Backus, Kehoe, Kydland

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Working P a ~ e r 213

RELATIVE PRICE MOVEMENTS IN DYNAMIC GENERAL

EQUILIBRIUM MODELS OF INTERNATIONAL TRADE

by David K. Backus Patrick J. Kehoe and Finn E. Kydland

David K. Backus is a professor of economics at

the Stern School of Business New York

University; Patrick J. Kehoe is a professor of

economics at the University of Pennsylvania and

a consultant at the Federal Reserve Bank of

Minneapolis; and Finn E. Kydland is a professor

of economics at Carnegie-Mellon University

Pittsburgh and a research associate of the

Federal Reserve Bank of Cleveland. The authors

thank the National Science Foundation the

Institute for Empirical Macroeconomics and the

Center for Japan-U.S. Business and Economic

Studies faculty fellowship program for financial

support. They also thank Ronald Jones Maury

Obstfeld and Chris Stefanadis for helpful

comments.

Working papers of the Federal Reserve Bank of

Cleveland are preliminary materials circulated

to stimulate discussion and critical comment.

The views stated herein are those of the authors

and not necessarily those of the Federal Reserve

Bank of Cleveland or of the Board of Governors

of the Federal Reserve System.

November 1992

clevelandfed.org/research/workpaper/index.cfm



BSTR CT

We examine the behavior of internati onal relati ve price s from th e perspective

of dynamic gene ral equilibrium theory with par tic ula r emphasis on th e

variability of the terms of trade and the relation between the terms of trade

and net exports. We highlight aspects of the theory th at a r e criti cal in

determining these properties cont rast our perspective with those associated

with the Marshall-Lerner condition and th e Harberger-Laursen-Metzler effect

and point out fea tur es of the d at a th at have proved diff icult t o explain

within existing dynamic general equilibrium models.




ntroduction

Relative prices are a central feature of both the pure theory of

inte rna tion al tr ad e and open-economy macroeconomics. Although th e emphasis

dif fe rs in the two branches of international economics t o a gr ea t exten t the

same theory underlies theo reti cal and empirical work in each. Applications

of dynamic genera l equilibrium theory or interna tional r ea l business cycle

theory continue thi s tradition by extending a t the aggrega te level several

of the fe atu re s of sta tic tra de theory to dynamic and stochastic settings.

What thes e applications of fe r we think is

deeper understanding of the

dynamics of tr ad e and relati ve prices.

The Marshall-Lerner condition is withou t question th e most common link

between tr ad e theory and interna tional macroeconomics. In tr ad e theory thi s

elasticity condition on import demand functions determines the direction of

many comparative statics exercises and serves as a stability condition on an

otherwise st at ic theory telling us whether a disequilibrium ad justme nt

process will succeed in establishing equilibrium. In interna tional

macroeconomics the same condition is used to establis h a positive

association between the trade balance and the terms of trade or real exchange

ra te . This is the level a t which the theory is presen ted in most textbooks

and indeed in th e popular Mundell-Fleming and Dornbusch macroeconomic

models of open economies.

The macroeconomic branch of inte rna tion al economics has al so developed

insights th at ar e largely independent of the theory of tra de . The absorp tion

approach focuses on the accounting relation connecting saving investment

and the balance of tra de. What distinguishes this work from sta tic tra de

theory is it s suggestion th at the tra de balance or the closely related

cu rr en t account re fle cts th e dynamic decisions by agen ts to lend or borrow

in international capital markets. critical development f or understanding




the relation between tra de and relative prices i s the recognition th at any

dependence of th e tra de balance on the terms of t ra de implies,

as

a matter of

accounting, a similar relation with international borrowing and lending.

This connection was noted by Harberger

1950)

and Laursen and Metzler

1950)

and later incorporated by Obstfeld

1982)

and Svensson and Razin

1983)

into

explicitly dynamic theories of the balance of trade. These la te r papers

emphasize th e influence of t er ms of tr ad e movements on perma nent income, and

hence on saving. They argue tha t persistent changes in th e te rms of tra de

have larger income effects than transitory changes, and thus give rise to

potentially different relations between the trade balance and the terms of

trade. The effect , in their analysis, is a comparison between two

deterministic equilibria.

We approach tra de and rela tiv e price dynamics fro m

a

somewhat different

theor etic al traditi on, th at of dynamic general equilibrium theory. Like much

of sta ti c tr ad e theory, we use competitive consumers and producers. Unlike

t ha t work, however, our theory i s explicitly dynamic. And unlike th e modern

approach t o th e Harberger-Laursen-Metzler

effect, we consider not comparisons

between dif fer ent det ermin istic equilibria, but propert ies of equilibria in

sto cha sti c theor etic al economies. We consider in th e theor y th e same

experiment th at applied economists consider in th e data : th e correlations

between trade and relative price variables along an equilibrium path.

Somewhat to our surprise, this approach leads to substantially different

views of trade and price behavior than suggested by earlier work.

The application of dynamic general equilibrium theor y t o intern atio nal

trade has also led, in a rapidly growing number of pa pers, t o attempt s to

quantify t he theory s properties and compare them t o proper ties of national

economies. These at te mp ts have led t o a clearer understanding of which

fea ture s of the dat a can be accounted for by the present st at e of theory and




which remain anomalous. This quantitative approach gen era tes sha rpe r

predictions than quali tat ive theory and helps to focus further theoretical

work on clearly defined issues.

We elaborate on the twin themes of theoretical development and

quantitat ive properties in the re st of the paper. We st ar t , in section

2

by

documenting some of the salient properties of aggregate trade and relative

prices for

a

number of industrialized countries. These prop ertie s make

explicit the obj ect s of int ere st in theoretical economies and serve

as

a

basis of comparison with the theory.

We develop the theory in

a

series of two-country worlds, highlighting

as

we go th e roles played by diff erent theoretical featur es. Section is

devoted t o an e xchange economy in which each count ry specia lizes in

a

single

tra ded good. Here, th e variability of relative price s and th e relation

between prices and trade are governed by

a

single parameter: the elastici ty

of substitution between foreign and domestic goods. Some of the quantit ative

properties of this economy change when we consider preferences that are not

additively separable between foreign and domestic goods and that favor

consumption of home goods. This aspec t of th e the ory i s developed in section

4. We find, among oth er things, th at agents risk aversion plays

a

role in

both the dynamics of trade and prices and the relation between these two

variables.

In section

5

we compare this theory with alternatives based on the

Marshall-Lerner condition and th e Harberger-Laursen-Metzler ef fe ct . We show

th at our elasticity condition is not relat ed t o the Marshall-Lerner

condition, which is always satisf ied in our symmetric economy. With res pec t

t o t h e Harberger-Laursen-Metzler effect , we find that the persistence of

shocks is orthogonal t o th e relation between relative p rices and th e balance

of trade: fo r given preference parameters, the correlation between tra de and




prices is the same whether pr ice changes la st one period or one hundred. In

both comparisons, dynamic general equilibrium theory provides a different

perspective on trade and price fluctuations than does earlier work.

In the remaining sections, we consider extensions of the theoretical

str uct ure t ha t change some of it s quantitative fe atu res and broaden the

theory s predictions. In section 6, we explore shocks to government spending

as well as to aggregate endowments.

s

one might expect, this extension has

the potential t o change equilibrium comovements considerably. We find, fo r

example, that the sign of the relation between the trade balance and the

te rm s of tr ad e depends on the relative sizes of shocks t o endowments and

government spending, a s well a s on the elasticit y of s ubsti tution.

In section

7,

we embed th e exchange st ru ctu re of ear li er sections into

an economy with endogenous labor supply and capita l formation. The cri tica l

element here is capita l formation . With th is modification, we find tha t the

dynamics of tr ade now reflect, to a large extent, cyclical fluctuations in

physical investment. The most strik ing result is an asymmetric

cross-correlation function fo r the trad e balance and the ter ms of trad e,

which we label the S-curve. This fe atur e does not aris e in exchange

economies, whereby construction investment is zero and the cross-correlation

function is symmetric. In th is sense, the dynamics of capital formation play

an important role in connecting the dynamics of the trade balance and the

rel ativ e price of foreign t o domestic goods.

We conclude with a f ew remarks on the st reng ths and weaknesses of

existi ng dynamic general equilibrium theor ies of international trade, and

suggestions for directions the theory might take in the future.

