vate sector can plausibly be modeled in line with a version of the intertemporal

appr oach that allows for so me liquidity-constrained consumers. 52

Ahmed's papers are distinctive in their use of long historical data series on

gove rnmen t expenditures from the United Kingdom. In the 1986 paper, Ah me d

looks at annual 1908-80 data to gauge the impact of U.K. government spending

on the current account (actually, the trade balance, TB). The 1987 paper ana-

lyzes a pre-World War I sample on public military spending and trade balances

running from 1732 to 1913. Ahmed argues that the expenditures accompany-

ing Britain's wars were largely exogenous and were almost certainly viewed as

temporary by the public. Thus, on the basis of the intertemporal approach, one

51The same problems arise in the macroeconomic iterature on estimating consumption functions.Deaton (1987), for example, argues that if income is stationary in growth rates (a hypothesis thatis difficult statistically to reject given the limited post-WWII time series), then consumption shouldmove more than one-for-one with income innovations. There is, on the other hand, no Deaton'sparadox if income is highly serially correlated but still stationary.

52Roubini (1988) combines the intertemporal approach with the tax-smoothing theory of govern-

ment deficits, finding mixed results for a sample of OECD countries.



Ch 34: The IntertemporaI Approach to the Current Account

1 8 5 4 P o u n d s M i l l io n s )

2 0

1783

i li tary S pend ing

15

1

C u r r e n t c c o u n t

01 7 01 1 7 2 2 1 7 4 3 1 7 6 4 t 7 8 5 1 8 0 6 1 8 2 7 1 8 48 t 8 6 9 1 8 9 0 1 9 1 1 1 9 3 2

Figure 4.2. United Kingdom: Military spending and current account, 1701-1938 (detrended annual

data).

might expect Bri tain to have been running external deficits during wars. 53 In the

twent ieth century, swings in British government spending have been dominated

by the two world wars, both of which were accompanied by large current-

account deficits. Figure 4.2 uses data from Ahmed s papers to graph military

spending against the current account over 1701-1938. 54 This 238-year sample

provides a more demanding testing ground than the twentieth century alone, as

the period is punctuated by many wars. 55

A negative correlation between surges in government spending and the cur-

S3The result that te mpora ry war-time increases in public spending should lead to an externaldeficit does not necessarily hold if the whole world is at war. In an all-encompassing global war,higher governmen t spending everywhere would push up world interest rates with current accountimplications that would depend mostly on countries net external asset holdings. This point illustratesthe distinction between global and country-specitic shocks emphasized in Section 3 above.

54Both series have had a 2 percent annual growth tre nd removed, as in Ahme d (1987). The current

account has been constructed from Ahme d s trade balance data using a 3 percent per annum sterlingrate of return on foreign assets starting from an assumed zero net foreign asset position in 1701.We thank Shaghil Ahmed for providing us with the data from his papers.

55The possible gain or loss of colonial territories and privileges, which was the motive for much

warfare before World War I, naturally could be expected to exert an additional wealth effect on

the current account• Ideally, this effect should be controlled for in estimation .




r e n t a c c o u n t i s f u l ly c o n s i s t e n t w i th t h e o r i e s o t h e r t h a n t h e i n t e r t e m p o r a l a p -

p r o a c h , f o r e x a m p l e , a K e y n e s i a n m u l t i p l i e r m o d e l . T o r e d u c e t h e s e t o f a l te r -

n a t i v e t h e o r i e s c o n si s te n t w i th t h e d a t a , A h m e d e x p l o r e s f o r m a l e c o n o m e t r i ct e st s. A r e p r e s e n t a t i v e r e s u l t f r o m A h m e d ( 19 8 6 ) is

T B t = - 0 . 2 1 ( G r - G t ) - 0 . 4 4 G t + e t; R 2 = 0 . 2 8 , D . W . = 2 . 3 2

0 . 0 5 ) 0 . 8 8 )

w h i c h i s e s t i m a t e d o v e r 1 9 0 8 - 80 . 56 T h i s r e g r e s s i o n s h o w s t h a t t h e t e m p o r a r y

c o m p o n e n t o f g o v e r n m e n t s p e n d i n g h a s a s ig n if ic a nt n e g a t i v e in f lu e n c e o n t h e

c u r r e n t a c c o u n t , w h e r e a s t h e p e r m a n e n t c o m p o n e n t i t s el f d o e s n o t , c o n s i s te n t

w i t h ( 4. 46 ). U n f o r t u n a t e l y , t h e r e g r e s s i o n ' s s p e c if i c a ti o n l e a v e s o p e n t h e p o s s i -

N l i t y t h a t G t i s t h e o n l y s ig n i fi c an t d e t e r m i n a n t o f t h e c u r r e n t a c c o u n t a n d t h a t

G t p l a y s n o r o l e a t al l - a s a n a t e m p o r a l K e y n e s i a n m o d e l w o u l d p r e d i c t .

U s i n g o u r e s t i m a t e d c u r r e n t a c c o u n t in p la c e o f t h e t r a d e b a l a n c e , w e h a v e

r u n a si m i l a r r e g r e s s i o n o n t h e 1 7 0 1 - 1 9 3 8 d a t a , b u t w h i l e k e e p i n g G t - G t in t h e

r e g r e s s i o n w e r e p la c e G t b y G t s o a s t o e n c o m p a s s t r a n s p a r e n t l y t h e i n t e r t e m -

p o r a l a n d K e y n e s i a n a l t e r n a t i v e s w i t h i n a s in g l e t e st . 87 T h e r e s u l t in g r e g r e s s i o n ,

r u n u s i n g a C o c h r a n e - O r c u t t c o r r e c t i o n f o r f i r s t- o r d e r s e r i a l c o r r e l a t i o n i s 58

C A t ---- - 0 .0 1 6 G t - G t ) - 0 .028 Gt + e t ; p = 0 .907

(0 .013 ) (0 .093 ) (0 .027 )

I n t h i s s p e c i f i c a t i o n , n e i t h e r c u r r e n t n o r p e r m a n e n t g o v e r n m e n t s p e n d i n g i s

i n d i v i d u a l l y s ig n i fi ca n t. A s u s u a l , i t is u n c l e a r w h e t h e r t h e i n t e r t e m p o r a l a p -

p r o a c h is s im p l y fa ls e , o r w h e t h e r t h e m a n y e x t r a n e o u s s im p l i fi c at io n s a n d m a i n -

t a i n e d h y p o t h e s e s i m p o s e d b y t h e e c o n o m e t r i c i a n a r e t o b l a m e . I t is t h e r e f o r e

u s e f u l to t u r n t o a n e w e r e m p i r i c a l a p p r o a c h b a s e d o n a l es s r e s t r i c ti v e f r a m e -

w o r k .