2 Firs t

ook

a t t he Da ta

Since the ultimate objective of our theory i s t o account f or empirical




regulari t ies, we st rt by looking

at

some of th e propert ies of international

relative prices. We focu s here on th re e variables. The ter ms of tr ade ,

denoted p, i s the ra t io of the import pr ice def la tor t o the export pr ice

defl ator , both taken fro m national income and product accounts. Net export s,

denoted nx, is the rat io of expo rts minus imports, in curr ent prices, t o

out put in cu rr ent prices . Real output , denoted y, i s GDP o r GNP, depending

on th e country, in base-year prices (generally 1985). All th ree variables

a re constructed w ith da ta tak en fr om the OECD s Quarter ly National Accounts

In table 4.1 we repo rt various propert ies of th e term s of t rad e fo r

th ree countries: Japan, the United Kingdom, and th e United Sta tes. These

stat ist i cs ref er to Hodrick-Prescott f i l tered variables, and both the term s

of trade and real output ar e logarithms. Many of t he same propert ies ar e

re po rt ed in Backus, Kehoe, an d Kydland (1992b) and Blackburn and Ravn (1991)

f o r additional developed countr ies and in Mendoza (1992) f o r developing

countr ies. The sample period in tab le 4.1 ru ns fr om 1955:2 t o 1989:4, which

enables us to look separately at the periods before and af te r the collapse of

Bretton Woods.

We see, fo r

a

st ar t , t ha t movements in the ter ms of t ra de have been both

variable and persistent . The standar d deviation of term s of tr ad e

f1uc;uations ran ges f ro m 2.71 percent in th e United Kingdom t o 5.97 per cent

in Japan. Both here and in our earli er paper, variabi lity of the ter ms of

tr ad e is considerably lar ger in Japan than in oth er countries. We a r e

unsure,

at

th is point, how much of thi s additional variability reflec ts tr u e

relative p rice movement and how much has t o do with differe nces in the manner

in which tr ad e pri ces a r e constructed. Both Alterman (1991) and Graboyes

(1991) ra ise questions concerning th e quality of c urr ent t ra de price s in th e

United States, and these problems may be greater in earlier periods and other

countries. Alterman (1991) estimat es th at improved price da ta exhibit about




30

percent less variability tha n those reported here. Nevertheless, we a r e

probably on safe ground in claiming substantial variability of the terms of

tr ad e in all countries. Persistence is evident in the autocorrelations,

which a r e generally in th e neighborhood of

0.8.

Table 4.1 also verifies that

the re has been much more variability of the te rms of t ra de since the advent

of floating exchange rat es than before,

a

feature stressed by Mussa 1986)

fo r rea l exchange ra te s rat ios of consumer price indexes converted

a t

spot

exchange rates) . Standard deviations of th e terms of trad e ar e typically two

t o three times larger in the l att er period.

We als o include, in tabl e 4.1, c orrel ation s of t he te rm s of t ra de with

net exports and rea l output. With respect to net exports, we find great er

coherence across periods, but litt le acros s countries. The ter ms of tr ad e

and net exports have generally been positively correlated in the United

St at es and negatively cor rel ate d in Japan and th e United Kingdom. We see in

tab le 4.2, which covers th e post-Bretton Woods period f o r 1 countries, that

th e United Sta te s is an outlier in thi s regard: The correlation between th e

tra de balance and the te rms of tra de i s negative fo r every other country.

With respect to output, th er e has been no regularity in th e correlation with

the terms of trade, either over time or across countries.

The contemporaneous correlation between net exports and the terms of

tra de fai ls to ca pture a n important regularity that appears when we examine

th e complete cross-correlation function: the correlations, tha t is, between

pt and n ~ ~ + ~ ,o r various lead s and lags k. The contemporaneous corre lati on

re fe rs to k=O. For positive k th e correlations perta in to net exports and

pa st prices, and fo r negative k th e reverse. We find f o r Japan and th e

United Kingdom that this function has an asymmetric S shape, which we call

the S-curve.

For Japan and the United Kingdom, this feature appears not only

in the postwar period

as a

whole, but in th e pre- and post-Bret ton Woods




subperiods as well. For the United Sta tes, the same pat ter n is evident only

in the earl ie r period. Our ea rli er paper (Backus, Kehoe, and Kydland, 1992b,

f igure

1

documents th is pa tte rn in eight of eleven countrie s.

In the remainder of the paper, we examine these properties from the

perspective of

a

series of successively more complex dynamic general

equilibrium models, bringing additional data to bear when the theory suggests

it. For now, we note th at th e ter ms of tra de has been highly variable and

persistent in all three countries, that i ts correlation with net exports is

generally negative, and th at the cross-correlation function fo r net exports

and the term s of t ra de is often asymmetric (the S-curve property).

Dynamic Exchange Economy

One of the simplest dynamic general equilibrium models of

a

world

economy has two countries tha t tra de specialized endowments. Let time t run

from an ini t ial date to

a

termina l da te T, possibly infinite . The

evolution of thi s endowment is st ochast ic, given by

a

Debreu tree th at we

describe in notation adapted from Lucas (1984). The st at e zL n element of

t

t h e s e t Z , denotes th e history of the economy fro m da te through t Each

t

of these possible s ta te s occurs with a probability n(z

1.

Country 1, which

we call the home country, is endowed with

a str ea m of positive quanti tie s of

t

the home good, denoted {y (z 1 or, in shorthand notation, simply (yl).

1

Likewise, co untry 2, t he fo reign country, i s endowed with th e positive

sequence (y of quan titi es of th e foreign good. We denote th e pric es of th e

2

t t t

domestic and foreign goods in st at e z by ql(z and q2(z

1.

As in section

t t t

2, we define the te rms of trad e, p(z = q ( z 1/q

(z 1, as

the relative price

2

1

of imports t o exports.

Each country is represented by

a

single consumer, who stands in for

a

larg e number of like agents. The preferen ces of th e consumer of country i




a re chara cterized by th e expected utility function

with O<p<l, U(c)

=

cl- /(l- ), and

p O

We re fe r to as the risk aversion

parameter.

Both agents consume composites of the foreign and domestic goods,

described by the Armington aggregator functions,

c (a b

=

G(al,bl), c (b ,a = G(b2,a2),

1 1 1 2 2 2

with

1-a 1-a

l / l -a)

G(a,b)

=

[wa + b

where a. and b. a r e th e quant ities of th e domestic and fore ign good consumed

by th e agen t of country i. Thus, th e agents of each country consume

combinations of fore ign and domestic goods, a s expressed in the function

G.

This theore tical device, due t o Armington (19691, is widely used in

computable st a ti c general equilibrium tr ad e models. In th is economy it is

equivalent to giving consumers preferences over foreign and domestic goods

directly. The two paramete rs,

a >O

and w>O, govern the elasticity of

subst itutio n and sha res of foreign and domestic goods. The elas ticit y is

cr=l/a. With w=l, th e two consumers have iden tica l pref eren ces, and with w>l

they exhibit a pref eren ce fo r home goods: If home and foreign goods sell fo r

the same price,

agents consume more of the home good than the foreign good.

The budget constr aint of t he domestic agent is

The foreign agent faces an analogous constraint.

A competitive equilibrium in th is economy cons ists of s tate -con tingent

quantities ( a b. and prices (q i) such tha t (i ) consumers maximize utility

i




given prices and budget constraints and (i i) quanti t ies sat isfy t he resource

constraints ,

t

f o r each st at e We find i t convenient t o compute an equilibrium using th e

Negishi-Mantel algo rithm in which, f o r any initial distri butio n of resou rces,

a competitive allocation is associated with a Par et o optimum. Each optimum

is the solution t o a problem of the form: For some choice of positive

welfare weights

A

,A

,

choose quantities

(a

a b b in each s ta te t o

1 2 1 2 1 2

maximize C.A.u subjec t t o the resource const raint s. The supporting price s

i

can then be identified with the Lagrange multipliers on the constraints or

derived fr om consumers fir st- ord er conditions. Backus (1992, secti on 2 )

describes th is procedure in similar conte xt and discusses alter nativ e

decentralization schemes.

For the optimum problem, let us denote the Lagrange multipliers on the

t t

t

resource constraints in state z

by ql(z

1

and q2(z fo r the domestic and

forei gn goods, respectively. The Lagrange multipliers correspond t o price s

in the associated competitive equilibrium. If, fo r each i, we define spot

t t

price functions i by qi(z 1 = /3t n(z t)~ i(z , then the optimum problem

t

separates into

a

number of identical problems, one fo r each sta te z , of the

form

t t t t t t

max

3

n(z

1

{AIU(G[al(z ), bl (z

11)

+ A2U(G[b2(z 1,a2(z 11))

{a bi}

subject to the resource constraints . The first -orde r conditions fo r each

s t a t e a r e




t t t t t

The ter ms of t rad e is p(z

=

q ( z )/q ( z

=

Q (z )/Ql(z

.

2 1

2

In this section, we rest ric t ourselves to the ca se of identical

pref eren ces, w=l, f o r which th e analysis can be done analytically. The

equilibrium allocation is then

f o r countries i=1,2, with consumption sh are s s

=

hi

i

l//,Y

.A

t ha t s um t o

one. Backus (1992) describes how th e wel far e weights, and hence th e shar es,

a r e relat ed t o the endowments. The properti es of intere st, however, do not

depend on th e choice of weights, so we can skip th is additional step. The

supporting prices are, up to

a

fa ct or of proportionality,

and the equilibrium terms of trade is

The tra de balance in country 1 is, in units of th e domestic good,

In equilibrium, the rati o of the tr ade balance to output (the form of the

trade variable used in table 4.1) is

Along any equilibrium path for this economy the welfare weights, hi, are

constant. The consumption shar es, s ar e functions of the welf are weights

i




alone, so they ar e constant

as

well. Thus, fluctuations in both the trad e

balance and t he ter ms of tr ad e ar e driven, along any equilibrium path, only

by movements in th e endowment rat io, y2/y1. In th is sense, equilib rium

prices and quantit ies are functions of a s ingle sta te variable, the r ati o

y2/y1, and ar e th us indirectly rela ted t o each other.

Although th e theory i s fairly simple, we can s ta rt t o compare some of

it s propert ies with those of the da ta in particula r, the variabil i ty and

persistence of th e terms of tr ade, p, and the correlation of th e term s of

tra de with net exports . Clearly, th e variabil i ty of p i s governed by the

variability of th e endowment rati o, y2/y1, and th e substitution par amet er,

cr=l/a. A given amount of variability of th e endowment ra ti o can produce as

much price variability as we like if cr i s smal l enough. As an exampl e,

consider th e standar d deviation of the US term s of tr ade reported in table

4.1: percent , fo r th e period as

a

whole . This ref ers to the s tandard

deviation of the Hodrick-Prescott fil ter ed logarithm. The stan dar d deviation

of the fi lte red logarithm of the ra tio of Japanese to US output is about 2.2.

To gene rate t he amount of pr ice variability we see in the United St ate s,

then, we need an elas tici ty of about cr=0.73 since 2.2/0.73=3.01. Thi s i s

only a rough calculation, s ince the da ta re fe r t o a world with more than one

country and in which a

large par t of t he variabil i ty of output appears in

investment, which i s obviously absent here. But i t is suggestive of th e role

played by th e elasticity of substitu tion in generat ing relative p rice

variability. As

a

rule, th e theory can produce any amount of price

variability we like if t he elasticity of su bstitutio n is

a

free parameter .

With rega rd to persistence, t he terms of tr ad e inherit s th e

autocor relation properties of th e endowment rati o. To continue our example,

the autocorrelation of t he Japan/US output ratio the fi l t ered logarithm,

tha t is) is 0.7, so the autocorrelation of th e terms of trad e, in our theory,




is

also 0.7. This is sl ightly less than we see fo r the US terms of t rad e in

table 4.1, but t he discrepancy

is

not large, either economically or

stat is t ically.

The final issue concerns the relat ion between th e tra de balance and th e

ter ms of trade. The contemporaneous relation

is

summarized by

roposition

I Let o=l in the Armington aggregator,

G

Then the relat ion

between th e tr ad e balance, nx /y and th e ter ms of tr ade , p,

is

governed by

1 1

c=l /a, th e elastic ity of substitution between forei gn and domestic goods. If

c>l , the two var iables a re posi tively re la ted; i f 6 1 , they a re negatively

related.

More precisely, consider tw o sta te s with endowment ra tio s x=y /y and

2 1

x1=y /y with x> xl . Since p is a decreasing function of the endowment

2 1

rati o, p< pl . Now consider the tr ad e balance. If c> l, then nx/y nx1 /y .

In this case, th e sta te with higher p also has higher nx/y and th e two

variables are, in thi s sense, positively related. If c<l, th e reverse is

t rue . A similar result is implicit in Stockman and Svensson (1987, section

5.3 .

If c= l, th e trade balance

is

constant, as noted recently by Cole and

Obstfeld (1991). Except f o r nonlinearities and nonstationarities, th e

correlation is ei ther +1 o r -1, unless c= l, when the tr ad e balance is

constant and the correlation is not defined.

The dynamics of the relation between trade and prices, like the dynamics

of prices, are determined completely by the dynamics of the endowment ratio.

Except fo r nonlinearities and nonstationarities, th e cross-correlation

funct ion for the t rad e balance and the terms of t ra de

is

the same

as

t h e

aut oco rre lat ion func tion of th e endowment rat io. By way of example, suppose

th e logarithm of th e endowment rat io

is AR(l), with autocorrelation p>O.

Then if c> l, the cross-correlation function fo r the tra de balance and the




te rm s of tr ad e is tent-shaped: The contemporaneous correlat ion is +1 and the

correlat ion between p and nx is p l k . If c< l, th e function is V-shaped.

t t+k

Even with other autocorrelat ion patterns, th e cross-correlat ion function will

be symmetric since th e autocorrelation function is. The exchange economy,

there fore, is incapable of reproducing the asymmetric correlat ion functio ns

pictured in figure 4.1.

4 Pr e f e r e n c e f o r Hom e Goo ds

When consumers in the two countries have preferences that favor their

resp ectiv e home goods (w>l in the Armington agg reg ato r GI the behavior of

tr ad e and price s changes somewhat. When pref erenc es f o r domestic and forei gn

goods ar e not addit ively separable, we find tha t th e risk aversion para meter,

7, a s well a s the elast ici ty of substi tut ion between foreign and domestic

goods, c=l/a, plays a role in the relat ion between the tr ad e balance and th e

terms of t rade .

The simplest case is y=a: risk aversion (7) is the inverse of t he

substi tut ion elast ici ty f o r foreign and domestic goods c=l/a). With this

restrict ion, preferences, including th e aggregator, ar e additively separable

between the foreign and domestic goods, simplifying the analysis

considerab ly. We compute an equilibrium, as before, fr om an optimum. The

reade r may verify th at th e equil ibrium allocations, f o r countries i=1,2, a re

a a

where the consumption shares, s1 (ohl)1/~[(whl)1/ +h~ 7~, s2 1-sa sb

1 1

b b

1

/ /[~11/ +(w~2)1/ l, an d s 1-5 a r e constant along any equilibrium

2 1

path. The only difference from t he symmetric case is th at the consumption

sha res now diff er acros s goods, with lar ger values of w leading to larger

a

shares of home good consumption,

s

and

sb

The supporting prices are

1 2




so the equilibrium terms of trade is

s

before, th e rela tive price p is driven by the endowment rati o. The only

change is the factor of proportionality, which does not affect the properties

of the logarithm of p. The variability of the term s of tr ad e is determin ed

by th e variability of t he endowment rati o, y2/y1, and the elas ticity of

substitution, cr=l/a

The tra de balance fo r country 1 in this economy, expressed a s a r at io t o

domestic output, is

We can se e tha t pre fere nce f or home goods (w>l) has th e e ff ec t of damping

fluctuations in the balance of trade, since larger values of

w

imply smaller

values of

sb

Comovements, however, do not change: The sign of the ef fe ct

1

of th e endowment ra ti o on the balance of tr ade once more hinges on whether

cr=l/a is greater or less than one and does not depend on any other

parame ters. Thus, the properties described in the previous section f o r

identical pref erences (w=l) apply to t hi s economy a s well.