4 .2 .3 . P r e s e n t - v a l u e m o d e l s o f t he c u r r e n t a c c o u n t

G h o s h ( 1 9 95 ) , O t t o ( 19 9 2 ), a n d S h e f fr i n a n d W o o ( 19 9 0 ) a p p l y a n a l t e r n a t i v e

m e t h o d o l o g y t h a t m a k e s u s e o f t h e in f o r m a t i o n e m b o d i e d i n p a s t c u r re n t a c-c o u n t s t o m a k e m o r e a c c u r a te p r e d i c ti o n s o f I7 , G , a n d [ . T h e s e s t u d i e s b u i l d o n

t h e m e t h o d o l o g y d e v e l o p e d b y C a m p b e l l ( 19 87 ) a n d b y C a m p b e l l a n d S h i ll e r

(19 87) . 59

56See Table 1, regression I (with p = 0.02) on p. 211.57To form G we us ed an autoregressive forecasting model of detrended government spending.58Similar results are obtained when we use the trade balance in place of the current account, as

Ahm ed (1987) does.59Campbell's (1987) study of private U.S. saving is especially relevant to the current-account

studies we a re a bout to discuss. Com parison with Cam pbell's results is difficult, how ever, becausehe examines a different question, the accumulation of private wealth of all kinds in response to

fluctuations in after-tax labor incom e.




D e f i n e

Q ~ Y - G - I

T h e s t a r t i n g p o i n t f o r t h e p r e s e n t - v a l u e m e t h o d o l o g y is a g a i n eq . ( 4. 46 ), e x -

p r e s s e d i n t h e f o r m

C A t = Q t - Q t (4.50)

T h e n e w v a r i a b l e Q c a n b e t h o u g h t o f a s t h e n e t p r i v a t e n o n i n t e r e s t c a s h f lo w.

A l t h o u g h t h e m a i n i n n o v a t i o n o f t h e C a m p b e l l - S h i l l e r a p p r o a c h d o e s n o t r e a ll y

r e q u i r e i t, G h o s h , S h e f f r i n - W o o , a n d O t t o a l l f o l l o w C a m p b e l l a n d S h i l l e r i n

r e w r i t i n g e q . ( 4 . 5 0 ) a s

C A t = - - E t ~ ~ A Q s (4.5:l)

s=t+l

w h e r e Q t = Q t - Q t - 1 i s t he d i f f e r e n c e o f t h e c a s h fl o w v a r i a b l e. E q u a t i o n

( 4. 51 ) s a y s t h a t t h e c u r r e n t a c c o u n t b a l a n c e t e n d s t o b e n e g a t i v e w h e n n e t

c a s h f l o w i s e x p e c t e d t o r i s e, a n d p o s i t i v e w h e n n e t c a s h f l o w is e x p e c t e d t o

f a l l . C o n d i t i o n a l e x p e c t a t i o n s a r e a s s u m e d t o b e l i n e a r p r o j e c t i o n s o n a v a i l a b l e

i n f o r m a t i o n .

W h a t a d v a n t a g e i s t h e r e t o e s t i m a t i n g e q . ( 4. 51 ), w h e r e Q t e n t e r s i n d i f -

f e r e n c e d f o r m , r a t h e r t h a n e q . ( 4 . 5 0 ) , w h e r e i t s l e v e l e n t e r s ? T h e d i f f e r e n c e d

v e r s i o n i s a p p r o p r i a t e i f o n e is c o n c e r n e d t h a t t h e r e i s a u n i t r o o t i n Q t , s o t h a tr e m o v a l o f a t i m e t r e n d is n o t s u f f i c ie n t f o r s t a t i o n a r i ty . 6° I f Q t i s i n d e e d I ( 1 )

( h a s a u n i t r o o t ) , t h e n , a s C a m p b e l l a n d S h i l l er h a v e e m p h a s i z e d , e q . ( 4 .5 1 )

a l lo w s o n e t o u s e t h e s t a t i o n a r y v a r i a b le z X Q t a s a r e g r e s s o r w i t h o u t h a v i n g t o

d i f f e r e n c e b o t h C A a n d Q , w h i c h i s i n e f f ic i e n t in t h e l i k e l y e v e n t t h a t C A is

s t a t io na r y . 61

T h e f u n d a m e n t a l d if f e re n c e b e t w e e n t he G h o s h , S h e f f r i n -W o o , a n d O t t o a p-

p r o a c h a n d e a r l i e r s tu d i e s c o n ce r n s h o w o n e p r o x i e s f o r p ri v a t e a g e n t s e x p e c-

t a t io n s o f f u t u r e v a l u e s o f Q . T h e b a s ic in s i g h t o f t h e C a m p b e l l - S h i l l e r m e t h o d -

o l o g y is t h a t a s lo n g t h e i n f o r m a t i o n s et u s e d b y t h e e c o n o m e t r i c i a n d o e s n o t

c o n t a i n a l l t h e i n f o r m a t i o n a v a i l a b l e t o p r i v a t e a g e n t s , t h e n p a s t v a l u e s o f C Ac o n t a i n i n f o r m a t i o n u s e fu l in c o n s t r u ct in g e s t i m a t e s o f a g e n t s e x p e c t a t i o n s o f

f u t u r e v a l u e s o f Q . O b v i o u s l y , i n c o r p o r a t i n g t h i s in s i g h t d o e s n t a c t u a l l y r e q u i r e

u s i n g f i r s t d i f f e r e n c e s , a s i n e q . 4 . 5 1 ) , r a t h e r t h a n l e v e l s , a s i n e q . ( 4 . 5 0 ) .

S u p p o s e , f o r e x a m p l e , t h a t o n e f o r m s e x p e c t a t io n s o f f u t u r e v a l u e s o f d~Qt

b y f ir st e s t im a t i n g a f i r s t- o r d e r V A R ( t h e g e n e r a l iz a t i o n t o h i g h e r - o r d e r V A R s

i s s t r a i g h t f o r w a r d )

6°Ghosh (1995) cannot re jec t the hypothes i s o f a unit roo t in Ot for h i s sample . Sheffr in and Woo

(1990) and O t to (1992) repo r t s im i la r re sul ts .