It should be clear , then, t ha t any influence of t he home pref eren ce

par am ete r, w, on price behavior must op erat e through nonseparabilities

between domestic and foreign goods dif fe ren t values of a and y. The

allocation of goods between countries is influenced, in this case, by the

sign of a-y. The fir st- ord er conditions do not admit a simple analytic

solution, but the intuition behind the equilibrium allocation is fairly

straightforward.

s

before, the variables of inter est ar e functions of the




endowment ratio , x=y /y In st at es with high values of x, the ra ti os of

2 1

forei gn t o domestic good consumption, b./ai, and t h e agg reg ate consumption

rat io, c /c a re also high: They a r e increasing functions, in other words,

1

of th e endowment ra ti o x. Neither prope rty

s

surprising: If th er e

s

relatively more of t he forei gn good, then in equilibrium both ag ent s consume

relatively more, and aggregate consumption favors the country whose

prefe rence s weight the foreign good more (country 2, since w>l). In simple

terms , let t he foreign and domestic goods be bananas and apples, an d suppose

th e foreign agent pre fer s bananas (w>l) and th e domestic agent pr ef er s

apples. Then the two statements are , f irs t , tha t in sta tes with relatively

more bananas, both agents consume relatively more bananas than apples and,

second, that aggregate consumption by the foreign agent, who has

a

stronger

preference f or bananas, r ise s proportionately more than consumption by the

domestic agent. Proofs of both of these statemen ts a r e included in th e

appendix.

From this starting point, we can deduce the effects on the relative

price of t he foreign good and th e balance of trad e. Consider th e price.

From th e first-orde r conditions, reported in the previous section, we see

th at th e terms of t r ade sat isf ies the relat ions

where for convenience we have dropped explicit dependence of variables on the

t

sta te, z Since b

/a

and b2/a2 a r e increasing functions of the endowment

1 1

rat io x , the terms of t r ade

s a

decreasing function. Thus, an incre ase in

th e rela tive supply of the forei gn good lowers it s rela tive price. With

somewhat great er e ffo rt we can chara cteri ze the magnitude of th e decline.

The first step is to relate the endowment ratio to bl/al.

The resource

const raint s imply




b

where s1=bl/y2 i s th e (possibly state-depen dent) sh ar e of fo reig n good

consumption by th e agen t of country 1. Thus, with

0 1 , the proportional

change in b /a can be either gre ate r or less tha n the proportional change in

1 1

x, depending on whether sb increases or decreases with x.

The second step

1

follows from th e first- orde r conditions fo r the foreign good:

Since c /c is an increa sing function of th e endowment rat io, sb is

2 1 1

increasing in x if p a , decreasing if ;r<a, and constant if ;r=a (thi s being

the additively separable case described earli er) . Thus, the (absolute value

of t he ) slope of t he relation between the logarithms of the term s of t ra de ,

p, and the endowment ratio , x, is gre ate r than if y>a, less than if y<a,

and equal to (a s we ve already seen) if y=a. Other things equal, gr ea te r

risk aversion tends to increase the variability of t he term s of tr ad e

relative t o tha t of the endowment ratio.

The contemporaneous relation between the trade balance and the terms of

trade is characterized by

Proposition

2

Let

w l

(preferen ce f o r home goods). Then the re exist s a

positive number cr* such that if cr>cr*, th e tr ade balance, nx /y is

1 1

positively rela ted t o the term s of t ra de , p, and if crccr*, th e two variables

a r e negatively rel ated . Furthermore, if ;r>l, then cr*<l.

Thus, the risk aversion parameter, ;r has an influence on comovements between

th e tr ad e balance and the terms of trad e. The proof consists largely of

expressing the ra tio of t he tr ad e balance to output in a convenient form. A s

in Proposition 1, both th e tra de balance and the te rms of tr ad e a re monotonic




functions of th e endowment rat io x=y /y The ter ms of trad e is , fo r al l

2 1

para mete r values, decreasing in x. As f o r th e tr ad e balance, we let

a

With w=l, s l is constant . Since bl/al is,

as

we have shown, increasing in

th e endowment ra ti o x=y /y th e proposition follows immediately with cr*=l.

2 1

a

With w>l, the dependence of

s

on x introduces an additional element of

1

dependence on x. If ;r>l and a<;r, sa is increasing in x. Thus, f o r as1 the

1

tr ad e balance is decreasing in x. Since th e solution is continuous in th e

parameters , this i s t rue f or values of a slightly greater than 1 as well .

For la rge values of a , however, th e trad e balance is increasing in x,

as

we

show in th e appendix (resu lt [A41). Thus, the re ar e numbers

a >l

and

cr*=l/a*<l t h a t divide regi ons of positive and negative comovement between th e

t rad e balance and the terms of t rade.

In sho rt, th is economy is much like th at of the previous section. It s

simi lari ties and differences a re illustrated by th e following example.

Example Let there be two states, with unconditional probabilities

1 2 1 2 ( Nonl inea ri ti es a r e i rr el evan t her e, s ince t w o poi nt s c a n a lw ays

be connected by a

str aig ht line.) Let the aggreg ate endowments (y y of

1 2

the domestic and foreign goods be (l+e, l-E) in state 1, (I-e, l+e) in state 2,

with e>O Thus, th e stan dard deviations of y and y a r e e and the s tandard

1 2

deviation of th e logarithm of the endowment ra ti o y /y is, f o r small e ,

2 1

approximately 2e.

The transition probabilities between states i and j a r e

The persistence parameter p governs the autocorrelation function for any

random variable adapted to the state , with the k-order autocorrelation equal

k

t o p




Case 1: identical pref eren ces

w=l ) .

The terms of t rade is

which equ al s [ 1 + ~ ) / 1 -~ )1 -~n s t a t e 1 and [ l - c ) / l + c l ~ - ~n state 2.

The

sta nda rd deviation of th e logarithm of p is, f o r small c, approximately

a 2c ). With

c=0.05

and a=5, the standard deviation is 0.500. The ratio of

the t rade balance t o output is

Thus, f or cr=l/a<l, th e correlation between p and tb

is

-1, and f o r cr>l t he

correlation is l. For a=l, the trade balance is zero in both sta te s and the

correlation is not defined. Note th at the persistence para meter , p, has no

bearing on this correlation. The cross-correlation function fo r the tr ad e

balance and the terms of trade has the form

where cr=l/a.

As noted earlier, this function is symmetric in k.

Case 2: pref eren ce f or home goods w>l ) . To make this concrete, let

c=0.05, w=2, and 7=2. With a=5, the stand ard deviation of th e logarithm of

th e ter ms of tr ad e is 0.497, slightly smaller than in th e case of identical

preferences. There is

a

cr it ic al value cr*=O.885<1 of t h e ela sti cit y of

substitution such th at f or cr>cr*, the tra de balance and th e te rms of tr ad e a r e

positively corr elat ed, and f o r crccr* they a r e negatively cor rela ted. The

cross-correlation function is

which remains symmetric.






These conditions together imply balanced trade:

Utility maximization by both agents, subje ct t o thei r respe ctive budget

constraints, res ult s in import demand functions, say a2 p) and bl p). These

functions define net exports

as a function of th e ter ms of trade :

This function is increasing in p if

*

>

1,

where

=

- abl/ap)[p/bl)

and

e

= aa2/ap) p/a2)

a r e th e domestic and foreign import elasticities. The inequality is th e

well-known Marshall-Lerner condition.

We now apply th is an alysi s t o our economy. The relevant import demand

funct ions a re

bl p)

=

yl/ p+pD)

where, as before , cr=l/a is the elasti city of substit ution between foreign and

domestic goods.

The import elasticities a re therefore

cr-1

E

= l+crp )/ p+pC),




Adding these two expressions, we find that for all positive p and cr,

E E 1.

In other words, t he Marshall-Lerner condition is always satisfi ed in this

economy, rega rdle ss of t he value of the elast icity of sub stitut ion between

foreign and domestic goods. This example illu stra tes more general result ,

cited by Eth ier 1988, secti on A.3 : The Marshall-Lerner condition is alwa ys

satisfied when consumers in the two countries have identical homothetic

preferences.

Clearly, the Marshall-Lerner condition ha s no connection with t he

elast icity condition of Proposition 1 and theref ore has no bearing on the

correlation between the tr ad e balance and the terms of t rad e fo r time series

da ta gener ated by economies like ours. The differe nce in res ul ts stems , we

think, f rom t he difference between dynamic modeling and the st at ic analysis

th at underlies th e Marshall-Lerner condition. Despite th e intuitive appeal

of t he la tt er, we find t ha t when the dynamics ar e worked out explicitly, we

get

a

differe nt int erpreta tion of this property of the data.

The theoretical s ta te of the art regarding the relation between the

tra de balance and the te rm s of tra de, however, is not th e Marshall-Lerner

condition but th e 1980s revival of th e Harberger-Laursen-Metzler effect

ini tia ted by Obstfeld 1982) and Svensson and Razin 1983). These pap ers ,

and others that followed, st rt with the central insight of the absorption

approach: th at trad e imbalances reflec t differences between saving and

investment. The theoretical economies of these two papers a r e deterministic

but share with ours the fe at ure tha t dynamics are explicit. They come,

however, to much different conclusions regarding the factors that lead to

positive association between the trad e balance and the te rm s of trad e. These

papers suggest th at two fac tors ar e critical in determining the pat tern of




comovements: the persistence of the shock and the form of dependence of the

discount fac to r, or rat e of time preference, on fut ure utility. Transi tory

shocks typically lead, in their analy sis, to movements in the ter ms of t ra de

and th e tr ad e balance of opposite sign. We find, in con tras t, th at the

relation between the trade balance and the terms of trade is independent of

the dynamics of prices.

The aforementioned papers also find that the effect of permanent shocks

depends on the behavior of the discount factor.

s

Svensson and Razin (1983,

p. 100) put it: A permanent terms- of-trad e deteri oratio n cause s a

deterioration or improvement in the real trade balance, depending on whether

the rate of time preference decreases or increases, respectively, with

th e level of welfar e. Obstfeld (1982) assumes th at th e ra te of time

preference is increasing in utility and therefore predicts a decline in the

t ra de balance. In his words (1982, p. 2511, ...an economy specialized in

production must experience a fall in aggregate spending and a current

[account] surplu s as a resu lt of an unanticipated, permanent worsening in it s

term s of trade . In both papers th ere is no eff ect of a permanent change in

price on the tra de balance if the ra te of time preference is constant. In

our economies, the rate of time preference is constant, fixed by the discount

fac tor

p

The conclusion should then be that permanent movements in the

ter ms of tr ad e have no effe ct on th e tr ad e balance. We find, instead, th at

th e relation between the trad e balance and the ter ms of tra de is determined

by th e elasticity of subs titution, reg ardles s of t he persistence of shocks.

s

in our analysis of t he Marshall-Lerner condition, t he diffe rence

between our approach and that of the

Harberger-Laursen-Metzler

l i tera ture

stems , in pa rt, f rom our definition of the issue. In our analysis, th e

relation between t he trad e balance and the te rms of tra de per tains to th e

correlation between these two variables for a single time series realization,




like the quarterly series for Japan, the United Kingdom, and the United

St at es described in table 4.1. This corresponds, in our theoretical

economies, t o th e corr elation between the t wo variabl es along an equilibrium

path. In t he anal ysis of Obstfeld 1982) and Svensson and Razin 19831,

however, the


effect pertains to a comparison

between two diff eren t deterministic equilibria: one in which th e te rm s of

tr ad e is high, and one in which it is low. Apparently these two thought

experiments emphasize much diff eren t fe at ur es of t he theory. We would argu e

th at our thought experiment is closer t o what we have in mind when we compare

theory and data. A closer look also suggests,

as

brought out in Backus

1992) and Stockman and Svensson 19871, th at th e theory re qui res expl icit

treatment of the stochastic structure of the economy, something that

deterministic analysis obviously cannot provide.

One way in which these t wo points of view might be reconciled

s

t o

consider economies in which agen ts have more limited ability t o hedge ris k

than they do in th e complete marke t economies of sections and 4. In th e

1980s analysis of th e


effect, income effects play a

central role. In our economies, however, ther e ar e no income eff ect s along

an equilibrium path. With complete marke ts, eac h age nt has a single, date-0

budget const rain t. As

a

result , each has

a

state-invariant marginal utility

of income, refle cte d in the const ant welf are weights of ou r optimum problem.

Backus 19921, Kehoe and Richardson 19851, an d Mendoza 1992) sug ges t t ha t

some of the flavor of the Harberger-Laursen-Metzler

l i terature may carry over

t o dynamic stoc has tic setti ngs wi th some types of mark et incompleteness.

In short, we find that explicit dynamic stochastic analysis of trade and

relative prices leads to much dif fere nt views of t he fa ct or s determining

the ir comovements. Even th e role of th a t textbook stan dard, the

Marshall-Lerner condition, may need to be reconsidered.




Government Spending

The theory thus f a r has focused on fluctuations in trad e and prices

arisi ng fro m movements in endowments. Here we consider an extension to th e

excha nge economy of section in which we have, in addit ion, exogenous shocks

t o government spending. Related anal yses have been provided by Baxte r

(1992), Buiter (19891, Hodrick (19881, Macklem (19901, Obstfe ld (1989),

Reynolds (1991), and Yi (1991). We fi nd thi s extension both int er es ti ng in

i t s own right and a useful ste p toward introducing

a

wide range of impulses

int o dynamic gener al equilibrium models of tra de: shocks, f o r example, to

ta xe s, ta ri ff s, and possibly even monetary policies. To keep th e analysis

simple, we res tr ic t ourselves t o the ca se of symmetric preferences

w=l

in

the Armington aggregator

GI.

In th is new economy, t he government i s an additi onal consumer of goods.

Let us sa y th at in st at e zt th e government of country i consumes th e quantity

g.(z of i ts home good. This spending is financed with lump-sum t ax es , say

r i (z .

An equilibrium then consists of quantities

(a

and b i , prices (qi) ,

i

and government policies (g. ,~.) such th at (i ) agent s maximize utility given

prices and budget constraints, ( ii) quantities satis fy th e resource

constraints,

and (iii) policies s atisf y governments' budget const raints.

With thi s stru ctu re, th e economy is equivalent t o one with net

endowments yi-gi, r at he r tha n y and we can apply most of th e re su lt s of

i

sec tio n with lit tle change. The equilibrium allocation includes




f o r i=1,2, with consumption shar es

s = x /'/z.x /'

for some choice of

i

J J

welfare weights

A

The equilibrium term s of t ra de i s

The variability of t he te rms of t ra de is governed, then, by th e variability

of th e net endowment rati o and the elasticity of substitution, cr=l/a. In

practice, th e addition of government purchases has li ttl e influence on the

variance of p, since g is only

a

fra cti on of out put and is generally less

variable. The same reasoning applies t o persistence: Introducing government

purchases of goods and services does litt le to change our prediction t ha t

relative prices retain the persistence of output ratios.

The most interes ting consequences of government purchases concern t rad e.

If w.=y.-g. i s th e endowment net of government purchases, ne t ex port s in

country 1 are

a

nxl(z

1 =

(1-sl)wl(z

1

[w2(z )/wl(z

11

slw2(z

The ratio of net exports to output is

1-a

nxl(z l/yl(z

1

= ((1-sll

-

sl[w2(z )/wl(z 11 } wl(z )/yl(z

1

In our earli er analysis, g was zero and the las t term was, therefore , one.

1

As

a

result, the effect of the endowment ratio on the trade balance, and the

association between movements in th e tr ad e balance, nx /y and the ter ms of

1 1

tr ad e, p, depended only on th e value of cr=l/a. Fo r cr<l th e asso ciat ion was

positive; for cr<l th e reverse. Here we find an additional fac to r, the ra ti o

of th e net endowment, w to to ta l output, y

1 1




We can ge t some idea of t he contri butions of outpu t and government

spending shocks on trade and price fluctuations by considering special cases.

Consider, fi rs t, th e case in which g is proportional t o y Then wl/yl is

1 1

constant, and the relation between the trade balance and the terms of trade

is determined by cr,

as

i t wa s in Proposition 1. With a>l (or u<l) , the t rade

balance and the te rms of tr ad e a re positively rel ated along an equilibrium

path; wit h cr<l, they a r e negatively relat ed. Alternatively, suppose outpu ts

y. ar e constant and g is th e only shock. Then the tra de balance and the

1

te rms of tr ad e a r e positively associated, re gardl ess of the value of cr. This

example is like many others in economics in which the comovement between two

endogenous variables depends on the source of their fluctuations.

This analysis suggests a second look

at

trade and price data, with

spec ial atte ntion paid t o government purchases. As we see in tab le 4.2,

there has been lit t le regularity across countries in either the variability

of government purchases relative to th at of r eal output, o r in the

corre latio n between these two variables. The same state ment applies to the

corre latio ns of government purchases with t he tra de balance and the t er ms of

tra de. That is not t o say th at government purchases have not played a role

in tr ad e and price behavior, but t ha t th is role i s not simple enough t o show

up in summary st at is ti cs of th is form. Froot and Rogoff (1991) document

somewhat stronger indications of

a

relation between government spending and

real exchange rates using different methods.