61Trehan and Walsh (199l ) d i scuss condi t ions under which s ta t ionar i ty of CA i s necessa ry for a

c oun t ry s i n t e r t e m pora l budge t ba l a nc e.



1 7 8 6 M O b s t fe l d a n d K R o g o f f

[ C A t - i ] Lez t

a n d t h e n m a k e s u s e o f it s i m p l i c a t i o n t h a t

E t k C A , + k ] = 4 ,3 4 , 4 ] L C A ] 4 . 5 3 )

t o f o r m a n e s t i m a t e d c u r r e n t a c c o u n t , C A t. 62 I f i i s t he 2 x 2 i den t i t y mat r ix

and ~ t he m at r ix o f t he 4 , s , t hen eq s . (4 .51 ) and (4 .53) imply t ha t

C - A t : - [ 1 0 ] [ ( l + r ) - - l ~ ] [ I _ ( 1 + r ) _ 1 ~ ] - 1 L C A t[ Q t[ A e l-~ [CbaQ q C A ] [ C A t ] (4.54)

I f t h e v e r s i o n o f t h e in t e r t em p o r a l ap p r o ach em b o d i e d i n ( 4 .5 1 ) is t r u e , t h en

t h e t h eo r e t i ca l l y p r ed i c t ed v a l u e o f [ eaQ @ cA ] i n ( 4 .5 4 ) i s s i mp l y [0 1 ] Th e

r e a s o n t h is r e s tr i c ti o n e m e r g e s is o b v i o u s w h e n t h e V A R c a p t u r e s a l l i n f o r ma-

t i o n p eo p l e u s e t o f o r ecas t f u t u r e ca s h flo w . Th e s am e r e s t r ic t i o n a l s o h o l d s

t ru e , h o w e v e r , w h e n t h e V A R c a p t u r e s o n l y a s u b s e t o f t h a t in f o r m a t i o n . T h e

r ea s o n i s t h a t - C A t c a p t u r e s t h e r e p r e s e n t a t i v e c o n s u m e r ' s b e s t e s ti m a t e o f t h e

p r e s e n t v a l u e o f f u t u r e ca s h - f lo w ch an g es , regardless o f w h a t o t h e r i n f o r m a t i o n

h e o r s h e h a s .

A p p l y i n g t h e a b o v e a p p ro a c h , S h e ff r in a n d W o o f in d t h a t t h e r e s tr i c ti o n

C A t = C A t is r e j e c t e d f o r C a n a d a , D e n m a r k , a n d t h e U . K . i n t h e i r 1 9 5 5 -

8 5 sa m p l e , a l t h o u g h i t is n o t r e j e c t e d fo r B e l g iu m . G h o s h , w h o s e s a m p l e p e r i o d

i s 1960-88 , f i nds t ha t t he r es t r i c t i on i s no t r e j ec t ed fo r t he U.S . , bu t t ha t i t f a i l s

f o r C a n a d a , G e r m a n y , J a p a n , a n d t h e U n i t e d K i n g d o m .

E q u a t i o n ( 4. 54 ) le a d s to a s t ri n g en t t e s t o f t h e m o d e l , b u t a n u m b e r o f m o r e

g en e r a l t e s t s l e s s s en s i t i v e t o ma i n t a i n ed h y p o t h es i s co u l d b e ap p l i ed . O n e b as i c

i mp l i ca t i o n o f t h e mo d e l i s t h a t C A t s h o u l d G r a n g e r - c a u s e A Q t . G h o s h f i n d s

t h a t i n h i s f u l l s amp l e , ev en t h i s w eak e r t e s t s t i l l i s p a s s ed o n l y b y t h e U n i t edS t a t e s d a t a . S h e f f r in a n d W o o a r r iv e a t m o r e p o s i t i v e r e su l ts . A n o t h e r a p p r o a c h

i s ad o p t ed b y O t t o ( 1 9 9 2 ) , w h o t e s t s t h e r e s t r i c t i o n t h a t

E t - 1 { C A , - A Q , - ( 1 + r C A t _ t } = 0

w h i ch f o l l o w s s tr a i g h t f o r w ar d l y f r o m eq . ( 4.5 1) . O t t o r e j ec t s t h e p r e s en t - v a l u e

m o d e l f o r C an ad a an d t h e U .S . a f t e r f in d i n g t h a t l ag g ed v a r i ab l e s h e l p in p r e -

d i c t i ng C A t - A Q t (1 + r C A t _ l .

6 2 O n c e a g a i n t h i s r e q u i r e s a c h o i c e o f t h e c o n s t a n t r e a l r i s k - f r e e i n t e r e s t r a t e r .



Ch 34: The Intertemporal Approach to the Current Account / 787

W h i l e t h e f o r m a l e v i d e n c e t h e r e f o r e i s v e r y m i x e d , 63 G h o s h , S h e f f r i n a n d

W o o , a n d O t t o a l l s t r e s s t h a t t h e i n f o r m a l e v i d e n c e o b t a i n e d b y s i m p l y l i n i n g

u p a c t u a l c u r r e n t a c c o u n t s w i t h t h e m o d e l ' s p r e d i c t i o n s c a n b e q u i t e i m p r e s s iv e .T h i s p e r s p e c t i v e is u s e f u l , b e c a u s e n o e m p i r i c a l m o d e l i s l i k e l y t o b e l i t e ra l l y

t r u e . I n F i g u r e 4 .3 , w e g r a p h t w o i l l u s t r a ti v e c a se s , S w e d e n a n d t h e U n i t e d

K i n g d o m , u s i n g p o s t w a r d a t a ; b o t h f i g ur e s a r e b a s e d o n a f i r s t - o r d e r V A R w i t h

A Q a n d C A a s d is c u s s ed a b o v e . T h e m o d e l p e r f o r m s v e r y w e l l fo r S w e d e n , b u t

p o o r l y f o r th e U n i t e d K i n g d o m . O n e p r o b l e m m i g h t b e t h a t th e m o d e l d o e s

n o t e x p l i c it l y i n c o r p o r a t e t h e e f f e c t s o f o i l p r i ce s c h a n g e s , w h i c h h a v e b e e n

i m p o r t a n t f o r B r i t a i n i n r e c e n t y e a r s .