7

Trade and Capital Formation

In th e exchange economies of sections and 4, we compared pro per tie s of

t h e da ta with analogous properties of tr ad e and relative prices in simple

theor etica l economies. This analysis brought up two questions th at deserve

a

close r look. We found, f o r one thing, th at the variability of th e te rm s of




tr ad e is governed by the variability of t he output ra tio and the elasticity

of substitution between foreign and domestic goods. By choosing a smal l

enough elasticity, th e theory can genera te literally any amount of relative

price variability. The question, in this case, is whether price variability

in the theory and the da ta a re close f or reasonable values of this

elastic ity. In anothe r res pec t, we found th at the exchange economy could

not, f o r any choice of parame ter values, mimic the data: th e cross-

correlation function fo r the tra de balance and the terms of trad e. In the

da ta this function is generally asymmetric, a fe atu re we document in figure

4.1 and label the S-curve. In th e exchange economy, however, th e function is

symmetric by construction, since both the trade balance and the terms of

tr ade a re functions of t he same st at e variable. The question here is whether

this property changes when we introduce physical capital formation.

The introduction of capital formation brings us closer to the theme of

th e absorption approach to the balance of payments: th at fluctua tions in

trade reflect differences between saving and investment.

s

a mat te r of pure

accounting, thi s connection i s undeniable, but i t als o shi ft s one s attenti on

away from within-period relativ e prices to the intertempora l decisions to

save and invest. Thus, Sachs (1981) argues tha t trad e deficits often re fle ct

investment booms and Stockman and Svensson (19871 tie both trade and relative

price s to flu ctu atio ns in, among othe r things, fixed capita l forma tion. We

continue this tradition by introducing capital formation to an economy that

is otherwise like our earlier ones. The str uc tur e is adapted fr om Backus,

Kehoe, and Kydland (1992b). The emphasis, as in earli er s ection s, i s on the

dynamics of the tr ad e balance and the term s of trade.

The theoretical economy has the following elements. There are , a s

before, two countries tha t specialize in differ ent goods. Prefe rence s of the

representative consumer in each country

i

are characterized by an expected




util ity function of t he for m

where c and n a r e consumption and hours worked in country i, U(c,l-n)

i t i t

[cp(l-n) - 1 -~/(1-7), and

720

The primary difference in preferences from

th e economy of section 3 is the appearance of leisure in agents uti l i ty

functions.

Goods in th e two countries, labeled

a

fo r country 1 and b fo r

country 2, a r e produced using capital, k, and labor , n, with lin ear

8

1-8

homogeneous production functio ns of th e same form , F(k,n) k n This

gives rise to the date- t resource constraints,

in countries 1 and 2, respectively. The qua ntit y y denote s GDP in country

i t

i, measured in units of th e local good, and

a

and bit denote uses of t he

i t

two goods in country i. If k and n ar e constant, this reduces to the pure

exchange setti ng of section 3, with productivity shocks giving ri se t o

proportionate output fluctuations.

The vector zt (zlt,z2t) is

a

stochastic

shock to productivity whose proper ties will be described shortly.

Consumption, i nvestme nt, and government spending in each country a r e

composites of the foreign and domestic goods, with

1-a 1-all/(l-a)

where, as before, G(a,b) [wa +b The para mete rs a a nd a r e

both positive, and the elastic ity of substitut ion between foreign an d

domestic goods is cr=l/a As noted earl ier, t his s tru ctu re i s widely used in




st at ic general equilibrium models of trad e. Capital stocks evolve according

t o

where 6 is the depreciation rate. Two differences between th is economy and

th e exchange economy of sections 3 5 ar e the introduction of capital

form ation and th e assumption here th at government spending may have some

foreign content.

Finally, th e underlying shocks to our economy a r e independent biva riat e

autoregressio ns. The technology shocks follow

Z

where is distr ibute d normally and independently over time with variance

vz

The correlation between the technology shocks, z and z is determined

1 2

by th e off-diagonal elements of and VZ

Similarly, shocks to government

spending are governed by

where g (g ,g and

cg

is distributed normally with variance V

t I t 2 t g

Technology shocks, z, and government spending shocks, g, are independent.

With these elements, and the parameter values listed in table 4.3, we

can approach th e behavior of the ter ms of trade. The critical parameters,

f o r our purposes, a r e the elastic ity of substitution, cr, which we s et equal

to 1.5, and th e steady-sta te rat io of imports t o GDP, which we se t equal to

0.15 by choosing appro pria tely. In th is benchmark version of th e economy,

foreign and domestic goods ar e bette r sub stitu tes than they would be with

Cobb-Douglas pref eren ces (cr=l) and imports a re , on a verage, 85 percent of

GDP. The choice of elasticit y is in the range of esti mates fr om a large

number of stu die s, a s documented by Whalley (1985, ch. 4). Est ima tes of t he




elasticity a r e generally close t o one, and often slightly larger. The import

sha re is slightly larger than we see in the United Stat es, Japan, o r an

aggre gate of European countries with intra-European tr ad e netted out), but

smaller than we see for most countries individually.

A number of properties of th e theoretical economy with alt erna tive

parameter settings a r e reported in table 4.4. Consider, fi rs t , fluctuations

in th e term s of trade . The standard deviation of the term s of t ra de with our

benchmark parameter values is 0.48 percent, which is a fa cto r of s ix less

tha n we see fo r th e United St at es in tab le 4.1. With smal ler values of cr,

the theoretical economy generates gre ate r variabili ty of the te rms of trade.

s

illustrated in fi gur e 4.2, the standa rd deviation of p gets lar ger as we

decrease c , and fo r cr less than 0. 03 the stan dard deviation exceeds

2.

Thus,

it appears that while the theory can produce as much variability in the terms

of trade as we see in the data, i t requires an elasticity of substitution

much smaller than most existing estimates.

The value of

cr required to match th e variability of th e terms of tr ad e

in US da ta i s substantially smaller in thi s model less than

0.03

than in

our calculation in section 3 fo r th e United Sta tes and Japan fo r which we

estimated t ha t w=0.73 would be sufficient) . Three fac to rs account f o r most

of this difference. The fi rs t is th at the theoretical economy has, in the

benchmark case, about 25 percent less variability in th e output rati o tha n we

calculated f o r Japan and th e United States. Modifications of the theory tha t

bring the magnitude of business cycles closer to th e da ta will also bring t he

theory and dat a closer together with respect t o price variabili ty. The

second fa ct or is capital formation. If we eliminate capi tal which we can do

by setting

8=0

in the production function), the economy generates

considerably grea te r price variability, despite less variability in the rat io

of outputs. The final fac tor is the import share. If the import sha re is




raised fro m 0.15 to 0.25, t he variability increases substantially a t every

value of cr For cr=1.5, the benchmark value, the standard deviation of the

relative price rise s from 0.48 to 0.58.

A

second property of the model is the contemporaneous correlation

between net exports and the term s of trade. In the data, th is correlation

has been positive for the United States and negative for Japan and the United

Kingdom (see table 4.1). In the theoretical economy we find, for the

benchmark parameter values, that the correlation is -0.41.

A s

we might

expect from Propositions 1 and 2, this correlation is sensitive to th e

elasti city of substit ution . We see in fig ure 4.3 th at the correl ation

increa ses with cr, and i s positive f o r elast ici tie s gr ea te r th an cr*=2.76.

This fe atu re, too, is strongly influenced by capita l formation. In the model

without cap ital (8 =0 ), th e economy is much like tha t described in Proposition

2, with a crit ica l elast ici ty cr*=0.94. For cr>cr*, th e tr ad e balance and th e

term s of tr ad e a r e positively correla ted; fo r crccr*, t he rev erse.

A thi rd proper ty of int eres t is the impact of government spending on the

correlation between the trad e balance and th e ter ms of trade. We see in

table 4.4 th at with only shocks to government spending, th e correl ation

between net ex ports and the terms of trad e shi fts from negative t o positive.

This mir ror s a simil ar resu lt in section 6. With shocks to both

productivity, z and government spending, g, we find that the former

dominate, in the sense t ha t t he economy s properties ar e similar t o those

with shocks to productivity alone.