I n d e e d , i f o n e e x t e n d s t h e d a t a o n G r e a t B r i t a in o v e r a l o n g e r h i s to r ic a l

p e r i o d , t h e m o d e l ' s p e r f o r m a n c e l o o k s m u c h b e t t e r . F o r a n n u a l B r i t i s h d a t a

o v e r t h e p e r i o d 1 8 7 0 -1 9 9 1 , a f i r s t- o r d e r V A R f o r d xQ a n d C A y i e l d s64

A Q t ] = [ 0 . 2 4 -0 .14] [AQt-11CA t ] - 0 . 1 1 0 .8 4 ] [CA _I ]

F i g u r e 4 . 4 i s c o n s t r u c t e d u s i n g t h e a b o v e e s t i m a t e s a n d a s s u m i n g a r e a l i n -

t e r e s t ra t e o f 4 p e r c e n t p e r a n n u m . E x t e n d i n g t h e d a t a s e t y i el d s a d r a m a t i c a l l y

b e t t e r f it t h a n w h e n o n e e s t im a t e s t h e m o d e l o v e r p o s t - W o r l d W a r I I d a t a a l o n e.

T h o u g h t h e v i s u a l e v i d e n c e i s f a ir l y s t ri k in g , t h e m o d e l s ti ll f ai ls a f o r m a l t e s t

o f t h e r e s t r i c t io n e m b o d i e d i n e q . (4 .5 4). F r o m t h e a b o v e V A R e s t i m a t e s , o n e

o b t a i n s [ ~ ) z x O ~ C A ] = [ -- 0 .2 6 0 .5 4 ], w h i c h d i f f e r s s i g n i f i c a n t l y f r o m t h e n u l lh y p o t h e s i s v a l u e o f [ 0 1 I

A c o m m o n t h e m e i n t h e g r a p h ic a l e v i d e n c e p r e s e n t e d b y G h o s h , S h e f f r i n -

W o o , a n d O t t o i s t h a t t h e a c t u a l c u r r e n t a c c o u n t is o f t e n f a r m o r e v o l a t i l e t h a n

t h e p r e d i c t e d c u r r e n t a c c o u n t . T h i s s e e m s t o c o n t r a d i c t t h e F e l d s t e i n - H o r i o k a

c o n c l u s io n t h a t c u r r e n t a c c o u n t m o v e m e n t s a r e r e l a t iv e l y s m a l l c o m p a r e d t o

w h a t o n e w o u l d e x p e c t i n th e o ry . G h o s h f o r m a l l y c o m p a r e s t h e v a r i an c e s o f th e

p r e d i c t e d a n d a c t u a l c u r r e n t a c c o u n t s e r i e s a n d f i n d s t h a t , e x c e p t i n t h e U . S .

c a s e ( w h e r e h e c a n n o t r e j e c t e q u a l i t y o f th e v a r i a n c e s ) , t h e v a r i a n c e o f t h e actuals e r i es i s h i g h e r. O t t o s i m i l a r l y f in d s t h a t C a n a d a ' s c u r r e n t a c c o u n t is s ix t i m e s a s

v o l a t i l e as t h e p r e d i c t e d s e ri e s. 65 G h o s h i n t e r p r e t s h i s f i n d i n g as e v i d e n c e o f t o o

6 3 G h o s h a n d O s t r y ( 1 9 9 5 ) a p p l y t h e p r e s e n t - v a l u e a p p r o a c h t o d e v e l o p i n g c o u n t r i e s a n d a r g u etha t , i f a ny th ing , i t p e r f o r m s be t t e r t ha n f o r i ndus t r i a l i z e d c oun t r i e s . The y f i nd t ha t a c r o s s a l a r ges a m p l e o f d e v e l o p i n g c o u n t r i e s , t h e l e v e l a n d v o l a ti l it y o f n e t c a p i t a l m o v e m e n t s p r e d i c t e d b ythe i r c onsum pt ion - sm oo th ing m ode l c lo se ly pa r a l l e l s t hose i n t he da t a . Th i s f i nd ing i s puz z l ing -d e v e l o p i n g c o u n t r i e s c a p i t a l m a r k e t s t e n d t o b e l es s o p e n t h a n t h o s e o f t h e i n d u s tr i a li z e d c o u n t r i es- bu t one pos s ib l e e xp la na t ion r e l i e s on t he d i s t i nc t i on be tw e e n g loba l a nd c oun t r y - spe c i f i c shoc kstha t w e m a k e be low . P la us ib ly , de ve lop in g c oun t r i e s a r e r e l a t i ve ly m o r e su sc e p t ib l e t o c oun t r y -spe c i f i c a s oppose d to g loba l shoc ks , so t ha t t he p r e se n t - va lue m ode l , w h ic h a s sum e s a g ive n a nd

c o n s t a n t r e a l i n t e r e s t r a t e , d o e s s o m e w h a t b e t t e r.

64H is to r i c a l da t a a r e f r om F e in s t e in ( 1972 ) a nd M a dd i son ( 1991 ) .

6S S he f fr i n a nd W oo s d a t a ( w h ic h the y ge n e r ous ly su pp l i e d t o u s ) y i e ld s im i l a r r e su l ts .




1985 Kronor per Capita

4000

3000

2000

1000

0

1000

2000

3000

Actual

kt

Predicted I l1952 1956 1960 1964 1968 1972 1976 1980 1984 1988

1985 Pounds per Capita

200

100

100

200

300

V V Predicted

19501954195819621966197019741978 19821986 1990

Figure 4.3. Sweden: Actu al and predicte d current account balance annual data).



Ch. 34: 7"he Intertempora Approach to the Current Account 1789

9 4 P o u n d s p e r C a p i ta

6

0

-2

-4

6.8 Pre dicte d A

10

121871 1 882 1893 1904 1915 1926 1937 1948 1959 197 0 1981 1991

Figure 4.4. Un ited K ingdom : Actual and predicted current accoun t balance (annual data).

m u c h c a p i ta l m o b i li ty , i n c o n t r a s t t o th e F e l d s t e i n - H o r i o k a c l a i m o f t o o l i t tl e.

O n e p o s s ib l e e x p l a n a t i o n o f t h e G h o s h - O t t o f in d in g s is t o v ie w t h e m a s r e l a t e dt o D e a t o n ' s p a r a d o x o f e x c es s iv e c o n s u m p t i o n s m o o t h n e ss . T h e D e a t o n p a r a d o x

c a n b e r e s o l v e d b y s t i p u la t in g t h a t i n c o m e , t h o u g h h i g h l y se r ia l ly c o r r e la t e d ,

d o e s n o t l i t e r a ll y c o n t a i n a u n i t ro o t . ( W h e n i n c o m e i s s t a t i o n a r y i n g ro w t h

r a t e s r a t h e r t h a n i n le v e ls , a s m a ll c h a n g e i n c u r r e n t i n c o m e c a n i m p l y a v e r y

l a r g e c h a n g e i n p e r m a n e n t i n c o m e a n d , h e n c e , i n p r e d i c t e d c o n s u m p t i o n . ) J u s t

a s t h e a s s u m p t i o n o f a u n i t r o o t i n i n c o m e c a n l e a d t o t h e c o n c l u s i o n t h a t

c o n s u m p t i o n i s t o o s m o o t h , i t c a n a l so p r o d u c e t h e r e s u l t t h a t s a v in g o r t h e

c u r r e n t a c c o u n t is t o o v o l a ti le . T h i s m a y h e l p e x p l ai n t h e G h o s h - O t t o v o l a t il i t y

r e s u l ts , t h o u g h f u r t h e r i n v e s t i g a t i o n is r e q u i r e d .

4.2.4. Glo bal versus country-speci fic shocks' and the current accou nt

O n e s h o r t c o m i n g o f th e s t ud i e s c o n s i d e r e d s o fa r is t h e i r im p l i c it a s s u m p t i o n

t h a t a l l s h o c k s t o c a s h f l o w a r e p u r e l y i d i o s y n c r a t i c . 66 I n r e a l i t y , e v e n a s m a l I

c o u n t r y ' s o u t p u t g r o w t h o r i n v e s t m e n t m a y b e h i g h l y c o r r e l a t e d w i t h t h a t in t h e

r e s t o f th e w o r l d . O u t p u t s h o c k s w h i c h i d e n t i c a l ly i m p a c t a l l c o u n t r i e s s h o u ld ,

h o w e v e r , e x p r e s s t h e m s e l v e s p r i m a r i l y t h r o u g h t h e g l o b a l i n t e r e s t ra t e , a n d n o t

66This criticism, of course, applies with equa l force to mu ch of the macro econo metric literature

on consumption.




i n i n d i v i d u a l c o u n t r i e s c u r r e n t a c c o u n t s . G l i c k a n d R o g o f f (1 99 5) a r g u e t h a t t h i s

i s su e is e m p i r i c a l ly im p o r t a n t a n d t r y t o c o n f r o n t i t. T h e i r m o d e l a l s o a t t e m p t s

t o t r a c e s h o c k s t o o u t p u t a n d i n v e s t m e n t b a c k t o c h a n g e s i n f a c t o r p r o d u c t i v i ty ,a l l o w i n g f o r m o r e s t r u c t u r e t h a n t h e e m p i r i c a l s t u d i e s j u s t d i s c u s s e d . 67 A s i m p l e r

v e r s i o n o f t h e G l i c k - R o g o f f f r a m e w o r k s u ff ic es t o i ll u s tr a t e th e i r m a i n p o i n t s .

L e t s l a b e l t h e c o u n t r y - s p e c if i c c o m p o n e n t o f c a s h f l ow Q~: a n d t h e g l o b a l

c o m p o n e n t Q W , s o t h a t

A Q = A Q c + A Q w

T h e g l o b a l c o m p o n e n t is t h e p a rt o f Q t h a t is p e r f e c tl y c o r re l a t e d w i t h a v e r a g e

w o r l d Q . T h e n , a s s u m i n g t h a t Q C is 1 (1 ), a n d t h a t i n i t i a l n e t f o r e i g n a s s e t p o -

s i t i o n s a r e z e r o , o n e c a n a f te r m a n y s t ep s ) s h o w t h a t e q . ( 4 . 5 1 ) i s r e p l a c e d b y

t h e a p p r o x i m a t e c u r r e n t - a c c o u n t e q u a t i o n 68

C A t = - E t -1-+-~r A Q,~ (4 .55)

s=t+l

w h e r e t h e i n t e r e s t r a t e u s e d i s t h a t p r e v a i l i n g a l o n g a n i n i ti a l s t e a d y - s t a t e p a t h .

A c c o r d i n g t o ( 4 .5 5 ) , o n l y c o u n t r y - s p e c i f i c s h o c k s a f f e c t c u r r e n t a c c o u n t s . 69

T o s e p a r a t e Q C f r o m Q W , G l i c k a n d R o g o f f c o n s i d e r a n n u a l d a t a f o r t h e G - 7

c o u n t r i e s o v e r 1 9 6 0 - 9 0 , t r e a t i n g th e s e c o u n t r i e s a s t h e w o r l d ( w h i c h , i n t e r m s o f

e c o n o m i c s iz e, is n t a b a d a p p r o x i m a t i o n f o r m o s t o f t h e i r s a m p l e p e r i o d ). T h e y

c o n s i d e r t w o a l t e r n a t iv e m e t h o d s o f s ep a r a t i n g s h o c k s i n t o l oc a l a n d g l o b a lc o m p o n e n t s . T h e s i m p l e s t i s t o f o r m Q C a s Q - Q W , w h e r e QW i s t a k e n t o b e

a m e a n - G N P w e i g h t e d a v e r a g e f o r t h e e n t i re g ro u p . T h e m o r e s o p h i s t ic a t e d

a p p r o a c h is t o r e g re s s e a c h c o u n t r y s A Q o n a n i n d e x o f t h e r e m a i n i n g c o u n -

t r i e s c a s h f lo w s , d e f i n i n g Q C a s t h e r e g r e s s i o n r e s i d u a l . G l i c k a n d R o g o f f f i n d

t h a t t h e t w o a p p r o a c h e s y i e l d s i m i l a r r e s u l t s f o r t h e i r u l t i m a t e c u r r e n t - a c c o u n t

a n d i n v e s t m e n t e q u a t i o n s . O v e r a l l , g l o b a l s h o c k s a p p e a r t o a c c o u n t f o r a v e r y

s i g n i fi c a n t p o r t i o n o f t o t a l p r o d u c t i v i t y s h o c k s i n t h e G - 7 c o u n t r i e s , r o u g h l y

5 0 p e r c e n t . 7° G l i c k a n d R o g o f f f in d t h a t t h e g l o b a l v e r s u s c o u n t r y - s p e c i fi c d is -

t i n c t io n g r e a t l y im p r o v e s t h e a b i li ty o f t h e i n t e r t e m p o r a l a p p r o a c h t o e x p l a i n

67Leiderman and Razin (1991) develop a model similar to Glick and Rogoff s, although they do

not distinguish between global and country-specific shocks.

68The derivation of equation (4.55) requires that the variances of the underlying productivity

shocks be constant. The global component of the shock, QW affects world interest rates but not the

current account.