Finally, we look a t the complete cross-correlation function fo r net

expo rts and the ter ms of tr ade.

A s

pictured in figure 4.4, this correlation

has the same asymmetric shape we documented fo r the d at a in fig ure 4.1. Some

intuition fo r thi s behavior i s provided by fig ure 4.5, in which we grap h the

dynamic responses t o a one-standard-deviation shock t o domestic productivity.




Following th is shock output and th e rela tive pri ce of forei gn goods both

increase . Consumption also rise s but by less tha n output. Investment grows

initially by much more than consumption as r esources a re t r ansfer red t o the

home country t o exploit its expected fu tu re productivity advantage. As

capital accumulates thi s resource tr an sf er diminishes. The tr ad e balance

which is the difference

a t

market prices between outpu t and th e sum of

consumption and investment exhibits an initia l period of de fici t followed

by surplus. These dynamic responses give ri se t o the asymmetric cross-

correlatio n function of figur e

4.4.

In shor t much of t he intuition f o r th is dynamic gene ral equilibrium

tr ad e model i s available fro m the exchange economy of section s 3 5. What the

exchange economy misses completely ar e the dynamics of t he rela tion between

the trade balance and the terms of trade: the asymmetric cross-correlation

function th at we documented in the da ta and labeled the S-curve. The

cross-correlation function between these two variables

is

symmetric in the

exchange economy fo r al l para mete r values. In th is section we have seen

th at t he dynamics of capital formatio n provide

a

plausible basis for an

asymmetric pattern.

8 Final houghts

We have argued t ha t a dynamic general equilibrium approach to aggregate

trade theory provides both

a

new level of understandin g of t he inte rrel atio ns

between trade and price movements and

a

framework in which these relations

can be quantif ied. With regard to the former we have seen th at the relation

between trade and price variables is much different from that suggested by

th e Marshall-Lerner condition cited in most textbooks. With re ga rd t o th e

lat ter we suggest th at t he dynamic relation between tra de and the relative

price of fo reign goods can be understood as

a

consequence of the dynamics of




capita l formation. Thus, the dynamics of tr ad e variables ar e inseparable

fr om th e dynamics of th e re st of the economy.

Future work will undoubtedly focus, however, not on these contributions,

but on dimensions in which the theory, in its current incarnation, provides a

relati vely poor approximation to the dynamics of act ual economies. The most

obvious example is the variab ility of th e te rm s of t rade . In the economy of

section 7, and in Stockman and Tes ar 1991) a s well, t he st and ard deviation

of the ter ms of t ra de i s substantially smaller than we estimate in the data.

This discrepancy between theory and da ta helps t o motivate theories in which

monetary policy influences rel ative price s Grilli and Roubini 1992,

Schlagenhauf and Wrase 19921 and in which inte rnatio nal mark et segmentation,

possibly in conjunction with imperf ect competition, also plays a pa rt Dumas

1992, Giovannini 1988, Lapham 1990). Ongoing research will likely tel l us

how important each of these features is, and how they modify the lessons of

the theory outlined above.




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P. Hooper and J.D. Richardson (eds. 1 International Economic

Transactions: Is su es in Measurement and Empirical Research.

Chicago:

University of Chicago Press.

Armington, P. 1969.

A

theory of demand for products distinguished by place

of production. IMF Staff Papers 27, 488-526.

Backus, D. 1992. Interp reting comovements in the tr ad e balance and th e

te rms of trade. Journal o f International Economics forthcoming.

Backus, D., Kehoe, P., and Kydland,

F.

1992a. Interna tional re al

business cycles. Journal o f Political Economy 100 (August), 745-775.

Backus, D., Kehoe, P., and Kydland, F. 1992b. Dynamics of th e t r ade

balance and th e ter ms of tr ade : The S-curve. Federa l Reserve Bank of

Cleveland, Working Paper 9211, October.

Baxter, M. 1992. Fiscal policy, specialization, and tr ad e in th e two-sector

model: The return of Ricardo? Journal o f Political Economy

100

(August), 713-744.

Blackburn, K., and Ravn,

M.

1991. Contemporary macroeconomic flu ctu ati ons:

An int ern ati onal perspective. Unpublished manu scr ipt , Januar y.

Buiter,

W.

1989. Budgetary Policy International and Intertemporal Trade in

the Global Economy. Amsterdam: North Holland.

Cole,

H.

and Obstfeld,

M.

1991. Commodity t r ade and internat iona l

risk-sharing. Journal o f Monetary Economics 28 (August), 3-24.

Dornbusch, R. 1980.

Open Economy Macroeconomics.

New York: Basic Books.

Dumas, B. 1992. Dynamic equilibrium and th e re al exchange ra t e in a

spatially separated world. Review o f Financia Stud ies 5, 153-180.

Ethier, W. J. 1988. Modern International Economics Second Edition. New York:

Norton.




Froot, K., and Rogoff, K. 1991. Government spending and the re al exchange

ra te in th e Bretton Woods era. Unpublished manuscript.

Giovannini, A. 1988. Exchange ra te s and tra ded goods prices. Journal of

International Economics

24, 45-68.

Graboyes, R. 1991. Internat ional tra de and payments data. Federal Reserve

Bank of Richmond,

Quarterly Review

77 (September/October), 20-31.

Grilli, V. and Roubini, N. 1992. Liquidity and exchange ra te s.

Journal of International Economics

32 (May), 339-352.

Harberger,

A.

1950. Currency deprecia tion, income, and the balance of

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Hodrick, R. 1988. US interna tional capi tal flow s: perspectives from

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Carnegie-Rochester Conference Serie s on

Public Policy

30 (Spring), 231-288.

Kehoe, P., and Richardson, P. 1985. Dynamics of the cu rr en t account:

The oret ical and empirica l analysis. Federal Reserve Bank of

Minneapolis, Working Paper.

Kemp, M. 1987. Marsha ll-Lerner condition.

The New Palgrave: Dictionary

of Economics.

London: Macmillan.

Krugman, P., and Obstfeld, M. 1991.

International Economics: Theory and

Policy

Second Edition. New York: HarperCollins .

Lapham, B. 1990. A dynamic, general equilibrium analysis of deviations from

the laws of one price. Unpublished manu script, Queen's University,

September.

Laursen , S., an d Metzler, L. 1950. Flexible exchange ra te s and th e the ory of

employment.

Review o f Economics and Statis tics

32, 281-299.

Lucas , R. 1984. Money in a theo ry of finance.

Carnegie-Rochester Conference

Series on Public Policy

21, 9-45.

Macklem, R.T. 1990. Terms-of-trade dist urbance s and fis cal policy in a small




open economy. Bank of Canada, Working Pape r 90-7, December.

Mendoza, E. 1992. The te rm s of tr ad e and economic fluc tuat ions. Unpublished

manuscript, International Monetary Fund, February.

Mussa,

M

1986. Nominal exchange r a t e regimes and the behavior of rea l

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A

Meltzer (eds.),

Real Business

Cy cles Real Exchange Rates and Actual Polic ies .

Carnegie-Rochester

Conference Series.

Obstfeld,

M

1982. Aggregate spending and th e ter ms of trade : Is the re

a

Laursen-Metzler effect?

Quarter ly Journal o f Economics

97 (May),

251-270.

Obstfeld,

M

1989. Fiscal deficits and relat ive prices in a growing

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Journal o f Monetary Economics

23 (May), 461-484.

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January.

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Stockma n, A., and Svensson, L. E.

0

1987. Capital flow s, investm ent, and

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Journal o f Monetary Economics

19, 171-201.

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A.

and Te sar , L. 1991. Tast es and technology in a two-country

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Journal o f Political

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91 (February), 97-125.




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J

1985. Trade Liberalization Among Major Trading Areas Cambridge,

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at

t h e NBER Universities

Conference, May.




APPENDIX: Proof o f Prop osit ion

The algebra behind Proposition 2 is straightforward but fair ly tedious.

We start by reducing th e economy to tw o equations in tw o unknowns. The

unknowns are the consumption shares of the first agent,

sa=a

/y and

1 1 1

b

s

=b /y The fir st- orde r conditions and resource c onstra ints then imply

1 1

2

and

b

a

where m=b

/a -xs

/s

>O

and v=2/a>0. With these substitutions, th e tw o

1 1 - 1 1

a

equations determine

s

and

sb

as

funct ions of t he endowment ra ti o x=y /y

1 1

2

1

Note th at if eith er w = l or a=;r, t he r ig ht side of (A21 is one and sa i s

1

constant.