69If initial net foreign asset positions are not zero, the interest-rate effects of global shocks can

redistribute income from debtors to creditors in a way that al ters curren t accounts. [Recall eq. (3.9)above.[ Gliek and Rogoff show that this effect is empiricaUy small.

7°Costello (1993) and Stockman (1988) have found, for slightly different country samples andindustry-level data, that global productivity or output shocks seem to be less correlated betweensimilar manufacturing industries in different countries than be tween different industries in the samecountry. That evidence apparently points to a greater role for country-specific shocks, and it remains

to reconcile it with the results discussed in the text.



C h . 3 4. T h e I n t e r t e m p o r a t A p p r o a c h t o th e C u r r e nt A c c o u n t 1791

a c t u a l c u r r e n t a c c o u n t s : t h e c o e f f ic i e n ts o n t h e g l o b a l s h o c k s a r e i n v a r i a b l y m u c h

s m a l l e r t h a n t h o s e o n t h e c o u n t r y - s p e c i fi c s h o c k s, a n d a r e u s u a l l y i n s ig n i f ic a n t .

4 . 2 . 5 . E x t e n s i o n s

T h e e m p i r i c a l c o n s u m p t i o n - s m o o t h i n g m o d e l s d i s c u s s e d s o f a r a l l i g n o r e t h c

p r e c a u t i o n a r y m o t i v e f o r sa v i n g, a s w a s r e m a r k e d e a r l i er . C a b a l l e r o ( 19 9 0) h a s

s h o w n , h o w e v e r , t h a t u n d e r s p e c i f i e d a s s u m p t i o n s o n e c a n o b t a i n c l o s e d - f o r m

c o n s u m p t i o n f u n c t i o n s b a s e d o n t h e p e r i o d u t i li t y f u n c t i o n u C ) - - e x p ( - u C ) ,

w h e r e v i s t h e c o e f f i c ie n t o f a b s o l u t e r i sk a v e r s i o n . T h u s , t h e r e is n o n e e d

t o r e l y e x c l u s iv e l y o n a l in e a r - q u a d r a t i c f o r m u l a t i o n f o r c l o s e d - f o r m s o l u ti o n s .

G h o s h a n d O s t r y ( 1 9 92 , 19 94 ) a p p l y C a b a l l e r o s r e s u lt s t o a d d a p r e c a u t i o n a r y

s a v i n g e f fe c t t o t h e p r e s e n t - v a l u e m o d e l o f t h e c u r r e n t a c c o u n t . 71 T h e k e y n e w

p a r a m e t e r a p p e a r i n g i n th e i r e x t e n d e d f r a m e w o r k i s o-g = V a r( ~ ) , w h e r e

~t = 0 t - - g r - I 0 t

is t h e d a t e - t i n n o v a t i o n t o e x p e c t e d p e r m a n e n t p r i v a t e c a s h flow . G h o s h a n d

O s t r y ( 1 9 9 2 ) l o o k a t q u a r t e r l y 1 9 5 5 - 9 0 t i m e - s e r i e s d a t a f o r C a n a d a , J a p a n , t h e

U n i t e d K i n g d o m , a n d t h e U n i t e d S t a t e s . B e c a u s e t h e y a r e l o o k i n g a t t i m e -

s e r ie s r a t h e r t h a n c r o s s -s e c t io n d a t a , t h e y m u s t n e g o t i a t e t h e d i f fi c u lt i ss u e o f

t i m e v a r i a t i o n i n ~ , w h i c h is a c o n d i t i o n a l v a r i a n c e i n a d y n a m i c s e t ti n g . L o n g

e n o u g h i n t e r v a l s m u s t b e a l l o w e d f o r a c c u r a t e m e a s u r e s o f o-~ , b u t i n t e r v a l ss h o u l d n o t b e s o l o n g a s t o p r e c l u d e e n o u g h d a t a p o i n t s f o r m e a n i n g f u l t i m e -

s e r i e s r e g r e s s i o n s . 72 U s i n g t w o - t o f i v e - y e a r i n t e r v a l s t o m e a s u r e o- , G h o s h

a n d O s t r y f i n d t h a t t h e i r p r e c a u t i o n a r y v a r i a b l e u s u a l l y e n t e r s s i g n i fi c a n tl y a n d

w i t h t h e c o r r e c t s i g n i n p r e s e n t - v a l u e c u r r e n t a c c o u n t r e g r e s si o n s . G h o s h a n d

O s t r y ( 19 9 4) f i n d s i m i l a r ly p o s i t i v e r e su l t s f o r d e v e l o p i n g c o u n t r i e s . T h e i r p o i n t

e s t i m a t e s s u g g e st t h a t p r e c a u t i o n a r y s a v i ng s a re o f th e o r d e r o f m a g n i t u d e o f 5

p e r c e n t o f i m p o r t s f o r t h e A f r i c a n r e g io n , 4 p e r c e n t f o r c o m m o d i t y e x p o r t e rs ,

a n d 1 4 p e r c e n t f o r f u e l e x p o r t e r s .

N o n e o f t h e e m p i r i c a l s t u d i e s d i s c u s s e d t h u s f a r d i s t i n g u i s h e s b e t w e e n d u r a -

b le s a n d n o n d u r a b l e s o r b e t w e e n t r a d e a b l e s a n d n o n t r a d e a b l e s . A s w e e m p h a -

s i z e d i n o u r t h e o r e t i c a l d i s c u s s i o n , b o t h d i s t i n c t i o n s c a n b e i m p o r t a n t f o r t h e

c u r r e n t a c c o u n t . B u r d a a n d G e r l a c h (1 99 3) a r g u e t h a t , i n t h e o r y , d u r a b l e - g o o d s

i m p o r t s a r e m u c h m o r e s e n si ti v e t o e x p e c te d m o v e m e n t s i n th e r e a l e x c h a n g e

r a t e ( b e c a u s e o f t h e r e s u l t i n g e x p e c t a t i o n s o f c a p i t a l g a i n o r l o ss ) t h a n a r c

n o n d u r a b l e s i m p o r t s . E s t i m a t i n g t h e i r m o d e l p o s e s a n u m b e r o f d i ff ic u lt ie s : i n

p a r t i c u la r , t h e t h e o r y ca ll s f o r a m e a s u r e o f t h e s t o c k o f c o n s u m e r d u r a b l e s ,

b u t t h i s is d i f f i c u l t t o o b t a i n i n p r a c t i c e . U s i n g a v e c t o r e r r o r - c o r r e c t i o n t i m e -

71An a l t e rna t ive theo re t ica l t r ea tm en t i s Rodr iguez 1993).