Preliminaries:

(a1

If we differentiate th e f ir st equation we get

a

Thus, s and

s

ar e positively relate d and we can use this relation t o

1

b

subst i tute out any d s s we get.

1

b

a

(b) Differentiate the rat io s

/s

1:

1 1

b

a

b a b a v

a

a

d ( s

/s

1

(S

/S

1

[(s

/S 10

-11 dsl/sl.

1 1 1 1 1 1

(c )

Differentiate

m:

b a v

a adm/m dx/x I s l / s l l w -11 dsl/sl.

(dl Inequalit ies. From (A11 and w>l:

b a v a b

s l / s l ) w -1 (sl-sll/(l-s:) > 0.




We now prove th e claims in th e tex t.

a

1.

We show t h a t s l is increasing in x if 7>a , and decreasing if 7 <a.

We diff erentia te (A2) and find, af te r rearrangement:

If we s ubs titu te the expression f or dm/m [( c) above1 we get a n equation of

t he f o r m

a

s o t ha t s l is incre asing in x if B/A>O, and decre asing other wise. The

coefficient of dx/x i s

a a

Since w>l, B has the same sign as 7-a. The coefficient of ds /s i s

1 1

a

Clearly if 7< a, A is posit ive and ds /dx is negative. If p a , then

1

1-a l+v 1-a 2+v) 1-a

A/7 = (w+m (l+w m

+

8 (1-w m

,

a b

where 8= s -s )(7-a)/;r<l. Combining ter ms makes it clea r th at A is positive

1 1

in th is case, too. Thus, the sign of dsa/dx is th e same as the sign of 7-a.

1

2. An immediate corollary is th at c /c is increasing in x: The fi rs t-

2 1

order conditions imply

The behavior of

sy

with respect to x implies th at the consumption ratio,

c

/C

is increasing in x,

as

claimed in the text.

2 1

3. We now show th a t b /a =m is increasing in x.

From (A31 we have

1 1




From the definition of B

Since A>O, m is increasing in x.

4. We tu rn to the dependence of t he tra de balance on x. A s in the

text ,

Differentiating, we find

which is positive if

From A4) and AS) we can show th at th is inequality holds fo r la rge enough a




Table

4.1

Properties of the Trade Balance and the Terms of Trade

Standard Auto-

Cross-

Dev.

( )

correlation Correlation

Country

Period

P

nx P

nx

(P,nx>

P,Y)

Japan

1955 89 5.97 .97 .87

.77 46 09

1955 70 2.17 .98 .73

.66 55 .41

1971 89

7.76 .94 .87 .83 51

27

United Kingdom 1955 89 2.71 1.08 .76 .66 54 .20

1955 70 1.51

.78

.38 .54 . 15 .56

1971 89 3.38 1.21 .79 .65 .60 .10

United States

1955 89 2.99 .45 .82 .80 .30 09

1955 70 1.31

.30 .65

.79 .28 .47

1971 89 3.84 .55 .84 .80 .30 23

Variables are p, the terms of trade, logarithm; nx, the ratio of net exports to output; y, real output,

logarithm. Data are quarterly from the OECD s Quarterly National Accounts Statistics refer to

Hodrick-Prescott filtered variables.

SOURCE: Authors calculat ions.




Table

4.2

The Trade Balance, the Terms of Trade, and Government Purchases

Standard

Deviation Cross-Correlations

Country

g @ nx> g , n x > g , ~ )

g , ~ )

Australia

1.47 1.90

.I1 .I5 .15 .17

Austria

1.27 .45

25 .I1

.28 .23

Canada 1.49 1.16 .06 .I5 .02 .22

France

.91 .66 50 l l .45 .24

Germany

1.47 1.22 .09 .I1 .I6 .23

Italy

1.70 .69 .66 . l l .42 .01

Japan

1.48 1.54

.51 .19

.35 .02

Switzerland 1.94

1.01 .61 . I5 .29 .28

United Kingdom 1.60

1.07

.60

.06 .01 .06

United States 1.93 1.47 .31 .28 .13 .12

The sample period is 1971:l to 1989:4. Variables are p, the terms of trade, loga-

rithm; nx the ratio of net exports to output; y, real output, logarithm; g, real

government purchases of goods and services, logarithm. Data are quarterly from the

O EC D Y s

Quarterly National Accounts

Statistics refer to Hodrick-Prescott filtered

variables.





Table 4.3

Benchmark Parameter Values

Preferences

Technology

Forcing Processes

0.36,

0 .025 , l l a 1 . 5 ,

import share 0 .1 5

var

~

var

E

0.008522,

C O ~ T E ~ , E ~0.258

gt 0

SOURCE:

Authors calculat ions.




Table 4.4

Properties of Theoretical Economies with Capital Formation

Standard

Deviation

( )

Autocorrelation Correlation

Economy

x

P

nx

P

WY) WP) @,P)

Benchmark .30

1.38 .48

.61 .63

.83

.64

-.41 .49

.02)

.

18) .M)

.07) .10)

.05)

.07) .08) .14)

Large Elasticity .33 1.41 .35 .63

.64

.88 -.57 -.05 .43

.03) .18) .05) .07) .18) .03) .08) .09) .14)

Small Elasticity .37 1.33 .76 .61 .63 .77 -.66 -.80 .51

.03)

.

18) .07) .07)

.

10) .05) .07) .09) .16)

Big Share .63 1.37 .58 .59 .64 .83 -.61 -.41 .52

.04)

.

18) .08) .07)

.

10) .04) .07) .07)

.

13)

Small Share .08 1.38 .43 .62 .63 .81 -.65 -.41 .48

.01) .18) .06) .07 .10) .05) .07) .08) .14)

Two Shocks .33 1.33 .57 .62 .65 .78 -.57 -.05 .39

.03)

.

15) .07) .08) .08) .06) .15) .17) .17)

Govt. Shocks .16 .17 .30 .67 .67 .67 -.55 1.00 -.55

.03) .02) .05) .ll) .08)

.

11) .13) .00) .13)

Variables are defined in Table 4.1. Statistics refer to Hodrick-Prescott filtered variables.

Entries are averages

over 20 simulations of 100 quarters each; numbers in parentheses are standard deviations. Parameters as in

Table 4.3, except large elasticity,

a

=

2.5; small elasticity, a = 0.5; big share, import share

=

0.25; small

share, import share

=

0.05; two shocks, mean of g = diag 0.2,0.2), B

=

diag 0.95,0.95), and V, =

diag 0.0042,0.0042);government shocks, as in two shocks plus

z =

1, all t.

SOURCE

Authors' calc~.llations.




Fig 4.1 S CURVES

IN TH

DATA

JAPAN

0.75

UNITED

KINGDOM

0.75

U

LL

0.75

UNITED STATES

0.50

--

\

/

LL

\

\

/

--

I _

PRE 72

-

POST 72

--

PRE 72

0.75

I

I I

I I I I I

I

I

I

I

I

I I I

I

I I I I

I I

I

I

I I

I

I

8 6 4 2 0 2 4 6 8

Lag

of p behind x

SOURCE: Authors calculations.

\ d-

POST 72

0.75

I

I

I I > I

I

I

I I

I I

I I

I I I 1 I I I I

I 1 1

I I




Fig 4 2

VARIABILmY

OF THE

T RMS

OF TR DE

lasticity of Substitution

SOURCE Authors calculations.




Fig. 4.3 CORRELATION OF THE TRADE BALANC E

0 8

AND TERMS OF TRADE

0 6

0 4

2

3 4 5 6

Elasticity o

Substitution





Fig.

4 4

S CURVE FOR

THE

BENCHMARK ECONOMY

Lag

of

p

over

nx

SOURCE Authors calculations.




Fig

4.5 DYNAMIC RESPONSES TO DOMESTIC

PRODUCTIVITY SHOCK

120

.

0 2 0 l ~ I 1 1 I I I 1 I I I I I I I I 1 I I I I I I I

1.00

s

0.80--

X

0.60

m

o

0.40

u

8

020

.

* OUTPUT

.

.

.

.

.

- - - _ - - - - - _

- - - - - - - - - _ _ -

PRODUCI M~

SHO K

--

2

I

4 4

4

TERMS

O

TRADE

4

4

4

4 4 2 .


Documents

Backus, Kehoe, Kydland