72An al ternat ive approa ch would be to ado pt an e xpl ic i t para m eter iz at ion of Var~ , ~: t) .



1792 M. O bstfeld and K. R ogoff

series specification including quarterly data on the current account, expected

permanent net income, the relative price of durables in terms of nondurables,

and a variable capturing expected changes in that price, Burda and Gerlachfind that the expected price changes have a significant correlation with the U.S.

current account over 1970-88. This finding, they argue, provides support for

the empirical role of the durables versus nondurables distinction. It is difficult

to compare these results with those of the empirical models discussed earlier

because the Burda-Gerlach setup, with its very general lag structure, imposes

much less theoretical structure. It would be interesting to pursue an alternative

approach based on eq. (3.23). 73

Rogoff (1992) incorporates nontraded goods into an empirical intertemporal

model, although his primary focus is on explaining the well-documented near

random-walk behavior of real exchange rates. His main result is that intertem-

poral consumption smoothing in traded goods might account for the persistence

of innovations in real exchange rates. In the simplest case, assume exogenous

output of tradeables and nontradeables, a Cobb-Douglas period utility function

[p = 1 in eq. (3.17)], and an intertemporal substitution elasticity, or, of 1. In this

case, as we saw earlier, people smooth their consumption of tradeables inde-

pendently of the evolution of their nontradeables consumption. As above, the

real exchange rate, the relative price of nontradeables on date t, depends on

G r t Y N t and consumers expenditure shares. A permanent shock to tradeables

output raises Ca- permanently and thereby permanently raises the relative priceof nontradeables. But even a t e m p o r a r y rise in traded-goods output raises Gr

permanently because of consumption smoothing. The model thus can explain

why the persistence in real exchange rate movements might be much greater

than that of the underlying exogenous shocks. A country s ability to borrow and

lend in international markets is the key to this result: it would not obtain absent

internationa l capital mobility. Rogoff (1992) applies his model to data for Japan

and the Uni ted States, finding some support, though further testing is required.

5 H o w u s e f u l i s t h e t h e o r y ?

Even in its most rudimentary forms, the intertemporal approach to the cur-

rent account has proved valuable for analyzing a host of important problems.

Without an intertemporal approach, it would be hard to analyze or evaluate

the current-account patterns that followed the two oil shocks of the 1970s. The

dynamic budget constraints emphasized throughout this chapter are also essen-

tial in analyzing episodes of capital-market disruption, such as the developing-

country debt crisis of the 1980s. True, the standard in tertemporal models must

7 For som e preliminary empirical results, see Obstfeld and Rogoff(1996), ch. 2.



C h 3 4 : T h e I n t e r te m p o r a l A p p r o a c h t o t h e C u r r e n t A c c o u n t 793

b e e x t e n d e d t o t a k e a c c o u n t o f d e f a u l t r i s k b u t , a s w e h a v e s e e n , t h e m a i n

q u a l i t a t i v e i n s ig h t s d o n o t c h a n g e . M o r e g e n e r a l l y , m o d e l s t h a t f a i l t o i n t e g r a t e

i n v e s t m e n t , s av i ng , a n d g r o w t h m a k e i t v i r t u a l ly i m p o s s i b le t o u n d e r s t a n d w h ys o m e c o u n t r i e s h a v e p e r s i s t e n t c u r r e n t a c c o u n t i m b a l a n c e s . W h y , f o r e x a m -

p l e , a re C a n a d a ' s a n d A u s t r a l i a ' s c u r r e n t a c c o u n t s p e r e n n i a l l y i n d ef ic it , a n d

J a p a n ' s i n s u r p lu s , d e s p i t e w i d e s w i n g s i n t h e i r c u r r e n c i e s ' r e a l e x c h a n g e r a t es '?

O v e r l a p p i n g - g e n e r a t i o n s v a r i a n t s o f t h e i n t e r t e m p o r a l m o d e l a r e i n d i s p e n s a b l e

f o r t h i n k i n g a b o u t h o w , s a y , t h e a g i n g o f J a p a n ' s p o p u l a t i o n c o u l d e v e n t u a l l y

l e a d t o a f a ll i n J a p a n ' s p e r s i s t e n t t r a d e s u r p lu s e s .

A s p o s i t i v e d e s c r i p t i o n s o f t h e c u r r e n t a c c o u n t , t h e s i m p l e i n t e r t e m p o r a l

t h e o r i e s a r e n o t w i t h o u t t h e i r l i m i t a ti o n s . A s w e s a w a b o v e , s i m p l e t i m e - s e r i e s

m o d e l s b a s e d o n c o n s u m p t i o n s m o o t h i n g s ee m t o w o r k f a i r ly w e l l f o r so m e

c o u n t r i e s ( f o r e x a m p l e , S w e d e n ) b u t , in o t h e r c a s es , c le a r l y m i s s m u c h o f th e

a c t i o n . F u r t h e r r e s e a r c h a l l o w i n g f o r t i m e - v a r y i n g i n t e r e s t r a t e s , m u l t i p l e g o o d s ,

d u r a b l e s , n o m i n a l p r i ce r ig i d it ie s , a n d s o m e l i q u i d i ty - c o n s t r a i n e d c o n s u m e r s

m a y l e a d t o b e t t e r d e s c r i p t iv e p o w e r . I f t h e s i m p l e s t in f i n i t e l y - li v e d r e p r e s e n t a -

t i v e a g e n t m o d e l s a r e t o b e b e l i e v e d , t h e n i t i s a p u z z l e t h a t r a t i o s o f f o r e i g n

d e b t t o o u t p u t s e l d o m e x c e e d 1 :1 w h e n p l au s i b le p a r a m e t e r e s t im a t e s s u g g e st

t h a t r a t i o s o f 5:1 o r 1 0:1 c o u l d e a s i l y be s u s t a i n a b l e a n d e v e n o p t i m a l .

O b s e r v e d d e b t - G D P r a ti o s a r e e a s i e r to r a t i o n a l iz e i n e c o n o m i e s w i t h fi ni te -

l i v e d d y n a s t i e s , b u t s u c h m o d e l s , w h i l e c a p a b l e o f e m b r a c i n g a w i d e r s e t o f

e m p i r i c a l p h e n o m e n a , a l s o p o s e e m p i r i c a l p u z zl e s. A f a i r l y r o b u s t i m p l i c a t i o n

i s t h a t g o v e r n m e n t d e f i c it s l e a d t o c u r r e n t - a c c o u n t d e f i c it s , b u t t h e e m p i r i c a l

e v i d e n c e s u p p o r t i n g t h i s p r e d i c t io n , w h i l e su g g e s t iv e , is h a r d l y a b a s is f o r s t r o n g

c o n c l u s io n s . T h e s t r i k in g i n d u s t r i a l - c o u n t r y c o r r e l a t i o n o b s e r v e d o v e r 1 9 7 6 - 19 8 5

i s n o t c l e a r l y e v i d e n t l a t e r o n . P r o m i s i n g d i r e c t i o n s f o r f u t u r e i n v e s t i g a t i o n i n -

c l u d e m o d e l s w i t h m o r e d e t a i l e d i n t e r g e n e r a t i o n a l s t ru c t u r e s a n d a m o r e c o m -

p r e h e n s i v e a c c o u n t i n g o f t h e i n t e r g e n e r a t i o n a l t r a n s f e r s i m p l i e d b y f i s c a l a n d

s o c i a l i n s u r a n c e p o l i c i e s .

T h e m o d e l s w e h a v e d i s c u s s e d i n t h i s c h a p t e r p r o v i d e o n l y a s t a r t i n g p o i n t .

O b v i o u s l y , t h e t a s k o f b u i l d i n g a n d e m p i r i c a ll y a p p l y i n g r i c h e r a n d m o r e r e a l is t i c

i n t e r t e m p o r a l m o d e l s w i ll n o t b e a n e a s y o n e . B u t t h e r e is n o a v o i d i n g th isc h a l l e n g e , s i n c e t h e t w o l e a d i n g a l t e r n a t i v e s t o t h e i n t e r t e m p o r a l m o d e l a r e

s e r i o u s l y f l aw e d .

O n e a l t e r n a t i v e t h a t h a s b e e n e x p l o r e d e x t e n s i v e l y i n r e c e n t r e s e a r c h i s t h e

c o m p l e t e m a r k e t s m o d e l , in w h i c h c o u n t r y -s p e c i f ic s h o c k s o f a ll ty p e s - t o h u -

m a n a s w e l l a s fi n a n c i a l w e a l t h , t o p e r s o n a l a s w e l l a s c o r p o r a t e t a x e s - c a n b e

i n s u r e d i n t e r n a t i o n a l l y . I f th i s a p p r o a c h i s c o r r e c t , o f c o u r s e , t h e n t h e c u r r e n t

a c c o u n t i s l i tt l e m o r e t h a n a n a c c o u n t i n g c o n v e n t i o n w i t h o u t m a j o r s i g n i fi c an c e

e v e n f o r a c o u n t r y ' s r e l a t i v e w e a l t h p o s i t i o n . ( S e e t h e d i s c u s s i o n i n S e c t i o n

3 . 2 . 1 . ) W e h a v e a r g u e d t h a t r e a l - w o r l d i n t e r n a t i o n a l c a p i t a l m a r k e t s a r e v e r y

f a r f r o m t h e f r i c ti o n l e s s , f u l l - i n f o r m a t i o n , c o m p l e t e - m a r k e t s i d e a l . F a c t o r s i no




hibiting complete domestic capital markets include moral hazard problems in

lending at the microeconomic level, finite lifetimes, and difficulties in insur-

ing labor income. In international markets, these problems are compoundedby sovereign default risk, difficulties in insuring national government spending

shocks, and cultural and institutional differences. Of course, it would be vastly

preferable to model explicitly these capital-market imperfections rather than

simply to assume limited asset trade, especially for understanding the impact

of government policy. We have discussed some work along these lines and pre-

sented a simple example. Until these models have been more fully developed,

however, the intertemporal model seems to provide a much closer description

of reality than does the complete markets model.

Complete-market models represent an extreme alternative to the intertem-

poral approach. At the opposite pole are variants of the open-economy IS-LM

model due to Mundell (1968) and Fleming (1962). This approach, which ignores

intertemporal choice and even intertemporal budget constraints, remains over-

whelmingly dominant in policy circles. But as a f ramework for addressing funda-

mentally dynamic phenomena such as the current account and government debt,

the Mundell-Fleming paradigm, even when jerry-rigged with dynamic add-ons,

is fatally handicapped.

The Mundell-Fleming approach offers no valid benchmark for evaluating ex-

ternal balance. In practice, policymakers often strive to avoid a negative current

account. Just as efficient international trade generally requires unbalanced tradeacross commodity groups, however, efficient trade across time often calls for

an unbalanced current account. The intertemporal approach identifies circum-

stances, for example, a transitory fall in output or a rise in domestic investment

productivity, that justify a current account deficit. On these issues, the Mundell -

Fleming approach has nothing to say.

Evaluating the real exchange rate consistent with full employment and exter-

nal balance is another prime concern of policy: intervention or realignment dc-

cisions may hinge on the determination that a currency's value is misaligned .

Since the Mundel l-Fleming approach has nothing to say about external balance,

it is, afortiori, unable to address the possibility of misalignment.Because it lacks microfoundations or even the most basic intertempora l bud-

get constraints, the Mundell-Fleming approach provides no grounds for nor-

mative judgment s on current accounts or international macroeconomic policies.

No economist would take seriously an assessment of tax, trade, or regulatory

policy based on a model with these shortcomings. The intertemporal approach

to the current account offers a viable framework for assessing macroeconomic

policy, one that must supplant the Mundell-F leming framework for normative

questions.

It is hard to portray Mundell-Fleming as a successful positive current-account

theory, either. Without denying the theory's empirical appeal in capturing short-



Ch . 34. T h e l n t e r t emp o r a l A p p r o a c h t o th e C u r r e n t A c c o u n t 7 9 5

r u n m a c r o e c o n o m i c d e v e l o p m e n t s o v e r s o m e e p i s o d e s t h e c o re m o d e l h a s n o

c le a r m u c h le s s t e s t a b l e p r e d i c t i o n s a b o u t c u r r e n t - a c c o u n t d y n a m i c s . A g a i n a s

i n t e r t e m p o r a l m o d e l s b e c o m e m o r e t r a c ta b l e a n d e n j o y w i d e r e m p i r ic a l t e st in git s e e m s t o u s th a t th e y m u s t u l t i m a t e l y c o m e t o s u p p l a n t m o d i f ie d M u n d e l l -

F l e m i n g m o d e l s f o r p o s i t iv e a s w e l l as n o r m a t i v e q u e s t i o n s .

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Ch. 34. The lntertemporal Approach to the Current Account 1799

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38 :183 - 198 .

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